diff --git a/.vscode/launch.json b/.vscode/launch.json new file mode 100644 index 0000000..6b76b4f --- /dev/null +++ b/.vscode/launch.json @@ -0,0 +1,15 @@ +{ + // Use IntelliSense to learn about possible attributes. + // Hover to view descriptions of existing attributes. + // For more information, visit: https://go.microsoft.com/fwlink/?linkid=830387 + "version": "0.2.0", + "configurations": [ + { + "name": "Python Debugger: Current File", + "type": "debugpy", + "request": "launch", + "program": "${file}", + "console": "integratedTerminal" + } + ] +} \ No newline at end of file diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..cc081ee --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,3 @@ +{ + "python-envs.defaultEnvManager": "ms-python.python:venv" +} \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/buses.csv b/examples/capacity_expansion/2bus/inputs/buses.csv deleted file mode 100644 index 7c8ea05..0000000 --- a/examples/capacity_expansion/2bus/inputs/buses.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,bus_type -north,slack -south,PQ \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/capacity_factors.csv b/examples/capacity_expansion/2bus/inputs/capacity_factors.csv deleted file mode 100644 index a9342d1..0000000 --- a/examples/capacity_expansion/2bus/inputs/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -cf_one,sc1,1,solar,1 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/generators.csv b/examples/capacity_expansion/2bus/inputs/generators.csv deleted file mode 100644 index 84c2430..0000000 --- a/examples/capacity_expansion/2bus/inputs/generators.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -gas_gen,gas,north,cf_one,0,10,0,0,200,200,10 -diesel_gen,diesel,south,cf_one,0,50,0,0,200,200,50 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/lines.csv b/examples/capacity_expansion/2bus/inputs/lines.csv deleted file mode 100644 index 5a71e96..0000000 --- a/examples/capacity_expansion/2bus/inputs/lines.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,efficiency -line,north,south,100,FALSE,,,,,1 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/loads.csv b/examples/capacity_expansion/2bus/inputs/loads.csv deleted file mode 100644 index 467cbfc..0000000 --- a/examples/capacity_expansion/2bus/inputs/loads.csv +++ /dev/null @@ -1,3 +0,0 @@ -bus,scenario,timepoint,load_MW -north,sc1,1,0 -south,sc1,1,120 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/scenarios.csv b/examples/capacity_expansion/2bus/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/2bus/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/timepoints.csv b/examples/capacity_expansion/2bus/inputs/timepoints.csv deleted file mode 100644 index 2d8d232..0000000 --- a/examples/capacity_expansion/2bus/inputs/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timeseries -1,winter \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/inputs/timeseries.csv b/examples/capacity_expansion/2bus/inputs/timeseries.csv deleted file mode 100644 index 11ad9c3..0000000 --- a/examples/capacity_expansion/2bus/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/costs_summary.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 3ff6b7d..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,1999.9999999999998 -cost_per_period_USD,0.0 -total_cost_USD,1999.9999999999998 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/emissions_per_scenario.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/energy_budget_constraints.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_built_capacity.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 3ff6b7d..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,1999.9999999999998 -cost_per_period_USD,0.0 -total_cost_USD,1999.9999999999998 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 8e25f56..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,3 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -gas_gen,sc1,1,100.0 -diesel_gen,sc1,1,19.999999999999996 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/line_flows.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index 5ef5602..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,2 +0,0 @@ -line,from_bus,to_bus,scenario,timepoint,existing_capacity_MW,net_flow_leaving_from_bus_MW,net_flow_arriving_at_to_bus_MW,flow_sent_at_from_bus_MW,flow_sent_at_to_bus_times_efficiency_MW,flow_sent_at_from_bus_times_efficiency_MW,flow_sent_at_to_bus_MW,built_capacity_MW,total_capacity_MW -line,north,south,sc1,1,100.0,100.0,100.0,100.0,-0.0,100.0,-0.0,0,100.0 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index e25caed..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,3 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -north,sc1,1,10.0 -south,sc1,1,50.0 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_balance_by_bus.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_balance_by_bus.csv deleted file mode 100644 index 407a9c0..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_balance_by_bus.csv +++ /dev/null @@ -1,3 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -north,sc1,1,100.0,0,0,0.0,100.0 -south,sc1,1,19.999999999999996,0,0,120.0,-100.0 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_budget_constraints.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/solver_status.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/solver_status.csv deleted file mode 100644 index 4a5b2b8..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.024181842803955078 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_built_capacity.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/capacity_expansion/2bus/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/capacity_expansion/2bus/sting_log.txt b/examples/capacity_expansion/2bus/sting_log.txt deleted file mode 100644 index 122231d..0000000 --- a/examples/capacity_expansion/2bus/sting_log.txt +++ /dev/null @@ -1,2803 +0,0 @@ -2026-02-11 13:37:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/inputs ... - - 'lines.csv' ... -2026-02-11 13:39:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/inputs ... - - 'lines.csv' ... - Added 1 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 2 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 2 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 10000.0 - Constraint=cMaxDispatch[Generator(id=1, name='diesel_gen', bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.2000000000e+01 nrm: 1e+04 Viol. con: 1e-17 var: 0e+00 - Dual. obj: 5.2000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 1e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.2000000000e+01 nrm: 1e+04 Viol. con: 1e-17 var: 0e+00 - Dual. obj: 5.2000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 1e-17 -> Time spent by solver: 0.21 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 52.0. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.24 seconds. - -2026-02-11 13:40:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/inputs ... - - 'lines.csv' ... - Added 1 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 2 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 2 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='diesel_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='diesel_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='diesel_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 10000.0 - Constraint=cMaxDispatch[Generator(id=0, name='diesel_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=1, name='gas_gen', bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=0, name='diesel_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.2000000000e+01 nrm: 1e+04 Viol. con: 4e-17 var: 0e+00 - Dual. obj: 5.2000000000e+01 nrm: 5e+01 Viol. con: 1e-17 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.2000000000e+01 nrm: 1e+04 Viol. con: 4e-17 var: 0e+00 - Dual. obj: 5.2000000000e+01 nrm: 5e+01 Viol. con: 1e-17 var: 2e-17 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 52.0. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-11 13:44:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/inputs ... - - 'lines.csv' ... - Added 1 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 2 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 2 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 19.999999999999996. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-13 15:16:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/inputs ... - - 'lines.csv' ... - Added 1 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 2 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options=Field(name=None,type=None,default=,default_factory=,init=True,repr=True,hash=None,compare=True,metadata=mappingproxy({}),kw_only=,_field_type=None)) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -2026-02-15 18:13:57 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timepoints', 'scenarios', 'timeseries'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' - - 'timeseries.csv' ... - Added 1 'timeseries' -2026-02-15 18:14:26 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timepoints', 'scenarios', 'timeseries'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' - - 'timeseries.csv' ... - Added 1 'timeseries' -2026-02-15 18:19:25 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -2026-02-15 18:21:15 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus -Rule failed when generating expression for Constraint cEnergyBalance with index (Bus(id=0, bus='north'), Scenario(id=0, name='sc1', type_='scenarios', probability=1.0), Timepoint(id=0, name='1', timeseries='winter')): -AttributeError: 'ConcreteModel' object has no attribute 'eGenAtBus' -Constructing component 'cEnergyBalance' from data=None failed: - AttributeError: 'ConcreteModel' object has no attribute 'eGenAtBus' -2026-02-15 18:22:31 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -2026-02-15 18:23:10 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -2026-02-15 18:23:50 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -2026-02-15 18:26:03 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.19 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 19.999999999999996. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -2026-02-15 18:26:34 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 19.999999999999996. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -2026-02-15 18:27:34 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 19.999999999999996. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 19:53:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-15 20:18:25 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-15 20:18:35 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-15 20:27:51 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-15 20:35:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-15 20:38:25 - ____ __ __ - / __/_/ /___/ /_ _____ _ - _\ \/_ __// _// \/ / _ `/ -/___/ /__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus ... - - 'generators.csv' ... - Added 2 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'buses.csv' ... - Added 2 'buses' - - 'loads.csv' ... - Added 2 'loads' - - 'lines.csv' ... - Added 1 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 2 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 2 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 2 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 2 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of line flows - Size: 2 variables - - Maximum flow constraints per line - Size: 3 constraints - - Energy balance at each bus - Size: 2 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 100.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=0, bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 20000.0 - Constraint=cMaxDispatch[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=0, name='gas_gen', bus='north'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.5 - Variable=vGEN[Generator(id=1, name='diesel_gen', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 4 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+01 nrm: 1e+04 Viol. con: 2e-17 var: 0e+00 - Dual. obj: 2.0000000000e+01 nrm: 5e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1999.9999999999995. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/2bus/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - diff --git a/examples/capacity_expansion/5bus_1h/inputs/buses.csv b/examples/capacity_expansion/5bus_1h/inputs/buses.csv deleted file mode 100644 index 121e77d..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,bus_type,zone -1,slack,center -2,PQ,north -3,PQ,south -4,PQ,south -5,PQ,south \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/capacity_factors.csv b/examples/capacity_expansion/5bus_1h/inputs/capacity_factors.csv deleted file mode 100644 index a9342d1..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -cf_one,sc1,1,solar,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/generators.csv b/examples/capacity_expansion/5bus_1h/inputs/generators.csv deleted file mode 100644 index 077e412..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -1,gas,1,cf_one,0,14,0,0,40,40,0 -2,gas,1,cf_one,0,15,0,0,170,170,0 -3,gas,3,cf_one,0,30,0,0,520,520,0 -4,gas,4,cf_one,0,40,0,0,200,200,0 -5,gas,5,cf_one,0,10,0,0,600,600,0 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/lines.csv b/examples/capacity_expansion/5bus_1h/inputs/lines.csv deleted file mode 100644 index 0274bda..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,400,FALSE,0.00281,0.0281,0,0.00712,-360,360 -2,1,4,1000,FALSE,0.00304,0.0304,0,0.00658,-360,360 -3,1,5,1000,FALSE,0.00064,0.0064,0,0.03126,-360,360 -4,2,3,1000,FALSE,0.00108,0.0108,0,0.01852,-360,360 -5,3,4,1000,FALSE,0.00297,0.0297,0,0.00674,-360,360 -6,4,5,240,FALSE,0.00297,0.0297,0,0.00674,-360,360 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/loads.csv b/examples/capacity_expansion/5bus_1h/inputs/loads.csv deleted file mode 100644 index 2288c24..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/loads.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,load_MW -1,sc1,1,0 -2,sc1,1,300 -3,sc1,1,300 -4,sc1,1,400 -5,sc1,1,0 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/scenarios.csv b/examples/capacity_expansion/5bus_1h/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/storage.csv b/examples/capacity_expansion/5bus_1h/inputs/storage.csv deleted file mode 100644 index abcb9eb..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus,name,c0_USD,c1_USDperMWh,c2_USDperMWh2,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,technology -1,cats_1,0,0,0,0,0,0,0,0,0,0,0.92,0.92,hydroelectric pumped storage \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/timepoints.csv b/examples/capacity_expansion/5bus_1h/inputs/timepoints.csv deleted file mode 100644 index 2d8d232..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timeseries -1,winter \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/inputs/timeseries.csv b/examples/capacity_expansion/5bus_1h/inputs/timeseries.csv deleted file mode 100644 index 11ad9c3..0000000 --- a/examples/capacity_expansion/5bus_1h/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 840cad1..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925381036 -cost_per_period_USD,0.0 -total_cost_USD,17479.896925381036 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/emissions_per_scenario.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/energy_budget_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_built_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 840cad1..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925381036 -cost_per_period_USD,0.0 -total_cost_USD,17479.896925381036 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index eef2ac8..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,323.49484626905166 -4,sc1,1,0.0 -5,sc1,1,466.5051537309485 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/line_flows.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index daf4a61..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,1,0.0,-4.060673079637738,249.7167650427273,175.22728030896712 -4,2,3,sc1,1,-4.060673079637738,-3.7464117296447834,-50.283234957272754,2.7306760151897604 -2,1,4,sc1,1,0.0,-3.28599929195582,186.7883886882213,106.06530253217578 -5,3,4,sc1,1,-3.7464117296447834,-3.28599929195582,-26.788388688220994,2.1313247724782833 -3,1,5,sc1,1,0.0,0.8388843033736129,-226.50515373094865,32.83493418667564 -6,4,5,sc1,1,-3.28599929195582,0.8388843033736129,-239.99999999999997,171.07199999999995 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index cc70b2d..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,16.97735882434225 -2,sc1,1,26.38445952181784 -3,sc1,1,30.00000000340988 -4,sc1,1,39.94273632600235 -5,sc1,1,10.00000000042757 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_balance_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_balance_by_bus.csv deleted file mode 100644 index 94d089b..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_balance_by_bus.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,1,210.0,0.0,0,0.0,209.99999999999991 -2,sc1,1,0.0,0.0,0,300.0,-300.0 -3,sc1,1,323.49484626905166,0.0,0,300.0,23.494846269051756 -4,sc1,1,0.0,0.0,0,400.0,-400.0000000000003 -5,sc1,1,466.5051537309485,0.0,0,0.0,466.50515373094856 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_budget_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/solver_status.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/solver_status.csv deleted file mode 100644 index db2540d..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.054229021072387695 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_built_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch_by_bus.csv deleted file mode 100644 index 87ea0dd..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion/storage_dispatch_by_bus.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,net_discharge_MW -1,sc1,1,0.0 -2,sc1,1,0.0 -3,sc1,1,0.0 -4,sc1,1,0.0 -5,sc1,1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/buses.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/buses.csv deleted file mode 100644 index b8b0857..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/buses.csv +++ /dev/null @@ -1,4 +0,0 @@ -id,name,type_,bus_type,zone,kron_removable_bus,base_power_MVA,base_voltage_kV,base_frequency_Hz,latitude,longitude,max_flow_MW,minimum_voltage_pu,maximum_voltage_pu -0,north,buses,zone_bus,north,,,,,,,1400.0,, -1,center,buses,zone_bus,center,,,,,,,2400.0,, -2,south,buses,zone_bus,south,,,,,,,3000.0,, diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/capacity_factors.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/capacity_factors.csv deleted file mode 100644 index 19f22a3..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,site,scenario,timepoint,capacity_factor,technology -0,,capacity_factors,cf_one,sc1,1,1.0,solar diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/generators.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/generators.csv deleted file mode 100644 index e6d99a0..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -id,name,type_,bus,minimum_active_power_MW,maximum_active_power_MW,minimum_reactive_power_MVAR,maximum_reactive_power_MVAR,base_power_MVA,base_voltage_kV,base_frequency_Hz,technology,site,cap_existing_power_MW,cap_max_power_MW,cost_fixed_power_USDperkW,cost_variable_USDperMWh,c0_USD,c1_USDperMWh,c2_USDperMWh2,emission_rate_tonneCO2perMWh,bus_id,expand_capacity,component_id,forced_dispatch_MW -0,1,generators,center,,,,,,,,gas,cf_one,40.0,40.0,0.0,0.0,0.0,14.0,0.0,,1,False,, -1,2,generators,center,,,,,,,,gas,cf_one,170.0,170.0,0.0,0.0,0.0,15.0,0.0,,1,False,, -2,3,generators,south,,,,,,,,gas,cf_one,520.0,520.0,0.0,0.0,0.0,30.0,0.0,,2,False,, -3,4,generators,south,,,,,,,,gas,cf_one,200.0,200.0,0.0,0.0,0.0,40.0,0.0,,2,False,, -4,5,generators,south,,,,,,,,gas,cf_one,600.0,600.0,0.0,0.0,0.0,10.0,0.0,,2,False,, diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/lines.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/lines.csv deleted file mode 100644 index f296b07..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/lines.csv +++ /dev/null @@ -1,5 +0,0 @@ -id,name,type_,from_bus,to_bus,r_pu,x_pu,g_pu,b_pu,expand_capacity,cap_existing_power_MW,cost_fixed_power_USDperkW,angle_max_deg,angle_min_deg,base_power_MVA,base_voltage_kV,base_frequency_Hz,decomposed,from_bus_id,to_bus_id,efficiency -0,1,lines,center,north,0.00281,0.0281,0.0,0.00712,False,400.0,0.0,360.0,-360.0,,,,False,1,0, -1,2,lines,center,south,0.00304,0.0304,0.0,0.00658,False,1000.0,0.0,360.0,-360.0,,,,False,1,2, -2,3,lines,center,south,0.00064,0.0064,0.0,0.03126,False,1000.0,0.0,360.0,-360.0,,,,False,1,2, -3,4,lines,north,south,0.00108,0.0108,0.0,0.01852,False,1000.0,0.0,360.0,-360.0,,,,False,0,2, diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/loads.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/loads.csv deleted file mode 100644 index 26a4e1b..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/loads.csv +++ /dev/null @@ -1,6 +0,0 @@ -id,name,type_,bus,timepoint,load_MW,scenario,load_MVAR -0,,loads,center,1,0.0,sc1, -1,,loads,north,1,300.0,sc1, -2,,loads,south,1,300.0,sc1, -3,,loads,south,1,400.0,sc1, -4,,loads,south,1,0.0,sc1, diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/scenarios.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/scenarios.csv deleted file mode 100644 index 0c17777..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,probability -0,sc1,scenarios,1.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/storage.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/storage.csv deleted file mode 100644 index a1f6099..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,technology,bus,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,c0_USD,c1_USDperMWh,c2_USDperMWh2,expand_capacity,bus_id -0,cats_1,storage,hydroelectric pumped storage,center,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.92,0.92,0.0,0.0,0.0,False,1 diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/timepoints.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/timepoints.csv deleted file mode 100644 index f144824..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,timeseries,timeseries_id,weight,duration_hr,prev_timepoint_id -0,1,timepoints,winter,0,1.0,1.0,0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/system_csv/timeseries.csv b/examples/capacity_expansion/5bus_1h/outputs/system_csv/timeseries.csv deleted file mode 100644 index 2853905..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/system_csv/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period,start,end,period,timepoint_selection_method -0,winter,timeseries,1.0,1,1.0,,,, diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/costs_summary.csv deleted file mode 100644 index 49b92be..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,14810.000000000007 -cost_per_period_USD,0.0 -total_cost_USD,14810.000000000007 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/dispatch_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/dispatch_by_bus.csv deleted file mode 100644 index b682140..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/dispatch_by_bus.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,dispatch_MW -north,sc1,1,0.0 -center,sc1,1,210.0 -south,sc1,1,790.0000000000002 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/emissions_per_scenario.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/energy_budget_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_built_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 49b92be..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,14810.000000000007 -cost_per_period_USD,0.0 -total_cost_USD,14810.000000000007 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index a0bc871..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,190.0000000000002 -4,sc1,1,0.0 -5,sc1,1,600.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch_by_bus.csv deleted file mode 100644 index 683e6c5..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/generator_dispatch_by_bus.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,dispatch_MW -south,sc1,1,790.0 -center,sc1,1,210.0 -north,sc1,1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/line_flows.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/line_flows.csv deleted file mode 100644 index 7b5d62e..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,5 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,center,north,sc1,1,1.60092703021851,0.0,98.45124471120732,27.23633971437274 -4,north,south,sc1,1,0.0,1.2596441732572838,-201.5487552887927,43.87165281913858 -2,center,south,sc1,1,1.60092703021851,1.2596441732572838,19.39978352848569,1.1441088668943982 -3,center,south,sc1,1,1.60092703021851,1.2596441732572838,92.14897176030702,5.434517117748391 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 49e88a2..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -north,sc1,1,30.00000000000001 -center,sc1,1,29.999999999999993 -south,sc1,1,30.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_balance_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_balance_by_bus.csv deleted file mode 100644 index a996d7c..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_balance_by_bus.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -north,sc1,1,0.0,0.0,0,300.0,-300.0 -center,sc1,1,210.0,0.0,0,0.0,210.00000000000006 -south,sc1,1,790.0000000000002,0.0,0,700.0,89.99999999999997 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_budget_constraints.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/solver_status.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/solver_status.csv deleted file mode 100644 index db3698c..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.010589122772216797 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_built_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_capacity.csv deleted file mode 100644 index 735d01f..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,built_power_capacity_MW,built_energy_capacity_MWh -cats_1,sc1,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch_by_bus.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch_by_bus.csv deleted file mode 100644 index b544025..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/storage_dispatch_by_bus.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,net_discharge_MW -south,sc1,1,0.0 -center,sc1,1,0.0 -north,sc1,1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_capacity.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 52befee..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,built_capacity_MW -1,sc1,0.0 -2,sc1,0.0 -3,sc1,0.0 -4,sc1,0.0 -5,sc1,0.0 diff --git a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_dispatch.csv b/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 95e0ecc..0000000 --- a/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,190.0 -4,sc1,1,0.0 -5,sc1,1,600.0 diff --git a/examples/capacity_expansion/5bus_1h/sting_log.txt b/examples/capacity_expansion/5bus_1h/sting_log.txt deleted file mode 100644 index 447d4e9..0000000 --- a/examples/capacity_expansion/5bus_1h/sting_log.txt +++ /dev/null @@ -1,17542 +0,0 @@ -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.18 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.22 seconds. - -2026-02-06 10:15:21 -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:15:21 -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'north', 'south', 'center'} - - System with new buses created: {'north', 'south', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 3 constraints - Size: 3 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:24:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:25:17 -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:25:17 -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 3 constraints - Size: 3 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:31:24 -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:31:24 -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:35:01 -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:35:01 -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'north', 'center', 'south'} - - System with new buses created: {'north', 'center', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:40:40 -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:40:40 -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:58:51 -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:58:51 -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 11:10:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpcfcds52g.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.22 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -2026-02-06 11:11:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpv08qruov.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:13:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpcmcb59in.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:13:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpdb6uksqh.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:14:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp1skdnd7v.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:14:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpo_kgi_h4.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:16:34 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp3ogsocec.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:21:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -2026-02-06 11:22:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 11:30:06 -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 11:30:06 -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. - -> Objective value: 14810.00 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-08 14:04:07 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.02 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.01 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.02 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.01 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.03 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.01 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.01 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.01 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.15 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.07 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.07 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.01 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.01 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.01 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.01 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.01 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.01 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.01 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.01 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.01 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.09 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.06 seconds. - -> Completed in 0.12 seconds. - - ->> Run completed in 0.44 seconds. - -2026-02-08 14:04:36 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.01 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.03 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.02 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.03 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.01 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.01 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.01 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.01 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.01 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.01 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.01 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.01 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.01 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.12 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.10 seconds. - -> Completed in 0.15 seconds. - - ->> Run completed in 0.33 seconds. - -2026-02-08 14:04:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpsxcv8cz3.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.18 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.24 seconds. - -2026-02-08 14:05:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.01 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.01 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.03 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpb1mu174f.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.10 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.02 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.02 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.21 seconds. - -2026-02-08 14:07:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpgl77cylq.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.07 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.12 seconds. - -2026-02-08 14:07:49 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.02 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmps328w1n9.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.11 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.20 seconds. - -2026-02-08 14:08:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.01 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.01 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.01 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.04 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.02 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpev0plb7b.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.11 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.02 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.14 seconds. - -> Completed in 0.17 seconds. - - ->> Run completed in 0.34 seconds. - -2026-02-08 14:08:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpx8rl3g0t.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.07 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.12 seconds. - -2026-02-08 14:10:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.01 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.01 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.01 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.04 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.02 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpzjiw2avg.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0x92a2bb3c -Coefficient statistics: - Matrix range [1e-02, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [3e+00, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 1.32e-13 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 2.65e-13 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 6.82e-14 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 3.23e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.09 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.02 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.09 seconds. - - ->> Run completed in 0.24 seconds. - -2026-02-08 22:42:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1', technology='gas', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=4, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=4, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4', technology='gas', site='cf_one', cap_existing_power_MW=200.0, cap_max_power_MW=200.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=40.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=3, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Could not locate the 'gurobi' executable, which is required for solver gurobi -2026-02-08 22:42:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1', technology='gas', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=4, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=4, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4', technology='gas', site='cf_one', cap_existing_power_MW=200.0, cap_max_power_MW=200.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=40.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=3, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.27 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.29 seconds. - -2026-02-08 22:42:52 -2026-02-08 22:42:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-08 22:42:52 -2026-02-08 22:42:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. - - 0 'inf' components. - - 0 'inf' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=520.0, cap_max_power_MW=520.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=30.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=520.0, cap_max_power_MW=520.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=30.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -222.5068568853514 - - Maximum coefficient: -222.5068568853514 - Constraint=cEnergyBalance[Bus(id=2, bus='center'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=2, bus='center'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=2, bus='center'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=2, bus='center'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=600.0, cap_max_power_MW=600.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=10.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=200.0, cap_max_power_MW=200.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=40.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south', technology='gas', site='cf_one', cap_existing_power_MW=200.0, cap_max_power_MW=200.0, cost_fixed_power_USDperkW=0.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=40.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 148.1. - -> Objective value: 148.1. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Run completed in 0.03 seconds. - - ->> Run completed in 0.03 seconds. - -2026-02-15 18:32:54 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -2026-02-15 18:33:06 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -2026-02-15 18:33:16 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.01 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.01 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.01 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.01 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.01 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.11 seconds. - -2026-02-15 18:33:16 -2026-02-15 18:33:16 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -2026-02-15 18:35:58 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:35:58 -2026-02-15 18:35:58 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:35:58 -2026-02-15 18:35:58 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. -2026-02-15 18:39:07 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:39:07 -2026-02-15 18:39:07 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:39:07 -2026-02-15 18:39:07 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timepoints', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timepoints', 'scenarios'] completed. - - New system has: - - New system has: -2026-02-15 18:45:05 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:45:05 -2026-02-15 18:45:05 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:45:05 -2026-02-15 18:45:05 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timepoints', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timepoints', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'timeseries' components. - - 0 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -2026-02-15 18:45:42 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:45:42 -2026-02-15 18:45:42 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:45:42 -2026-02-15 18:45:42 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:47:11 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 18:47:11 -2026-02-15 18:47:11 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:47:11 -2026-02-15 18:47:11 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'center', 'south', 'north'} - - System with new buses created: {'center', 'south', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:48:24 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:48:24 -2026-02-15 18:48:24 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:48:24 -2026-02-15 18:48:24 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'north', 'center', 'south'} - - System with new buses created: {'north', 'center', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:50:24 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:50:25 -2026-02-15 18:50:25 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:50:25 -2026-02-15 18:50:25 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:51:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:51:38 -2026-02-15 18:51:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:51:38 -2026-02-15 18:51:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -2026-02-15 18:51:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 22.31 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 22.33 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 22.42 seconds. - -2026-02-15 18:52:18 -2026-02-15 18:52:18 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:52:18 -2026-02-15 18:52:18 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'center', 'south', 'north'} - - System with new buses created: {'center', 'south', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:53:27 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 3.23 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.01 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.02 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 3.25 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.07 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 3.35 seconds. - -2026-02-15 18:53:30 -2026-02-15 18:53:30 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:53:30 -2026-02-15 18:53:30 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:55:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 18:55:56 -2026-02-15 18:55:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:55:56 -2026-02-15 18:55:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -2026-02-15 18:57:19 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 174.79896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 18:57:19 -2026-02-15 18:57:19 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:57:19 -2026-02-15 18:57:19 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'center', 'south', 'north'} - - System with new buses created: {'center', 'south', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -278.9478509254434 - - Maximum coefficient: -278.9478509254434 - Constraint=cEnergyBalance[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 148.10000000000008. - -> Objective value: 148.10000000000008. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-15 18:59:02 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-15 18:59:02 -2026-02-15 18:59:02 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 18:59:02 -2026-02-15 18:59:02 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] -System created with attributes: ['case_directory', 'components', 'type_to_class', 'class_to_type', 'generators', 'capacity_factors', 'storage', 'infinite_sources', 'buses', 'loads', 'lines', 'branch_series_rl', 'shunt_parallel_rl', 'timeseries', 'timepoints', 'scenarios'] - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -222.5068568853514 - - Maximum coefficient: -222.5068568853514 - Constraint=cEnergyBalance[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.000000000007. - -> Objective value: 14810.000000000007. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-15 19:51:17 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-15 19:51:17 -2026-02-15 19:51:17 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System initialization completed. -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 19:51:17 -2026-02-15 19:51:17 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System initialization completed. -System initialization completed. - - System with new buses created: {'center', 'south', 'north'} - - System with new buses created: {'center', 'south', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. - - 0 'energy_budgets' components. - - 0 'energy_budgets' components. - - 0 'carbon_policies' components. - - 0 'carbon_policies' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -278.9478509254434 - - Maximum coefficient: -278.9478509254434 - Constraint=cEnergyBalance[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=1, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 9e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.000000000007. - -> Objective value: 14810.000000000007. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-15 20:14:43 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 20:14:43 -2026-02-15 20:14:43 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 20:14:43 -2026-02-15 20:14:43 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. - - 0 'energy_budgets' components. - - 0 'energy_budgets' components. - - 0 'carbon_policies' components. - - 0 'carbon_policies' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -278.9478509254434 - - Maximum coefficient: -278.9478509254434 - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.000000000011. - -> Objective value: 14810.000000000011. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-15 20:14:54 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 20:14:54 -2026-02-15 20:14:54 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 20:14:54 -2026-02-15 20:14:54 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. - - 0 'energy_budgets' components. - - 0 'energy_budgets' components. - - 0 'carbon_policies' components. - - 0 'carbon_policies' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -278.9478509254434 - - Maximum coefficient: -278.9478509254434 - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 3e-12 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.000000000011. - -> Objective value: 14810.000000000011. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -System: -System: - - generators: 5 components - - generators: 5 components - - capacity_factors: 1 components - - capacity_factors: 1 components - - storage: 1 components - - storage: 1 components - - buses: 5 components - - buses: 5 components - - loads: 5 components - - loads: 5 components - - lines: 6 components - - lines: 6 components - - timeseries: 1 components - - timeseries: 1 components - - timepoints: 1 components - - timepoints: 1 components - - scenarios: 1 components - - scenarios: 1 components -System: -System: - - generators: 5 components - - generators: 5 components - - capacity_factors: 1 components - - capacity_factors: 1 components - - storage: 1 components - - storage: 1 components - - buses: 5 components - - buses: 5 components - - loads: 5 components - - loads: 5 components - - lines: 6 components - - lines: 6 components - - timeseries: 1 components - - timeseries: 1 components - - timepoints: 1 components - - timepoints: 1 components - - scenarios: 1 components - - scenarios: 1 components -2026-02-15 20:15:54 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 20:15:55 -2026-02-15 20:15:55 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 20:15:55 -2026-02-15 20:15:55 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. - - 0 'energy_budgets' components. - - 0 'energy_budgets' components. - - 0 'carbon_policies' components. - - 0 'carbon_policies' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=2, name='3', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -222.5068568853514 - - Maximum coefficient: -222.5068568853514 - Constraint=cEnergyBalance[Bus(id=2, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=2, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=2, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=2, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.0. - -> Objective value: 14810.0. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-15 20:16:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.4e+02 6.3e-01 1.0e+02 0.00e+00 3.655204504e+02 3.357894549e+02 7.4e+01 0.00 -1 1.1e+02 1.7e-01 2.7e+01 2.05e+00 1.836206104e+02 1.868615957e+02 1.9e+01 0.00 -2 1.7e+01 2.5e-02 4.0e+00 1.36e+00 1.549697112e+02 1.553911501e+02 2.9e+00 0.00 -3 6.7e+00 9.7e-03 1.6e+00 1.00e+00 1.511044133e+02 1.513554053e+02 1.1e+00 0.00 -4 1.2e+00 1.7e-03 2.8e-01 -8.37e-01 1.618720919e+02 1.664080188e+02 2.0e-01 0.00 -5 8.4e-01 1.2e-03 2.0e-01 1.02e+00 1.662532913e+02 1.686530752e+02 1.4e-01 0.00 -6 1.0e-01 1.5e-04 2.5e-02 8.01e-01 1.738862797e+02 1.740213695e+02 1.8e-02 0.00 -7 2.9e-03 4.2e-06 6.9e-04 1.04e+00 1.747733946e+02 1.747739454e+02 4.9e-04 0.00 -8 1.3e-05 1.8e-08 3.0e-06 1.01e+00 1.747988150e+02 1.747988194e+02 2.2e-06 0.00 -9 1.3e-09 1.8e-12 3.1e-10 1.00e+00 1.747989692e+02 1.747989692e+02 2.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896924e+02 nrm: 5e+04 Viol. con: 9e-08 var: 0e+00 - Dual. obj: 1.7479896924e+02 nrm: 6e+01 Viol. con: 1e-13 var: 5e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e+02 nrm: 5e+04 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 1.7479896927e+02 nrm: 6e+01 Viol. con: 0e+00 var: 9e-08 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925381036. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 20:16:38 -2026-02-15 20:16:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-15 20:16:38 -2026-02-15 20:16:38 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. - - System with new buses created: {'north', 'center', 'south'} - - System with new buses created: {'north', 'center', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - Cloning components: ['capacity_factors', 'timepoints', 'timeseries', 'scenarios'] completed. - - New system has: - - New system has: - - 5 'generators' components. - - 5 'generators' components. - - 1 'capacity_factors' components. - - 1 'capacity_factors' components. - - 1 'storage' components. - - 1 'storage' components. - - 0 'infinite_sources' components. - - 0 'infinite_sources' components. - - 3 'buses' components. - - 3 'buses' components. - - 5 'loads' components. - - 5 'loads' components. - - 4 'lines' components. - - 4 'lines' components. - - 0 'branch_series_rl' components. - - 0 'branch_series_rl' components. - - 0 'shunt_parallel_rl' components. - - 0 'shunt_parallel_rl' components. - - 1 'timeseries' components. - - 1 'timeseries' components. - - 1 'timepoints' components. - - 1 'timepoints' components. - - 1 'scenarios' components. - - 1 'scenarios' components. - - 0 'energy_budgets' components. - - 0 'energy_budgets' components. - - 0 'carbon_policies' components. - - 0 'carbon_policies' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be grouped and summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=1, bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='center'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -278.9478509254434 - - Maximum coefficient: -278.9478509254434 - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=2, bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxCharge[Storage(id=0),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 60000.0 - - Maximum RHS: 60000.0 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='south'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 1.4810000000e+02 nrm: 6e+04 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 - Dual. obj: 1.4810000000e+02 nrm: 3e+01 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.000000000007. - -> Objective value: 14810.000000000007. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/buses.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/buses.csv deleted file mode 100644 index 7238617..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,bus_type -1,slack -2,PQ -3,PQ -4,PQ -5,PQ \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/capacity_factors.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/capacity_factors.csv deleted file mode 100644 index a9342d1..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -cf_one,sc1,1,solar,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/generators.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/generators.csv deleted file mode 100644 index 077e412..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -1,gas,1,cf_one,0,14,0,0,40,40,0 -2,gas,1,cf_one,0,15,0,0,170,170,0 -3,gas,3,cf_one,0,30,0,0,520,520,0 -4,gas,4,cf_one,0,40,0,0,200,200,0 -5,gas,5,cf_one,0,10,0,0,600,600,0 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/lines.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/lines.csv deleted file mode 100644 index 1fba0a2..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,100,FALSE,0,0.01,0,0,-360,360 -2,1,4,200,FALSE,0,0.01,0,0,-360,360 -3,1,5,100,FALSE,0,0.01,0,0,-360,360 -4,2,3,200,FALSE,0,0.01,0,0,-360,360 -5,3,4,100,FALSE,0,0.01,0,0,-360,360 -6,4,5,200,FALSE,0,0.01,0,0,-360,360 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/loads.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/loads.csv deleted file mode 100644 index 346e5bd..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/loads.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,load_MW -1,sc1,1,300 -2,sc1,1,0 -3,sc1,1,300 -4,sc1,1,400 -5,sc1,1,0 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/scenarios.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/storage.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/storage.csv deleted file mode 100644 index abcb9eb..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus,name,c0_USD,c1_USDperMWh,c2_USDperMWh2,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,technology -1,cats_1,0,0,0,0,0,0,0,0,0,0,0.92,0.92,hydroelectric pumped storage \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/timepoints.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/timepoints.csv deleted file mode 100644 index 2d8d232..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timeseries -1,winter \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/inputs/timeseries.csv b/examples/capacity_expansion/5bus_kron_1h/inputs/timeseries.csv deleted file mode 100644 index 11ad9c3..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 2a862b6..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,20810.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,20810.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index aa1232c..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,Capacity_MW diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 2a862b6..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,20810.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,20810.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index b310916..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -generator,timepoint,Dispatch_MW diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_built_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_built_capacity.csv deleted file mode 100644 index 0755db9..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1,7 +0,0 @@ -line,capacity_MW -1,0.0 -2,0.0 -3,0.0 -4,0.0 -5,0.0 -6,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_capacities.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_capacities.csv deleted file mode 100644 index 51ec659..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_capacities.csv +++ /dev/null @@ -1,7 +0,0 @@ -line_pi,Capacity_MW -1,400.0 -2,0.0 -3,0.0 -4,0.0 -5,0.0 -6,240.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 49ae0c0..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_flows.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index ea31521..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,1,0.0,0.5837590765688607,-35.8990801047472,3.621370506151428 -4,2,3,sc1,1,0.5837590765688607,0.8081219956771774,-35.899080104747206,1.3918434685564212 -2,1,4,sc1,1,0.0,-1.84041282307742,104.61589160573493,33.27123372044716 -5,3,4,sc1,1,0.8081219956771774,-1.84041282307742,154.1009198952528,70.52886773231245 -3,1,5,sc1,1,0.0,0.5878234541534619,-158.71681150098775,16.12225680194565 -6,4,5,sc1,1,-1.84041282307742,0.5878234541534619,-141.28318849901223,59.28398987676884 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index e135596..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -1,sc1,1,0.0 -2,sc1,1,0.0 -3,sc1,1,0.0 -4,sc1,1,0.0 -5,sc1,1,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 83f7d37..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index f0f1175..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,30.000000008185214 -2,sc1,1,30.00000000648072 -3,sc1,1,30.00000000552379 -4,sc1,1,30.00000000929578 -5,sc1,1,10.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices_USDperMWh.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices_USDperMWh.csv deleted file mode 100644 index b5cd5b9..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/local_marginal_prices_USDperMWh.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,-4.9544594476215404e-8 -2,sc1,1,1.7865926206089043e-6 -3,sc1,1,1.4610694710779029e-6 -4,sc1,1,5.658808098676484e-7 -5,sc1,1,1.3794769633506266e-8 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index 4402961..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -cats_1,sc1,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 66a951d..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,Capacity_MW -1,sc1,0.0 -2,sc1,0.0 -3,sc1,0.0 -4,sc1,0.0 -5,sc1,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 775b689..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,490.00000000000006 -4,sc1,1,0.0 -5,sc1,1,300.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/costs_summary.csv deleted file mode 100644 index 2a862b6..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,20810.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,20810.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_capacity.csv deleted file mode 100644 index aa1232c..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,Capacity_MW diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 2a862b6..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,20810.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,20810.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index b310916..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -generator,timepoint,Dispatch_MW diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_built_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_flows.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_flows.csv deleted file mode 100644 index d0cfc1d..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -Y_kron_f1-t3,1,3,sc1,1,0.0,0.8080333493539349,-35.902395596013704,5.012134044707489 -Y_kron_f1-t4,1,4,sc1,1,0.0,-1.840444486002598,104.61769144385102,33.272378543644095 -Y_kron_f3-t4,3,4,sc1,1,0.8080333493539349,-1.840444486002598,154.09760440398634,70.52583289865099 -Y_kron_f1-t5,1,5,sc1,1,0.0,0.5878178407816852,-158.71529584783735,16.121948887082585 -Y_kron_f4-t5,4,5,sc1,1,-1.840444486002598,0.5878178407816852,-141.28470415216262,59.28526185327143 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding.csv deleted file mode 100644 index 854f842..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,5 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -1,sc1,1,0.0 -3,sc1,1,0.0 -4,sc1,1,0.0 -5,sc1,1,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 83f7d37..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 58dd816..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,5 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,30.000000009503577 -3,sc1,1,30.00000000475768 -4,sc1,1,30.000000012016958 -5,sc1,1,10.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index 4402961..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -cats_1,sc1,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_capacity.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 66a951d..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,Capacity_MW -1,sc1,0.0 -2,sc1,0.0 -3,sc1,0.0 -4,sc1,0.0 -5,sc1,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_dispatch.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 775b689..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,490.00000000000006 -4,sc1,1,0.0 -5,sc1,1,300.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv deleted file mode 100644 index c1d2585..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv +++ /dev/null @@ -1,6 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,3,100.0 -1,4,200.0 -1,5,100.0 -3,4,100.0 -4,5,200.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_optimization.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_optimization.csv deleted file mode 100644 index 9555edc..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_line_capacity_via_optimization.csv +++ /dev/null @@ -1,6 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,3,83.3333333333333 -1,4,200.0 -1,5,100.0 -3,4,99.99999999999999 -4,5,175.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_removable_buses.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_removable_buses.csv deleted file mode 100644 index aa67fed..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/kron_removable_buses.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus -2 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv deleted file mode 100644 index ca414ff..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,300.0,0.0,100.0,100.0,100.0 -3,0.0,200.0,100.0,0.0,100.0 -4,100.0,100.0,300.0,100.0,0.0 -5,100.0,0.0,100.0,200.0,0.0 -2,100.0,100.0,0.0,0.0,200.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_conductance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_conductance_matrix.csv deleted file mode 100644 index 0dda322..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_conductance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,0.0,0.0,0.0,0.0,0.0 -3,0.0,0.0,0.0,0.0,0.0 -4,0.0,0.0,0.0,0.0,0.0 -5,0.0,0.0,0.0,0.0,0.0 -2,0.0,0.0,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_susceptance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_susceptance_matrix.csv deleted file mode 100644 index f798d8f..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/original_system_susceptance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,-300.0,0.0,100.0,100.0,100.0 -3,0.0,-200.0,100.0,0.0,100.0 -4,100.0,100.0,-300.0,100.0,0.0 -5,100.0,0.0,100.0,-200.0,0.0 -2,100.0,100.0,0.0,0.0,-200.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv deleted file mode 100644 index 15e5cc9..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,5 -1,250.0,50.0,100.0,100.0 -3,50.0,150.0,100.0,0.0 -4,100.0,100.0,300.0,100.0 -5,100.0,0.0,100.0,200.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_conductance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_conductance_matrix.csv deleted file mode 100644 index 4b272d7..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_conductance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,5 -1,0.0,0.0,0.0,0.0 -3,0.0,0.0,0.0,0.0 -4,0.0,0.0,0.0,0.0 -5,0.0,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_susceptance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_susceptance_matrix.csv deleted file mode 100644 index e7d50f4..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/reduced_susceptance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,5 -1,-250.0,50.0,100.0,100.0 -3,50.0,-150.0,100.0,0.0 -4,100.0,100.0,-300.0,100.0 -5,100.0,0.0,100.0,-200.0 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_absolute_admittance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_absolute_admittance_matrix.csv deleted file mode 100644 index a1850c2..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,223.57188682712035,0.0,32.73148652006543,155.4745609703108,35.41057616405655 -3,0.0,125.61087425062001,33.50293569730603,0.0,92.13307316759158 -4,32.73148652006543,33.50293569730603,99.7173974886193,33.50293569730603,0.0 -5,155.4745609703108,0.0,33.50293569730603,188.93968529222374,0.0 -2,35.41057616405655,92.13307316759158,0.0,0.0,127.51813660361303 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_conductance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_conductance_matrix.csv deleted file mode 100644 index 7adc9dc..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_conductance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,22.250685688535143,0.0,-3.2569046378322044,-15.470297029702971,-3.523484020999965 -3,0.0,12.5012501250125,-3.3336667000033335,0.0,-9.167583425009166 -4,-3.2569046378322044,-3.3336667000033335,9.924238037838872,-3.3336667000033335,0.0 -5,-15.470297029702971,0.0,-3.3336667000033335,18.803963729706304,0.0 -2,-3.523484020999965,-9.167583425009166,0.0,0.0,12.691067446009132 diff --git a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_susceptance_matrix.csv b/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_susceptance_matrix.csv deleted file mode 100644 index 7a25817..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/outputs/kron_reduction/system_susceptance_matrix.csv +++ /dev/null @@ -1,6 +0,0 @@ -Index,1,3,4,5,2 -1,-222.4618968853514,0.0,32.56904637832204,154.7029702970297,35.234840209999646 -3,0.0,-124.98724125012501,33.33666700003334,0.0,91.67583425009167 -4,32.56904637832204,33.33666700003334,-99.22232037838872,33.33666700003334,0.0 -5,154.7029702970297,0.0,33.33666700003334,-188.00163729706304,0.0 -2,35.234840209999646,91.67583425009167,0.0,0.0,-126.88503446009132 diff --git a/examples/capacity_expansion/5bus_kron_1h/sting_log.txt b/examples/capacity_expansion/5bus_kron_1h/sting_log.txt deleted file mode 100644 index 2fbe35a..0000000 --- a/examples/capacity_expansion/5bus_kron_1h/sting_log.txt +++ /dev/null @@ -1,31599 +0,0 @@ -2026-01-11 11:34:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.01 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 11:34:18 -2026-01-11 11:34:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1470110.00 USD. -> Objective value: 1470110.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.03 seconds. - ->> Run completed in 0.03 seconds. -2026-01-11 11:44:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 11:44:19 -2026-01-11 11:44:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1470110.00 USD. -> Objective value: 1470110.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.03 seconds. - ->> Run completed in 0.03 seconds. -2026-01-11 12:18:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 26 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.4701100000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.4701100000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1470110.00 USD. -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.06 seconds. -2026-01-11 12:18:40 -2026-01-11 12:18:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 1.4701100000e+00 nrm: 5e-03 Viol. con: 0e+00 var: 4e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1470110.00 USD. -> Objective value: 1470110.00 USD. -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.03 seconds. - ->> Run completed in 0.03 seconds. -2026-01-11 12:19:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.02 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.01 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.02 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 26 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.4701100000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4701100000e+00 nrm: 4e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.4701100000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1470110.00 USD. -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.13 seconds. -2026-01-11 12:20:01 -2026-01-11 12:20:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. -2026-01-11 12:22:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.06 seconds. -2026-01-11 12:22:08 -2026-01-11 12:22:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 13 - Constraints : 13 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:45:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...Rule failed for Expression 'eGenTotalCost' with index None: -TypeError: unsupported operand type(s) for *: 'ExpressionData' and 'NoneType'Constructing component 'eGenTotalCost' from data=None failed: - TypeError: unsupported operand type(s) for *: 'ExpressionData' and 'NoneType'2026-01-11 12:49:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 20 after factor : 21 -Factor - dense dim. : 0 flops : 2.17e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.6e+02 2.6e+02 3.8e+01 0.00e+00 3.849054605e+01 1.127261451e+00 2.5e-01 0.00 -1 1.1e+01 8.0e+00 1.2e+00 -9.77e-01 2.830526693e+01 6.810623011e+00 7.7e-03 0.00 -2 5.7e-01 4.2e-01 6.0e-02 -3.38e-01 4.893203248e+00 7.998857189e+00 4.0e-04 0.00 -3 2.0e-01 1.5e-01 2.1e-02 8.51e-01 2.684913050e+00 4.022176809e+00 1.4e-04 0.00 -4 3.7e-02 2.7e-02 3.9e-03 9.23e-01 1.472916033e+00 1.537927876e+00 2.6e-05 0.00 -5 1.3e-02 9.2e-03 1.3e-03 1.10e+00 6.587088901e-01 6.716763294e-01 8.9e-06 0.00 -6 2.8e-03 2.0e-03 2.9e-04 1.03e+00 5.078650989e-01 5.103609306e-01 1.9e-06 0.00 -7 6.8e-05 4.9e-05 7.1e-06 9.90e-01 4.762609246e-01 4.761857460e-01 4.8e-08 0.00 -8 7.3e-09 5.3e-09 7.7e-10 1.00e+00 4.751101302e-01 4.751101209e-01 5.1e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.7511013021e-01 nrm: 4e+02 Viol. con: 1e-05 var: 0e+00 - Dual. obj: 4.7510994646e-01 nrm: 5e-03 Viol. con: 6e-10 var: 3e-07 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.7511000000e-01 nrm: 4e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 4.7511017195e-01 nrm: 5e-03 Viol. con: 3e-09 var: 2e-06 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 475110.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 12:49:03 -2026-01-11 12:49:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 27 - Scalar variables : 27 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4Eliminator terminated. -Eliminator terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 3 -Optimizer - Constraints : 3 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 9 conic : 0 -Optimizer - Scalar variables : 9 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 6 after factor : 6 -Factor - nonzeros before factor : 6 after factor : 6 Factor - dense dim. : 0 flops : 4.60e+01 -Factor - dense dim. : 0 flops : 4.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.3e+03 5.8e-01 8.4e+01 0.00e+00 8.632096985e+00 2.644307046e+01 1.0e+02 0.00 -0 1.3e+03 5.8e-01 8.4e+01 0.00e+00 8.632096985e+00 2.644307046e+01 1.0e+02 0.00 1 4.3e+02 1.9e-01 2.8e+01 3.79e+00 3.632169133e+00 2.605251832e+01 3.4e+01 0.00 -1 4.3e+02 1.9e-01 2.8e+01 3.79e+00 3.632169133e+00 2.605251832e+01 3.4e+01 0.00 2 7.0e+01 3.1e-02 4.5e+00 1.32e+00 2.634465267e+00 5.066847265e+00 5.5e+00 0.00 -2 7.0e+01 3.1e-02 4.5e+00 1.32e+00 2.634465267e+00 5.066847265e+00 5.5e+00 0.00 3 1.2e+01 5.2e-03 7.6e-01 1.17e+00 1.406934135e+00 1.708725247e+00 9.2e-01 0.00 -3 1.2e+01 5.2e-03 7.6e-01 1.17e+00 1.406934135e+00 1.708725247e+00 9.2e-01 0.00 4 2.1e+00 9.4e-04 1.4e-01 1.02e+00 1.149522124e+00 1.195177207e+00 1.7e-01 0.00 -4 2.1e+00 9.4e-04 1.4e-01 1.02e+00 1.149522124e+00 1.195177207e+00 1.7e-01 0.00 5 2.9e-02 1.3e-05 1.9e-03 1.00e+00 1.120937096e+00 1.121464732e+00 2.3e-03 0.00 -5 2.9e-02 1.3e-05 1.9e-03 1.00e+00 1.120937096e+00 1.121464732e+00 2.3e-03 0.00 6 2.9e-06 1.3e-09 1.9e-07 1.00e+00 1.120710023e+00 1.120710076e+00 2.3e-07 0.00 -6 2.9e-06 1.3e-09 1.9e-07 1.00e+00 1.120710023e+00 1.120710076e+00 2.3e-07 0.00 7 2.9e-10 1.3e-13 1.9e-11 1.00e+00 1.120710000e+00 1.120710000e+00 2.3e-11 0.00 -7 2.9e-10 1.3e-13 1.9e-11 1.00e+00 1.120710000e+00 1.120710000e+00 2.3e-11 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 2 Time: 0.00 -Primal. Iterations: 2 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 8e-11 var: 0e+00 - Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 8e-11 var: 0e+00 Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 8e-15 var: 3e-14 - Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 8e-15 var: 3e-14 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 2e-14 var: 9e-14 - Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 2e-14 var: 9e-14 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1120710.00 USD. -> Objective value: 1120710.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.01 seconds]. -ok [0.01 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:52:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.4e+03 3.6e-01 9.1e+01 0.00e+00 7.150676667e+00 2.493688668e+01 1.1e+02 0.00 -1 3.4e+02 5.3e-02 1.3e+01 3.45e+00 1.835247329e+00 1.148401131e+00 1.6e+01 0.00 -2 3.8e+01 5.9e-03 1.5e+00 1.40e+00 8.692492356e-01 8.109740394e-01 1.8e+00 0.00 -3 3.9e+00 6.0e-04 1.5e-01 1.12e+00 5.310626305e-01 5.224564329e-01 1.8e-01 0.00 -4 3.7e-02 5.7e-06 1.4e-03 1.02e+00 4.752629994e-01 4.751727984e-01 1.7e-03 0.00 -5 3.7e-06 5.8e-10 1.4e-07 1.00e+00 4.751100156e-01 4.751100065e-01 1.7e-07 0.00 -6 3.7e-10 5.7e-14 1.4e-11 1.00e+00 4.751100000e-01 4.751100000e-01 1.7e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.7511000000e-01 nrm: 5e+02 Viol. con: 8e-11 var: 0e+00 - Dual. obj: 4.7511000000e-01 nrm: 5e-03 Viol. con: 1e-14 var: 1e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.7511000000e-01 nrm: 4e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 4.7511000001e-01 nrm: 5e-03 Viol. con: 7e-14 var: 7e-14 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 475110.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 12:52:57 -2026-01-11 12:52:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 27 - Scalar variables : 27 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4Eliminator terminated. -Eliminator terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 3 -Optimizer - Constraints : 3 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 9 conic : 0 -Optimizer - Scalar variables : 9 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 6 after factor : 6 -Factor - nonzeros before factor : 6 after factor : 6 Factor - dense dim. : 0 flops : 4.60e+01 -Factor - dense dim. : 0 flops : 4.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.3e+03 5.8e-01 8.4e+01 0.00e+00 8.632096985e+00 2.644307046e+01 1.0e+02 0.00 -0 1.3e+03 5.8e-01 8.4e+01 0.00e+00 8.632096985e+00 2.644307046e+01 1.0e+02 0.00 1 4.3e+02 1.9e-01 2.8e+01 3.79e+00 3.632169133e+00 2.605251832e+01 3.4e+01 0.00 -1 4.3e+02 1.9e-01 2.8e+01 3.79e+00 3.632169133e+00 2.605251832e+01 3.4e+01 0.00 2 7.0e+01 3.1e-02 4.5e+00 1.32e+00 2.634465267e+00 5.066847265e+00 5.5e+00 0.00 -2 7.0e+01 3.1e-02 4.5e+00 1.32e+00 2.634465267e+00 5.066847265e+00 5.5e+00 0.00 3 1.2e+01 5.2e-03 7.6e-01 1.17e+00 1.406934135e+00 1.708725247e+00 9.2e-01 0.00 -3 1.2e+01 5.2e-03 7.6e-01 1.17e+00 1.406934135e+00 1.708725247e+00 9.2e-01 0.00 4 2.1e+00 9.4e-04 1.4e-01 1.02e+00 1.149522124e+00 1.195177207e+00 1.7e-01 0.00 -4 2.1e+00 9.4e-04 1.4e-01 1.02e+00 1.149522124e+00 1.195177207e+00 1.7e-01 0.00 5 2.9e-02 1.3e-05 1.9e-03 1.00e+00 1.120937096e+00 1.121464732e+00 2.3e-03 0.00 -5 2.9e-02 1.3e-05 1.9e-03 1.00e+00 1.120937096e+00 1.121464732e+00 2.3e-03 0.00 6 2.9e-06 1.3e-09 1.9e-07 1.00e+00 1.120710023e+00 1.120710076e+00 2.3e-07 0.00 -6 2.9e-06 1.3e-09 1.9e-07 1.00e+00 1.120710023e+00 1.120710076e+00 2.3e-07 0.00 7 2.9e-10 1.3e-13 1.9e-11 1.00e+00 1.120710000e+00 1.120710000e+00 2.3e-11 0.00 -7 2.9e-10 1.3e-13 1.9e-11 1.00e+00 1.120710000e+00 1.120710000e+00 2.3e-11 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 2 Time: 0.00 -Primal. Iterations: 2 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 8e-11 var: 0e+00 - Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 8e-11 var: 0e+00 Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 8e-15 var: 3e-14 - Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 8e-15 var: 3e-14 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 1.1207100000e+00 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 2e-14 var: 9e-14 - Dual. obj: 1.1207100000e+00 nrm: 5e-03 Viol. con: 2e-14 var: 9e-14 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1120710.00 USD. -> Objective value: 1120710.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:54:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.01 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 12:54:10 -2026-01-11 12:54:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 13 - Constraints : 13 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 27 - Scalar variables : 27 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 - Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 - Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 376710.00 USD. -> Objective value: 376710.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.01 seconds]. -ok [0.01 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:54:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 12:54:20 -2026-01-11 12:54:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 13 - Constraints : 13 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 27 - Scalar variables : 27 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 - Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 - Primal. obj: 3.7671000000e-01 nrm: 5e+02 Viol. con: 6e-14 var: 0e+00 Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 - Dual. obj: 3.7671000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 6e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 376710.00 USD. -> Objective value: 376710.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.03 seconds. - ->> Run completed in 0.03 seconds. -2026-01-11 12:58:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 4e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 12:58:16 -2026-01-11 12:58:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 13 - Constraints : 13 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 - Dual. obj: 1.4810000000e-02 nrm: 5e-03 Viol. con: 0e+00 var: 3e-17 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:59:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.00 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 12:59:09 -2026-01-11 12:59:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 12:59:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 12:59:15 -2026-01-11 12:59:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.03 seconds. - ->> Run completed in 0.03 seconds. -2026-01-11 13:12:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.09 seconds. -2026-01-11 13:12:30 -2026-01-11 13:12:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Kron reduction will remove 1 buses out of 5 total buses.> Kron reduction will remove 1 buses out of 5 total buses. Completed 'get_remove_buses' in 0.00 seconds. Completed 'get_remove_buses' in 0.00 seconds.> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 13:13:23 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 13:13:23 -2026-01-11 13:13:23 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Kron reduction will remove 1 buses out of 5 total buses.> Kron reduction will remove 1 buses out of 5 total buses. Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.01 seconds]. -ok [0.01 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.02 seconds. - Total: 0.02 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 13:13:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.00 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 13:13:58 -2026-01-11 13:13:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Kron reduction will remove 1 buses out of 5 total buses. -> Kron reduction will remove 1 buses out of 5 total buses. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 28 - Scalar variables : 28 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus results ... - Bus results ...ok [0.01 seconds]. -ok [0.01 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -2026-01-11 16:13:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...Rule failed for Expression 'eCostPerTp' with index Timepoint(name='1', timeseries='winter', id=0, timeseries_id=0, weight=1.0, duration_hr=1.0, prev_timepoint_id=0): -TypeError: attribute name must be string, not 'IndexedExpression'Constructing component 'eCostPerTp' from data=None failed: - TypeError: attribute name must be string, not 'IndexedExpression'2026-01-11 16:14:46 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...2026-01-11 16:17:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... ok [0.00 seconds]. - - 'buses.csv' ... ok [0.00 seconds]. - - 'timeseries.csv' ... ok [0.00 seconds]. - - 'timepoints.csv' ... ok [0.00 seconds]. - - 'scenarios.csv' ... ok [0.00 seconds]. - - 'loads.csv' ... ok [0.00 seconds]. - - 'generators.csv' ... ok [0.00 seconds]. - - 'capacity_factors.csv' ... ok [0.00 seconds]. - - 'storage.csv' ... ok [0.00 seconds]. - Total: 0.01 seconds. -> Constructing capacity expansion model: - - Generators variables and constraints ...ok [0.00 seconds]. - - Storage variables and constraints ...ok [0.00 seconds]. - - Bus variables and constraints ...ok [0.00 seconds]. - - Objective function ...ok [0.00 seconds]. - Total: 0.01 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ...ok [0.01 seconds]. - - Storage results ...ok [0.01 seconds]. - - Bus results ...ok [0.01 seconds]. - Total: 0.02 seconds. - ->> Run completed in 0.10 seconds. -2026-01-11 16:17:12 -2026-01-11 16:17:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== -> System initialization ...> System initialization ...... ok. -... ok. -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs -> Load components via CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs - - 'lines.csv' ... - 'lines.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'buses.csv' ... - 'buses.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timeseries.csv' ... - 'timeseries.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'timepoints.csv' ... - 'timepoints.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'scenarios.csv' ... - 'scenarios.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'loads.csv' ... - 'loads.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'generators.csv' ... - 'generators.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'capacity_factors.csv' ... - 'capacity_factors.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - - 'storage.csv' ... - 'storage.csv' ... ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. -> Kron reduction will remove 1 buses out of 5 total buses. -> Kron reduction will remove 1 buses out of 5 total buses. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Kron reduction completed. -> Kron reduction completed. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Constructing capacity expansion model: -> Constructing capacity expansion model: - - Generators variables and constraints ... - Generators variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage variables and constraints ... - Storage variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Bus variables and constraints ... - Bus variables and constraints ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Objective function ... - Objective function ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.00 seconds. - Total: 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem Name : - Name : Objective sense : minimize - Objective sense : minimize Type : LO (linear optimization problem) - Type : LO (linear optimization problem) Constraints : 17 - Constraints : 17 Affine conic cons. : 0 - Affine conic cons. : 0 Disjunctive cons. : 0 - Disjunctive cons. : 0 Cones : 0 - Cones : 0 Scalar variables : 23 - Scalar variables : 23 Matrix variables : 0 - Matrix variables : 0 Integer variables : 0 - Integer variables : 0 -Optimizer started. -Optimizer started.Presolve started. -Presolve started.Eliminator started. -Eliminator started.Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3Eliminator terminated. -Eliminator terminated.Linear dependency checker started. -Linear dependency checker started.Linear dependency checker terminated. -Linear dependency checker terminated.Eliminator started. -Eliminator started.Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0Eliminator terminated. -Eliminator terminated.Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 Optimizer - threads : 24 -Optimizer - threads : 24 Optimizer - solved problem : the primal -Optimizer - solved problem : the primal Optimizer - Constraints : 4 -Optimizer - Constraints : 4 Optimizer - Cones : 0 -Optimizer - Cones : 0 Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.00 -Factor - setup time : 0.00 Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 Basis identification started. -Basis identification started.Basis identification initialization started. -Basis identification initialization started.Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00Primal basis identification phase started. -Primal basis identification phase started.Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00Dual basis identification phase started. -Dual basis identification phase started.Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00Initialization. Time: 0.00 -Initialization. Time: 0.00 Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - -Interior-point solution summary -Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 -Basic solution summary -Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL - Solution status : OPTIMAL Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 > Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - Generators results ...ok [0.00 seconds]. -ok [0.00 seconds]. - - Storage results ... - Storage results ...ok [0.01 seconds]. -ok [0.01 seconds]. - - Bus results ... - Bus results ...ok [0.00 seconds]. -ok [0.00 seconds]. - Total: 0.01 seconds. - Total: 0.01 seconds. - ->> Run completed in 0.04 seconds. - ->> Run completed in 0.04 seconds. -> Read of component data from csv files. initializing ... -2026-01-11 23:54:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.01 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.01 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.01 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.40 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.01 seconds. - ->> Run completed in 0.41 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-11 23:54:58 -2026-01-11 23:54:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. initializing ... -2026-01-11 23:57:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.02 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.01 seconds. - - Bus results ... - Completed in 0.02 seconds. -> Export of results completed in 0.03 seconds. - ->> Run completed in 0.11 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-11 23:57:48 -2026-01-11 23:57:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. initializing ... -2026-01-11 23:59:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.01 seconds. - ->> Run completed in 0.06 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-11 23:59:09 -2026-01-11 23:59:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. initializing ... -2026-01-11 23:59:41 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.02 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.01 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.01 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.01 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.01 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.01 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.01 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.01 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.01 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.01 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.01 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.01 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.01 seconds. - - Bus results ... - Completed in 0.02 seconds. -> Export of results completed in 0.03 seconds. - ->> Run completed in 0.11 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-11 23:59:42 -2026-01-11 23:59:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. initializing ... -2026-01-12 00:00:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.04 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-12 00:00:57 -2026-01-12 00:00:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. initializing ... -2026-01-12 00:01:39 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.04 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-12 00:01:39 -2026-01-12 00:01:39 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Identifying buses for Kron reduction... -> Identifying buses for Kron reduction... -> Total number of buses: 5 -> Total number of buses: 5 -> Buses with either generation, load or storage: 4 -> Buses with either generation, load or storage: 4 -> Kron reduction will remove 1 buses out of 5 total buses. -> Kron reduction will remove 1 buses out of 5 total buses. -> Reduction of the system via Kron reduction. initializing ... -> Reduction of the system via Kron reduction. initializing ... -> Performing Kron reduction... - -> Performing Kron reduction... - -> Original system has 5 buses and 6 lines. - -> Original system has 5 buses and 6 lines. - -> Reduced system has 4 buses and 4 lines. -> Reduced system has 4 buses and 4 lines. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Constructing capacity expansion model ... -> Constructing capacity expansion model ... - - Generators variables and constraints ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage variables and constraints ... - - Storage variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus variables and constraints ... - - Bus variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Objective function ... - - Objective function ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - - Generators results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage results ... - - Storage results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus results ... - - Bus results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -> Read of component data from csv files. initializing ... -2026-01-12 00:05:26 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.02 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.03 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.06 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-12 00:05:26 -2026-01-12 00:05:26 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Identifying buses for Kron reduction... -> Identifying buses for Kron reduction... -> Total number of buses: 5 -> Total number of buses: 5 -> Buses with either generation, load or storage: 4 -> Buses with either generation, load or storage: 4 -> Kron reduction will remove 1 buses out of 5 total buses. -> Kron reduction will remove 1 buses out of 5 total buses. -> Reduction of the system via Kron reduction. initializing ... -> Reduction of the system via Kron reduction. initializing ... - - Original system has 5 buses and 6 lines. - - - Original system has 5 buses and 6 lines. - - - Reduced system has 4 buses and 4 lines. - - Reduced system has 4 buses and 4 lines. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Constructing capacity expansion model ... -> Constructing capacity expansion model ... - - Generators variables and constraints ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage variables and constraints ... - - Storage variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus variables and constraints ... - - Bus variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Objective function ... - - Objective function ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - - Generators results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage results ... - - Storage results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus results ... - - Bus results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -> Read of component data from csv files. initializing ... -2026-01-12 00:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.03 seconds. - -> Read of component data from csv files. initializing ... -> Read of component data from csv files. initializing ... -2026-01-12 00:06:45 -2026-01-12 00:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Read of component data from csv files. completed in 0.00 seconds. -> Identify removable buses for Kron reduction. initializing ... -> Identify removable buses for Kron reduction. initializing ... -> Identifying buses for Kron reduction... -> Identifying buses for Kron reduction... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Identify removable buses for Kron reduction. completed in 0.00 seconds. -> Identify removable buses for Kron reduction. completed in 0.00 seconds. -> Reduction of the system via Kron reduction. initializing ... -> Reduction of the system via Kron reduction. initializing ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Reduced system has 4 buses and 4 lines. - - Reduced system has 4 buses and 4 lines. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Reduction of the system via Kron reduction. completed in 0.00 seconds. -> Constructing capacity expansion model ... -> Constructing capacity expansion model ... - - Generators variables and constraints ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage variables and constraints ... - - Storage variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus variables and constraints ... - - Bus variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Objective function ... - - Objective function ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - - Generators results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage results ... - - Storage results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus results ... - - Bus results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -> Initializing Read of component data from csv files. ... -2026-01-12 00:08:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Completed Read of component data from csv files. in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.04 seconds. - -> Initializing Read of component data from csv files. ... -> Initializing Read of component data from csv files. ... -2026-01-12 00:08:01 -2026-01-12 00:08:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Completed Read of component data from csv files. in 0.00 seconds. -> Completed Read of component data from csv files. in 0.00 seconds. -> Initializing Identify removable buses for Kron reduction. ... -> Initializing Identify removable buses for Kron reduction. ... -> Identifying buses for Kron reduction... -> Identifying buses for Kron reduction... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed Identify removable buses for Kron reduction. in 0.00 seconds. -> Completed Identify removable buses for Kron reduction. in 0.00 seconds. -> Initializing Reduction of the system via Kron reduction. ... -> Initializing Reduction of the system via Kron reduction. ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Reduced system has 4 buses and 4 lines. - - Reduced system has 4 buses and 4 lines. -> Completed Reduction of the system via Kron reduction. in 0.00 seconds. -> Completed Reduction of the system via Kron reduction. in 0.00 seconds. -> Constructing capacity expansion model ... -> Constructing capacity expansion model ... - - Generators variables and constraints ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage variables and constraints ... - - Storage variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus variables and constraints ... - - Bus variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Objective function ... - - Objective function ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - - Generators results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage results ... - - Storage results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus results ... - - Bus results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -> Initializing read of component data from csv files ... -2026-01-12 00:10:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Completed read of component data from csv files in 0.00 seconds. -> Constructing capacity expansion model ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - - Storage variables and constraints ... - Completed in 0.00 seconds. - - Bus variables and constraints ... - Completed in 0.00 seconds. - - Objective function ... - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion : - - Generators results ... - Completed in 0.00 seconds. - - Storage results ... - Completed in 0.00 seconds. - - Bus results ... - Completed in 0.00 seconds. -> Export of results completed in 0.01 seconds. - ->> Run completed in 0.04 seconds. - -> Initializing read of component data from csv files ... -> Initializing read of component data from csv files ... -2026-01-12 00:10:48 -2026-01-12 00:10:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: -> Loading components via CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs: - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Completed read of component data from csv files in 0.00 seconds. -> Completed read of component data from csv files in 0.00 seconds. -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Identifying buses for Kron reduction... -> Identifying buses for Kron reduction... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed identify removable buses for Kron reduction in 0.00 seconds. -> Completed identify removable buses for Kron reduction in 0.00 seconds. -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Reduced system has 4 buses and 4 lines. - - Reduced system has 4 buses and 4 lines. -> Completed reduction of the system via Kron reduction in 0.00 seconds. -> Completed reduction of the system via Kron reduction in 0.00 seconds. -> Constructing capacity expansion model ... -> Constructing capacity expansion model ... - - Generators variables and constraints ... - - Generators variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage variables and constraints ... - - Storage variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus variables and constraints ... - - Bus variables and constraints ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Objective function ... - - Objective function ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Construction completed in 0.00 seconds. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.1e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : -> Exporting results in /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion : - - Generators results ... - - Generators results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Storage results ... - - Storage results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - Bus results ... - - Bus results ... - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. -> Export of results completed in 0.00 seconds. - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-14 18:13:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.01 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-14 18:13:38 -2026-01-14 18:13:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Reduced system has 4 buses and 5 lines. - - Reduced system has 4 buses and 5 lines. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 10 variables - Size: 10 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 4 variables - Size: 4 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 5 constraints - Size: 5 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 4 expressions - Size: 4 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 1 expressions - Size: 1 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 5 variables - Size: 5 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 2 constraints - Size: 2 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 1 constraints - Size: 1 constraints - - State of charge constraints - - State of charge constraints - Size: 5 constraints - Size: 5 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 4 variables - Size: 4 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 4 constraints - Size: 4 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 4 constraints - Size: 4 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.09 seconds. - - ->> Run completed in 0.09 seconds. - -2026-01-16 16:51:41 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-16 16:51:41 -2026-01-16 16:51:41 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -2026-01-16 16:52:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.01 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.04 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-16 16:52:17 -2026-01-16 16:52:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 -2026-01-16 16:52:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-01-16 16:52:56 -2026-01-16 16:52:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... -2026-01-16 16:53:26 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.01 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-16 16:53:26 -2026-01-16 16:53:26 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. -Rule failed when generating expression for Constraint cFlowPerExpLine with index LinePiModel(id=0, name='1', from_bus='1', to_bus='2', r_pu=0.00281, x_pu=0.0281, g_pu=0.0, b_pu=0.00712, expand_capacity=False, cap_existing_power_MW=100.0, cost_fixed_power_USDperkW=0.0, angle_max_deg=360.0, angle_min_deg=-360.0, sbase_VA=None, vbase_V=None, fbase_Hz=None, decomposed=False, from_bus_id=0, to_bus_id=4): -KeyError: "Index '1' is not valid for indexed component 'vTHETA'" -Rule failed when generating expression for Constraint cFlowPerExpLine with index LinePiModel(id=0, name='1', from_bus='1', to_bus='2', r_pu=0.00281, x_pu=0.0281, g_pu=0.0, b_pu=0.00712, expand_capacity=False, cap_existing_power_MW=100.0, cost_fixed_power_USDperkW=0.0, angle_max_deg=360.0, angle_min_deg=-360.0, sbase_VA=None, vbase_V=None, fbase_Hz=None, decomposed=False, from_bus_id=0, to_bus_id=4): -KeyError: "Index '1' is not valid for indexed component 'vTHETA'" -Constructing component 'cFlowPerExpLine' from data=None failed: - KeyError: "Index '1' is not valid for indexed component 'vTHETA'" -Constructing component 'cFlowPerExpLine' from data=None failed: - KeyError: "Index '1' is not valid for indexed component 'vTHETA'" -2026-01-16 16:55:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-16 16:55:55 -2026-01-16 16:55:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.10 seconds. - -> Completed in 0.10 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 10 variables - Size: 10 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 4 variables - Size: 4 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 5 constraints - Size: 5 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 4 expressions - Size: 4 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 1 expressions - Size: 1 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 5 variables - Size: 5 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 2 constraints - Size: 2 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 1 constraints - Size: 1 constraints - - State of charge constraints - - State of charge constraints - Size: 5 constraints - Size: 5 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 4 variables - Size: 4 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 4 constraints - Size: 4 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 4 constraints - Size: 4 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.15 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-16 17:00:36 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-16 17:00:36 -2026-01-16 17:00:36 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - -> Completed in 0.06 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 10 variables - Size: 10 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 4 variables - Size: 4 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 5 constraints - Size: 5 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 4 expressions - Size: 4 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 1 expressions - Size: 1 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 5 variables - Size: 5 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 2 constraints - Size: 2 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 1 constraints - Size: 1 constraints - - State of charge constraints - - State of charge constraints - Size: 5 constraints - Size: 5 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 1 expressions - Size: 1 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 4 variables - Size: 4 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 4 constraints - Size: 4 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 4 constraints - Size: 4 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 17 - Constraints : 17 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.15 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-16 17:01:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.09 seconds. - -2026-01-16 17:01:18 -2026-01-16 17:01:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - -> Completed in 0.06 seconds. - -2026-01-16 17:01:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': False, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 5 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 5 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 6 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 25 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.80e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e+03 7.3e-01 1.8e+02 0.00e+00 1.193358064e+01 3.539378078e+01 2.0e+02 0.00 -1 7.3e+02 2.1e-01 5.3e+01 3.91e+00 3.929896377e+00 4.896996964e+01 6.0e+01 0.00 -2 1.1e+02 3.1e-02 7.7e+00 1.18e+00 2.695255073e+00 8.252283329e+00 8.7e+00 0.00 -3 2.0e+01 5.9e-03 1.5e+00 8.34e-01 1.830968368e+00 1.543452199e+00 1.7e+00 0.00 -4 7.1e+00 2.1e-03 5.1e-01 8.48e-01 5.726139383e-01 4.688788045e-01 5.8e-01 0.00 -5 2.2e-01 6.4e-05 1.6e-02 9.96e-01 2.529525306e-02 2.204015439e-02 1.8e-02 0.00 -6 3.1e-02 9.2e-06 2.3e-03 9.97e-01 2.324711836e-02 2.277874736e-02 2.6e-03 0.00 -7 6.5e-03 1.9e-06 4.7e-04 9.28e-01 2.107184597e-02 2.097309075e-02 5.3e-04 0.00 -8 1.1e-03 3.3e-07 8.2e-05 1.00e+00 2.089676477e-02 2.087966414e-02 9.2e-05 0.00 -9 3.4e-07 1.0e-10 2.5e-08 1.00e+00 2.081002198e-02 2.081001674e-02 2.8e-08 0.00 -10 3.4e-11 1.0e-14 2.5e-12 1.00e+00 2.081000000e-02 2.081000000e-02 2.8e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000002e-02 nrm: 5e+02 Viol. con: 1e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 3e-15 var: 5e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0810000004e-02 nrm: 5e-03 Viol. con: 3e-15 var: 6e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-16 17:01:50 -2026-01-16 17:01:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal attempts : 1 successes : 1 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Presolve started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal deps. : 0 dual deps. : 0 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 6 variables. - Size: 6 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 6 constraints. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : DUAL_INFEASIBLE - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - -2026-01-16 17:02:23 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.06 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving capacity expansion model... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.10 seconds. - -> Completed in 0.11 seconds. - -2026-01-16 17:05:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.09 seconds. - -> Completed in 0.10 seconds. - -2026-01-16 17:10:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 17:21:23 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 17:22:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 17:24:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 17:24:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -2026-01-16 17:25:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -2026-01-16 17:25:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.05 seconds. -2026-01-16 17:29:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: 1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: 1.00. -> Time spent by solver: 0.05 seconds. -2026-01-16 17:57:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.9e-01 1.1e+00 1.2e+00 0.00e+00 6.497420217e-01 -1.467295079e-01 4.5e-01 0.00 -1 2.2e-02 8.2e-02 9.4e-02 2.35e+00 3.211566864e-05 -2.187002813e-02 3.4e-02 0.00 -2 1.2e-05 4.5e-05 5.2e-05 1.10e+00 4.810411150e-06 -1.712449179e-05 1.9e-05 0.00 -3 1.2e-09 4.5e-09 5.2e-09 1.00e+00 4.810221073e-10 -1.712370773e-09 1.9e-09 0.00 -4 1.2e-13 4.5e-13 5.2e-13 1.00e+00 4.810221056e-14 -1.712397427e-13 1.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.8102210557e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -7.6200223566e-14 nrm: 3e-01 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.05 seconds. -2026-01-16 17:58:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.9e-01 1.1e+00 1.2e+00 0.00e+00 6.497420217e-01 -1.467295079e-01 4.5e-01 0.00 -1 2.2e-02 8.2e-02 9.4e-02 2.35e+00 3.211566864e-05 -2.187002813e-02 3.4e-02 0.00 -2 1.2e-05 4.5e-05 5.2e-05 1.10e+00 4.810411150e-06 -1.712449179e-05 1.9e-05 0.00 -3 1.2e-09 4.5e-09 5.2e-09 1.00e+00 4.810221073e-10 -1.712370773e-09 1.9e-09 0.00 -4 1.2e-13 4.5e-13 5.2e-13 1.00e+00 4.810221056e-14 -1.712397427e-13 1.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.8102210557e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -7.6200223566e-14 nrm: 3e-01 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.06 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.417961979e-01 -1.711735576e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.177024137e-05 -2.033758042e-02 3.4e-02 0.00 -2 1.5e-05 5.4e-05 6.2e-05 1.08e+00 3.262974881e-06 -2.384391733e-05 2.2e-05 0.00 -3 1.5e-09 5.4e-09 6.2e-09 1.00e+00 3.262851072e-10 -2.384267947e-09 2.2e-09 0.00 -4 1.5e-13 5.4e-13 6.2e-13 1.00e+00 3.262851057e-14 -2.384310450e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.2628510575e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.4099578995e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.1e-01 1.1e+00 1.1e+00 0.00e+00 6.840711975e-01 -2.266462213e-02 4.2e-01 0.00 -1 7.9e-03 4.0e-02 4.2e-02 2.22e+00 3.511354547e-05 -1.057471602e-02 1.6e-02 0.00 -2 3.3e-05 1.7e-04 1.8e-04 1.26e+00 1.417515839e-05 -6.435645898e-05 6.7e-05 0.00 -3 3.3e-09 1.7e-08 1.8e-08 1.00e+00 1.428776261e-09 -6.429515558e-09 6.7e-09 0.00 -4 3.3e-13 1.7e-12 1.8e-12 1.00e+00 1.428776245e-13 -6.429515126e-13 6.7e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4287762455e-13 nrm: 2e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: -6.4384925706e-13 nrm: 3e-01 Viol. con: 0e+00 var: 8e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 8e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e-01 1.1e+00 1.2e+00 0.00e+00 6.649326599e-01 -9.543708695e-02 4.4e-01 0.00 -1 1.8e-02 7.7e-02 8.5e-02 2.32e+00 3.300131291e-05 -2.250675504e-02 3.1e-02 0.00 -2 1.3e-05 5.6e-05 6.2e-05 1.15e+00 9.686393208e-06 -1.850827845e-06 2.3e-05 0.00 -3 1.3e-09 5.6e-09 6.2e-09 1.00e+00 9.686208129e-10 -1.850929747e-10 2.3e-09 0.00 -4 1.3e-13 5.6e-13 6.2e-13 1.00e+00 9.686215449e-14 -1.850930166e-14 2.3e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.6862154491e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -1.9858333140e-14 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.427795589e-01 -1.682398476e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.180997433e-05 -2.055249994e-02 3.4e-02 0.00 -2 1.5e-05 5.3e-05 6.2e-05 1.08e+00 3.425562201e-06 -2.330799249e-05 2.2e-05 0.00 -3 1.5e-09 5.3e-09 6.2e-09 1.00e+00 3.425430017e-10 -2.330678464e-09 2.2e-09 0.00 -4 1.5e-13 5.3e-13 6.2e-13 1.00e+00 3.425430001e-14 -2.330706883e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4254300007e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.3555344471e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.11 seconds. - -> Completed in 0.11 seconds. - -2026-01-16 17:58:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.9e-01 1.1e+00 1.2e+00 0.00e+00 6.497420217e-01 -1.467295079e-01 4.5e-01 0.00 -1 2.2e-02 8.2e-02 9.4e-02 2.35e+00 3.211566864e-05 -2.187002813e-02 3.4e-02 0.00 -2 1.2e-05 4.5e-05 5.2e-05 1.10e+00 4.810411150e-06 -1.712449179e-05 1.9e-05 0.00 -3 1.2e-09 4.5e-09 5.2e-09 1.00e+00 4.810221073e-10 -1.712370773e-09 1.9e-09 0.00 -4 1.2e-13 4.5e-13 5.2e-13 1.00e+00 4.810221056e-14 -1.712397427e-13 1.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.8102210557e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -7.6200223566e-14 nrm: 3e-01 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.417961979e-01 -1.711735576e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.177024137e-05 -2.033758042e-02 3.4e-02 0.00 -2 1.5e-05 5.4e-05 6.2e-05 1.08e+00 3.262974881e-06 -2.384391733e-05 2.2e-05 0.00 -3 1.5e-09 5.4e-09 6.2e-09 1.00e+00 3.262851072e-10 -2.384267947e-09 2.2e-09 0.00 -4 1.5e-13 5.4e-13 6.2e-13 1.00e+00 3.262851057e-14 -2.384310450e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.2628510575e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.4099578995e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.1e-01 1.1e+00 1.1e+00 0.00e+00 6.840711975e-01 -2.266462213e-02 4.2e-01 0.00 -1 7.9e-03 4.0e-02 4.2e-02 2.22e+00 3.511354547e-05 -1.057471602e-02 1.6e-02 0.00 -2 3.3e-05 1.7e-04 1.8e-04 1.26e+00 1.417515839e-05 -6.435645898e-05 6.7e-05 0.00 -3 3.3e-09 1.7e-08 1.8e-08 1.00e+00 1.428776261e-09 -6.429515558e-09 6.7e-09 0.00 -4 3.3e-13 1.7e-12 1.8e-12 1.00e+00 1.428776245e-13 -6.429515126e-13 6.7e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4287762455e-13 nrm: 2e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: -6.4384925706e-13 nrm: 3e-01 Viol. con: 0e+00 var: 8e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 8e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e-01 1.1e+00 1.2e+00 0.00e+00 6.649326599e-01 -9.543708695e-02 4.4e-01 0.00 -1 1.8e-02 7.7e-02 8.5e-02 2.32e+00 3.300131291e-05 -2.250675504e-02 3.1e-02 0.00 -2 1.3e-05 5.6e-05 6.2e-05 1.15e+00 9.686393208e-06 -1.850827845e-06 2.3e-05 0.00 -3 1.3e-09 5.6e-09 6.2e-09 1.00e+00 9.686208129e-10 -1.850929747e-10 2.3e-09 0.00 -4 1.3e-13 5.6e-13 6.2e-13 1.00e+00 9.686215449e-14 -1.850930166e-14 2.3e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.6862154491e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -1.9858333140e-14 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.427795589e-01 -1.682398476e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.180997433e-05 -2.055249994e-02 3.4e-02 0.00 -2 1.5e-05 5.3e-05 6.2e-05 1.08e+00 3.425562201e-06 -2.330799249e-05 2.2e-05 0.00 -3 1.5e-09 5.3e-09 6.2e-09 1.00e+00 3.425430017e-10 -2.330678464e-09 2.2e-09 0.00 -4 1.5e-13 5.3e-13 6.2e-13 1.00e+00 3.425430001e-14 -2.330706883e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4254300007e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.3555344471e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.10 seconds. - -> Completed in 0.10 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.20 seconds. - -2026-01-16 17:59:34 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.9e-01 1.1e+00 1.2e+00 0.00e+00 6.497420217e-01 -1.467295079e-01 4.5e-01 0.00 -1 2.2e-02 8.2e-02 9.4e-02 2.35e+00 3.211566864e-05 -2.187002813e-02 3.4e-02 0.00 -2 1.2e-05 4.5e-05 5.2e-05 1.10e+00 4.810411150e-06 -1.712449179e-05 1.9e-05 0.00 -3 1.2e-09 4.5e-09 5.2e-09 1.00e+00 4.810221073e-10 -1.712370773e-09 1.9e-09 0.00 -4 1.2e-13 4.5e-13 5.2e-13 1.00e+00 4.810221056e-14 -1.712397427e-13 1.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 4.8102210557e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -7.6200223566e-14 nrm: 3e-01 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.417961979e-01 -1.711735576e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.177024137e-05 -2.033758042e-02 3.4e-02 0.00 -2 1.5e-05 5.4e-05 6.2e-05 1.08e+00 3.262974881e-06 -2.384391733e-05 2.2e-05 0.00 -3 1.5e-09 5.4e-09 6.2e-09 1.00e+00 3.262851072e-10 -2.384267947e-09 2.2e-09 0.00 -4 1.5e-13 5.4e-13 6.2e-13 1.00e+00 3.262851057e-14 -2.384310450e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.2628510575e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.4099578995e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.1e-01 1.1e+00 1.1e+00 0.00e+00 6.840711975e-01 -2.266462213e-02 4.2e-01 0.00 -1 7.9e-03 4.0e-02 4.2e-02 2.22e+00 3.511354547e-05 -1.057471602e-02 1.6e-02 0.00 -2 3.3e-05 1.7e-04 1.8e-04 1.26e+00 1.417515839e-05 -6.435645898e-05 6.7e-05 0.00 -3 3.3e-09 1.7e-08 1.8e-08 1.00e+00 1.428776261e-09 -6.429515558e-09 6.7e-09 0.00 -4 3.3e-13 1.7e-12 1.8e-12 1.00e+00 1.428776245e-13 -6.429515126e-13 6.7e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4287762455e-13 nrm: 2e+02 Viol. con: 7e-14 var: 0e+00 - Dual. obj: -6.4384925706e-13 nrm: 3e-01 Viol. con: 0e+00 var: 8e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 8e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.5e-01 1.1e+00 1.2e+00 0.00e+00 6.649326599e-01 -9.543708695e-02 4.4e-01 0.00 -1 1.8e-02 7.7e-02 8.5e-02 2.32e+00 3.300131291e-05 -2.250675504e-02 3.1e-02 0.00 -2 1.3e-05 5.6e-05 6.2e-05 1.15e+00 9.686393208e-06 -1.850827845e-06 2.3e-05 0.00 -3 1.3e-09 5.6e-09 6.2e-09 1.00e+00 9.686208129e-10 -1.850929747e-10 2.3e-09 0.00 -4 1.3e-13 5.6e-13 6.2e-13 1.00e+00 9.686215449e-14 -1.850930166e-14 2.3e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.6862154491e-14 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: -1.9858333140e-14 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e-01 1.1e+00 1.3e+00 0.00e+00 6.427795589e-01 -1.682398476e-01 4.5e-01 0.00 -1 2.3e-02 8.2e-02 9.4e-02 2.35e+00 3.180997433e-05 -2.055249994e-02 3.4e-02 0.00 -2 1.5e-05 5.3e-05 6.2e-05 1.08e+00 3.425562201e-06 -2.330799249e-05 2.2e-05 0.00 -3 1.5e-09 5.3e-09 6.2e-09 1.00e+00 3.425430017e-10 -2.330678464e-09 2.2e-09 0.00 -4 1.5e-13 5.3e-13 6.2e-13 1.00e+00 3.425430001e-14 -2.330706883e-13 2.2e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4254300007e-14 nrm: 1e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.3555344471e-13 nrm: 3e-01 Viol. con: 0e+00 var: 3e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:07:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.06 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:07:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 5e-01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:23:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.06 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:23:41 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:33:44 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 18:35:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. -2026-01-16 18:42:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.05. -> Time spent by solver: 0.05 seconds. -2026-01-16 18:42:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. -2026-01-16 18:50:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.09 seconds. - -> Completed in 0.10 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.19 seconds. - -2026-01-16 18:53:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.05 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.10 seconds. - -> Completed in 0.10 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.05 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.22 seconds. - -2026-01-16 19:46:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.10 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.02 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.08 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.08 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.11 seconds. - -> Completed in 0.12 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.02 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.32 seconds. - -2026-01-16 19:48:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.05. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.08 seconds. - -> Completed in 0.08 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-16 19:48:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.1, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 3 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.05. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.08 seconds. - -> Completed in 0.08 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 10 variables - - Decision variables of load shedding - Size: 4 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 5 constraints - - Dispatch at bus expressions - Size: 4 expressions - - Generation cost per timepoint expressions - Size: 1 expressions - - Load shedding cost expressions - Size: 1 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 5 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 2 constraints - - Maximum state of charge constraints - Size: 1 constraints - - State of charge constraints - Size: 5 constraints - - Storage cost per timepoint expressions - Size: 1 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 4 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 0 constraints - - Line cost per period expression - - Maximum flow constraints per bus - Size: 4 constraints - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 4 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 17 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 11 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 10 -Factor - dense dim. : 0 flops : 7.60e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.6e+03 7.0e-01 1.8e+02 0.00e+00 1.111971474e+01 3.508246490e+01 2.1e+02 0.00 -1 6.9e+02 1.9e-01 4.9e+01 3.74e+00 3.704302877e+00 4.049388415e+01 5.5e+01 0.00 -2 1.2e+02 3.1e-02 8.1e+00 1.16e+00 2.500682083e+00 8.078758838e+00 9.2e+00 0.00 -3 3.2e+01 8.6e-03 2.2e+00 7.35e-01 2.565248179e+00 2.231573501e+00 2.5e+00 0.00 -4 1.2e+01 3.1e-03 8.1e-01 7.88e-01 7.811436683e-01 6.626525438e-01 9.1e-01 0.00 -5 6.7e-01 1.8e-04 4.7e-02 9.78e-01 2.755231655e-02 2.047961290e-02 5.3e-02 0.00 -6 3.9e-02 1.1e-05 2.7e-03 1.00e+00 2.348630060e-02 2.307494886e-02 3.1e-03 0.00 -7 8.6e-03 2.3e-06 6.1e-04 9.13e-01 2.108880161e-02 2.099041007e-02 6.9e-04 0.00 -8 1.9e-03 5.1e-07 1.3e-04 1.00e+00 2.093213914e-02 2.090864546e-02 1.5e-04 0.00 -9 1.2e-06 3.2e-10 8.2e-08 9.99e-01 2.081007228e-02 2.081005676e-02 9.3e-08 0.00 -10 1.2e-10 3.2e-14 8.2e-12 1.00e+00 2.081000001e-02 2.081000001e-02 9.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000007e-02 nrm: 5e+02 Viol. con: 4e-11 var: 0e+00 - Dual. obj: 2.0810000000e-02 nrm: 5e-03 Viol. con: 1e-14 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0810000000e-02 nrm: 5e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0810000006e-02 nrm: 5e-03 Viol. con: 8e-15 var: 5e-15 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 20810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-16 19:50:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 0 - - Kron reduction will remove 0 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 5 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 2. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.03. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 2 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: -2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.02. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.9997000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: -2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -5.9994000000e-02 nrm: 2e+02 Viol. con: 9e-19 var: 0e+00 - Dual. obj: -5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 19:53:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 0 - - Kron reduction will remove 0 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 5 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 2. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 2 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.02. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 19:54:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': 2, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Buses with at most 2 neighbors: 0 - - Kron reduction will remove 0 buses out of 5 total buses. -> Completed in 0.02 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 5 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 2. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.8381000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.8381000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 2 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.1816000000e-02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.1816000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.02. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 19:58:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0197000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 5.0197000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-17 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.05. -> Time spent by solver: 0.06 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.1408000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.1408000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.4640000000e-03 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 6.4640000000e-03 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.9997000000e-02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.9997000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 2e-33 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.9994000000e-02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 5.9994000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.06. -> Time spent by solver: 0.01 seconds. -2026-01-16 22:02:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.02 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 127.79. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 22:04:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -127.79. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -200.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 22:07:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -Rule failed when generating expression for Constraint cAngleDiff with index Bus(id=0, bus='1'): -PyomoException: Cannot convert non-constant Pyomo expression (-1.5707963267948966 <= vTHETA[Bus(id=0, bus='1')]) to bool. -This error is usually caused by using a Var, unit, or mutable Param in a -Boolean context such as an "if" statement, or when checking container -membership or equality. For example, - >>> m.x = Var() - >>> if m.x >= 1: - ... pass -and - >>> m.y = Var() - >>> if m.y in [m.x, m.y]: - ... pass -would both cause this exception. -Constructing component 'cAngleDiff' from data=None failed: - PyomoException: Cannot convert non-constant Pyomo expression (-1.5707963267948966 <= vTHETA[Bus(id=0, bus='1')]) to bool. -This error is usually caused by using a Var, unit, or mutable Param in a -Boolean context such as an "if" statement, or when checking container -membership or equality. For example, - >>> m.x = Var() - >>> if m.x >= 1: - ... pass -and - >>> m.y = Var() - >>> if m.y in [m.x, m.y]: - ... pass -would both cause this exception. -2026-01-16 22:08:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -127.79. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -200.00. -> Time spent by solver: 0.01 seconds. -2026-01-16 22:08:46 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -127.79. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:09:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:15:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -127.79. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:17:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 127.79. -> Time spent by solver: 0.05 seconds. -2026-01-16 22:17:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: -1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : DUAL_INFEASIBLE - Solution status : DUAL_INFEASIBLE_CER - Primal. obj: -1.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: unbounded - - message from solver: Problem is dual infeasible The solution is a certificate of dual infeasibility. -> Time spent by solver: 0.04 seconds. -> Solver finished with status: warning, termination condition: unbounded. -> Objective value: -1.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:18:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: -1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: -1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: -127.79. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:18:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:19:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.0000000000e+01 nrm: 2e+02 Viol. con: 2e-16 var: 0e+00 - Dual. obj: 9.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.0000000000e+01 nrm: 2e+02 Viol. con: 2e-16 var: 0e+00 - Dual. obj: 9.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 90.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:21:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:22:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:23:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 127.79. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:23:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -2026-01-16 22:23:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -2026-01-16 22:23:49 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2778931361e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.2778931361e+02 nrm: 1e+00 Viol. con: 0e+00 var: 5e-14 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 127.79. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:25:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5557862721e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 2.5557862721e+02 nrm: 2e+00 Viol. con: 0e+00 var: 1e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5557862721e+02 nrm: 2e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 2.5557862721e+02 nrm: 2e+00 Viol. con: 0e+00 var: 1e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 255.58. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:31:41 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5557862721e+02 nrm: 3e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 2.5557862721e+02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5557862721e+02 nrm: 3e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 2.5557862721e+02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 -> Time spent by solver: 0.07 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 255.58. -> Time spent by solver: 0.07 seconds. -2026-01-16 22:35:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5001923247e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.5001923247e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5001923247e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.5001923247e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.02. -> Time spent by solver: 0.04 seconds. -2026-01-16 22:38:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. -2026-01-16 22:50:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5001923247e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.5001923247e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5001923247e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.5001923247e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.02. -> Time spent by solver: 0.06 seconds. -2026-01-16 23:03:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:07:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:09:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 23:09:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 23:23:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. -2026-01-16 23:24:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.0000000000e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 3.0000000000e-02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.03. -> Time spent by solver: 0.06 seconds. -2026-01-16 23:26:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.3333333333e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e-02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.3333333333e-02 nrm: 1e+00 Viol. con: 0e+00 var: 1e-16 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.01. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:30:26 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.6666666667e-01 nrm: 2e+01 Viol. con: 4e-19 var: 7e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.6666666667e-01 nrm: 2e+01 Viol. con: 4e-19 var: 7e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.67. -> Time spent by solver: 0.06 seconds. -2026-01-16 23:33:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0000000000e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.0000000000e-01 nrm: 1e+01 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0000000000e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.0000000000e-01 nrm: 1e+01 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.60. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:34:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.6666666667e-01 nrm: 2e+01 Viol. con: 4e-19 var: 7e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e-01 nrm: 2e+02 Viol. con: 3e-17 var: 0e+00 - Dual. obj: 6.6666666667e-01 nrm: 2e+01 Viol. con: 4e-19 var: 7e-15 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.67. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:37:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 2e+02 Viol. con: 5e-16 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 2e+03 Viol. con: 0e+00 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 2e+02 Viol. con: 5e-16 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 2e+03 Viol. con: 0e+00 var: 5e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:38:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 14 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 8 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 2e-17 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 2e-17 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:39:23 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -Rule failed when generating expression for Objective oMaximizeAngleDiff with index None: -AttributeError: 'ConcreteModel' object has no attribute 'z' -Constructing component 'oMaximizeAngleDiff' from data=None failed: - AttributeError: 'ConcreteModel' object has no attribute 'z' -2026-01-16 23:39:35 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:39:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-16 23:39:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 5e+03 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 7e-17 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 7e-17 var: 2e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 2 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 4 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 3 after factor : 3 -Factor - dense dim. : 0 flops : 2.10e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 1.0e+04 2.0e+00 0.00e+00 -9.954959469e+01 -1.040397018e+02 2.5e+00 0.00 -1 2.2e+00 5.5e+01 1.1e-02 -9.90e-01 -5.208245134e+01 -2.867979311e+02 1.4e-02 0.00 -2 1.2e+00 3.0e+01 5.9e-03 1.10e+00 1.322280211e+02 7.399868482e+01 7.4e-03 0.00 -3 2.1e-01 5.2e+00 1.1e-03 1.33e+00 1.906762202e+02 1.906119016e+02 1.3e-03 0.00 -4 8.8e-03 2.2e-01 4.4e-05 1.45e+00 1.996652377e+02 1.996440210e+02 5.5e-05 0.00 -5 1.1e-06 2.8e-05 5.6e-09 1.02e+00 1.999999546e+02 1.999999500e+02 7.0e-09 0.00 -6 1.1e-10 2.8e-09 4.4e-13 1.00e+00 2.000000000e+02 2.000000000e+02 7.0e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-09 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 3e-11 var: 1e-07 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 4e-07 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 00:02:49 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 00:14:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 9e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 9e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 5e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 00:15:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 00:28:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 9e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 9e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 5e-13 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 00:34:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 7 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 7 lines. - - Kron system has 4 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 3.3e+03 3.3e+02 0.00e+00 -3.664530980e+02 -3.574291996e+01 1.3e+00 0.00 -1 9.5e-01 7.9e+00 8.0e-01 -9.88e-01 -1.013473657e+02 -1.618829471e+02 3.2e-03 0.00 -2 1.4e-01 1.2e+00 1.2e-01 7.25e-01 5.897929548e+01 5.435464429e+01 4.8e-04 0.00 -3 9.1e-02 7.6e-01 7.6e-02 9.22e-01 6.862918837e+01 6.534762102e+01 3.1e-04 0.00 -4 7.9e-02 6.6e-01 6.6e-02 9.58e-01 8.422126637e+01 8.225783879e+01 2.7e-04 0.00 -5 5.2e-02 4.4e-01 4.4e-02 1.00e+00 8.998965572e+01 8.874626304e+01 1.8e-04 0.00 -6 2.8e-02 2.4e-01 2.4e-02 8.81e-01 8.805045381e+01 8.730008964e+01 9.5e-05 0.00 -7 2.8e-04 2.3e-03 2.3e-04 1.02e+00 9.988295677e+01 9.987764189e+01 9.3e-07 0.00 -8 2.8e-08 2.3e-07 2.3e-08 1.00e+00 9.999998828e+01 9.999998774e+01 9.3e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 3 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.9999988275e+01 nrm: 2e+02 Viol. con: 6e-06 var: 0e+00 - Dual. obj: 9.9999996538e+01 nrm: 1e+00 Viol. con: 2e-08 var: 3e-05 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 3e-18 var: 9e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 1.0e+03 0.00e+00 -8.010797105e+02 1.944310805e+02 4.0e+00 0.00 -1 9.6e-01 2.4e+01 2.4e+00 -9.88e-01 -2.221601818e+02 -4.010694539e+02 9.7e-03 0.00 -2 1.4e-01 3.4e+00 3.4e-01 7.21e-01 1.726956665e+02 1.598951406e+02 1.4e-03 0.00 -3 3.0e-02 7.4e-01 7.5e-02 9.45e-01 1.962299117e+02 1.949285351e+02 3.0e-04 0.00 -4 7.8e-04 2.0e-02 2.0e-03 1.01e+00 1.998793416e+02 1.998737652e+02 7.9e-06 0.00 -5 8.3e-08 2.1e-06 2.1e-07 1.00e+00 1.999999852e+02 1.999999850e+02 8.4e-10 0.00 -6 8.3e-12 2.1e-10 2.1e-11 1.00e+00 2.000000000e+02 2.000000000e+02 8.4e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-09 var: 0e+00 - Dual. obj: 2.0000000001e+02 nrm: 1e+00 Viol. con: 2e-11 var: 3e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 1e-11 var: 4e-07 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 1.3e+04 1.3e+03 0.00e+00 -1.200719466e+03 1.274294044e+02 5.3e+00 0.00 -1 1.0e+00 3.4e+01 3.4e+00 -9.88e-01 -3.458606284e+02 -5.623066587e+02 1.4e-02 0.00 -2 1.7e-01 5.7e+00 5.8e-01 6.89e-01 1.332807864e+02 1.155274901e+02 2.3e-03 0.00 -3 9.5e-03 3.2e-01 3.2e-02 9.02e-01 1.293750762e+02 1.333963090e+02 1.3e-04 0.00 -4 6.9e-06 2.3e-04 2.3e-05 1.01e+00 1.333319770e+02 1.333348422e+02 9.2e-08 0.00 -5 6.9e-10 2.3e-08 2.3e-09 1.00e+00 1.333333332e+02 1.333333335e+02 9.2e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333320e+02 nrm: 1e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.3333333416e+02 nrm: 1e+00 Viol. con: 2e-09 var: 3e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.3333333333e+02 nrm: 1e+00 Viol. con: 5e-26 var: 2e-21 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 133.33. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 3.8e-01 0.00e+00 2.982797032e+02 2.938904942e+02 4.0e+00 0.00 -1 8.5e-01 2.1e+01 8.2e-04 -9.88e-01 7.636880622e+01 -3.952040104e+02 8.6e-03 0.00 -2 1.6e-01 4.1e+00 1.6e-04 7.97e-01 1.098342697e+02 5.358252438e+01 1.6e-03 0.00 -3 3.8e-03 9.5e-02 3.6e-06 1.15e+00 1.001215365e+02 1.001160216e+02 3.8e-05 0.00 -4 4.9e-07 1.2e-05 4.7e-10 1.01e+00 1.000000028e+02 9.999999625e+01 4.9e-09 0.00 -5 4.9e-11 1.2e-09 4.1e-14 1.00e+00 1.000000000e+02 1.000000000e+02 4.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 9e-09 var: 0e+00 - Dual. obj: 1.0000000004e+02 nrm: 1e+00 Viol. con: 9e-11 var: 1e-07 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 2e-11 var: 1e-06 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 3.3e+03 1.2e+00 0.00e+00 6.627324161e+01 6.371675297e+01 1.3e+00 0.00 -1 8.1e-01 6.7e+00 2.5e-03 -9.88e-01 1.629938636e+01 -1.434872020e+02 2.7e-03 0.00 -2 1.6e-01 1.3e+00 4.9e-04 8.35e-01 6.034614213e+01 4.089793565e+01 5.3e-04 0.00 -3 4.2e-02 3.5e-01 1.3e-04 1.12e+00 8.857505481e+01 8.412592131e+01 1.4e-04 0.00 -4 1.0e-03 8.6e-03 3.2e-06 1.02e+00 9.997110909e+01 9.986351610e+01 3.5e-06 0.00 -5 1.1e-07 9.1e-07 3.3e-10 1.00e+00 9.999999620e+01 9.999998502e+01 3.7e-10 0.00 -6 1.1e-11 9.1e-11 3.4e-14 1.00e+00 1.000000000e+02 1.000000000e+02 3.7e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 3 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-09 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 7e-12 var: 1e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 4e-13 var: 8e-08 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 4.8e-01 0.00e+00 -9.945979279e+01 -1.039490018e+02 4.0e+00 0.00 -1 8.0e-01 2.0e+01 9.7e-04 -9.88e-01 -2.402412183e+01 -5.032403207e+02 8.1e-03 0.00 -2 1.4e-01 3.4e+00 1.6e-04 8.39e-01 1.176070433e+02 7.004076643e+01 1.4e-03 0.00 -3 1.8e-02 4.5e-01 2.2e-05 1.11e+00 1.984498881e+02 1.935563204e+02 1.8e-04 0.00 -4 3.6e-05 8.9e-04 4.3e-08 1.06e+00 1.999926682e+02 1.999905801e+02 3.6e-07 0.00 -5 3.6e-09 8.9e-08 4.3e-12 1.00e+00 1.999999993e+02 1.999999991e+02 3.6e-11 0.00 -6 5.9e-13 1.5e-11 3.4e-11 1.00e+00 2.000000000e+02 2.000000000e+02 3.6e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 9e-12 var: 2e-09 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 1e-12 var: 3e-08 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 01:03:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 7 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 7 lines. - - Kron system has 4 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 3.3e+03 3.3e+02 0.00e+00 -3.664530980e+02 -3.574291996e+01 1.3e+00 0.00 -1 9.5e-01 7.9e+00 8.0e-01 -9.88e-01 -1.013473657e+02 -1.618829471e+02 3.2e-03 0.00 -2 1.4e-01 1.2e+00 1.2e-01 7.25e-01 5.897929548e+01 5.435464429e+01 4.8e-04 0.00 -3 9.1e-02 7.6e-01 7.6e-02 9.22e-01 6.862918837e+01 6.534762102e+01 3.1e-04 0.00 -4 7.9e-02 6.6e-01 6.6e-02 9.58e-01 8.422126637e+01 8.225783879e+01 2.7e-04 0.00 -5 5.2e-02 4.4e-01 4.4e-02 1.00e+00 8.998965572e+01 8.874626304e+01 1.8e-04 0.00 -6 2.8e-02 2.4e-01 2.4e-02 8.81e-01 8.805045381e+01 8.730008964e+01 9.5e-05 0.00 -7 2.8e-04 2.3e-03 2.3e-04 1.02e+00 9.988295677e+01 9.987764189e+01 9.3e-07 0.00 -8 2.8e-08 2.3e-07 2.3e-08 1.00e+00 9.999998828e+01 9.999998774e+01 9.3e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 3 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.9999988275e+01 nrm: 2e+02 Viol. con: 6e-06 var: 0e+00 - Dual. obj: 9.9999996538e+01 nrm: 1e+00 Viol. con: 2e-08 var: 3e-05 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 3e-18 var: 9e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 1.0e+03 0.00e+00 -8.010797105e+02 1.944310805e+02 4.0e+00 0.00 -1 9.6e-01 2.4e+01 2.4e+00 -9.88e-01 -2.221601818e+02 -4.010694539e+02 9.7e-03 0.00 -2 1.4e-01 3.4e+00 3.4e-01 7.21e-01 1.726956665e+02 1.598951406e+02 1.4e-03 0.00 -3 3.0e-02 7.4e-01 7.5e-02 9.45e-01 1.962299117e+02 1.949285351e+02 3.0e-04 0.00 -4 7.8e-04 2.0e-02 2.0e-03 1.01e+00 1.998793416e+02 1.998737652e+02 7.9e-06 0.00 -5 8.3e-08 2.1e-06 2.1e-07 1.00e+00 1.999999852e+02 1.999999850e+02 8.4e-10 0.00 -6 8.3e-12 2.1e-10 2.1e-11 1.00e+00 2.000000000e+02 2.000000000e+02 8.4e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-09 var: 0e+00 - Dual. obj: 2.0000000001e+02 nrm: 1e+00 Viol. con: 2e-11 var: 3e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 1e-11 var: 4e-07 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 1.3e+04 1.3e+03 0.00e+00 -1.200719466e+03 1.274294044e+02 5.3e+00 0.00 -1 1.0e+00 3.4e+01 3.4e+00 -9.88e-01 -3.458606284e+02 -5.623066587e+02 1.4e-02 0.00 -2 1.7e-01 5.7e+00 5.8e-01 6.89e-01 1.332807864e+02 1.155274901e+02 2.3e-03 0.00 -3 9.5e-03 3.2e-01 3.2e-02 9.02e-01 1.293750762e+02 1.333963090e+02 1.3e-04 0.00 -4 6.9e-06 2.3e-04 2.3e-05 1.01e+00 1.333319770e+02 1.333348422e+02 9.2e-08 0.00 -5 6.9e-10 2.3e-08 2.3e-09 1.00e+00 1.333333332e+02 1.333333335e+02 9.2e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333320e+02 nrm: 1e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.3333333416e+02 nrm: 1e+00 Viol. con: 2e-09 var: 3e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.3333333333e+02 nrm: 1e+00 Viol. con: 5e-26 var: 2e-21 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 133.33. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 3.8e-01 0.00e+00 2.982797032e+02 2.938904942e+02 4.0e+00 0.00 -1 8.5e-01 2.1e+01 8.2e-04 -9.88e-01 7.636880622e+01 -3.952040104e+02 8.6e-03 0.00 -2 1.6e-01 4.1e+00 1.6e-04 7.97e-01 1.098342697e+02 5.358252438e+01 1.6e-03 0.00 -3 3.8e-03 9.5e-02 3.6e-06 1.15e+00 1.001215365e+02 1.001160216e+02 3.8e-05 0.00 -4 4.9e-07 1.2e-05 4.7e-10 1.01e+00 1.000000028e+02 9.999999625e+01 4.9e-09 0.00 -5 4.9e-11 1.2e-09 4.1e-14 1.00e+00 1.000000000e+02 1.000000000e+02 4.9e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 9e-09 var: 0e+00 - Dual. obj: 1.0000000004e+02 nrm: 1e+00 Viol. con: 9e-11 var: 1e-07 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 2e-11 var: 1e-06 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 3 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 3.3e+03 1.2e+00 0.00e+00 6.627324161e+01 6.371675297e+01 1.3e+00 0.00 -1 8.1e-01 6.7e+00 2.5e-03 -9.88e-01 1.629938636e+01 -1.434872020e+02 2.7e-03 0.00 -2 1.6e-01 1.3e+00 4.9e-04 8.35e-01 6.034614213e+01 4.089793565e+01 5.3e-04 0.00 -3 4.2e-02 3.5e-01 1.3e-04 1.12e+00 8.857505481e+01 8.412592131e+01 1.4e-04 0.00 -4 1.0e-03 8.6e-03 3.2e-06 1.02e+00 9.997110909e+01 9.986351610e+01 3.5e-06 0.00 -5 1.1e-07 9.1e-07 3.3e-10 1.00e+00 9.999999620e+01 9.999998502e+01 3.7e-10 0.00 -6 1.1e-11 9.1e-11 3.4e-14 1.00e+00 1.000000000e+02 1.000000000e+02 3.7e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 3 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 2e-09 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 7e-12 var: 1e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 4e-13 var: 8e-08 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 9 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 7 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 7.20e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 9.9e+03 4.8e-01 0.00e+00 -9.945979279e+01 -1.039490018e+02 4.0e+00 0.00 -1 8.0e-01 2.0e+01 9.7e-04 -9.88e-01 -2.402412183e+01 -5.032403207e+02 8.1e-03 0.00 -2 1.4e-01 3.4e+00 1.6e-04 8.39e-01 1.176070433e+02 7.004076643e+01 1.4e-03 0.00 -3 1.8e-02 4.5e-01 2.2e-05 1.11e+00 1.984498881e+02 1.935563204e+02 1.8e-04 0.00 -4 3.6e-05 8.9e-04 4.3e-08 1.06e+00 1.999926682e+02 1.999905801e+02 3.6e-07 0.00 -5 3.6e-09 8.9e-08 4.3e-12 1.00e+00 1.999999993e+02 1.999999991e+02 3.6e-11 0.00 -6 5.9e-13 1.5e-11 3.4e-11 1.00e+00 2.000000000e+02 2.000000000e+02 3.6e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 9e-12 var: 2e-09 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 1e-12 var: 3e-08 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 21:10:34 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 7 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.07 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 7 lines. - - Kron system has 4 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 5.8333333333e+01 nrm: 1e+00 Viol. con: 5e-17 var: 1e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 5.8333333333e+01 nrm: 1e+00 Viol. con: 5e-17 var: 1e-12 -> Time spent by solver: 0.08 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 58.33. -> Time spent by solver: 0.08 seconds. -2026-01-17 21:10:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 7 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 7 lines. - - Kron system has 4 buses and 6 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 5.8333333333e+01 nrm: 1e+00 Viol. con: 5e-17 var: 1e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 5.8333333333e+01 nrm: 1e+00 Viol. con: 5e-17 var: 1e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 58.33. -> Time spent by solver: 0.04 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.3333333333e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.3333333333e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.3333333333e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 133.33. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the dual -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 16 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.32e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.2e+02 2.0e-01 3.2e+02 0.00e+00 2.375287017e+01 3.001802370e+02 3.9e+01 0.00 -1 5.6e+00 9.4e-03 1.5e+01 1.44e+00 9.883366943e+01 1.088481870e+02 1.9e+00 0.00 -2 1.2e-01 2.1e-04 3.3e-01 1.14e+00 9.997613330e+01 1.002172442e+02 4.1e-02 0.00 -3 2.0e-05 3.3e-08 5.3e-05 1.03e+00 9.999999553e+01 1.000000325e+02 6.6e-06 0.00 -4 1.4e-08 9.4e-11 5.0e-08 1.00e+00 1.000000000e+02 1.000000000e+02 1.0e-09 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.9999999997e+01 nrm: 1e+02 Viol. con: 1e-08 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 7e-11 var: 5e-07 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.9999999997e+01 nrm: 1e+02 Viol. con: 7e-09 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 3e-16 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 3 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 8 -Optimizer - solved problem : the dual -Optimizer - Constraints : 3 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 13 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 6 after factor : 6 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.1e+02 2.7e-01 2.8e+02 0.00e+00 -2.678555888e+01 1.959032130e+02 5.5e+01 0.00 -1 5.1e+01 4.5e-02 4.5e+01 2.03e+00 5.280457442e+01 7.063396771e+01 8.9e+00 0.00 -2 3.7e+00 3.3e-03 3.3e+00 1.14e+00 5.775120772e+01 5.933082084e+01 6.5e-01 0.00 -3 2.6e-02 2.3e-05 2.4e-02 1.09e+00 5.833050841e+01 5.834264556e+01 4.6e-03 0.00 -4 4.2e-06 3.7e-09 3.8e-06 1.00e+00 5.833333288e+01 5.833333483e+01 7.5e-07 0.00 -5 6.8e-10 6.1e-13 6.1e-10 1.00e+00 5.833333333e+01 5.833333333e+01 1.2e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 5.8333333334e+01 nrm: 1e+00 Viol. con: 6e-14 var: 5e-09 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.8333333333e+01 nrm: 1e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 5.8333333333e+01 nrm: 1e+00 Viol. con: 2e-17 var: 1e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 58.33. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 7 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 8 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 21:12:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7500000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.7500000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7500000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 1.7500000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 175.00. -> Time spent by solver: 0.02 seconds. -2026-01-17 21:13:49 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.02 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-12 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.03 seconds. -> Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 21:14:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:16:36 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 13 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 2 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 1e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:17:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 5 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 12 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 2e-13 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:19:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:19:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 2e-14 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 4 to bus 5. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7500000000e+02 nrm: 2e+02 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 1.7500000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7500000000e+02 nrm: 2e+02 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 1.7500000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 175.00. -> Time spent by solver: 0.01 seconds. -2026-01-17 21:19:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:20:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 11 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 1 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:24:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 3 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 10 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 8.3333333333e+01 nrm: 1e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 8.3333333333e+01 nrm: 1e+00 Viol. con: 0e+00 var: 2e-12 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 83.33. -> Time spent by solver: 0.04 seconds. -2026-01-17 21:24:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/capacity_expansion/5bus_kron_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 5 - - Buses with either generation, load or storage: 4 - - Kron reduction will remove 1 buses out of 5 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 5 buses and 6 lines. - - Kron system has 4 buses and 5 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 6 variables. - - Constraints of angle differences for original system. - Size: 6 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 8 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 7 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. diff --git a/examples/capacity_expansion/5bus_sequential/inputs/buses.csv b/examples/capacity_expansion/5bus_sequential/inputs/buses.csv deleted file mode 100644 index 121e77d..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,bus_type,zone -1,slack,center -2,PQ,north -3,PQ,south -4,PQ,south -5,PQ,south \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/capacity_factors.csv b/examples/capacity_expansion/5bus_sequential/inputs/capacity_factors.csv deleted file mode 100644 index a9342d1..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -cf_one,sc1,1,solar,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/generators.csv b/examples/capacity_expansion/5bus_sequential/inputs/generators.csv deleted file mode 100644 index 68aff97..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -1,gas,1,cf_one,0,14,0,14,0,40,14 -2,gas,1,cf_one,0,15,0,15,0,170,15 -3,gas,3,cf_one,0,30,0,30,0,520,30 -4,gas,4,cf_one,0,40,0,40,0,200,40 -5,gas,5,cf_one,0,10,0,10,0,600,10 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/lines.csv b/examples/capacity_expansion/5bus_sequential/inputs/lines.csv deleted file mode 100644 index 0274bda..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,400,FALSE,0.00281,0.0281,0,0.00712,-360,360 -2,1,4,1000,FALSE,0.00304,0.0304,0,0.00658,-360,360 -3,1,5,1000,FALSE,0.00064,0.0064,0,0.03126,-360,360 -4,2,3,1000,FALSE,0.00108,0.0108,0,0.01852,-360,360 -5,3,4,1000,FALSE,0.00297,0.0297,0,0.00674,-360,360 -6,4,5,240,FALSE,0.00297,0.0297,0,0.00674,-360,360 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/loads.csv b/examples/capacity_expansion/5bus_sequential/inputs/loads.csv deleted file mode 100644 index 2288c24..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/loads.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,load_MW -1,sc1,1,0 -2,sc1,1,300 -3,sc1,1,300 -4,sc1,1,400 -5,sc1,1,0 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/scenarios.csv b/examples/capacity_expansion/5bus_sequential/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/storage.csv b/examples/capacity_expansion/5bus_sequential/inputs/storage.csv deleted file mode 100644 index abcb9eb..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus,name,c0_USD,c1_USDperMWh,c2_USDperMWh2,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,technology -1,cats_1,0,0,0,0,0,0,0,0,0,0,0.92,0.92,hydroelectric pumped storage \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/timepoints.csv b/examples/capacity_expansion/5bus_sequential/inputs/timepoints.csv deleted file mode 100644 index 2d8d232..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timeseries -1,winter \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/inputs/timeseries.csv b/examples/capacity_expansion/5bus_sequential/inputs/timeseries.csv deleted file mode 100644 index 11ad9c3..0000000 --- a/examples/capacity_expansion/5bus_sequential/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 7dd75ea..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925381036 -cost_per_period_USD,17479896.92538104 -total_cost_USD,17497376.82230642 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/emissions_per_scenario.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/energy_budget_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv deleted file mode 100644 index f6ad435..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,built_capacity_MW -1,40.0 -2,170.0 -3,323.4948462690518 -4,-0.0 -5,466.5051537309484 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 7dd75ea..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925381036 -cost_per_period_USD,17479896.92538104 -total_cost_USD,17497376.82230642 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index b5be056..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -1,sc1,1,40.0 -2,sc1,1,170.0 -3,sc1,1,323.4948462690518 -4,sc1,1,0.0 -5,sc1,1,466.50515373094834 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/line_flows.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index b5cfbd4..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,1,0.0,-4.060673079637736,249.7167650427272,175.22728030896698 -4,2,3,sc1,1,-4.060673079637736,-3.746411729644781,-50.28323495727288,2.730676015189774 -2,1,4,sc1,1,0.0,-3.2859992919558163,186.78838868822112,106.06530253217561 -5,3,4,sc1,1,-3.746411729644781,-3.2859992919558163,-26.78838868822104,2.1313247724782904 -3,1,5,sc1,1,0.0,0.8388843033736121,-226.50515373094842,32.834934186675575 -6,4,5,sc1,1,-3.2859992919558163,0.8388843033736121,-239.9999999999997,171.07199999999955 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 3930a10..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,16994.336181834202 -2,sc1,1,26410.84397850411 -3,sc1,1,30030.00000000001 -4,sc1,1,39982.67905911374 -5,sc1,1,10010.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_balance_by_bus.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_balance_by_bus.csv deleted file mode 100644 index dbbbb20..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_balance_by_bus.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,1,210.0,0.0,0,0.0,209.9999999999999 -2,sc1,1,0.0,0.0,0,300.0,-300.00000000000006 -3,sc1,1,323.4948462690518,0.0,0,300.0,23.494846269051827 -4,sc1,1,0.0,0.0,0,400.0,-399.99999999999983 -5,sc1,1,466.50515373094834,0.0,0,0.0,466.50515373094817 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_budget_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/solver_status.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/solver_status.csv deleted file mode 100644 index 816cacb..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.02855706214904785 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/costs_summary.csv deleted file mode 100644 index f818424..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925380977 -cost_per_period_USD,0.0 -total_cost_USD,17479.896925380977 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/emissions_per_scenario.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/energy_budget_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_built_capacity.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_costs_summary.csv deleted file mode 100644 index f818424..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,17479.896925380977 -cost_per_period_USD,0.0 -total_cost_USD,17479.896925380977 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_dispatch.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_dispatch.csv deleted file mode 100644 index c799a35..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/generator_dispatch.csv +++ /dev/null @@ -1,6 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -1,sc1,1,39.99999999999901 -2,sc1,1,170.00000000000188 -3,sc1,1,323.49484626904876 -4,sc1,1,0.0 -5,sc1,1,466.50515373095027 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/line_flows.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/line_flows.csv deleted file mode 100644 index 1188341..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/line_flows.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,1,0.0,-4.060673079637762,249.71676504272875,175.22728030896917 -4,2,3,sc1,1,-4.060673079637762,-3.7464117296448167,-50.283234957271226,2.7306760151895944 -2,1,4,sc1,1,0.0,-3.285999291955828,186.78838868822174,106.06530253217632 -5,3,4,sc1,1,-3.7464117296448167,-3.285999291955828,-26.788388688222472,2.1313247724785187 -3,1,5,sc1,1,0.0,0.8388843033736165,-226.50515373094964,32.83493418667593 -6,4,5,sc1,1,-3.285999291955828,0.8388843033736165,-240.00000000000063,171.07200000000088 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/local_marginal_prices.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/local_marginal_prices.csv deleted file mode 100644 index 263f86a..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/local_marginal_prices.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,1,Not available -2,sc1,1,Not available -3,sc1,1,Not available -4,sc1,1,Not available -5,sc1,1,Not available diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_balance_by_bus.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_balance_by_bus.csv deleted file mode 100644 index d3ec926..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_balance_by_bus.csv +++ /dev/null @@ -1,6 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,1,210.00000000000088,0.0,0,0.0,210.00000000000085 -2,sc1,1,0.0,0.0,0,300.0,-299.99999999999994 -3,sc1,1,323.49484626904876,0.0,0,300.0,23.494846269048743 -4,sc1,1,0.0,0.0,0,400.0,-399.99999999999994 -5,sc1,1,466.50515373095027,0.0,0,0.0,466.50515373095027 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_budget_constraints.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/solver_status.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/solver_status.csv deleted file mode 100644 index 110fdd3..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,gurobi -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.05384087562561035 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_built_capacity.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_costs_summary.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_dispatch.csv b/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_dispatch.csv deleted file mode 100644 index 8f5b8a3..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/cost_production/storage_dispatch.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,sc1,1,0.0,0.0,0.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/buses.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/buses.csv deleted file mode 100644 index 72fa015..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -id,name,type_,zone,bus_type,kron_removable_bus,base_power_MVA,base_voltage_kV,base_frequency_Hz,latitude,longitude,max_flow_MW,minimum_voltage_pu,maximum_voltage_pu -0,1,buses,center,slack,,,,,,,2400.0,, -1,2,buses,north,PQ,,,,,,,1400.0,, -2,3,buses,south,PQ,,,,,,,2000.0,, -3,4,buses,south,PQ,,,,,,,2240.0,, -4,5,buses,south,PQ,,,,,,,1240.0,, diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/capacity_factors.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/capacity_factors.csv deleted file mode 100644 index 2a3b3fe..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/capacity_factors.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,zone,site,scenario,timepoint,capacity_factor,technology -0,,capacity_factors,,cf_one,sc1,1,1.0,solar diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/generators.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/generators.csv deleted file mode 100644 index 8c11078..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -id,name,type_,zone,bus,minimum_active_power_MW,maximum_active_power_MW,minimum_reactive_power_MVAR,maximum_reactive_power_MVAR,base_power_MVA,base_voltage_kV,base_frequency_Hz,technology,site,cap_existing_power_MW,cap_max_power_MW,cost_fixed_power_USDperkW,cost_variable_USDperMWh,c0_USD,c1_USDperMWh,c2_USDperMWh2,emission_rate_tonneCO2perMWh,bus_id,expand_capacity,component_id,forced_dispatch_MW -0,1,generators,,1,,,,,,,,gas,cf_one,40.0,40.0,14.0,14.0,0.0,14.0,0.0,,0,false,, -1,2,generators,,1,,,,,,,,gas,cf_one,170.0,170.0,15.0,15.0,0.0,15.0,0.0,,0,false,, -2,3,generators,,3,,,,,,,,gas,cf_one,323.4948462690518,520.0,30.0,30.0,0.0,30.0,0.0,,2,false,, -3,4,generators,,4,,,,,,,,gas,cf_one,0.0,200.0,40.0,40.0,0.0,40.0,0.0,,3,false,, -4,5,generators,,5,,,,,,,,gas,cf_one,466.5051537309484,600.0,10.0,10.0,0.0,10.0,0.0,,4,false,, diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/lines.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/lines.csv deleted file mode 100644 index bc81d3c..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -id,name,type_,zone,from_bus,to_bus,r_pu,x_pu,g_pu,b_pu,expand_capacity,cap_existing_power_MW,cost_fixed_power_USDperkW,angle_max_deg,angle_min_deg,base_power_MVA,base_voltage_kV,base_frequency_Hz,decomposed,from_bus_id,to_bus_id,efficiency -0,1,lines,,1,2,0.00281,0.0281,0.0,0.00712,false,400.0,0.0,360.0,-360.0,,,,false,0,1, -1,2,lines,,1,4,0.00304,0.0304,0.0,0.00658,false,1000.0,0.0,360.0,-360.0,,,,false,0,3, -2,3,lines,,1,5,0.00064,0.0064,0.0,0.03126,false,1000.0,0.0,360.0,-360.0,,,,false,0,4, -3,4,lines,,2,3,0.00108,0.0108,0.0,0.01852,false,1000.0,0.0,360.0,-360.0,,,,false,1,2, -4,5,lines,,3,4,0.00297,0.0297,0.0,0.00674,false,1000.0,0.0,360.0,-360.0,,,,false,2,3, -5,6,lines,,4,5,0.00297,0.0297,0.0,0.00674,false,240.0,0.0,360.0,-360.0,,,,false,3,4, diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/loads.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/loads.csv deleted file mode 100644 index 1bf3ba3..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/loads.csv +++ /dev/null @@ -1,6 +0,0 @@ -id,name,type_,zone,bus,timepoint,load_MW,scenario,load_MVAR -0,,loads,,1,1,0.0,sc1, -1,,loads,,2,1,300.0,sc1, -2,,loads,,3,1,300.0,sc1, -3,,loads,,4,1,400.0,sc1, -4,,loads,,5,1,0.0,sc1, diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/scenarios.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/scenarios.csv deleted file mode 100644 index a3ef146..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,zone,probability -0,sc1,scenarios,,1.0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/storage.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/storage.csv deleted file mode 100644 index 29500fc..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,zone,technology,bus,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,c0_USD,c1_USDperMWh,c2_USDperMWh2,expand_capacity,bus_id -0,cats_1,storage,,hydroelectric pumped storage,1,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.92,0.92,0.0,0.0,0.0,false,0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timepoints.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timepoints.csv deleted file mode 100644 index e80447e..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timepoints.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,zone,timeseries,timeseries_id,weight,duration_hr,prev_timepoint_id -0,1,timepoints,,winter,0,1.0,1.0,0 diff --git a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timeseries.csv b/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timeseries.csv deleted file mode 100644 index 0f1035c..0000000 --- a/examples/capacity_expansion/5bus_sequential/outputs/input_data_for_cost_production/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -id,name,type_,zone,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period,start,end,period,timepoint_selection_method -0,winter,timeseries,,1.0,1,1.0,,,, diff --git a/examples/capacity_expansion/5bus_sequential/sting_log.txt b/examples/capacity_expansion/5bus_sequential/sting_log.txt deleted file mode 100644 index 962a94a..0000000 --- a/examples/capacity_expansion/5bus_sequential/sting_log.txt +++ /dev/null @@ -1,14873 +0,0 @@ -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.18 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.22 seconds. - -2026-02-06 10:15:21 -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:15:21 -2026-02-06 10:15:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'north', 'south', 'center'} - - System with new buses created: {'north', 'south', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 3 constraints - Size: 3 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 4e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:24:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per bus - Size: 5 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 19 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 7e-22 var: 6e-17 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:25:17 -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:25:17 -2026-02-06 10:25:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'center', 'north', 'south'} - - System with new buses created: {'center', 'north', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=False, bus_max_flow_expansion=False, bus_max_flow=True, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 3 constraints - Size: 3 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:31:24 -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:31:24 -2026-02-06 10:31:24 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:35:01 -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:35:01 -2026-02-06 10:35:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'north', 'center', 'south'} - - System with new buses created: {'north', 'center', 'south'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:40:40 -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:40:40 -2026-02-06 10:40:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 10:58:51 -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 10:58:51 -2026-02-06 10:58:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'center', 'north'} - - System with new buses created: {'south', 'center', 'north'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 1e-17 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. -> Objective value: 14810.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 11:10:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpcfcds52g.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.22 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -2026-02-06 11:11:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpv08qruov.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:13:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpcmcb59in.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:13:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpdb6uksqh.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:14:15 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp1skdnd7v.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:14:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpo_kgi_h4.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:16:34 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp3ogsocec.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xd4ca6805 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 8 rows and 18 columns -Presolve time: 0.00s -Presolved: 4 rows, 8 columns, 18 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 6.000e+00 - Factor NZ : 1.000e+01 - Factor Ops : 3.000e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 -1.45768059e+02 2.00966885e-02 0.00e+00 4.60e+01 5.21e+01 0s - 1 -6.89922627e+01 2.29802740e-02 0.00e+00 6.08e+00 6.11e+00 0s - 2 -2.45165571e-01 2.29144547e-02 0.00e+00 0.00e+00 2.35e-02 0s - 3 4.33334015e-03 2.21055926e-02 0.00e+00 0.00e+00 1.52e-03 0s - 4 1.61013129e-02 1.75423861e-02 0.00e+00 0.00e+00 1.11e-04 0s - 5 1.74317501e-02 1.75030058e-02 0.00e+00 7.21e-14 5.50e-06 0s - 6 1.74780178e-02 1.74823347e-02 0.00e+00 8.25e-14 3.34e-07 0s - 7 1.74798208e-02 1.74798983e-02 0.00e+00 1.88e-13 5.99e-09 0s - 8 1.74798969e-02 1.74798969e-02 0.00e+00 1.37e-13 6.36e-15 0s - -Barrier solved model in 8 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 11:21:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -2026-02-06 11:22:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 20 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 13 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 7.4e+02 5.3e-01 8.6e+01 0.00e+00 5.317106115e-02 2.008031974e+01 1.1e+02 0.00 -1 1.5e+02 1.1e-01 1.8e+01 3.08e+00 2.559061933e-02 2.466445804e+01 2.2e+01 0.00 -2 1.9e+00 1.4e-03 2.3e-01 1.16e+00 2.287060515e-02 5.505723559e-02 2.8e-01 0.00 -3 1.1e-01 7.9e-05 1.3e-02 1.10e+00 2.321017279e-02 2.300019069e-02 1.6e-02 0.00 -4 3.4e-02 2.4e-05 4.0e-03 4.25e-01 1.762762433e-02 1.691732143e-02 4.9e-03 0.00 -5 1.5e-03 1.1e-06 1.7e-04 1.02e+00 1.759688411e-02 1.756167147e-02 2.1e-04 0.00 -6 7.8e-05 5.6e-08 9.2e-06 1.01e+00 1.748886053e-02 1.748700284e-02 1.1e-05 0.00 -7 1.4e-06 1.0e-09 1.7e-07 9.93e-01 1.748017151e-02 1.748014040e-02 2.1e-07 0.00 -8 2.3e-10 1.7e-13 2.8e-11 9.98e-01 1.747989696e-02 1.747989696e-02 3.4e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896962e-02 nrm: 5e+02 Viol. con: 2e-07 var: 0e+00 - Dual. obj: 1.7479896940e-02 nrm: 6e-05 Viol. con: 7e-14 var: 4e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7479896925e-02 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7479896966e-02 nrm: 6e-05 Viol. con: 0e+00 var: 9e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 11:30:06 -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -> Initializing creation of a zonal system where buses are grouped by their zone attribute ... -2026-02-06 11:30:06 -2026-02-06 11:30:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed - - System with new buses created: {'south', 'north', 'center'} - - System with new buses created: {'south', 'north', 'center'} - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Re-assigning bus, from_bus, to_bus attributes in system components completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - Cloning components: ['cf', 'tp', 'ts', 'sc'] completed. - - New system has: - - New system has: - - 0 'gfli_a' components. - - 0 'gfli_a' components. - - 0 'gfli_b' components. - - 0 'gfli_b' components. - - 0 'gfmi_c' components. - - 0 'gfmi_c' components. - - 0 'inf_src' components. - - 0 'inf_src' components. - - 4 'line_pi' components. - - 4 'line_pi' components. - - 0 'se_rl' components. - - 0 'se_rl' components. - - 0 'pa_rc' components. - - 0 'pa_rc' components. - - 3 'bus' components. - - 3 'bus' components. - - 1 'ts' components. - - 1 'ts' components. - - 1 'tp' components. - - 1 'tp' components. - - 1 'sc' components. - - 1 'sc' components. - - 5 'load' components. - - 5 'load' components. - - 5 'gen' components. - - 5 'gen' components. - - 1 'cf' components. - - 1 'cf' components. - - 1 'ess' components. - - 1 'ess' components. - - 0 'energy_budget' components. - - 0 'energy_budget' components. - - 0 'carbon_policy' components. - - 0 'carbon_policy' components. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 3 expressions - Size: 3 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 4 constraints - Size: 4 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. -There are multiple load entries for the same bus, scenario, and timepoint. They will be summed. - - Decision variables of bus angles - - Decision variables of bus angles - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 4 constraints - Size: 4 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 3 constraints - Size: 3 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 16 - Constraints : 16 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 11 - Scalar variables : 11 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Primal. obj: 1.4810000000e-02 nrm: 7e+02 Viol. con: 5e-13 var: 0e+00 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 - Dual. obj: 1.4810000000e-02 nrm: 3e-05 Viol. con: 0e+00 var: 7e-16 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 14810.00 USD. - -> Objective value: 14810.00 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_1h/outputs/zonal_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-02-06 12:13:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-06 12:13:08 -2026-02-06 12:13:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpbqeqaphm.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpbqeqaphm.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc46566cd -Model fingerprint: 0xc46566cd -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [2e+02, 1e+03] - RHS range [2e+02, 1e+03] -Presolve removed 8 rows and 9 columns -Presolve removed 8 rows and 9 columns -Presolve time: 0.00s -Presolve time: 0.00s - - -Barrier solved model in 0 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 0 iterations and 0.00 seconds (0.00 work units) -Model is infeasible -Model is infeasible -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Model was proven to be infeasible. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Model was proven to be infeasible. -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.11 seconds. -> Time spent by solver: 0.11 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Solver finished with status: warning, termination condition: infeasible. -evaluating object as numeric value: vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -evaluating object as numeric value: vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -evaluating object as numeric value: obj - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -evaluating object as numeric value: obj - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -2026-02-06 12:19:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpw_bhzlvk.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc46566cd -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [2e+02, 1e+03] -Presolve removed 8 rows and 9 columns -Presolve time: 0.00s - -Barrier solved model in 0 iterations and 0.00 seconds (0.00 work units) -Model is infeasible -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Model was proven to be infeasible. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: infeasible. -evaluating object as numeric value: vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -evaluating object as numeric value: obj - (object: ) -No value for uninitialized VarData object vGEN[Generator(id=0, name='1', technology='gas', bus='1', site='cf_one', cap_existing_power_MW=40.0, cap_max_power_MW=40.0, cost_fixed_power_USDperkW=14.0, cost_variable_USDperMWh=14.0, c0_USD=0.0, c1_USDperMWh=14.0, c2_USDperMWh2=0.0, emission_rate_tonneCO2perMWh=None, bus_id=0, expand_capacity=False),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='1', timeseries='winter')] -2026-02-06 12:30:00 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpeosampmf.pyomo.lp -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s - -Barrier statistics: - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - - Objective Residual -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 - -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-02-06 12:34:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 12:34:21 -2026-02-06 12:34:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp2plp3zh5.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp2plp3zh5.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:38:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 12:38:54 -2026-02-06 12:38:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpevw0h5yn.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpevw0h5yn.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:40:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 12:40:50 -2026-02-06 12:40:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp8o3ux_lw.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp8o3ux_lw.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:41:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 12:41:21 -2026-02-06 12:41:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpjqbsybsp.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpjqbsybsp.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:50:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 12:50:06 -2026-02-06 12:50:06 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp5pauw3w3.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp5pauw3w3.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:51:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 12:51:03 -2026-02-06 12:51:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp2keo1puy.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmp2keo1puy.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 12:58:39 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 12:58:39 -2026-02-06 12:58:39 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmphzlx2oan.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmphzlx2oan.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 13:02:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-02-06 13:02:20 -2026-02-06 13:02:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -2026-02-06 13:03:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 13:03:31 -2026-02-06 13:03:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -2026-02-06 13:03:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 13:03:57 -2026-02-06 13:03:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpdccbuvs7.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpdccbuvs7.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-06 14:13:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 1 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 5 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.9e+02 5.4e-01 9.0e+01 0.00e+00 5.084368530e+01 6.422271835e+01 1.0e+02 0.00 -1 1.3e+02 1.0e-01 1.7e+01 2.99e+00 2.477372408e+01 4.807401228e+01 1.9e+01 0.00 -2 2.8e+01 2.2e-02 3.6e+00 1.09e+00 1.799022880e+01 2.263385435e+01 4.1e+00 0.00 -3 3.8e+00 3.0e-03 5.0e-01 1.05e+00 1.767699405e+01 1.825240635e+01 5.7e-01 0.00 -4 6.1e-01 4.8e-04 8.0e-02 1.05e+00 1.754622417e+01 1.761129758e+01 9.2e-02 0.00 -5 1.0e-01 7.8e-05 1.3e-02 1.06e+00 1.750814629e+01 1.751733970e+01 1.5e-02 0.00 -6 2.3e-02 1.8e-05 2.9e-03 9.58e-01 1.749889328e+01 1.750093474e+01 3.4e-03 0.00 -7 2.5e-05 1.9e-08 3.2e-06 1.00e+00 1.749737976e+01 1.749737899e+01 3.7e-06 0.00 -8 2.5e-09 1.9e-12 3.2e-10 1.00e+00 1.749737682e+01 1.749737682e+01 3.7e-10 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376823e+01 nrm: 5e+02 Viol. con: 2e-06 var: 0e+00 - Dual. obj: 1.7497376822e+01 nrm: 6e-02 Viol. con: 8e-13 var: 5e-13 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 - Dual. obj: 1.7497376823e+01 nrm: 6e-02 Viol. con: 0e+00 var: 1e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82 USD. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-06 14:13:32 -2026-02-06 14:13:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Added 6 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'bus' components. - Added 5 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'tp' components. - Added 1 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'load' components. - Added 5 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'gen' components. - Added 5 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'cf' components. - Added 1 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=[], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpzwnrx1t_.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpzwnrx1t_.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc4a412e0 -Model fingerprint: 0xc4a412e0 -Coefficient statistics: -Coefficient statistics: - Matrix range [9e-01, 2e+04] - Matrix range [9e-01, 2e+04] - Objective range [1e-05, 4e-05] - Objective range [1e-05, 4e-05] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [4e+01, 1e+03] - RHS range [4e+01, 1e+03] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 0 2.54824422e+01 1.74798969e-02 6.42e-02 2.16e-14 2.83e-02 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 1 2.49191707e-02 1.74800696e-02 1.88e-05 6.18e-03 5.35e-04 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - 2 1.74798988e-02 1.74798969e-02 4.66e-12 6.17e-09 5.35e-10 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798988e-02 -Optimal objective 1.74798988e-02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.90 USD. - -> Objective value: 17479.90 USD. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-15 20:00:22 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxDispatch[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 600.0 - Constraint=cCapGenNonVar[Generator(id=4, name='5', bus='5')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 400.0 - Variable=vCAP[Generator(id=3, name='4', bus='4')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.0e+02 4.0e+02 1.6e+02 0.00e+00 9.385424073e+02 7.762745216e+02 2.6e-01 0.00 -1 1.3e+02 8.7e+01 3.6e+01 -9.91e-01 3.196335151e+03 3.037620512e+03 5.7e-02 0.00 -2 9.0e+00 6.0e+00 2.5e+00 -9.54e-01 3.856673463e+04 3.845798105e+04 3.9e-03 0.00 -3 3.6e+00 2.4e+00 9.8e-01 -9.82e-01 8.684316398e+03 8.571563981e+03 1.6e-03 0.00 -4 3.4e+00 2.3e+00 9.2e-01 -9.02e-01 1.132815806e+04 1.121908265e+04 1.5e-03 0.00 -5 6.9e-01 4.6e-01 1.9e-01 -9.01e-01 3.886258921e+04 3.889687291e+04 3.0e-04 0.00 -6 7.9e-02 5.3e-02 2.2e-02 -5.25e-01 1.272207414e+05 1.274782304e+05 3.5e-05 0.00 -7 2.1e-03 1.4e-03 5.8e-04 5.66e-01 1.733188922e+05 1.733356516e+05 9.4e-07 0.00 -8 5.7e-06 3.8e-06 1.5e-06 1.01e+00 1.749694974e+05 1.749695403e+05 2.5e-09 0.00 -9 5.8e-10 3.8e-10 1.1e-10 1.00e+00 1.749737678e+05 1.749737678e+05 2.5e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376779e+05 nrm: 5e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 1.7497376779e+05 nrm: 6e+04 Viol. con: 3e-08 var: 1e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+05 nrm: 5e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 1.7497376822e+05 nrm: 6e+04 Viol. con: 0e+00 var: 9e-10 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82230642. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 20:00:22 -2026-02-15 20:00:22 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System initialization completed. -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -2026-02-15 20:02:31 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cMaxDispatch[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Maximum RHS: 600.0 - Constraint=cCapGenNonVar[Generator(id=4, name='5', bus='5')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 400.0 - Variable=vCAP[Generator(id=3, name='4', bus='4')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.0e+02 4.0e+02 1.6e+02 0.00e+00 9.385424073e+02 7.762745216e+02 2.6e-01 0.00 -1 1.3e+02 8.7e+01 3.6e+01 -9.91e-01 3.196335151e+03 3.037620512e+03 5.7e-02 0.00 -2 9.0e+00 6.0e+00 2.5e+00 -9.54e-01 3.856673463e+04 3.845798105e+04 3.9e-03 0.00 -3 3.6e+00 2.4e+00 9.8e-01 -9.82e-01 8.684316398e+03 8.571563981e+03 1.6e-03 0.00 -4 3.4e+00 2.3e+00 9.2e-01 -9.02e-01 1.132815806e+04 1.121908265e+04 1.5e-03 0.00 -5 6.9e-01 4.6e-01 1.9e-01 -9.01e-01 3.886258921e+04 3.889687291e+04 3.0e-04 0.00 -6 7.9e-02 5.3e-02 2.2e-02 -5.25e-01 1.272207414e+05 1.274782304e+05 3.5e-05 0.00 -7 2.1e-03 1.4e-03 5.8e-04 5.66e-01 1.733188922e+05 1.733356516e+05 9.4e-07 0.00 -8 5.7e-06 3.8e-06 1.5e-06 1.01e+00 1.749694974e+05 1.749695403e+05 2.5e-09 0.00 -9 5.8e-10 3.8e-10 1.1e-10 1.00e+00 1.749737678e+05 1.749737678e+05 2.5e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376779e+05 nrm: 5e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 1.7497376779e+05 nrm: 6e+04 Viol. con: 3e-08 var: 1e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+05 nrm: 5e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 1.7497376822e+05 nrm: 6e+04 Viol. con: 0e+00 var: 9e-10 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82230642. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-02-15 20:02:31 -2026-02-15 20:02:31 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -System initialization completed. -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: 0.0 - - Minimum RHS: 0.0 - Constraint=cMaxDispatch[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - Bound=upper - - Maximum RHS: 46650.51537309484 - - Maximum RHS: 46650.51537309484 - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatch[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Academic license - for non-commercial use only - expires 2026-12-23 -Academic license - for non-commercial use only - expires 2026-12-23 -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpmbu3a_f4.pyomo.lp -Read LP format model from file /var/folders/g0/dqv0hkx15ylc7p0dmzlbtf5m0000gp/T/tmpmbu3a_f4.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) -Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[arm] - Darwin 25.2.0 25C56) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0xc2909948 -Model fingerprint: 0xc2909948 -Coefficient statistics: -Coefficient statistics: - Matrix range [1e-02, 2e+02] - Matrix range [1e-02, 2e+02] - Objective range [1e-01, 4e-01] - Objective range [1e-01, 4e-01] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [2e+00, 5e+04] - RHS range [2e+00, 5e+04] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 4.35560184e+02 1.74798969e+02 8.22e-02 5.41e-13 7.01e-02 0s - 0 4.35560184e+02 1.74798969e+02 8.22e-02 5.41e-13 7.01e-02 0s - 1 1.75395733e+02 1.74799441e+02 1.88e-04 2.20e-02 1.85e-03 0s - 1 1.75395733e+02 1.74799441e+02 1.88e-04 2.20e-02 1.85e-03 0s - 2 1.74798970e+02 1.74798969e+02 9.79e-11 2.36e-08 1.99e-09 0s - 2 1.74798970e+02 1.74798969e+02 9.79e-11 2.36e-08 1.99e-09 0s - - -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 2 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798970e+02 -Optimal objective 1.74798970e+02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.31 seconds. -> Time spent by solver: 0.31 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.89692543603. - -> Objective value: 17479.89692543603. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.34 seconds. - - ->> Run completed in 0.34 seconds. - -2026-03-23 10:11:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch for non-variable generators (capacity factor of 1) - Size: 0 constraints - - Constraints on dispatch for variable generators - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of carbon policy constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of constraint on transmission capacity expansion ... -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: -2.4 - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cCapGenNonVar[Generator(id=4, name='5', bus='5')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 400.0 - Variable=vCAP[Generator(id=3, name='4', bus='4')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.0e+02 4.0e+02 1.6e+02 0.00e+00 9.385424073e+02 7.762745216e+02 2.6e-01 0.00 -1 1.3e+02 8.7e+01 3.6e+01 -9.91e-01 3.196335151e+03 3.037620512e+03 5.7e-02 0.00 -2 9.0e+00 6.0e+00 2.5e+00 -9.54e-01 3.856673463e+04 3.845798105e+04 3.9e-03 0.00 -3 3.6e+00 2.4e+00 9.8e-01 -9.82e-01 8.684316398e+03 8.571563981e+03 1.6e-03 0.00 -4 3.4e+00 2.3e+00 9.2e-01 -9.02e-01 1.132815806e+04 1.121908265e+04 1.5e-03 0.00 -5 6.9e-01 4.6e-01 1.9e-01 -9.01e-01 3.886258921e+04 3.889687291e+04 3.0e-04 0.00 -6 7.9e-02 5.3e-02 2.2e-02 -5.25e-01 1.272207414e+05 1.274782304e+05 3.5e-05 0.00 -7 2.1e-03 1.4e-03 5.8e-04 5.66e-01 1.733188922e+05 1.733356516e+05 9.4e-07 0.00 -8 5.7e-06 3.8e-06 1.5e-06 1.01e+00 1.749694974e+05 1.749695403e+05 2.5e-09 0.00 -9 5.8e-10 3.8e-10 1.1e-10 1.00e+00 1.749737678e+05 1.749737678e+05 2.5e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376779e+05 nrm: 5e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 1.7497376779e+05 nrm: 6e+04 Viol. con: 3e-08 var: 1e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+05 nrm: 5e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 1.7497376822e+05 nrm: 6e+04 Viol. con: 0e+00 var: 9e-10 -> Time spent by solver: 0.22 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82230642. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export transmission capacity expansion results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.27 seconds. - -2026-03-23 10:11:04 -2026-03-23 10:11:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch for non-variable generators (capacity factor of 1) - - Constraints on dispatch for non-variable generators (capacity factor of 1) - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch for variable generators - - Constraints on dispatch for variable generators - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of carbon policy constraints ... -> Initializing construction of carbon policy constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of constraint on transmission capacity expansion ... -> Initializing construction of constraint on transmission capacity expansion ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: -2.4 - - Minimum RHS: -2.4 - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - Bound=lower - - Maximum RHS: 46.65051537309484 - - Maximum RHS: 46.65051537309484 - Constraint=cMaxDispatchCf[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatchCf[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Set parameter LicenseID to value 2773173 -Set parameter LicenseID to value 2773173 -Academic license - for non-commercial use only - expires 2027-01-31 -Academic license - for non-commercial use only - expires 2027-01-31 -Read LP format model from file /var/folders/jg/04wfkrv505j8zgw99yb4_ql00000gq/T/tmpmwgk96kt.pyomo.lp -Read LP format model from file /var/folders/jg/04wfkrv505j8zgw99yb4_ql00000gq/T/tmpmwgk96kt.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 25.3.0 25D2128) -Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 25.3.0 25D2128) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Non-default parameters: -Non-default parameters: -FeasibilityTol 1e-05 -FeasibilityTol 1e-05 -Method 2 -Method 2 -BarHomogeneous 1 -BarHomogeneous 1 -Crossover 0 -Crossover 0 - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0x0a9452fc -Model fingerprint: 0x0a9452fc -Coefficient statistics: -Coefficient statistics: - Matrix range [1e-02, 2e+02] - Matrix range [1e-02, 2e+02] - Objective range [1e-01, 4e-01] - Objective range [1e-01, 4e-01] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [2e+00, 5e+01] - RHS range [2e+00, 5e+01] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.19866584e+02 1.74798969e+02 7.48e-01 3.28e-14 1.12e-01 0s - 0 2.19866584e+02 1.74798969e+02 7.48e-01 3.28e-14 1.12e-01 0s - 1 1.75644503e+02 1.74804762e+02 1.40e-02 6.95e-03 4.88e-03 0s - 1 1.75644503e+02 1.74804762e+02 1.40e-02 6.95e-03 4.88e-03 0s - 2 1.74798969e+02 1.74798963e+02 1.40e-12 6.44e-06 6.10e-06 0s - 2 1.74798969e+02 1.74798963e+02 1.40e-12 6.44e-06 6.10e-06 0s - 3 1.74798969e+02 1.74798969e+02 5.16e-10 7.05e-09 1.19e-08 0s - 3 1.74798969e+02 1.74798969e+02 5.16e-10 7.05e-09 1.19e-08 0s - 4 1.74798969e+02 1.74798969e+02 4.59e-13 4.20e-13 7.75e-12 0s - 4 1.74798969e+02 1.74798969e+02 4.59e-13 4.20e-13 7.75e-12 0s - - -Barrier solved model in 4 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 4 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e+02 -Optimal objective 1.74798969e+02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.31 seconds. -> Time spent by solver: 0.31 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925380977. - -> Objective value: 17479.896925380977. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export transmission capacity expansion results to CSV files ... -> Initializing export transmission capacity expansion results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.34 seconds. - - ->> Run completed in 0.34 seconds. - -2026-03-23 10:11:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - Added 5 'generators' - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - - 'storage.csv' ... - Added 1 'storage' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 5 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 1 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='quadratic', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 5 generators - - Decision variables of capacity expansion for generators - Size: 5 variables - - Decision variables of dispatch - Size: 5 variables - - Constraints on capacity expansion for generators - Size: 5 constraints - - Constraints on dispatch for non-variable generators (capacity factor of 1) - Size: 0 constraints - - Constraints on dispatch for variable generators - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - - Expressions for generation cost per timepoint - Size: 1 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 2 variables - - Decision variables of state of charge - Size: 1 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 2 constraints - - Constraints on maximum state of charge - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - - Expressions for storage cost per timepoint - Size: 1 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of bus angles - Size: 5 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 6 constraints - - Energy balance at each bus - Size: 5 constraints -> Completed in 0.00 seconds. - -> Initializing construction of carbon policy constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of constraint on transmission capacity expansion ... -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: -2.4 - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cCapGenNonVar[Generator(id=4, name='5', bus='5')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 400.0 - Variable=vCAP[Generator(id=3, name='4', bus='4')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 25 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 18 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 4 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 8 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 10 after factor : 10 -Factor - dense dim. : 0 flops : 1.00e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.0e+02 4.0e+02 1.6e+02 0.00e+00 9.385424073e+02 7.762745216e+02 2.6e-01 0.00 -1 1.3e+02 8.7e+01 3.6e+01 -9.91e-01 3.196335151e+03 3.037620512e+03 5.7e-02 0.00 -2 9.0e+00 6.0e+00 2.5e+00 -9.54e-01 3.856673463e+04 3.845798105e+04 3.9e-03 0.00 -3 3.6e+00 2.4e+00 9.8e-01 -9.82e-01 8.684316398e+03 8.571563981e+03 1.6e-03 0.00 -4 3.4e+00 2.3e+00 9.2e-01 -9.02e-01 1.132815806e+04 1.121908265e+04 1.5e-03 0.00 -5 6.9e-01 4.6e-01 1.9e-01 -9.01e-01 3.886258921e+04 3.889687291e+04 3.0e-04 0.00 -6 7.9e-02 5.3e-02 2.2e-02 -5.25e-01 1.272207414e+05 1.274782304e+05 3.5e-05 0.00 -7 2.1e-03 1.4e-03 5.8e-04 5.66e-01 1.733188922e+05 1.733356516e+05 9.4e-07 0.00 -8 5.7e-06 3.8e-06 1.5e-06 1.01e+00 1.749694974e+05 1.749695403e+05 2.5e-09 0.00 -9 5.8e-10 3.8e-10 1.1e-10 1.00e+00 1.749737678e+05 1.749737678e+05 2.5e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376779e+05 nrm: 5e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 1.7497376779e+05 nrm: 6e+04 Viol. con: 3e-08 var: 1e-06 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.7497376822e+05 nrm: 5e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 1.7497376822e+05 nrm: 6e+04 Viol. con: 0e+00 var: 9e-10 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17497376.82230642. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export transmission capacity expansion results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-03-23 10:11:48 -2026-03-23 10:11:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - System initialization completed. - System initialization completed. -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 5 'generators' - Added 5 'generators' - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 1 'capacity_factors' - Added 1 'capacity_factors' - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'storage' - Added 1 'storage' - - 'buses.csv' ... - - 'buses.csv' ... - Added 5 'buses' - Added 5 'buses' - - 'loads.csv' ... - - 'loads.csv' ... - Added 5 'loads' - Added 5 'loads' - - 'lines.csv' ... - - 'lines.csv' ... - Added 6 'lines' - Added 6 'lines' - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'timeseries' - Added 1 'timeseries' - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 1 'timepoints' - Added 1 'timepoints' - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'scenarios' - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Initializing upload built capacities from a previous capex solution ... -> Initializing upload built capacities from a previous capex solution ... -> Updated existing capacities for 5 generators based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 5 generators based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/generator_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -> Updated existing capacities for 0 storage units based on input file /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion/storage_built_capacity.csv -No file named 'line_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'line_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built line capacities. -No file named 'bus_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -No file named 'bus_built_capacity.csv' found in /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/capacity_expansion. Skipping upload of built bus capacities. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=False, single_storage_injection=False, generation_capacity_expansion=False, storage_capacity_expansion=False, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -Solver settings: SolverSettings(solver_name='gurobi', tee=True, solver_options={'BarHomogeneous': 1, 'FeasibilityTol': 1e-05, 'CrossOver': 0, 'Method': 2}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - - Set of capacity-expandable generators - Size: 0 generators - Size: 0 generators - - Decision variables of capacity expansion for generators - - Decision variables of capacity expansion for generators - Size: 0 variables - Size: 0 variables - - Decision variables of dispatch - - Decision variables of dispatch - Size: 5 variables - Size: 5 variables - - Constraints on capacity expansion for generators - - Constraints on capacity expansion for generators - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch for non-variable generators (capacity factor of 1) - - Constraints on dispatch for non-variable generators (capacity factor of 1) - Size: 0 constraints - Size: 0 constraints - - Constraints on dispatch for variable generators - - Constraints on dispatch for variable generators - Size: 5 constraints - Size: 5 constraints - - Constraints on forced dispatch requirements specified for certain generators - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - Size: 0 constraints - - Expressions for dispatch at any bus - - Expressions for dispatch at any bus - Size: 5 expressions - Size: 5 expressions - - Expressions for emission per timepoint per scenario expression - - Expressions for emission per timepoint per scenario expression - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per timepoint - - Expressions for generation cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expressions for generation cost per period - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - - Decision variables of discharge and charge - Size: 2 variables - Size: 2 variables - - Decision variables of state of charge - - Decision variables of state of charge - Size: 1 variables - Size: 1 variables - - Set of capacity-expandable storage units - - Set of capacity-expandable storage units - Size: 0 storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - - Decision variables of power and energy capacity expansion - Size: 0 variables - Size: 0 variables - - Constraints on power capacity expansion - - Constraints on power capacity expansion - Size: 0 constraints - Size: 0 constraints - - Constraints on storage dispatch - - Constraints on storage dispatch - Size: 2 constraints - Size: 2 constraints - - Constraints on maximum state of charge - - Constraints on maximum state of charge - Size: 1 constraints - Size: 1 constraints - - Constraints on evolution of state of charge across timepoints - - Constraints on evolution of state of charge across timepoints - Size: 6 constraints - Size: 6 constraints - - Expressions for storage cost per timepoint - - Expressions for storage cost per timepoint - Size: 1 expressions - Size: 1 expressions - - Expression for storage cost per period - - Expression for storage cost per period - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Load data processing - - Decision variables of bus angles - - Decision variables of bus angles - Size: 5 variables - Size: 5 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Maximum flow constraints per line - - Maximum flow constraints per line - Size: 6 constraints - Size: 6 constraints - - Energy balance at each bus - - Energy balance at each bus - Size: 5 constraints - Size: 5 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of carbon policy constraints ... -> Initializing construction of carbon policy constraints ... - - Annual carbon policy constraint - - Annual carbon policy constraint - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... -> Initializing construction of energy budget constraints ... - - Constraint for power budget - - Constraint for power budget - Size: 0 constraints - Size: 0 constraints - - Constraint for energy budget - - Constraint for energy budget - Size: 0 constraints - Size: 0 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of constraint on transmission capacity expansion ... -> Initializing construction of constraint on transmission capacity expansion ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - - RHS extremes: - - RHS extremes: - - Minimum RHS: -2.4 - - Minimum RHS: -2.4 - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cFlowPerNonExpLine[LinePiModel(id=5, from_bus='4', to_bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=lower - Bound=lower - - Maximum RHS: 46.65051537309484 - - Maximum RHS: 46.65051537309484 - Constraint=cMaxDispatchCf[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Constraint=cMaxDispatchCf[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Bound=upper - - Bound=upper - - - Objective coefficient extremes: - - Objective coefficient extremes: - - Minimum coefficient: 0.1 - - Minimum coefficient: 0.1 - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=4, name='5', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - - Maximum coefficient: 0.4 - - Maximum coefficient: 0.4 - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] - Variable=vGEN[Generator(id=3, name='4', bus='4'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Set parameter Username -Set parameter Username -Set parameter LicenseID to value 2773173 -Set parameter LicenseID to value 2773173 -Academic license - for non-commercial use only - expires 2027-01-31 -Academic license - for non-commercial use only - expires 2027-01-31 -Read LP format model from file /var/folders/jg/04wfkrv505j8zgw99yb4_ql00000gq/T/tmp8743p3bv.pyomo.lp -Read LP format model from file /var/folders/jg/04wfkrv505j8zgw99yb4_ql00000gq/T/tmp8743p3bv.pyomo.lp -Reading time = 0.00 seconds -Reading time = 0.00 seconds -x1: 26 rows, 12 columns, 48 nonzeros -x1: 26 rows, 12 columns, 48 nonzeros -Set parameter BarHomogeneous to value 1 -Set parameter BarHomogeneous to value 1 -Set parameter FeasibilityTol to value 1e-05 -Set parameter FeasibilityTol to value 1e-05 -Set parameter Crossover to value 0 -Set parameter Crossover to value 0 -Set parameter Method to value 2 -Set parameter Method to value 2 -Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 25.3.0 25D2128) -Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 25.3.0 25D2128) - - -CPU model: Apple M2 Ultra -CPU model: Apple M2 Ultra -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads -Thread count: 24 physical cores, 24 logical processors, using up to 24 threads - - -Non-default parameters: -Non-default parameters: -FeasibilityTol 1e-05 -FeasibilityTol 1e-05 -Method 2 -Method 2 -BarHomogeneous 1 -BarHomogeneous 1 -Crossover 0 -Crossover 0 - - -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Optimize a model with 26 rows, 12 columns and 48 nonzeros -Model fingerprint: 0x0a9452fc -Model fingerprint: 0x0a9452fc -Coefficient statistics: -Coefficient statistics: - Matrix range [1e-02, 2e+02] - Matrix range [1e-02, 2e+02] - Objective range [1e-01, 4e-01] - Objective range [1e-01, 4e-01] - Bounds range [0e+00, 0e+00] - Bounds range [0e+00, 0e+00] - RHS range [2e+00, 5e+01] - RHS range [2e+00, 5e+01] -Presolve removed 9 rows and 21 columns -Presolve removed 9 rows and 21 columns -Presolve time: 0.00s -Presolve time: 0.00s -Presolved: 3 rows, 5 columns, 9 nonzeros -Presolved: 3 rows, 5 columns, 9 nonzeros -Ordering time: 0.00s -Ordering time: 0.00s - - -Barrier statistics: -Barrier statistics: - AA' NZ : 3.000e+00 - AA' NZ : 3.000e+00 - Factor NZ : 6.000e+00 - Factor NZ : 6.000e+00 - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Factor Ops : 1.400e+01 (less than 1 second per iteration) - Threads : 1 - Threads : 1 - - - Objective Residual - Objective Residual -Iter Primal Dual Primal Dual Compl Time -Iter Primal Dual Primal Dual Compl Time - 0 2.19866584e+02 1.74798969e+02 7.48e-01 3.28e-14 1.12e-01 0s - 0 2.19866584e+02 1.74798969e+02 7.48e-01 3.28e-14 1.12e-01 0s - 1 1.75644503e+02 1.74804762e+02 1.40e-02 6.95e-03 4.88e-03 0s - 1 1.75644503e+02 1.74804762e+02 1.40e-02 6.95e-03 4.88e-03 0s - 2 1.74798969e+02 1.74798963e+02 1.40e-12 6.44e-06 6.10e-06 0s - 2 1.74798969e+02 1.74798963e+02 1.40e-12 6.44e-06 6.10e-06 0s - 3 1.74798969e+02 1.74798969e+02 5.16e-10 7.05e-09 1.19e-08 0s - 3 1.74798969e+02 1.74798969e+02 5.16e-10 7.05e-09 1.19e-08 0s - 4 1.74798969e+02 1.74798969e+02 4.59e-13 4.20e-13 7.75e-12 0s - 4 1.74798969e+02 1.74798969e+02 4.59e-13 4.20e-13 7.75e-12 0s - - -Barrier solved model in 4 iterations and 0.00 seconds (0.00 work units) -Barrier solved model in 4 iterations and 0.00 seconds (0.00 work units) -Optimal objective 1.74798969e+02 -Optimal objective 1.74798969e+02 - - -Could not load duals, i.e., shadow prices, from solver. -Could not load duals, i.e., shadow prices, from solver. -> Time spent by solver: 0.05 seconds. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 17479.896925380977. - -> Objective value: 17479.896925380977. - -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/cost_production -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/5bus_sequential/outputs/cost_production -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export carbon policy results to CSV files ... -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing export transmission capacity expansion results to CSV files ... -> Initializing export transmission capacity expansion results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - - ->> Run completed in 0.08 seconds. - diff --git a/examples/capacity_expansion/energy_budgets/inputs/buses.csv b/examples/capacity_expansion/energy_budgets/inputs/buses.csv deleted file mode 100644 index 121e77d..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,bus_type,zone -1,slack,center -2,PQ,north -3,PQ,south -4,PQ,south -5,PQ,south \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/energy_budget_regions.csv b/examples/capacity_expansion/energy_budgets/inputs/energy_budget_regions.csv deleted file mode 100644 index 3643a8b..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/energy_budget_regions.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,budget_region -hydro_1,hydro_zone -hydro_2,hydro_zone -hydro_3,hydro_zone \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/energy_budget_terms.csv b/examples/capacity_expansion/energy_budgets/inputs/energy_budget_terms.csv deleted file mode 100644 index 9bfa8e0..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/energy_budget_terms.csv +++ /dev/null @@ -1,4 +0,0 @@ -budget_term,timepoint -hydro_basic,tp_1 -hydro_basic,tp_2 -hydro_basic,tp_3 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/energy_budgets.csv b/examples/capacity_expansion/energy_budgets/inputs/energy_budgets.csv deleted file mode 100644 index 170e5ec..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/energy_budgets.csv +++ /dev/null @@ -1,2 +0,0 @@ -budget_term,budget_region,budget_constraint_energy_GWh,budget_constraint_power_GW -hydro_basic,hydro_zone,1.7,0.6 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/generators.csv b/examples/capacity_expansion/energy_budgets/inputs/generators.csv deleted file mode 100644 index 87692fb..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,technology,bus,site,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -gas_1,gas,1,no_capacity_factor,0,200,200,60 -gas_2,gas,1,no_capacity_factor,0,200,200,50 -hydro_1,hydro,3,no_capacity_factor,0,520,520,5 -hydro_2,hydro,4,no_capacity_factor,0,400,400,5 -hydro_3,hydro,5,no_capacity_factor,0,600,600,1 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/lines.csv b/examples/capacity_expansion/energy_budgets/inputs/lines.csv deleted file mode 100644 index 1aed44e..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg,efficiency -1,1,2,400,FALSE,0.00281,0.0281,0,0.00712,-360,360,0.98 -2,1,4,1000,FALSE,0.00304,0.0304,0,0.00658,-360,360,0.98 -3,1,5,1000,FALSE,0.00064,0.0064,0,0.03126,-360,360,0.98 -4,2,3,1000,FALSE,0.00108,0.0108,0,0.01852,-360,360,0.98 -5,3,4,1000,FALSE,0.00297,0.0297,0,0.00674,-360,360,0.98 -6,4,5,240,FALSE,0.00297,0.0297,0,0.00674,-360,360,0.98 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/loads.csv b/examples/capacity_expansion/energy_budgets/inputs/loads.csv deleted file mode 100644 index 75f9c32..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/loads.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,load_MW -1,sc1,tp_1,10 -2,sc1,tp_1,300 -3,sc1,tp_1,300 -4,sc1,tp_1,100 -5,sc1,tp_1,0 -1,sc1,tp_2,20 -2,sc1,tp_2,100 -3,sc1,tp_2,200 -4,sc1,tp_2,500 -5,sc1,tp_2,10 -1,sc1,tp_3,5 -2,sc1,tp_3,300 -3,sc1,tp_3,100 -4,sc1,tp_3,600 -5,sc1,tp_3,5 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/scenarios.csv b/examples/capacity_expansion/energy_budgets/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/timepoints.csv b/examples/capacity_expansion/energy_budgets/inputs/timepoints.csv deleted file mode 100644 index 84f4d23..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -tp_1,winter -tp_2,winter -tp_3,winter \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/inputs/timeseries.csv b/examples/capacity_expansion/energy_budgets/inputs/timeseries.csv deleted file mode 100644 index b290cbd..0000000 --- a/examples/capacity_expansion/energy_budgets/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,start,end,timepoint_duration_hr,timeseries_scale_to_period,number_of_timepoints -winter,1,3,1,1,3 \ No newline at end of file diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/costs_summary.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 153eed0..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,97567.56266917972 -cost_per_period_USD,0.0 -total_cost_USD,97567.56266917972 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/emissions_per_scenario.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/energy_budget_constraints.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/energy_budget_constraints.csv deleted file mode 100644 index 5d29145..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/energy_budget_constraints.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh -sc1,hydro_zone,hydro_basic,1.7,1.7000000000000002 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_built_capacity.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_costs_summary.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 9e8b370..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,47567.5626691774 -cost_per_period_USD,0.0 -total_cost_USD,47567.5626691774 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_dispatch.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 1ad54db..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,16 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -gas_1,sc1,tp_1,0.0 -gas_1,sc1,tp_2,40.00000000000081 -gas_1,sc1,tp_3,200.0 -gas_2,sc1,tp_1,200.0 -gas_2,sc1,tp_2,200.0 -gas_2,sc1,tp_3,200.0 -hydro_1,sc1,tp_1,0.0 -hydro_1,sc1,tp_2,0.0 -hydro_1,sc1,tp_3,0.0 -hydro_2,sc1,tp_1,0.0 -hydro_2,sc1,tp_2,137.5126515240672 -hydro_2,sc1,tp_3,229.37801577027147 -hydro_3,sc1,tp_1,510.00000000000057 -hydro_3,sc1,tp_2,452.4873484759324 -hydro_3,sc1,tp_3,370.6219842297285 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/line_flows.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index 37f9af6..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,19 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,tp_1,0.0,-5.946263886901561,365.6738064862688,375.74570502794165 -1,1,2,sc1,tp_2,0.0,-3.75050555529943,230.64257973402385,149.4807588376872 -1,1,2,sc1,tp_3,0.0,-5.083143846238037,312.59503354124985,274.5809905349809 -4,2,3,sc1,tp_1,-5.946263886901561,-6.356713594504666,65.6738064862686,4.658092767067524 -4,2,3,sc1,tp_2,-3.75050555529943,-4.566998637112146,130.64257973402388,18.43288233072565 -4,2,3,sc1,tp_3,-5.083143846238037,-5.161860584475803,12.595033541249887,0.17132565949762643 -2,1,4,sc1,tp_1,0.0,-2.329345796251413,132.4086554262511,53.29743817663459 -5,3,4,sc1,tp_1,-6.356713594504666,-2.329345796251413,-234.32619351373134,163.07903195090498 -2,1,4,sc1,tp_2,0.0,-3.374951615989252,191.844768741909,111.88542249265512 -5,3,4,sc1,tp_2,-4.566998637112146,-3.374951615989252,-69.35742026597624,14.28704168547522 -2,1,4,sc1,tp_3,0.0,-3.659630116575727,208.0269506884782,131.5566451267495 -5,3,4,sc1,tp_3,-5.161860584475803,-3.659630116575727,-87.40496645875022,22.689695640116096 -3,1,5,sc1,tp_1,0.0,1.1410139556917256,-308.08246191252016,60.745474136370845 -6,4,5,sc1,tp_1,-2.329345796251413,1.1410139556917256,-201.9175380874802,121.08895579630779 -3,1,5,sc1,tp_2,0.0,0.7499319793401816,-202.4873484759323,26.240720827400732 -6,4,5,sc1,tp_2,-3.374951615989252,0.7499319793401816,-239.99999999999997,171.07199999999995 -3,1,5,sc1,tp_3,0.0,0.46525347875370565,-125.62198422972847,10.099765069961055 -6,4,5,sc1,tp_3,-3.659630116575727,0.46525347875370565,-239.99999999999997,171.07199999999995 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index ef00432..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -1,sc1,tp_1,0.0 -1,sc1,tp_2,0.0 -1,sc1,tp_3,0.0 -2,sc1,tp_1,0.0 -2,sc1,tp_2,0.0 -2,sc1,tp_3,0.0 -3,sc1,tp_1,0.0 -3,sc1,tp_2,0.0 -3,sc1,tp_3,0.0 -4,sc1,tp_1,0.0 -4,sc1,tp_2,0.0 -4,sc1,tp_3,10.000000000000465 -5,sc1,tp_1,0.0 -5,sc1,tp_2,0.0 -5,sc1,tp_3,0.0 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index de853f4..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -total_cost_USD,50000.00000000233 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/local_marginal_prices.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index ef02486..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,tp_1,59.06790631987785 -1,sc1,tp_2,60.0 -1,sc1,tp_3,4996.932093680123 -2,sc1,tp_1,59.06790631987951 -2,sc1,tp_2,61.25667882782273 -2,sc1,tp_3,4998.188772507944 -3,sc1,tp_1,59.06790631987951 -3,sc1,tp_2,61.73967282570356 -3,sc1,tp_3,4998.671766505825 -4,sc1,tp_1,59.0679063198786 -4,sc1,tp_2,63.0679063198777 -4,sc1,tp_3,5000.0 -5,sc1,tp_1,59.06790631987769 -5,sc1,tp_2,59.06790631987769 -5,sc1,tp_3,4996.0 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_balance_by_bus.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_balance_by_bus.csv deleted file mode 100644 index 4659270..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_balance_by_bus.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,tp_1,200.0,0,0.0,10.0,189.99999999999972 -1,sc1,tp_2,240.0000000000008,0,0.0,20.0,220.0000000000006 -1,sc1,tp_3,400.0,0,0.0,5.0,394.99999999999955 -2,sc1,tp_1,0.0,0,0.0,300.0,-300.00000000000017 -2,sc1,tp_2,0.0,0,0.0,100.0,-100.0 -2,sc1,tp_3,0.0,0,0.0,300.0,-299.99999999999994 -3,sc1,tp_1,0.0,0,0.0,300.0,-299.9999999999999 -3,sc1,tp_2,0.0,0,0.0,200.0,-200.00000000000014 -3,sc1,tp_3,0.0,0,0.0,100.0,-100.00000000000011 -4,sc1,tp_1,0.0,0,0.0,100.0,-99.99999999999996 -4,sc1,tp_2,137.5126515240672,0,0.0,500.0,-362.4873484759327 -4,sc1,tp_3,229.37801577027147,0,10.000000000000465,600.0,-360.62198422972796 -5,sc1,tp_1,510.00000000000057,0,0.0,0.0,510.00000000000034 -5,sc1,tp_2,452.4873484759324,0,0.0,10.0,442.4873484759322 -5,sc1,tp_3,370.6219842297285,0,0.0,5.0,365.62198422972847 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_budget_constraints.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_budget_constraints.csv deleted file mode 100644 index bb725b5..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/power_budget_constraints.csv +++ /dev/null @@ -1,4 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW -sc1,hydro_zone,hydro_basic,tp_1,0.6,0.5100000000000006 -sc1,hydro_zone,hydro_basic,tp_2,0.6,0.5899999999999996 -sc1,hydro_zone,hydro_basic,tp_3,0.6,0.6000000000000001 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/solver_status.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/solver_status.csv deleted file mode 100644 index 7d8c5dc..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.21393990516662598 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_built_capacity.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_costs_summary.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_dispatch.csv b/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/capacity_expansion/energy_budgets/sting_log.txt b/examples/capacity_expansion/energy_budgets/sting_log.txt deleted file mode 100644 index 09fedae..0000000 --- a/examples/capacity_expansion/energy_budgets/sting_log.txt +++ /dev/null @@ -1,4379 +0,0 @@ -2026-02-13 11:45:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -2026-02-13 11:47:11 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... -2026-02-13 11:47:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables -Rule failed for Expression 'eFlowAtBus' with index (Bus(id=0, bus='1'), Scenario(name='sc1', probability=1.0, id=0), Timepoint(id=0, name='tp_1', timeseries='winter')): -TypeError: unsupported operand type(s) for *: 'NoneType' and 'VarData' -Constructing component 'eFlowAtBus' from data=None failed: - TypeError: unsupported operand type(s) for *: 'NoneType' and 'VarData' -2026-02-13 11:48:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget -2026-02-13 11:49:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget -2026-02-13 11:49:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 85 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 34 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 85 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 97 after factor : 103 -Factor - dense dim. : 0 flops : 8.91e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.5e+02 4.8e+01 7.2e+03 0.00e+00 1.521324261e+03 -5.679656909e+03 3.9e+00 0.00 -1 2.8e+02 1.4e+01 2.1e+03 -9.33e-01 2.272105783e+03 -4.335100038e+03 1.1e+00 0.00 -2 1.1e+01 5.5e-01 8.3e+01 -7.42e-01 9.488495747e+02 -5.665059903e+02 4.5e-02 0.00 -3 2.3e+00 1.2e-01 1.8e+01 5.92e-01 5.669998789e+02 1.839647509e+02 9.5e-03 0.00 -4 5.1e-01 2.6e-02 3.9e+00 8.95e-01 4.138099591e+02 3.257020645e+02 2.1e-03 0.00 -5 1.5e-01 7.4e-03 1.1e+00 9.72e-01 3.626991165e+02 3.368714056e+02 6.0e-04 0.00 -6 3.8e-02 1.9e-03 2.9e-01 9.92e-01 3.497199326e+02 3.430604227e+02 1.6e-04 0.00 -7 9.2e-03 4.6e-04 7.0e-02 9.97e-01 3.466213095e+02 3.450089501e+02 3.8e-05 0.00 -8 4.5e-04 2.2e-05 3.4e-03 1.00e+00 3.455505863e+02 3.454719368e+02 1.8e-06 0.00 -9 6.0e-08 3.0e-09 4.5e-07 1.00e+00 3.455018131e+02 3.455018026e+02 2.4e-10 0.00 -10 6.0e-12 3.0e-13 4.5e-11 1.00e+00 3.455018067e+02 3.455018067e+02 2.4e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 4 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 3e-15 var: 7e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 1e-13 var: 8e-13 -> Time spent by solver: 0.20 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 345.5018067086792. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.24 seconds. - -2026-02-13 11:51:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.03 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.01 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 85 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 34 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 85 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 97 after factor : 103 -Factor - dense dim. : 0 flops : 8.91e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.5e+02 4.8e+01 7.2e+03 0.00e+00 1.521324261e+03 -5.679656909e+03 3.9e+00 0.00 -1 2.8e+02 1.4e+01 2.1e+03 -9.33e-01 2.272105783e+03 -4.335100038e+03 1.1e+00 0.00 -2 1.1e+01 5.5e-01 8.3e+01 -7.42e-01 9.488495747e+02 -5.665059903e+02 4.5e-02 0.00 -3 2.3e+00 1.2e-01 1.8e+01 5.92e-01 5.669998789e+02 1.839647509e+02 9.5e-03 0.00 -4 5.1e-01 2.6e-02 3.9e+00 8.95e-01 4.138099591e+02 3.257020645e+02 2.1e-03 0.00 -5 1.5e-01 7.4e-03 1.1e+00 9.72e-01 3.626991165e+02 3.368714056e+02 6.0e-04 0.00 -6 3.8e-02 1.9e-03 2.9e-01 9.92e-01 3.497199326e+02 3.430604227e+02 1.6e-04 0.00 -7 9.2e-03 4.6e-04 7.0e-02 9.97e-01 3.466213095e+02 3.450089501e+02 3.8e-05 0.00 -8 4.5e-04 2.2e-05 3.4e-03 1.00e+00 3.455505863e+02 3.454719368e+02 1.8e-06 0.00 -9 6.0e-08 3.0e-09 4.5e-07 1.00e+00 3.455018131e+02 3.455018026e+02 2.4e-10 0.00 -10 6.0e-12 3.0e-13 4.5e-11 1.00e+00 3.455018067e+02 3.455018067e+02 2.4e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 4 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 3e-15 var: 7e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 1e-13 var: 8e-13 -> Time spent by solver: 0.10 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 345.5018067086792. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 4.12 seconds. - -> Initializing export energy budget results to CSV files ... -2026-02-13 11:52:21 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.03 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.01 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 0 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 85 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 34 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 85 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 97 after factor : 103 -Factor - dense dim. : 0 flops : 8.91e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.5e+02 4.8e+01 7.2e+03 0.00e+00 1.521324261e+03 -5.679656909e+03 3.9e+00 0.00 -1 2.8e+02 1.4e+01 2.1e+03 -9.33e-01 2.272105783e+03 -4.335100038e+03 1.1e+00 0.00 -2 1.1e+01 5.5e-01 8.3e+01 -7.42e-01 9.488495747e+02 -5.665059903e+02 4.5e-02 0.00 -3 2.3e+00 1.2e-01 1.8e+01 5.92e-01 5.669998789e+02 1.839647509e+02 9.5e-03 0.00 -4 5.1e-01 2.6e-02 3.9e+00 8.95e-01 4.138099591e+02 3.257020645e+02 2.1e-03 0.00 -5 1.5e-01 7.4e-03 1.1e+00 9.72e-01 3.626991165e+02 3.368714056e+02 6.0e-04 0.00 -6 3.8e-02 1.9e-03 2.9e-01 9.92e-01 3.497199326e+02 3.430604227e+02 1.6e-04 0.00 -7 9.2e-03 4.6e-04 7.0e-02 9.97e-01 3.466213095e+02 3.450089501e+02 3.8e-05 0.00 -8 4.5e-04 2.2e-05 3.4e-03 1.00e+00 3.455505863e+02 3.454719368e+02 1.8e-06 0.00 -9 6.0e-08 3.0e-09 4.5e-07 1.00e+00 3.455018131e+02 3.455018026e+02 2.4e-10 0.00 -10 6.0e-12 3.0e-13 4.5e-11 1.00e+00 3.455018067e+02 3.455018067e+02 2.4e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 4 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 3e-15 var: 7e-12 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.4550180671e+02 nrm: 6e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 3.4550180671e+02 nrm: 6e+01 Viol. con: 1e-13 var: 8e-13 -> Time spent by solver: 0.10 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 345.5018067086792. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -2026-02-13 11:52:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget -2026-02-13 11:53:00 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget -Rule failed when generating expression for Constraint cPowerBudget with index (EnergyBudget(id=0, budget_region='hydro_zone', budget_term='hydro_basic', budget_constraint_energy_GWh=2.0), Timepoint(id=0, name='tp_1', timeseries='winter'), Scenario(name='sc1', probability=1.0, id=0)): -TypeError: construct_capacity_expansion_model..cPowerBudget_rule() takes 3 positional arguments but 4 were given -Constructing component 'cPowerBudget' from data=None failed: - TypeError: construct_capacity_expansion_model..cPowerBudget_rule() takes 3 positional arguments but 4 were given -2026-02-13 11:53:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 65.59 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 65.61 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 88 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 37 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 88 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 112 after factor : 118 -Factor - dense dim. : 0 flops : 1.03e+03 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.6e+02 4.8e+01 7.3e+03 0.00e+00 1.513900294e+03 -5.742061883e+03 4.1e+00 0.00 -1 2.3e+02 1.2e+01 1.8e+03 -9.19e-01 2.385229815e+03 -4.008681392e+03 9.9e-01 0.00 -2 3.2e+01 1.6e+00 2.4e+02 -6.81e-01 1.454542453e+03 -1.723063001e+03 1.4e-01 0.00 -3 1.6e+01 8.0e-01 1.2e+02 1.27e-01 1.124692590e+03 -8.917292047e+02 6.8e-02 0.00 -4 9.1e+00 4.6e-01 6.9e+01 3.34e-01 1.043791185e+03 -4.040413954e+02 3.9e-02 0.00 -5 3.1e+00 1.6e-01 2.4e+01 4.50e-01 8.793814694e+02 2.167685343e+02 1.3e-02 0.00 -6 1.8e+00 8.9e-02 1.3e+01 -7.23e-02 1.212933436e+03 6.615825873e+02 7.6e-03 0.00 -7 2.6e-01 1.3e-02 2.0e+00 8.47e-01 1.437474664e+03 1.350029315e+03 1.1e-03 0.00 -8 5.5e-02 2.7e-03 4.1e-01 9.42e-01 1.445478834e+03 1.426790241e+03 2.3e-04 0.00 -9 8.6e-03 4.3e-04 6.5e-02 9.85e-01 1.450390267e+03 1.447442094e+03 3.7e-05 0.00 -10 3.1e-04 1.6e-05 2.4e-03 9.96e-01 1.451334500e+03 1.451226830e+03 1.3e-06 0.00 -11 5.8e-08 2.9e-09 4.4e-07 1.00e+00 1.451361427e+03 1.451361407e+03 2.5e-10 0.00 -12 5.8e-12 2.9e-13 4.7e-11 1.00e+00 1.451361433e+03 1.451361433e+03 2.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 0e+00 var: 1e-11 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 2e-11 var: 2e-11 -> Time spent by solver: 0.12 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1451.361432736361. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -evaluating object as numeric value: cPowerBudget - (object: ) -'IndexedConstraint' object is not callable -evaluating object as numeric value: cPowerBudget - (object: ) -'IndexedConstraint' object is not callable -2026-02-13 12:17:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 6.04 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 6.06 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 88 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 37 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 88 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 112 after factor : 118 -Factor - dense dim. : 0 flops : 1.03e+03 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.6e+02 4.8e+01 7.3e+03 0.00e+00 1.513900294e+03 -5.742061883e+03 4.1e+00 0.00 -1 2.3e+02 1.2e+01 1.8e+03 -9.19e-01 2.385229815e+03 -4.008681392e+03 9.9e-01 0.00 -2 3.2e+01 1.6e+00 2.4e+02 -6.81e-01 1.454542453e+03 -1.723063001e+03 1.4e-01 0.00 -3 1.6e+01 8.0e-01 1.2e+02 1.27e-01 1.124692590e+03 -8.917292047e+02 6.8e-02 0.00 -4 9.1e+00 4.6e-01 6.9e+01 3.34e-01 1.043791185e+03 -4.040413954e+02 3.9e-02 0.00 -5 3.1e+00 1.6e-01 2.4e+01 4.50e-01 8.793814694e+02 2.167685343e+02 1.3e-02 0.00 -6 1.8e+00 8.9e-02 1.3e+01 -7.23e-02 1.212933436e+03 6.615825873e+02 7.6e-03 0.00 -7 2.6e-01 1.3e-02 2.0e+00 8.47e-01 1.437474664e+03 1.350029315e+03 1.1e-03 0.00 -8 5.5e-02 2.7e-03 4.1e-01 9.42e-01 1.445478834e+03 1.426790241e+03 2.3e-04 0.00 -9 8.6e-03 4.3e-04 6.5e-02 9.85e-01 1.450390267e+03 1.447442094e+03 3.7e-05 0.00 -10 3.1e-04 1.6e-05 2.4e-03 9.96e-01 1.451334500e+03 1.451226830e+03 1.3e-06 0.00 -11 5.8e-08 2.9e-09 4.4e-07 1.00e+00 1.451361427e+03 1.451361407e+03 2.5e-10 0.00 -12 5.8e-12 2.9e-13 4.7e-11 1.00e+00 1.451361433e+03 1.451361433e+03 2.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 0e+00 var: 1e-11 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 2e-11 var: 2e-11 -> Time spent by solver: 0.08 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1451.361432736361. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -2026-02-13 12:18:34 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 1.65 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 1.66 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 88 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 37 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 88 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 112 after factor : 118 -Factor - dense dim. : 0 flops : 1.03e+03 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.6e+02 4.8e+01 7.3e+03 0.00e+00 1.513900294e+03 -5.742061883e+03 4.1e+00 0.00 -1 2.3e+02 1.2e+01 1.8e+03 -9.19e-01 2.385229815e+03 -4.008681392e+03 9.9e-01 0.00 -2 3.2e+01 1.6e+00 2.4e+02 -6.81e-01 1.454542453e+03 -1.723063001e+03 1.4e-01 0.00 -3 1.6e+01 8.0e-01 1.2e+02 1.27e-01 1.124692590e+03 -8.917292047e+02 6.8e-02 0.00 -4 9.1e+00 4.6e-01 6.9e+01 3.34e-01 1.043791185e+03 -4.040413954e+02 3.9e-02 0.00 -5 3.1e+00 1.6e-01 2.4e+01 4.50e-01 8.793814694e+02 2.167685343e+02 1.3e-02 0.00 -6 1.8e+00 8.9e-02 1.3e+01 -7.23e-02 1.212933436e+03 6.615825873e+02 7.6e-03 0.00 -7 2.6e-01 1.3e-02 2.0e+00 8.47e-01 1.437474664e+03 1.350029315e+03 1.1e-03 0.00 -8 5.5e-02 2.7e-03 4.1e-01 9.42e-01 1.445478834e+03 1.426790241e+03 2.3e-04 0.00 -9 8.6e-03 4.3e-04 6.5e-02 9.85e-01 1.450390267e+03 1.447442094e+03 3.7e-05 0.00 -10 3.1e-04 1.6e-05 2.4e-03 9.96e-01 1.451334500e+03 1.451226830e+03 1.3e-06 0.00 -11 5.8e-08 2.9e-09 4.4e-07 1.00e+00 1.451361427e+03 1.451361407e+03 2.5e-10 0.00 -12 5.8e-12 2.9e-13 4.7e-11 1.00e+00 1.451361433e+03 1.451361433e+03 2.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 0e+00 var: 1e-11 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 2e-11 var: 2e-11 -> Time spent by solver: 0.10 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1451.361432736361. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -2026-02-13 12:18:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 3.18 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 3.20 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 88 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 37 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 88 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 112 after factor : 118 -Factor - dense dim. : 0 flops : 1.03e+03 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.6e+02 4.8e+01 7.3e+03 0.00e+00 1.513900294e+03 -5.742061883e+03 4.1e+00 0.00 -1 2.3e+02 1.2e+01 1.8e+03 -9.19e-01 2.385229815e+03 -4.008681392e+03 9.9e-01 0.00 -2 3.2e+01 1.6e+00 2.4e+02 -6.81e-01 1.454542453e+03 -1.723063001e+03 1.4e-01 0.00 -3 1.6e+01 8.0e-01 1.2e+02 1.27e-01 1.124692590e+03 -8.917292047e+02 6.8e-02 0.00 -4 9.1e+00 4.6e-01 6.9e+01 3.34e-01 1.043791185e+03 -4.040413954e+02 3.9e-02 0.00 -5 3.1e+00 1.6e-01 2.4e+01 4.50e-01 8.793814694e+02 2.167685343e+02 1.3e-02 0.00 -6 1.8e+00 8.9e-02 1.3e+01 -7.23e-02 1.212933436e+03 6.615825873e+02 7.6e-03 0.00 -7 2.6e-01 1.3e-02 2.0e+00 8.47e-01 1.437474664e+03 1.350029315e+03 1.1e-03 0.00 -8 5.5e-02 2.7e-03 4.1e-01 9.42e-01 1.445478834e+03 1.426790241e+03 2.3e-04 0.00 -9 8.6e-03 4.3e-04 6.5e-02 9.85e-01 1.450390267e+03 1.447442094e+03 3.7e-05 0.00 -10 3.1e-04 1.6e-05 2.4e-03 9.96e-01 1.451334500e+03 1.451226830e+03 1.3e-06 0.00 -11 5.8e-08 2.9e-09 4.4e-07 1.00e+00 1.451361427e+03 1.451361407e+03 2.5e-10 0.00 -12 5.8e-12 2.9e-13 4.7e-11 1.00e+00 1.451361433e+03 1.451361433e+03 2.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 0e+00 var: 1e-11 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 2e-11 var: 2e-11 -> Time spent by solver: 0.11 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1451.361432736361. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 2.81 seconds. - -> Completed in 2.83 seconds. - - ->> Run completed in 6.15 seconds. - -2026-02-13 12:21:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='transport', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of line flows - Size: 36 variables - - Maximum flow constraints per line - Size: 54 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.0098 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vFLOW_SENT_AT_TO_BUS[LinePiModel(id=0, from_bus='1', to_bus='2'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 1 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 1000.0 - Constraint=cFlowPerNonExpLine1[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 88 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 66 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 37 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 88 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 112 after factor : 118 -Factor - dense dim. : 0 flops : 1.03e+03 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 9.6e+02 4.8e+01 7.3e+03 0.00e+00 1.513900294e+03 -5.742061883e+03 4.1e+00 0.00 -1 2.3e+02 1.2e+01 1.8e+03 -9.19e-01 2.385229815e+03 -4.008681392e+03 9.9e-01 0.00 -2 3.2e+01 1.6e+00 2.4e+02 -6.81e-01 1.454542453e+03 -1.723063001e+03 1.4e-01 0.00 -3 1.6e+01 8.0e-01 1.2e+02 1.27e-01 1.124692590e+03 -8.917292047e+02 6.8e-02 0.00 -4 9.1e+00 4.6e-01 6.9e+01 3.34e-01 1.043791185e+03 -4.040413954e+02 3.9e-02 0.00 -5 3.1e+00 1.6e-01 2.4e+01 4.50e-01 8.793814694e+02 2.167685343e+02 1.3e-02 0.00 -6 1.8e+00 8.9e-02 1.3e+01 -7.23e-02 1.212933436e+03 6.615825873e+02 7.6e-03 0.00 -7 2.6e-01 1.3e-02 2.0e+00 8.47e-01 1.437474664e+03 1.350029315e+03 1.1e-03 0.00 -8 5.5e-02 2.7e-03 4.1e-01 9.42e-01 1.445478834e+03 1.426790241e+03 2.3e-04 0.00 -9 8.6e-03 4.3e-04 6.5e-02 9.85e-01 1.450390267e+03 1.447442094e+03 3.7e-05 0.00 -10 3.1e-04 1.6e-05 2.4e-03 9.96e-01 1.451334500e+03 1.451226830e+03 1.3e-06 0.00 -11 5.8e-08 2.9e-09 4.4e-07 1.00e+00 1.451361427e+03 1.451361407e+03 2.5e-10 0.00 -12 5.8e-12 2.9e-13 4.7e-11 1.00e+00 1.451361433e+03 1.451361433e+03 2.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 3e-10 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 0e+00 var: 1e-11 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.4513614327e+03 nrm: 6e+02 Viol. con: 6e-14 var: 0e+00 - Dual. obj: 1.4513614327e+03 nrm: 5e+03 Viol. con: 2e-11 var: 2e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1451.361432736361. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-13 12:21:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 52 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.457164112e+04 -1.040611000e+03 2.3e+00 0.00 -1 5.3e+01 7.0e+02 1.6e+03 -9.88e-01 1.432986786e+04 -4.665863089e+02 2.4e-01 0.00 -2 9.9e+00 1.3e+02 3.0e+02 -8.67e-01 8.383298413e+03 -2.966779476e+03 4.4e-02 0.00 -3 4.9e+00 6.4e+01 1.5e+02 -5.25e-01 7.367785999e+03 -1.904227117e+03 2.2e-02 0.00 -4 1.4e+00 1.8e+01 4.1e+01 -2.07e-01 4.236864371e+03 -2.916489284e+02 6.2e-03 0.00 -5 8.7e-01 1.1e+01 2.6e+01 4.73e-01 3.203871133e+03 6.183988111e+01 3.9e-03 0.00 -6 6.5e-01 8.6e+00 2.0e+01 6.52e-01 2.727608229e+03 2.614966617e+02 2.9e-03 0.00 -7 1.1e-01 1.4e+00 3.2e+00 7.36e-01 1.261363602e+03 8.113079666e+02 4.8e-04 0.00 -8 2.0e-02 2.7e-01 6.1e-01 9.83e-01 9.999667655e+02 9.146845563e+02 9.1e-05 0.00 -9 3.2e-03 4.2e-02 9.5e-02 9.88e-01 9.355095500e+02 9.220951814e+02 1.4e-05 0.00 -10 2.3e-04 3.0e-03 6.9e-03 1.00e+00 9.266443762e+02 9.256752681e+02 1.0e-06 0.00 -11 1.8e-05 2.4e-04 5.5e-04 1.00e+00 9.258289523e+02 9.257511655e+02 8.2e-08 0.00 -12 4.4e-09 5.8e-08 1.3e-07 1.00e+00 9.257688514e+02 9.257688328e+02 2.0e-11 0.00 -13 4.4e-13 5.8e-12 1.3e-10 1.00e+00 9.257688361e+02 9.257688361e+02 2.0e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883608e+02 nrm: 6e+02 Viol. con: 3e-12 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 3e-12 var: 2e-10 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883606e+02 nrm: 6e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 1e-10 var: 4e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 925.7688360598107. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-13 12:23:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 52 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.457164112e+04 -1.040611000e+03 2.3e+00 0.00 -1 5.3e+01 7.0e+02 1.6e+03 -9.88e-01 1.432986786e+04 -4.665863089e+02 2.4e-01 0.00 -2 9.9e+00 1.3e+02 3.0e+02 -8.67e-01 8.383298413e+03 -2.966779476e+03 4.4e-02 0.00 -3 4.9e+00 6.4e+01 1.5e+02 -5.25e-01 7.367785999e+03 -1.904227117e+03 2.2e-02 0.00 -4 1.4e+00 1.8e+01 4.1e+01 -2.07e-01 4.236864371e+03 -2.916489284e+02 6.2e-03 0.00 -5 8.7e-01 1.1e+01 2.6e+01 4.73e-01 3.203871133e+03 6.183988111e+01 3.9e-03 0.00 -6 6.5e-01 8.6e+00 2.0e+01 6.52e-01 2.727608229e+03 2.614966617e+02 2.9e-03 0.00 -7 1.1e-01 1.4e+00 3.2e+00 7.36e-01 1.261363602e+03 8.113079666e+02 4.8e-04 0.00 -8 2.0e-02 2.7e-01 6.1e-01 9.83e-01 9.999667655e+02 9.146845563e+02 9.1e-05 0.00 -9 3.2e-03 4.2e-02 9.5e-02 9.88e-01 9.355095500e+02 9.220951814e+02 1.4e-05 0.00 -10 2.3e-04 3.0e-03 6.9e-03 1.00e+00 9.266443762e+02 9.256752681e+02 1.0e-06 0.00 -11 1.8e-05 2.4e-04 5.5e-04 1.00e+00 9.258289523e+02 9.257511655e+02 8.2e-08 0.00 -12 4.4e-09 5.8e-08 1.3e-07 1.00e+00 9.257688514e+02 9.257688328e+02 2.0e-11 0.00 -13 4.4e-13 5.8e-12 1.3e-10 1.00e+00 9.257688361e+02 9.257688361e+02 2.0e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883608e+02 nrm: 6e+02 Viol. con: 3e-12 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 3e-12 var: 2e-10 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883606e+02 nrm: 6e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 1e-10 var: 4e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 925.7688360598107. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-13 12:28:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 52 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.457164112e+04 -1.040611000e+03 2.3e+00 0.00 -1 5.3e+01 7.0e+02 1.6e+03 -9.88e-01 1.432986786e+04 -4.665863089e+02 2.4e-01 0.00 -2 9.9e+00 1.3e+02 3.0e+02 -8.67e-01 8.383298413e+03 -2.966779476e+03 4.4e-02 0.00 -3 4.9e+00 6.4e+01 1.5e+02 -5.25e-01 7.367785999e+03 -1.904227117e+03 2.2e-02 0.00 -4 1.4e+00 1.8e+01 4.1e+01 -2.07e-01 4.236864371e+03 -2.916489284e+02 6.2e-03 0.00 -5 8.7e-01 1.1e+01 2.6e+01 4.73e-01 3.203871133e+03 6.183988111e+01 3.9e-03 0.00 -6 6.5e-01 8.6e+00 2.0e+01 6.52e-01 2.727608229e+03 2.614966617e+02 2.9e-03 0.00 -7 1.1e-01 1.4e+00 3.2e+00 7.36e-01 1.261363602e+03 8.113079666e+02 4.8e-04 0.00 -8 2.0e-02 2.7e-01 6.1e-01 9.83e-01 9.999667655e+02 9.146845563e+02 9.1e-05 0.00 -9 3.2e-03 4.2e-02 9.5e-02 9.88e-01 9.355095500e+02 9.220951814e+02 1.4e-05 0.00 -10 2.3e-04 3.0e-03 6.9e-03 1.00e+00 9.266443762e+02 9.256752681e+02 1.0e-06 0.00 -11 1.8e-05 2.4e-04 5.5e-04 1.00e+00 9.258289523e+02 9.257511655e+02 8.2e-08 0.00 -12 4.4e-09 5.8e-08 1.3e-07 1.00e+00 9.257688514e+02 9.257688328e+02 2.0e-11 0.00 -13 4.4e-13 5.8e-12 1.3e-10 1.00e+00 9.257688361e+02 9.257688361e+02 2.0e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883608e+02 nrm: 6e+02 Viol. con: 3e-12 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 3e-12 var: 2e-10 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.2576883606e+02 nrm: 6e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.2576883606e+02 nrm: 5e+03 Viol. con: 1e-10 var: 4e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 925.7688360598107. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - -2026-02-13 12:29:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/inputs ... - - 'lines.csv' ... - Added 6 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 5 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 15 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 5 'gen' components. - Completed in 0.00 seconds. - - 'energy_budget_constraints.csv' ... - Added 1 'energy_budget' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(name='sc1', probability=1.0, id=0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 52 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.457203097e+04 -1.038472085e+03 2.3e+00 0.00 -1 5.6e+01 7.3e+02 1.7e+03 -9.88e-01 1.486393375e+04 2.664990695e+01 2.5e-01 0.00 -2 9.0e+00 1.2e+02 2.7e+02 -8.68e-01 9.655652712e+03 -1.221929826e+03 4.0e-02 0.00 -3 2.9e+00 3.8e+01 8.8e+01 -4.48e-01 5.814621941e+03 -1.365299478e+03 1.3e-02 0.00 -4 2.7e-01 3.6e+00 8.2e+00 4.25e-02 1.838645874e+03 7.308124489e+02 1.2e-03 0.00 -5 4.6e-02 6.0e-01 1.4e+00 9.57e-01 1.137718194e+03 9.494388939e+02 2.0e-04 0.00 -6 1.2e-02 1.6e-01 3.7e-01 9.93e-01 1.016313579e+03 9.653533196e+02 5.5e-05 0.00 -7 1.7e-03 2.3e-02 5.2e-02 9.99e-01 9.812298038e+02 9.740280288e+02 7.8e-06 0.00 -8 2.1e-04 2.8e-03 6.4e-03 1.00e+00 9.765168581e+02 9.756289073e+02 9.6e-07 0.00 -9 1.3e-05 1.7e-04 4.0e-04 1.00e+00 9.757171820e+02 9.756615617e+02 5.9e-08 0.00 -10 2.2e-09 2.9e-08 6.7e-08 1.00e+00 9.756756340e+02 9.756756246e+02 1.0e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567563399e+02 nrm: 5e+02 Viol. con: 1e-08 var: 0e+00 - Dual. obj: 9.7567562459e+02 nrm: 5e+03 Viol. con: 3e-09 var: 3e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567562669e+02 nrm: 5e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.7567562669e+02 nrm: 5e+03 Viol. con: 1e-12 var: 7e-11 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 975.6756266917898. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.07 seconds. - -2026-02-15 19:37:03 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 48 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 18 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 45 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 60 after factor : 63 -Factor - dense dim. : 0 flops : 6.69e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 6.0e+02 6.8e+03 1.5e+04 0.00e+00 1.475722915e+04 -6.502214940e+01 2.1e+00 0.00 -1 4.8e+01 5.4e+02 1.2e+03 -9.90e-01 1.234218248e+04 -1.634279018e+03 1.6e-01 0.00 -2 1.1e+01 1.2e+02 2.7e+02 -8.88e-01 3.263777593e+03 -8.615664474e+03 3.7e-02 0.00 -3 1.6e+00 1.8e+01 3.9e+01 -6.26e-01 2.469504110e+03 -2.838618145e+03 5.4e-03 0.00 -4 1.7e-01 1.9e+00 4.1e+00 3.14e-01 6.068748782e+02 -1.654084774e+02 5.7e-04 0.00 -5 3.0e-02 3.5e-01 7.5e-01 9.12e-01 1.651582860e+02 1.776073249e+01 1.0e-04 0.00 -6 7.7e-03 8.8e-02 1.9e-01 9.82e-01 8.740417956e+01 4.961565018e+01 2.7e-05 0.00 -7 3.3e-03 3.8e-02 8.2e-02 9.95e-01 6.930420744e+01 5.298191082e+01 1.1e-05 0.00 -8 2.6e-04 3.0e-03 6.5e-03 9.98e-01 5.632455231e+01 5.503901978e+01 9.0e-07 0.00 -9 3.1e-07 3.5e-06 7.6e-06 1.00e+00 5.550115275e+01 5.549959207e+01 1.1e-09 0.00 -10 3.1e-11 3.5e-10 7.6e-10 1.00e+00 5.550000012e+01 5.549999996e+01 1.1e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 3 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.5500000115e+01 nrm: 6e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 5.5499999959e+01 nrm: 5e+01 Viol. con: 2e-11 var: 5e-10 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.5500000000e+01 nrm: 6e+02 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 5.5500000185e+01 nrm: 5e+01 Viol. con: 5e-08 var: 1e-07 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 5550.000000000003. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.09 seconds. - -2026-02-15 19:42:36 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -2026-02-15 19:43:56 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' -2026-02-15 19:45:45 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' - - 'energy_budgets.csv' ... - Added 1 'energy_budgets' -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -2026-02-15 19:46:07 - ______  __  - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - /  /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -System initialization completed. -> Loading system components from CSV files from /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' - - 'energy_budgets.csv' ... - Added 1 'energy_budgets' -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, policies=['sting.policies.energy_budgets'], write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cEnergyBalance[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.0 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - Maximum RHS: 600.0 - Constraint=cMaxDispatch[Generator(id=4, name='hydro_3', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=upper - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(id=0, name='sc1', type_='scenarios', probability=1.0),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -MOSEK warning 500 (MSK_RES_WRN_LICENSE_EXPIRE): The license expires in 3 days. -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 52 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 45 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.457203097e+04 -1.038472085e+03 2.3e+00 0.00 -1 5.6e+01 7.3e+02 1.7e+03 -9.88e-01 1.486393375e+04 2.664990695e+01 2.5e-01 0.00 -2 9.0e+00 1.2e+02 2.7e+02 -8.68e-01 9.655652712e+03 -1.221929826e+03 4.0e-02 0.00 -3 2.9e+00 3.8e+01 8.8e+01 -4.48e-01 5.814621941e+03 -1.365299478e+03 1.3e-02 0.00 -4 2.7e-01 3.6e+00 8.2e+00 4.25e-02 1.838645874e+03 7.308124489e+02 1.2e-03 0.00 -5 4.6e-02 6.0e-01 1.4e+00 9.57e-01 1.137718194e+03 9.494388939e+02 2.0e-04 0.00 -6 1.2e-02 1.6e-01 3.7e-01 9.93e-01 1.016313579e+03 9.653533196e+02 5.5e-05 0.00 -7 1.7e-03 2.3e-02 5.2e-02 9.99e-01 9.812298038e+02 9.740280288e+02 7.8e-06 0.00 -8 2.1e-04 2.8e-03 6.4e-03 1.00e+00 9.765168581e+02 9.756289073e+02 9.6e-07 0.00 -9 1.3e-05 1.7e-04 4.0e-04 1.00e+00 9.757171820e+02 9.756615617e+02 5.9e-08 0.00 -10 2.2e-09 2.9e-08 6.7e-08 1.00e+00 9.756756340e+02 9.756756246e+02 1.0e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567563399e+02 nrm: 5e+02 Viol. con: 1e-08 var: 0e+00 - Dual. obj: 9.7567562459e+02 nrm: 5e+03 Viol. con: 3e-09 var: 3e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567562669e+02 nrm: 5e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.7567562669e+02 nrm: 5e+03 Viol. con: 1e-12 var: 7e-11 -> Time spent by solver: 0.15 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 97567.56266917898. - -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.20 seconds. - -2026-02-26 12:01:15 -> Initializing system ... - System initialization completed. -> Loading system components from CSV files from /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets ... - - 'generators.csv' ... - Added 5 'generators' - - 'buses.csv' ... - Added 5 'buses' - - 'loads.csv' ... - Added 15 'loads' - - 'lines.csv' ... - Added 6 'lines' - - 'timeseries.csv' ... - Added 1 'timeseries' - - 'timepoints.csv' ... - Added 3 'timepoints' - - 'scenarios.csv' ... - Added 1 'scenarios' - - 'energy_budgets.csv' ... - Added 1 'energy_budgets' -> Post system initialization completed in 0.01 seconds. -> Completed in: 0.02 seconds. - - ->> Starting capacity expansion... - -Model settings: ModelSettings(generator_type_costs='linear', load_shedding=True, single_storage_injection=False, generation_capacity_expansion=True, storage_capacity_expansion=True, line_capacity_expansion=False, line_capacity=True, power_flow='dc', bus_max_flow_expansion=False, bus_max_flow=False, angle_difference_limits=False, write_model_file=False, kron_equivalent_flow_constraints=False) -Solver settings: SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Set of capacity-expandable generators - Size: 0 generators - - Decision variables of capacity expansion for generators - Size: 0 variables - - Decision variables of dispatch - Size: 15 variables - - Constraints on capacity expansion for generators - Size: 0 constraints - - Constraints on dispatch based on capacity factors and existing/built capacity - Size: 15 constraints - - Constraints on forced dispatch requirements specified for certain generators - Size: 0 constraints - - Expressions for dispatch at any bus - Size: 15 expressions - - Expressions for emission per timepoint per scenario expression - Size: 3 expressions - - Expressions for generation cost per timepoint - Size: 3 expressions - - Expressions for generation cost per period -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables of discharge and charge - Size: 0 variables - - Decision variables of state of charge - Size: 0 variables - - Set of capacity-expandable storage units - Size: 0 storage units - - Decision variables of power and energy capacity expansion - Size: 0 variables - - Constraints on power capacity expansion - Size: 0 constraints - - Constraints on storage dispatch - Size: 0 constraints - - Constraints on maximum state of charge - Size: 0 constraints - - Constraints on evolution of state of charge across timepoints - Size: 15 constraints - - Expressions for storage cost per timepoint - Size: 3 expressions - - Expression for storage cost per period - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data processing - - Decision variables of load shedding - Size: 15 variables - - Decision variables of bus angles - Size: 15 variables - - Power flow per bus expressions - - Maximum flow constraints per line - Size: 18 constraints - - Energy balance at each bus - Size: 15 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.01 seconds. - -> Initializing construction of carbon policy constraints ... - - Annual carbon policy constraint - Size: 0 constraints -> Completed in 0.00 seconds. - -> Initializing construction of energy budget constraints ... - - Constraint for power budget - Size: 3 constraints - - Constraint for energy budget - Size: 1 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Initializing inspection of coefficients in the model ... - - Matrix coefficient extremes: - - Minimum coefficient: 0.01 - Constraint=cMaxDispatch[Generator(id=0, name='gas_1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vGEN[Generator(id=0, name='gas_1', bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: -188.03963729706305 - Constraint=cEnergyBalance[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - Variable=vTHETA[Bus(id=4, bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - - - RHS extremes: - - Minimum RHS: 0.017 - Constraint=cEnergyBudget[EnergyBudget(id=0, budget_region='hydro_zone', budget_term='hydro_basic', budget_constraint_energy_GWh=1.7),Scenario(id=0, name='sc1')] - Bound=upper - - Maximum RHS: -10.0 - Constraint=cFlowPerNonExpLine[LinePiModel(id=1, from_bus='1', to_bus='4'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - Bound=lower - - - Objective coefficient extremes: - - Minimum coefficient: 0.01 - Variable=vGEN[Generator(id=4, name='hydro_3', bus='5'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] - - Maximum coefficient: 50.0 - Variable=vSHED[Bus(id=0, bus='1'),Scenario(id=0, name='sc1'),Timepoint(id=0, name='tp_1', timeseries='winter')] -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 53 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 46 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 22 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 49 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 85 after factor : 87 -Factor - dense dim. : 0 flops : 8.77e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 5.2e+02 6.8e+03 1.6e+04 0.00e+00 1.454138719e+04 -1.191622373e+03 2.3e+00 0.00 -1 3.7e+01 4.8e+02 1.1e+03 -9.89e-01 1.400245941e+04 -5.930010131e+02 1.6e-01 0.00 -2 8.7e+00 1.2e+02 2.7e+02 -8.22e-01 6.907314648e+03 -4.395029738e+03 3.8e-02 0.00 -3 3.0e+00 3.9e+01 9.1e+01 -5.21e-01 5.597060919e+03 -2.086636378e+03 1.3e-02 0.00 -4 2.6e-01 3.5e+00 8.0e+00 6.65e-02 1.611887233e+03 5.076566490e+02 1.2e-03 0.00 -5 5.7e-02 7.5e-01 1.7e+00 9.57e-01 1.138657566e+03 8.974946086e+02 2.5e-04 0.00 -6 1.1e-02 1.5e-01 3.4e-01 9.99e-01 1.012945840e+03 9.652084041e+02 4.9e-05 0.00 -7 2.3e-03 3.1e-02 7.1e-02 1.00e+00 9.823826725e+02 9.724474797e+02 1.0e-05 0.00 -8 1.2e-03 1.5e-02 3.6e-02 1.00e+00 9.795323180e+02 9.745183324e+02 5.2e-06 0.00 -9 2.0e-04 2.6e-03 6.0e-03 1.00e+00 9.764332491e+02 9.755974105e+02 8.6e-07 0.00 -10 1.2e-05 1.6e-04 3.7e-04 1.00e+00 9.757151432e+02 9.756628353e+02 5.3e-08 0.00 -11 1.9e-09 2.5e-08 5.7e-08 1.00e+00 9.756756332e+02 9.756756250e+02 8.3e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567563317e+02 nrm: 5e+02 Viol. con: 8e-09 var: 0e+00 - Dual. obj: 9.7567562498e+02 nrm: 6e+04 Viol. con: 3e-07 var: 3e-08 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 9.7567562669e+02 nrm: 5e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 9.7567562669e+02 nrm: 6e+04 Viol. con: 1e-12 var: 9e-11 -> Time spent by solver: 0.21 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 97567.56266917972. - -> Initializing export all results to CSV files ... -- Directory: /Users/adamsedlak/Documents/Python/STING/examples/capacity_expansion/energy_budgets/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing export carbon policy results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing export energy budget results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.26 seconds. - diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/buses.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/buses.csv deleted file mode 100644 index 121e77d..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/buses.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,bus_type,zone -1,slack,center -2,PQ,north -3,PQ,south -4,PQ,south -5,PQ,south \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/generators.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/generators.csv deleted file mode 100644 index 87692fb..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/generators.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,technology,bus,site,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -gas_1,gas,1,no_capacity_factor,0,200,200,60 -gas_2,gas,1,no_capacity_factor,0,200,200,50 -hydro_1,hydro,3,no_capacity_factor,0,520,520,5 -hydro_2,hydro,4,no_capacity_factor,0,400,400,5 -hydro_3,hydro,5,no_capacity_factor,0,600,600,1 \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/lines.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/lines.csv deleted file mode 100644 index 424412a..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/lines.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,cost_fixed_power_USDperkW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg,efficiency -1,1,2,10,10,TRUE,0.00281,0.0281,0,0.00712,-360,360,0.98 -2,1,4,10,20,TRUE,0.00304,0.0304,0,0.00658,-360,360,0.98 -3,1,5,20,20,TRUE,0.00064,0.0064,0,0.03126,-360,360,0.98 -4,2,3,20,20,TRUE,0.00108,0.0108,0,0.01852,-360,360,0.98 -5,3,4,20,20,TRUE,0.00297,0.0297,0,0.00674,-360,360,0.98 -6,4,5,20,10,TRUE,0.00297,0.0297,0,0.00674,-360,360,0.98 \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/loads.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/loads.csv deleted file mode 100644 index 75f9c32..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/loads.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,load_MW -1,sc1,tp_1,10 -2,sc1,tp_1,300 -3,sc1,tp_1,300 -4,sc1,tp_1,100 -5,sc1,tp_1,0 -1,sc1,tp_2,20 -2,sc1,tp_2,100 -3,sc1,tp_2,200 -4,sc1,tp_2,500 -5,sc1,tp_2,10 -1,sc1,tp_3,5 -2,sc1,tp_3,300 -3,sc1,tp_3,100 -4,sc1,tp_3,600 -5,sc1,tp_3,5 \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/scenarios.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/scenarios.csv deleted file mode 100644 index 3ea9ffa..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -sc1,1 \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/timepoints.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/timepoints.csv deleted file mode 100644 index 84f4d23..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -tp_1,winter -tp_2,winter -tp_3,winter \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/inputs/timeseries.csv b/examples/capacity_expansion/transmission_capacity_policy/inputs/timeseries.csv deleted file mode 100644 index b290cbd..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,start,end,timepoint_duration_hr,timeseries_scale_to_period,number_of_timepoints -winter,1,3,1,1,3 \ No newline at end of file diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/costs_summary.csv deleted file mode 100644 index 4538e3d..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,4001430.80671787 -cost_per_period_USD,176372.64112908384 -total_cost_USD,4177803.4478469538 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/emissions_per_scenario.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/energy_budget_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_costs_summary.csv deleted file mode 100644 index 61232a5..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,10074.857358820802 -cost_per_period_USD,0.0 -total_cost_USD,10074.857358820802 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_dispatch.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_dispatch.csv deleted file mode 100644 index cb47d60..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/generator_dispatch.csv +++ /dev/null @@ -1,16 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -gas_1,sc1,tp_1,0.0 -gas_1,sc1,tp_2,0.0 -gas_1,sc1,tp_3,0.0 -gas_2,sc1,tp_1,0.0 -gas_2,sc1,tp_2,27.637268786765848 -gas_2,sc1,tp_3,12.637268580071416 -hydro_1,sc1,tp_1,317.8114480343996 -hydro_1,sc1,tp_2,235.86440989970126 -hydro_1,sc1,tp_3,135.86440989769255 -hydro_2,sc1,tp_1,97.87878698242977 -hydro_2,sc1,tp_2,400.0 -hydro_2,sc1,tp_3,400.0 -hydro_3,sc1,tp_1,24.30976443004219 -hydro_3,sc1,tp_2,52.362725987038445 -hydro_3,sc1,tp_3,47.362725990741616 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_built_capacity.csv deleted file mode 100644 index 35ea23a..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_built_capacity.csv +++ /dev/null @@ -1,7 +0,0 @@ -line,built_capacity_MW -1,0.0 -2,7.637268889936002 -3,0.0 -4,0.0 -5,0.0 -6,2.36272633303638 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_costs_summary.csv deleted file mode 100644 index f577077..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -cost_per_period_USD,176372.64112908384 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_flows.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_flows.csv deleted file mode 100644 index f15ae75..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/line_flows.csv +++ /dev/null @@ -1,19 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,tp_1,0.0,-0.1626111535138981,10.000000103179833,0.28100000579870665 -1,1,2,sc1,tp_2,0.0,-0.16261115171474572,9.999999992538443,0.2809999995806605 -1,1,2,sc1,tp_3,0.0,-0.16261115334504003,10.000000092795672,0.28100000521511675 -4,2,3,sc1,tp_1,-0.1626111535138981,-0.03761468089480709,-20.00000000533625,0.43200000023052604 -4,2,3,sc1,tp_2,-0.16261115171474572,-0.03761467909651677,-20.000000005198316,0.43200000022456725 -4,2,3,sc1,tp_3,-0.16261115334504003,-0.03761468075929958,-20.00000000000001,0.4320000000000005 -2,1,4,sc1,tp_1,0.0,-5.282568853548162e-9,3.002808085517117e-7,2.74112434512788e-16 -5,3,4,sc1,tp_1,-0.03761468089480709,-5.282568853548162e-9,-2.1885519768749244,0.014225586473784926 -2,1,4,sc1,tp_2,0.0,-0.31027652998871214,17.637268889936003,0.9456626918435493 -5,3,4,sc1,tp_2,-0.03761467909651677,-0.31027652998871214,15.864409916493805,0.7474881209356845 -2,1,4,sc1,tp_3,0.0,-0.31027652998871214,17.637268889936003,0.9456626918435493 -5,3,4,sc1,tp_3,-0.03761468075929958,-0.31027652998871214,15.864409819747348,0.7474881118188214 -3,1,5,sc1,tp_1,0.0,0.07407198314124853,-19.99999983441397,0.25599999576099763 -6,4,5,sc1,tp_1,-5.282568853548162e-9,0.07407198314124853,-4.309764581440605,0.05516499011989655 -3,1,5,sc1,tp_2,0.0,0.0740719824395785,-19.99999964495771,0.2559999909109175 -6,4,5,sc1,tp_2,-0.31027652998871214,0.0740719824395785,-22.36272632935299,1.4852718407781664 -3,1,5,sc1,tp_3,0.0,0.07407198244506867,-19.9999996464401,0.25599999094886666 -6,4,5,sc1,tp_3,-0.31027652998871214,0.07407198244506867,-22.36272632967243,1.485271840820599 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding.csv deleted file mode 100644 index 6537e51..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -1,sc1,tp_1,0.0 -1,sc1,tp_2,0.0 -1,sc1,tp_3,0.0 -2,sc1,tp_1,269.9999998914839 -2,sc1,tp_2,70.00000000226325 -2,sc1,tp_3,269.9999999072043 -3,sc1,tp_1,0.0 -3,sc1,tp_2,0.0 -3,sc1,tp_3,0.0 -4,sc1,tp_1,0.0 -4,sc1,tp_2,44.13559499666499 -4,sc1,tp_3,144.13559507419328 -5,sc1,tp_1,0.0 -5,sc1,tp_2,0.0 -5,sc1,tp_3,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding_costs_summary.csv deleted file mode 100644 index b2ad191..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -total_cost_USD,3991355.949359049 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/local_marginal_prices.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/local_marginal_prices.csv deleted file mode 100644 index bbc2cf7..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/local_marginal_prices.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,tp_1,9.094276094275301 -1,sc1,tp_2,50.0 -1,sc1,tp_3,50.0 -2,sc1,tp_1,4999.999999999999 -2,sc1,tp_2,5000.000000000001 -2,sc1,tp_3,5000.0 -3,sc1,tp_1,5.0 -3,sc1,tp_2,5.0 -3,sc1,tp_3,5.0 -4,sc1,tp_1,5.0 -4,sc1,tp_2,5000.0 -4,sc1,tp_3,5000.0 -5,sc1,tp_1,1.0 -5,sc1,tp_2,1.0 -5,sc1,tp_3,1.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_balance_by_bus.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_balance_by_bus.csv deleted file mode 100644 index ee2f4a2..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_balance_by_bus.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,tp_1,0.0,0,0.0,10.0,-9.999999430953329 -1,sc1,tp_2,27.637268786765848,0,0.0,20.0,7.637269237516735 -1,sc1,tp_3,12.637268580071416,0,0.0,5.0,7.637269336291576 -2,sc1,tp_1,0.0,0,269.9999998914839,300.0,-30.00000010851608 -2,sc1,tp_2,0.0,0,70.00000000226325,100.0,-29.999999997736754 -2,sc1,tp_3,0.0,0,269.9999999072043,300.0,-30.000000092795677 -3,sc1,tp_1,317.8114480343996,0,0.0,300.0,17.81144802846132 -3,sc1,tp_2,235.86440989970126,0,0.0,200.0,35.86440992169212 -3,sc1,tp_3,135.86440989769255,0,0.0,100.0,35.86440981974736 -4,sc1,tp_1,97.87878698242977,0,0.0,100.0,-2.1212129048464896 -4,sc1,tp_2,400.0,0,44.13559499666499,500.0,-55.8644051357828 -4,sc1,tp_3,400.0,0,144.13559507419328,600.0,-55.86440503935578 -5,sc1,tp_1,24.30976443004219,0,0.0,0.0,24.309764415854577 -5,sc1,tp_2,52.362725987038445,0,0.0,10.0,42.362725974310706 -5,sc1,tp_3,47.362725990741616,0,0.0,5.0,42.36272597611253 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_budget_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/solver_status.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/solver_status.csv deleted file mode 100644 index eb241f1..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.014853477478027344 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_dispatch.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/transmission_capacity_expansion_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/transmission_capacity_expansion_constraints.csv deleted file mode 100644 index 0bf6bca..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_10/transmission_capacity_expansion_constraints.csv +++ /dev/null @@ -1,2 +0,0 @@ -transmission_policy_id,built_transmission_capacity_MW,built_transmission_capacity_cap_MW -0,9.999995222972382,10 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/annual_carbon_cap_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/annual_carbon_cap_constraints.csv deleted file mode 100644 index a80b7c0..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/annual_carbon_cap_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,carbon_policy_id,carbon_cap_tonneCO2peryear,dispatched_emissions_tonneCO2peryear diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/costs_summary.csv deleted file mode 100644 index 874f646..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,3926416.9910138557 -cost_per_period_USD,251081.53078202996 -total_cost_USD,4177498.5217958856 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/emissions_per_scenario.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/emissions_per_scenario.csv deleted file mode 100644 index 4ab5f63..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/emissions_per_scenario.csv +++ /dev/null @@ -1,2 +0,0 @@ -scenario,emissions_tonneCO2peryear -sc1,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/energy_budget_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/energy_budget_constraints.csv deleted file mode 100644 index 3854691..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/energy_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,budget_constraint_energy_GWh,dispatched_energy_GWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_built_capacity.csv deleted file mode 100644 index 04d1b3d..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -generator,built_capacity_MW diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_costs_summary.csv deleted file mode 100644 index 46ba207..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,10352.29524865964 -cost_per_period_USD,0.0 -total_cost_USD,10352.29524865964 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_dispatch.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_dispatch.csv deleted file mode 100644 index 2a8e4ad..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/generator_dispatch.csv +++ /dev/null @@ -1,16 +0,0 @@ -generator,scenario,timepoint,dispatch_MW -gas_1,sc1,tp_1,0.0 -gas_1,sc1,tp_2,0.0 -gas_1,sc1,tp_3,0.0 -gas_2,sc1,tp_1,0.0 -gas_2,sc1,tp_2,30.108153078203003 -gas_2,sc1,tp_3,15.108153078202955 -hydro_1,sc1,tp_1,317.8114478114479 -hydro_1,sc1,tp_2,238.3935304234805 -hydro_1,sc1,tp_3,138.3935304234806 -hydro_2,sc1,tp_1,97.87878787878782 -hydro_2,sc1,tp_2,400.0 -hydro_2,sc1,tp_3,400.0 -hydro_3,sc1,tp_1,24.309764309764336 -hydro_3,sc1,tp_2,54.89184692179701 -hydro_3,sc1,tp_3,49.89184692179702 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_built_capacity.csv deleted file mode 100644 index 88bf4eb..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_built_capacity.csv +++ /dev/null @@ -1,7 +0,0 @@ -line,built_capacity_MW -1,0.0 -2,10.108153078202996 -3,0.0 -4,0.0 -5,0.0 -6,4.891846921797005 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_costs_summary.csv deleted file mode 100644 index fd01434..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -cost_per_period_USD,251081.53078202996 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_flows.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_flows.csv deleted file mode 100644 index 6fe6e35..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/line_flows.csv +++ /dev/null @@ -1,19 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,sc1,tp_1,0.0,-0.16261115183607863,9.999999999999982,0.28099999999999903 -1,1,2,sc1,tp_2,0.0,-0.16261115183607885,9.999999999999995,0.2809999999999997 -1,1,2,sc1,tp_3,0.0,-0.16261115183607783,9.99999999999993,0.28099999999999614 -4,2,3,sc1,tp_1,-0.16261115183607863,-0.03761467925033828,-20.0,0.432 -4,2,3,sc1,tp_2,-0.16261115183607885,-0.03761467925033853,-19.99999999999999,0.43199999999999955 -4,2,3,sc1,tp_3,-0.16261115183607783,-0.037614679250337284,-20.00000000000003,0.4320000000000012 -2,1,4,sc1,tp_1,0.0,-4.1503694149353723e-16,2.3592239273284573e-14,1.6920450119408497e-30 -5,3,4,sc1,tp_1,-0.03761467925033828,-4.1503694149353723e-16,-2.188552188552149,0.014225589225588713 -2,1,4,sc1,tp_2,0.0,-0.3537445621837035,20.108153078202992,1.2291869734579912 -5,3,4,sc1,tp_2,-0.03761467925033853,-0.3537445621837035,18.393530423480506,1.0048162254753237 -2,1,4,sc1,tp_3,0.0,-0.3537445621837035,20.108153078202992,1.2291869734579912 -5,3,4,sc1,tp_3,-0.037614679250337284,-0.3537445621837035,18.393530423480577,1.0048162254753314 -3,1,5,sc1,tp_1,0.0,0.07407198375451282,-20.0,0.256 -6,4,5,sc1,tp_1,-4.1503694149353723e-16,0.07407198375451282,-4.309764309764334,0.05516498316498377 -3,1,5,sc1,tp_2,0.0,0.07407198375451282,-20.0,0.256 -6,4,5,sc1,tp_2,-0.3537445621837035,0.07407198375451282,-24.891846921797004,1.8402240082391796 -3,1,5,sc1,tp_3,0.0,0.07407198375451288,-20.000000000000014,0.2560000000000004 -6,4,5,sc1,tp_3,-0.3537445621837035,0.07407198375451288,-24.891846921797008,1.8402240082391803 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding.csv deleted file mode 100644 index 20bd72c..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -1,sc1,tp_1,0.0 -1,sc1,tp_2,0.0 -1,sc1,tp_3,0.0 -2,sc1,tp_1,270.0 -2,sc1,tp_2,70.00000000000001 -2,sc1,tp_3,270.00000000000006 -3,sc1,tp_1,0.0 -3,sc1,tp_2,0.0 -3,sc1,tp_3,0.0 -4,sc1,tp_1,0.0 -4,sc1,tp_2,36.60646957651954 -4,sc1,tp_3,136.60646957651963 -5,sc1,tp_1,0.0 -5,sc1,tp_2,0.0 -5,sc1,tp_3,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding_costs_summary.csv deleted file mode 100644 index dc3bd0f..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -total_cost_USD,3916064.6957651963 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/local_marginal_prices.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/local_marginal_prices.csv deleted file mode 100644 index 0c3608b..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/local_marginal_prices.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,sc1,tp_1,9.094276094274392 -1,sc1,tp_2,50.0 -1,sc1,tp_3,50.0 -2,sc1,tp_1,5000.0 -2,sc1,tp_2,5000.000000000001 -2,sc1,tp_3,5000.0 -3,sc1,tp_1,5.0 -3,sc1,tp_2,5.0 -3,sc1,tp_3,5.0 -4,sc1,tp_1,5.0 -4,sc1,tp_2,5000.0 -4,sc1,tp_3,5000.0 -5,sc1,tp_1,1.0 -5,sc1,tp_2,1.0 -5,sc1,tp_3,1.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_balance_by_bus.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_balance_by_bus.csv deleted file mode 100644 index 94d6fe3..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_balance_by_bus.csv +++ /dev/null @@ -1,16 +0,0 @@ -bus,scenario,timepoint,generator_dispatch_MW,storage_dispatch_MW,load_shedding_MW,load_MW,net_line_leaving_flow_MW -1,sc1,tp_1,0.0,0,0.0,10.0,-9.999999999999996 -1,sc1,tp_2,30.108153078203003,0,0.0,20.0,10.108153078202987 -1,sc1,tp_3,15.108153078202955,0,0.0,5.0,10.10815307820291 -2,sc1,tp_1,0.0,0,270.0,300.0,-29.999999999999975 -2,sc1,tp_2,0.0,0,70.00000000000001,100.0,-29.999999999999982 -2,sc1,tp_3,0.0,0,270.00000000000006,300.0,-29.999999999999954 -3,sc1,tp_1,317.8114478114479,0,0.0,300.0,17.81144781144785 -3,sc1,tp_2,238.3935304234805,0,0.0,200.0,38.39353042348049 -3,sc1,tp_3,138.3935304234806,0,0.0,100.0,38.393530423480605 -4,sc1,tp_1,97.87878787878782,0,0.0,100.0,-2.121212121212208 -4,sc1,tp_2,400.0,0,36.60646957651954,500.0,-63.393530423480506 -4,sc1,tp_3,400.0,0,136.60646957651963,600.0,-63.393530423480584 -5,sc1,tp_1,24.309764309764336,0,0.0,0.0,24.309764309764333 -5,sc1,tp_2,54.89184692179701,0,0.0,10.0,44.891846921797004 -5,sc1,tp_3,49.89184692179702,0,0.0,5.0,44.891846921797026 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_budget_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_budget_constraints.csv deleted file mode 100644 index fb2d993..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/power_budget_constraints.csv +++ /dev/null @@ -1 +0,0 @@ -scenario,budget_region,budget_term,timepoint,budget_constraint_power_GW,dispatched_power_GW diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/solver_status.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/solver_status.csv deleted file mode 100644 index a9a090e..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -solver_name,mosek_direct -solver_status,ok -termination_condition,optimal -time_spent_seconds,0.033751726150512695 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_built_capacity.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_built_capacity.csv deleted file mode 100644 index a096c6b..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,built_power_capacity_MW,built_energy_capacity_MWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_costs_summary.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_costs_summary.csv deleted file mode 100644 index 4f27acf..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -cost_per_timepoint_USD,0.0 -cost_per_period_USD,0.0 -total_cost_USD,0.0 diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_dispatch.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/transmission_capacity_expansion_constraints.csv b/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/transmission_capacity_expansion_constraints.csv deleted file mode 100644 index 3051afb..0000000 --- a/examples/capacity_expansion/transmission_capacity_policy/outputs/tx_cap_15/transmission_capacity_expansion_constraints.csv +++ /dev/null @@ -1,2 +0,0 @@ -transmission_policy_id,built_transmission_capacity_MW,built_transmission_capacity_cap_MW -0,15.0,15 diff --git a/examples/kron_reduction/3bus_in_series/inputs/buses.csv b/examples/kron_reduction/3bus_in_series/inputs/buses.csv deleted file mode 100644 index 04bc9e8..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/buses.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,bus_type -1,slack -2,PQ -3,PQ \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/capacity_factors.csv b/examples/kron_reduction/3bus_in_series/inputs/capacity_factors.csv deleted file mode 100644 index efcc040..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/capacity_factors.csv +++ /dev/null @@ -1,4 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -solar_cf,1,1,solar,0 -solar_cf,1,2,solar,1 -solar_cf,1,3,solar,0.8 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/generators.csv b/examples/kron_reduction/3bus_in_series/inputs/generators.csv deleted file mode 100644 index 54a5988..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/generators.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -g1,solar,1,solar_cf,0,0.01,0,10,100,100,0 -g2,coal,1,no_capacity_factor,0,5,0,5,100,100,10 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/lines.csv b/examples/kron_reduction/3bus_in_series/inputs/lines.csv deleted file mode 100644 index a1fd322..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/lines.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,300,FALSE,0,0.01,0,0,-360,360 -2,3,2,150,FALSE,0,0.01,0,0,-360,360 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/loads.csv b/examples/kron_reduction/3bus_in_series/inputs/loads.csv deleted file mode 100644 index a39ede0..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/loads.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_MW -3,1,1,100 -3,1,2,200 -3,1,3,100 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/scenarios.csv b/examples/kron_reduction/3bus_in_series/inputs/scenarios.csv deleted file mode 100644 index ad1b9ef..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -1,1 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/storage.csv b/examples/kron_reduction/3bus_in_series/inputs/storage.csv deleted file mode 100644 index d8a2d78..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/storage.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus,name,c0_USD,c1_USDperMWh,c2_USDperMWh2,cap_existing_energy_MWh,cap_existing_power_MW,cap_max_power_MW,cost_fixed_energy_USDperkWh,cost_fixed_power_USDperkW,cost_variable_USDperMWh,duration_hr,efficiency_charge,efficiency_discharge,technology -1,storage,0,0.01,0,200,50,50,0,0,0.01,4,1,1,regular \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/timepoints.csv b/examples/kron_reduction/3bus_in_series/inputs/timepoints.csv deleted file mode 100644 index efad3f9..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -1,winter -2,winter -3,winter \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/inputs/timeseries.csv b/examples/kron_reduction/3bus_in_series/inputs/timeseries.csv deleted file mode 100644 index 7442139..0000000 --- a/examples/kron_reduction/3bus_in_series/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,3,1 \ No newline at end of file diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index ce4ba70..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251699.99999999985 -CostPerPeriod_USD,0.0 -TotalCost_USD,251699.99999999985 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 7de9dc7..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1699.9999999999998 -CostPerPeriod_USD,0.0 -TotalCost_USD,1699.9999999999998 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 99ca07c..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,99.99999999999999 -g2,2,50.0 -g2,3,19.999999999999993 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_flows.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index feb527d..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,7 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,1,1,0.0,-0.5729577951308232,99.99999999999999,0.0 -2,3,2,1,1,-1.1459155902616465,-0.5729577951308232,-99.99999999999999,0.0 -1,1,2,1,2,0.0,-0.8594366926962348,150.0,0.0 -2,3,2,1,2,-1.7188733853924696,-0.8594366926962348,-150.0,0.0 -1,1,2,1,3,0.0,-0.5729577951308232,99.99999999999999,0.0 -2,3,2,1,3,-1.1459155902616465,-0.5729577951308232,-99.99999999999999,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index 21c984f..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -3,1,1,0.0 -3,1,2,49.99999999999997 -3,1,3,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 3bf2e98..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,249999.99999999985 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 0e8167c..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,10 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.00000000030413 -1,1,2,9.999999999523311 -1,1,3,10.000000000173584 -2,1,1,10.000000000304905 -2,1,2,9.999999999523308 -2,1,3,10.000000000173932 -3,1,1,10.000000000304905 -3,1,2,5000.0 -3,1,3,10.000000000173932 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index ec70f34..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -storage,1,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index d43eb6b..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -storage,1,1,0.0,0.0,0.0 -storage,1,2,0.0,0.0,0.0 -storage,1,3,0.0,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv deleted file mode 100644 index 79e4fa9..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251700.00000000003 -CostPerPeriod_USD,0.0 -TotalCost_USD,251700.00000000003 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index d759a3c..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1700.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,1700.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 5b36919..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,100.0 -g2,2,50.00000000000001 -g2,3,20.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_flows.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_flows.csv deleted file mode 100644 index d3c5807..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -Y_kron_f1-t3,1,3,1,1,0.0,-1.1459155902616465,100.0,0.0 -Y_kron_f1-t3,1,3,1,2,0.0,-1.7188733853924696,150.0,0.0 -Y_kron_f1-t3,1,3,1,3,0.0,-1.1459155902616465,100.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv deleted file mode 100644 index 3ba1970..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -3,1,1,0.0 -3,1,2,50.00000000000001 -3,1,3,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 2ec90c0..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,250000.00000000003 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index ba2b24f..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.007101233811568 -1,1,2,9.999999998374138 -1,1,3,10.00000000061817 -3,1,1,10.007101233811568 -3,1,2,5000.0 -3,1,3,10.00000000061817 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index ec70f34..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -storage,1,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index d43eb6b..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -storage,1,1,0.0,0.0,0.0 -storage,1,2,0.0,0.0,0.0 -storage,1,3,0.0,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv deleted file mode 100644 index 2225899..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv +++ /dev/null @@ -1,2 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,3,150.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_removable_buses.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_removable_buses.csv deleted file mode 100644 index aa67fed..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/kron_removable_buses.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus -2 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv deleted file mode 100644 index 6a61430..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,4 +0,0 @@ -Index,1,3,2 -1,100.0,0.0,100.0 -3,0.0,100.0,100.0 -2,100.0,100.0,200.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv deleted file mode 100644 index a08d222..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv +++ /dev/null @@ -1,4 +0,0 @@ -Index,1,3,2 -1,0.0,0.0,0.0 -3,0.0,0.0,0.0 -2,0.0,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv deleted file mode 100644 index 300bde4..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv +++ /dev/null @@ -1,4 +0,0 @@ -Index,1,3,2 -1,-100.0,0.0,100.0 -3,0.0,-100.0,100.0 -2,100.0,100.0,-200.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv deleted file mode 100644 index 367cd64..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_absolute_admittance_matrix.csv +++ /dev/null @@ -1,3 +0,0 @@ -Index,1,3 -1,50.0,50.0 -3,50.0,50.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_conductance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_conductance_matrix.csv deleted file mode 100644 index 5b62e2a..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_conductance_matrix.csv +++ /dev/null @@ -1,3 +0,0 @@ -Index,1,3 -1,0.0,0.0 -3,0.0,0.0 diff --git a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv b/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv deleted file mode 100644 index 3c4f29f..0000000 --- a/examples/kron_reduction/3bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv +++ /dev/null @@ -1,3 +0,0 @@ -Index,1,3 -1,-50.0,50.0 -3,50.0,-50.0 diff --git a/examples/kron_reduction/3bus_in_series/sting_log.txt b/examples/kron_reduction/3bus_in_series/sting_log.txt deleted file mode 100644 index 23ebcbd..0000000 --- a/examples/kron_reduction/3bus_in_series/sting_log.txt +++ /dev/null @@ -1,35490 +0,0 @@ -2026-01-17 22:09:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/3bus/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-17 22:09:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/3bus/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. -2026-01-17 22:10:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/3bus/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:22:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/3bus/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. -2026-01-18 10:52:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.05 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.06 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.08 seconds. - -2026-01-18 10:52:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. -2026-01-18 11:18:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:18:17 -2026-01-18 11:18:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints -Rule failed when generating expression for Constraint cMaxGenVar with index (Generator(id=0, name='1', technology='solar', bus='1', site='solar', cap_existing_power_MW=100.0, cap_max_power_MW=150.0, cost_fixed_power_USDperkW=10.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=0.01, c2_USDperMWh2=0.0, bus_id=0, expand_capacity=True), Scenario(name='1', probability=1.0, id=0), Timepoint(name='1', timeseries='winter', id=0, timeseries_id=0, weight=1.0, duration_hr=1.0, prev_timepoint_id=2)): -KeyError: ('solar', '1', '1') -Rule failed when generating expression for Constraint cMaxGenVar with index (Generator(id=0, name='1', technology='solar', bus='1', site='solar', cap_existing_power_MW=100.0, cap_max_power_MW=150.0, cost_fixed_power_USDperkW=10.0, cost_variable_USDperMWh=0.0, c0_USD=0.0, c1_USDperMWh=0.01, c2_USDperMWh2=0.0, bus_id=0, expand_capacity=True), Scenario(name='1', probability=1.0, id=0), Timepoint(name='1', timeseries='winter', id=0, timeseries_id=0, weight=1.0, duration_hr=1.0, prev_timepoint_id=2)): -KeyError: ('solar', '1', '1') -Constructing component 'cMaxGenVar' from data=None failed: - KeyError: ('solar', '1', '1') -Constructing component 'cMaxGenVar' from data=None failed: - KeyError: ('solar', '1', '1') -2026-01-18 11:19:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:19:17 -2026-01-18 11:19:17 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 6 constraints - Size: 6 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 28 - Constraints : 28 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 1 -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:19:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:19:51 -2026-01-18 11:19:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 1 -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:21:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:21:52 -2026-01-18 11:21:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'quadratic', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 1 -Freed constraints in eliminator : 1 -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:22:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 4 variables. - - Constraints of angle differences for original system. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 4 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 5 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.03 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:22:33 -2026-01-18 11:22:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:24:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 4 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 33 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 7 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 16 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 15 after factor : 18 -Factor - dense dim. : 0 flops : 1.14e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.3e+02 5.1e-01 3.5e+01 0.00e+00 4.123546030e+00 1.396414401e+01 4.5e+01 0.00 -1 9.0e+01 1.4e-01 9.5e+00 4.01e+00 1.981484808e+00 2.362760408e+01 1.2e+01 0.00 -2 7.4e+00 1.1e-02 7.8e-01 1.16e+00 1.675916894e+00 3.099404178e+00 1.0e+00 0.00 -3 2.2e+00 3.4e-03 2.3e-01 1.05e+00 1.343029345e+00 1.725988179e+00 3.0e-01 0.00 -4 1.4e-02 2.2e-05 1.5e-03 1.02e+00 1.250666820e+00 1.251868356e+00 1.9e-03 0.00 -5 1.5e-05 2.3e-08 1.6e-06 1.00e+00 1.250003709e+00 1.250004996e+00 2.0e-06 0.00 -6 3.1e-06 4.9e-09 3.3e-07 9.87e-01 1.250001810e+00 1.250002045e+00 4.3e-07 0.00 -7 1.9e-08 2.8e-11 1.9e-09 1.00e+00 1.250001502e+00 1.250001503e+00 2.4e-09 0.00 -8 2.0e-12 2.8e-15 1.9e-13 1.00e+00 1.250001500e+00 1.250001500e+00 2.4e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2500015000e+00 nrm: 2e+02 Viol. con: 6e-13 var: 0e+00 - Dual. obj: 1.2500015000e+00 nrm: 5e-03 Viol. con: 9e-16 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2500015000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.2500015000e+00 nrm: 5e-03 Viol. con: 2e-16 var: 2e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1250001.50 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:24:16 -2026-01-18 11:24:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:24:16 -2026-01-18 11:24:16 -2026-01-18 11:24:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 6e-20 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:27:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': False, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 4 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 24 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 7 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 5.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 5.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:27:25 -2026-01-18 11:27:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:27:25 -2026-01-18 11:27:25 -2026-01-18 11:27:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': False, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': False, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': False, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - Size: 4 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 21 - Scalar variables : 21 - Scalar variables : 21 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. -Presolve started. -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Problem status : PRIMAL_INFEASIBLE - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Solution status : PRIMAL_INFEASIBLE_CER - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Problem status : PRIMAL_INFEASIBLE - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Solution status : PRIMAL_INFEASIBLE_CER - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Solver finished with status: warning, termination condition: infeasible. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:28:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 4 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 33 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 7 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 16 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 15 after factor : 18 -Factor - dense dim. : 0 flops : 1.14e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.3e+02 5.1e-01 3.5e+01 0.00e+00 4.123542646e+00 1.396414102e+01 4.5e+01 0.00 -1 9.0e+01 1.4e-01 9.5e+00 4.01e+00 1.981483320e+00 2.362760250e+01 1.2e+01 0.00 -2 7.4e+00 1.1e-02 7.8e-01 1.16e+00 1.675915378e+00 3.099405720e+00 1.0e+00 0.00 -3 2.2e+00 3.4e-03 2.3e-01 1.05e+00 1.343026142e+00 1.725978369e+00 3.0e-01 0.00 -4 1.4e-02 2.2e-05 1.5e-03 1.02e+00 1.250665291e+00 1.251866765e+00 1.9e-03 0.00 -5 1.5e-05 2.3e-08 1.6e-06 1.00e+00 1.250002209e+00 1.250003496e+00 2.0e-06 0.00 -6 3.1e-06 4.9e-09 3.3e-07 9.87e-01 1.250000310e+00 1.250000545e+00 4.3e-07 0.00 -7 1.8e-08 2.8e-11 1.9e-09 1.00e+00 1.250000002e+00 1.250000003e+00 2.4e-09 0.00 -8 4.5e-09 3.0e-15 1.8e-11 1.00e+00 1.250000000e+00 1.250000000e+00 2.4e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2500000000e+00 nrm: 2e+02 Viol. con: 2e-09 var: 0e+00 - Dual. obj: 1.2500000000e+00 nrm: 5e-03 Viol. con: 9e-16 var: 1e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.2500000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.2500000000e+00 nrm: 5e-03 Viol. con: 2e-16 var: 1e-14 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1250000.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 11:28:32 -2026-01-18 11:28:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:28:33 -2026-01-18 11:28:33 -2026-01-18 11:28:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:29:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 4 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 33 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 9 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 19 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 21 after factor : 27 -Factor - dense dim. : 0 flops : 1.73e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.4e+02 5.7e-01 3.4e+01 0.00e+00 3.853024944e+00 1.355624781e+01 4.4e+01 0.00 -1 8.9e+01 1.5e-01 9.0e+00 4.10e+00 1.524734610e+00 2.456550816e+01 1.2e+01 0.00 -2 1.4e+01 2.3e-02 1.4e+00 1.17e+00 1.111123769e+00 4.024610273e+00 1.8e+00 0.00 -3 1.5e+00 2.6e-03 1.6e-01 1.11e+00 5.031806496e-01 7.448256573e-01 2.0e-01 0.00 -4 5.5e-01 9.3e-04 5.5e-02 1.03e+00 4.383772086e-01 5.169614379e-01 7.1e-02 0.00 -5 2.3e-02 3.9e-05 2.3e-03 1.02e+00 3.766757463e-01 3.796452635e-01 3.0e-03 0.00 -6 1.2e-05 2.1e-08 1.2e-06 1.00e+00 3.750024446e-01 3.750038895e-01 1.6e-06 0.00 -7 1.5e-06 2.6e-09 1.5e-07 1.00e+00 3.750011195e-01 3.750012669e-01 2.0e-07 0.00 -8 1.5e-10 2.6e-13 1.6e-11 1.00e+00 3.750010000e-01 3.750010000e-01 2.0e-11 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.7500100001e-01 nrm: 2e+02 Viol. con: 5e-11 var: 0e+00 - Dual. obj: 3.7500100001e-01 nrm: 5e-03 Viol. con: 7e-14 var: 8e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.7500100000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 3.7500100002e-01 nrm: 5e-03 Viol. con: 8e-14 var: 8e-14 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 375001.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:29:54 -2026-01-18 11:29:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:29:54 -2026-01-18 11:29:54 -2026-01-18 11:29:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:31:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 1 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 4 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 0 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 31 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 33 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 7 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 16 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 15 after factor : 18 -Factor - dense dim. : 0 flops : 1.14e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 3.3e+02 5.4e-01 3.5e+01 0.00e+00 3.882038685e+00 1.371846741e+01 4.5e+01 0.00 -1 8.9e+01 1.4e-01 9.4e+00 4.00e+00 1.865051148e+00 2.348437024e+01 1.2e+01 0.00 -2 1.3e+01 2.1e-02 1.4e+00 1.16e+00 1.551537081e+00 4.234163579e+00 1.7e+00 0.00 -3 2.3e+00 3.7e-03 2.4e-01 1.07e+00 1.173533846e+00 1.593399282e+00 3.1e-01 0.00 -4 1.7e-01 2.8e-04 1.8e-02 1.01e+00 1.111320377e+00 1.140951578e+00 2.4e-02 0.00 -5 5.6e-04 9.1e-07 5.9e-05 9.94e-01 1.100020642e+00 1.100018154e+00 7.6e-05 0.00 -6 1.0e-05 1.6e-08 1.1e-06 1.00e+00 1.100001798e+00 1.100001754e+00 1.4e-06 0.00 -7 2.1e-06 3.4e-09 2.2e-07 9.88e-01 1.100000230e+00 1.100000216e+00 2.8e-07 0.00 -8 4.2e-08 6.8e-11 4.4e-09 1.00e+00 1.100000006e+00 1.100000006e+00 5.7e-09 0.00 -9 4.5e-12 7.2e-15 4.6e-13 1.00e+00 1.100000000e+00 1.100000000e+00 6.0e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.1000000000e+00 nrm: 2e+02 Viol. con: 1e-12 var: 0e+00 - Dual. obj: 1.1000000000e+00 nrm: 5e-03 Viol. con: 2e-15 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.1000000000e+00 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.1000000000e+00 nrm: 5e-03 Viol. con: 7e-16 var: 3e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 1100000.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:31:30 -2026-01-18 11:31:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:31:30 -2026-01-18 11:31:30 -2026-01-18 11:31:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 1 'gen' components. - Added 1 'gen' components. - Added 1 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 4 variables - Size: 4 variables - Size: 4 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 22 - Constraints : 22 - Constraints : 22 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 27 - Scalar variables : 27 - Scalar variables : 27 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 11:33:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 7 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 18 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 15 after factor : 18 -Factor - dense dim. : 0 flops : 1.18e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.8e+01 0.00e+00 3.249961007e+00 1.287051948e+01 4.7e+01 0.00 -1 1.2e+02 1.9e-01 1.1e+01 4.37e+00 1.364969501e+00 2.711761911e+01 1.4e+01 0.00 -2 1.4e+01 2.3e-02 1.3e+00 1.17e+00 1.032213972e+00 3.576318947e+00 1.7e+00 0.00 -3 3.1e+00 5.0e-03 2.9e-01 1.07e+00 5.254988327e-01 1.023722120e+00 3.7e-01 0.00 -4 7.6e-01 1.2e-03 7.3e-02 1.02e+00 3.720281721e-01 4.869670164e-01 9.1e-02 0.00 -5 3.2e-02 5.1e-05 3.0e-03 1.00e+00 3.539603346e-01 3.574886614e-01 3.8e-03 0.00 -6 4.3e-05 6.9e-08 4.1e-06 1.00e+00 3.515039565e-01 3.515073388e-01 5.1e-06 0.00 -7 9.9e-06 1.6e-08 9.4e-07 1.00e+00 3.515016557e-01 3.515024045e-01 1.2e-06 0.00 -8 1.8e-06 2.8e-09 1.7e-07 1.00e+00 3.515007325e-01 3.515008472e-01 2.1e-07 0.00 -9 2.9e-09 4.7e-12 2.8e-10 1.00e+00 3.515006002e-01 3.515006003e-01 3.5e-10 0.00 -10 2.4e-13 4.7e-16 2.7e-14 1.00e+00 3.515006000e-01 3.515006000e-01 3.5e-14 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 2 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.5150060000e-01 nrm: 2e+02 Viol. con: 1e-13 var: 0e+00 - Dual. obj: 3.5150060000e-01 nrm: 5e-03 Viol. con: 1e-16 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 3.5150060000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 3.5150060000e-01 nrm: 5e-03 Viol. con: 2e-17 var: 2e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 351500.60 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:33:02 -2026-01-18 11:33:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:33:02 -2026-01-18 11:33:02 -2026-01-18 11:33:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 25 - Constraints : 25 - Constraints : 25 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:33:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:33:59 -2026-01-18 11:33:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:33:59 -2026-01-18 11:33:59 -2026-01-18 11:33:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 25 - Constraints : 25 - Constraints : 25 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:47:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 11:47:25 -2026-01-18 11:47:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:47:25 -2026-01-18 11:47:25 -2026-01-18 11:47:25 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 25 - Constraints : 25 - Constraints : 25 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 2.0000000000e+00 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+00 nrm: 1e-02 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Objective value: 2000000.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 11:48:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions -2026-01-18 11:48:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions -2026-01-18 11:49:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 11:49:02 -2026-01-18 11:49:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. -2026-01-18 11:49:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.04 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.13 seconds. - -2026-01-18 11:49:09 -2026-01-18 11:49:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 11:49:09 -2026-01-18 11:49:09 -2026-01-18 11:49:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -2026-01-18 12:23:07 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 12:23:07 -2026-01-18 12:23:07 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. -2026-01-18 12:25:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 12:25:53 -2026-01-18 12:25:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-18 12:25:53 -2026-01-18 12:25:53 -2026-01-18 12:25:53 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -2026-01-18 12:28:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 12:28:19 -2026-01-18 12:28:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.06 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 12:28:19 -2026-01-18 12:28:19 -2026-01-18 12:28:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -2026-01-18 12:28:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 12:28:30 -2026-01-18 12:28:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.06 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 12:28:30 -2026-01-18 12:28:30 -2026-01-18 12:28:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 25 - Constraints : 25 - Constraints : 25 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 12:40:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 12:40:29 -2026-01-18 12:40:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 12:40:29 -2026-01-18 12:40:29 -2026-01-18 12:40:29 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 28 - Constraints : 28 - Constraints : 28 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 12:43:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 12:43:28 -2026-01-18 12:43:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-18 12:43:28 -2026-01-18 12:43:28 -2026-01-18 12:43:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -2026-01-18 12:45:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 12:45:38 -2026-01-18 12:45:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 12:45:38 -2026-01-18 12:45:38 -2026-01-18 12:45:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -2026-01-18 12:45:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 1 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 34 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 4e-19 var: 8e-09 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 12:45:52 -2026-01-18 12:45:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-18 12:45:52 -2026-01-18 12:45:52 -2026-01-18 12:45:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 1 constraints - Size: 1 constraints - Size: 1 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 28 - Constraints : 28 - Constraints : 28 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Constraints : 8 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Scalar variables : 20 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - nonzeros before factor : 17 after factor : 20 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -Factor - dense dim. : 0 flops : 1.30e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -0 4.1e+02 6.8e-01 3.6e+01 0.00e+00 3.463478084e+00 1.290784876e+01 4.6e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -1 1.1e+02 1.9e-01 1.0e+01 4.47e+00 1.226118151e+00 2.854207839e+01 1.3e+01 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -2 1.9e+01 3.2e-02 1.7e+00 1.15e+00 7.561038459e-01 4.742030613e+00 2.2e+00 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -3 1.7e+00 2.8e-03 1.5e-01 1.08e+00 4.765309260e-02 3.126384993e-01 1.9e-01 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -4 1.2e-01 1.9e-04 1.0e-02 1.01e+00 1.332461346e-02 2.614753340e-02 1.3e-02 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -5 1.3e-02 2.2e-05 1.2e-03 1.00e+00 3.611141188e-03 5.015519196e-03 1.5e-03 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -6 6.0e-04 9.8e-07 5.3e-05 1.00e+00 2.251750286e-03 2.302287720e-03 6.7e-05 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -7 4.1e-05 6.7e-08 3.6e-06 1.00e+00 2.204836285e-03 2.208265241e-03 4.6e-06 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -8 5.9e-06 9.7e-09 5.2e-07 1.01e+00 2.200867869e-03 2.201229285e-03 6.5e-07 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -9 4.1e-07 6.8e-10 3.6e-08 1.01e+00 2.200050734e-03 2.200073948e-03 4.6e-08 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -10 1.3e-10 2.1e-13 1.1e-11 1.00e+00 2.200000018e-03 2.200000018e-03 1.4e-11 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -11 3.6e-10 2.3e-17 1.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 1.4e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 1e-10 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - Dual. obj: 2.2000000000e-03 nrm: 1e-02 Viol. con: 6e-18 var: 6e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 - Dual. obj: 2.2008481667e-03 nrm: 1e-02 Viol. con: 0e+00 var: 8e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 12:46:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 3e-19 var: 9e-09 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 12:46:52 -2026-01-18 12:46:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 12:46:52 -2026-01-18 12:46:52 -2026-01-18 12:46:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 12:54:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 3e-19 var: 9e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -2026-01-18 12:54:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 3e-19 var: 9e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -2026-01-18 12:57:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 3e-19 var: 9e-09 -> Time spent by solver: 0.24 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.28 seconds. - -2026-01-18 12:57:38 -2026-01-18 12:57:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 12:57:38 -2026-01-18 12:57:38 -2026-01-18 12:57:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:01:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 8e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 3e-19 var: 9e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:01:59 -2026-01-18 13:01:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:01:59 -2026-01-18 13:01:59 -2026-01-18 13:01:59 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Objective value: 200.00. -> Objective value: 200.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -0 4.1e+02 6.7e-01 3.8e+01 0.00e+00 2.703581512e+00 1.238194724e+01 4.8e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -1 1.1e+02 1.8e-01 1.0e+01 4.39e+00 9.891899792e-01 2.789247478e+01 1.3e+01 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -2 2.0e+01 3.2e-02 1.8e+00 1.14e+00 6.286888875e-01 4.750240399e+00 2.3e+00 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 1.9e-01 1.08e+00 4.399749327e-02 3.738171596e-01 2.4e-01 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -4 2.4e-01 4.0e-04 2.3e-02 1.01e+00 2.348991526e-02 5.198152638e-02 2.8e-02 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -5 2.0e-02 3.3e-05 1.9e-03 1.00e+00 4.229289151e-03 6.559980060e-03 2.3e-03 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -6 2.3e-03 3.8e-06 2.2e-04 1.00e+00 2.394012124e-03 2.616828421e-03 2.7e-04 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -7 5.1e-05 8.3e-08 4.7e-06 1.00e+00 2.205650491e-03 2.210458297e-03 5.9e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -8 9.1e-06 1.5e-08 8.4e-07 1.01e+00 2.201261033e-03 2.201918830e-03 1.1e-06 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -9 8.5e-07 1.4e-09 7.9e-08 1.01e+00 2.200095789e-03 2.200149777e-03 9.9e-08 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -10 6.8e-10 1.1e-12 6.3e-11 1.00e+00 2.200000094e-03 2.200000088e-03 7.9e-11 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -11 2.4e-12 1.1e-16 6.3e-15 1.00e+00 2.200000000e-03 2.200000000e-03 7.9e-15 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 7e-13 var: 0e+00 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - Dual. obj: 2.2000000000e-03 nrm: 5e-03 Viol. con: 3e-17 var: 3e-17 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 2.2000000000e-03 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 - Dual. obj: 2.2009104866e-03 nrm: 5e-03 Viol. con: 0e+00 var: 9e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Objective value: 2200.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:06:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 9 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 1e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 1e-19 var: 7e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 13:06:56 -2026-01-18 13:06:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:06:56 -2026-01-18 13:06:56 -2026-01-18 13:06:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:56:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - Dual. obj: 1.0000000002e+00 nrm: 2e-02 Viol. con: 0e+00 var: 1e-14 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 1.0000000002e+00 nrm: 2e-02 Viol. con: 0e+00 var: 1e-14 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 13:56:18 -2026-01-18 13:56:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:56:18 -2026-01-18 13:56:18 -2026-01-18 13:56:18 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 25 - Scalar variables : 25 - Scalar variables : 25 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:57:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 1.0000000002e+00 nrm: 2e-02 Viol. con: 0e+00 var: 1e-14 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 1.0000000002e+00 nrm: 2e-02 Viol. con: 0e+00 var: 1e-14 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-18 13:57:40 -2026-01-18 13:57:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:57:40 -2026-01-18 13:57:40 -2026-01-18 13:57:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 25 - Scalar variables : 25 - Scalar variables : 25 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:57:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus -2026-01-18 13:58:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus -2026-01-18 13:59:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus -2026-01-18 14:00:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus -2026-01-18 14:00:08 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions -Rule failed for Expression 'eShedCostPerTp' with index Timepoint(id=0, name='1', timeseries='winter'): -KeyError: "Index '('3', Scenario(name='1', probability=1.0, id=0), Timepoint(id=0, name='1', timeseries='winter'))' is not valid for indexed component 'vSHED'" -Constructing component 'eShedCostPerTp' from data=None failed: - KeyError: "Index '('3', Scenario(name='1', probability=1.0, id=0), Timepoint(id=0, name='1', timeseries='winter'))' is not valid for indexed component 'vSHED'" -2026-01-18 14:00:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions -Rule failed for Expression 'eShedCostPerTp' with index Timepoint(id=0, name='1', timeseries='winter'): -KeyError: "Index '('3', Scenario(name='1', probability=1.0, id=0), Timepoint(id=0, name='1', timeseries='winter'))' is not valid for indexed component 'vSHED'" -Constructing component 'eShedCostPerTp' from data=None failed: - KeyError: "Index '('3', Scenario(name='1', probability=1.0, id=0), Timepoint(id=0, name='1', timeseries='winter'))' is not valid for indexed component 'vSHED'" -2026-01-18 14:01:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 14:01:45 -2026-01-18 14:01:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 14:01:45 -2026-01-18 14:01:45 -2026-01-18 14:01:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 25 - Scalar variables : 25 - Scalar variables : 25 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 14:02:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 14:02:28 -2026-01-18 14:02:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 14:02:28 -2026-01-18 14:02:28 -2026-01-18 14:02:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 25 - Scalar variables : 25 - Scalar variables : 25 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 14:03:40 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints -2026-01-18 14:06:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 14:06:14 -2026-01-18 14:06:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 14:06:14 -2026-01-18 14:06:14 -2026-01-18 14:06:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. - - Kron reduction will remove 2 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 25 - Scalar variables : 25 - Scalar variables : 25 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 14:07:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 9 variables - - Decision variables of load shedding - Size: 9 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 37 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 14:07:13 -2026-01-18 14:07:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 14:07:13 -2026-01-18 14:07:13 -2026-01-18 14:07:13 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 31 - Scalar variables : 31 - Scalar variables : 31 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:11:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 9 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.08 seconds. - -2026-01-18 14:11:09 -2026-01-18 14:11:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 14:11:09 -2026-01-18 14:11:09 -2026-01-18 14:11:09 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 4 variables. - Size: 4 variables. - Size: 4 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 4 - Constraints : 4 - Constraints : 4 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 5 - Scalar variables : 5 - Scalar variables : 5 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 27 - Constraints : 27 - Constraints : 27 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 28 - Scalar variables : 28 - Scalar variables : 28 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-19 15:48:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.03 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.01 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. -> Completed in 1.25 seconds. - -> Completed in 1.26 seconds. - - ->> Run completed in 1.30 seconds. - -2026-01-19 15:48:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 3 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. - - 'storage.csv' ... - Added 1 'ess' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 9 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 11 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 6 constraints - - Maximum state of charge constraints - Size: 3 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 9 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 6 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 9 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 31 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.9e+02 4.7e+01 5.8e+01 0.00e+00 5.939745551e+01 2.012468091e+00 9.2e-01 0.00 -1 1.4e+00 3.4e-01 4.3e-01 -8.70e-01 6.721394006e+00 1.195262886e+01 6.7e-03 0.00 -2 1.3e-01 3.3e-02 4.1e-02 8.60e-01 9.448262115e-01 1.326995962e+00 6.5e-04 0.00 -3 4.3e-02 1.1e-02 1.3e-02 8.76e-01 3.500381501e-01 4.337931498e-01 2.1e-04 0.00 -4 9.6e-03 2.4e-03 3.0e-03 8.94e-01 2.629548604e-01 2.827002973e-01 4.7e-05 0.00 -5 5.6e-05 1.4e-05 1.7e-05 9.83e-01 2.521710509e-01 2.521102644e-01 2.8e-07 0.00 -6 3.2e-06 8.0e-07 9.9e-07 1.00e+00 2.517151675e-01 2.517083231e-01 1.6e-08 0.00 -7 1.0e-07 2.6e-08 3.2e-08 1.00e+00 2.517018647e-01 2.517016421e-01 5.1e-10 0.00 -8 1.4e-08 3.4e-09 4.2e-09 1.00e+00 2.517001361e-01 2.517001020e-01 6.7e-11 0.00 -9 1.3e-10 3.3e-11 4.1e-11 1.00e+00 2.517000016e-01 2.517000012e-01 6.5e-13 0.00 -10 1.3e-14 4.1e-15 4.1e-15 1.00e+00 2.517000000e-01 2.517000000e-01 6.5e-17 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 2 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.01 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 4e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 5e-16 var: 7e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 3e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 8e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.02 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.02 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.10 seconds. - -2026-01-19 15:48:55 -2026-01-19 15:48:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 1.18 seconds. - -> Completed in 1.18 seconds. - -> Completed in 1.18 seconds. - -> Completed in 1.18 seconds. - - ->> Run completed in 1.19 seconds. - - ->> Run completed in 1.19 seconds. - -2026-01-19 15:48:56 -2026-01-19 15:48:56 -2026-01-19 15:48:56 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Added 2 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 3 'bus' components. - Added 3 'bus' components. - Added 3 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'storage.csv' ... - - 'storage.csv' ... - - 'storage.csv' ... - Added 1 'ess' components. - Added 1 'ess' components. - Added 1 'ess' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 3 - - Total number of buses: 3 - - Total number of buses: 3 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. - - Kron reduction will remove 1 buses out of 3 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Original system has 3 buses and 2 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 1.15 seconds. - -> Completed in 1.15 seconds. - -> Completed in 1.15 seconds. - -> Completed in 1.15 seconds. - -> Completed in 1.15 seconds. - -> Completed in 1.15 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 11 variables - Size: 11 variables - Size: 11 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 28 - Scalar variables : 28 - Scalar variables : 28 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Scalar variables : 17 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - nonzeros before factor : 12 after factor : 12 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -Factor - dense dim. : 0 flops : 8.40e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -0 4.0e+02 6.4e-01 3.9e+01 0.00e+00 2.617340248e+00 1.224328117e+01 4.8e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -1 1.0e+02 1.6e-01 9.7e+00 4.45e+00 1.080609797e+00 2.890636539e+01 1.2e+01 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -2 1.1e+01 1.8e-02 1.1e+00 1.10e+00 6.131011462e-01 3.176584559e+00 1.3e+00 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -3 2.0e+00 3.3e-03 2.0e-01 1.04e+00 2.847588747e-01 7.195862430e-01 2.4e-01 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -4 1.7e-02 2.7e-05 1.6e-03 1.01e+00 2.526901306e-01 2.541590317e-01 2.0e-03 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -5 2.0e-03 3.3e-06 2.0e-04 1.00e+00 2.517658471e-01 2.519162254e-01 2.5e-04 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -6 1.5e-05 2.4e-08 1.4e-06 1.00e+00 2.517019337e-01 2.517030023e-01 1.8e-06 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -7 2.9e-06 4.7e-09 2.8e-07 1.00e+00 2.517002291e-01 2.517003981e-01 3.5e-07 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -8 7.0e-08 1.1e-10 6.8e-09 9.99e-01 2.517000072e-01 2.517000108e-01 8.5e-09 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -9 8.0e-12 1.2e-14 7.3e-13 1.00e+00 2.517000000e-01 2.517000000e-01 9.1e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Primal. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 2e-12 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 3e-15 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 - Dual. obj: 2.5170071012e-01 nrm: 5e-03 Viol. con: 0e+00 var: 7e-09 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/3bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 1.21 seconds. - - ->> Run completed in 1.21 seconds. - - ->> Run completed in 1.21 seconds. - diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/buses.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/buses.csv deleted file mode 100644 index c2ab77b..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/buses.csv +++ /dev/null @@ -1,5 +0,0 @@ -name,bus_type -1,slack -2,PQ -3,PQ -4,PQ \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/capacity_factors.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/capacity_factors.csv deleted file mode 100644 index efcc040..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/capacity_factors.csv +++ /dev/null @@ -1,4 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -solar_cf,1,1,solar,0 -solar_cf,1,2,solar,1 -solar_cf,1,3,solar,0.8 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/generators.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/generators.csv deleted file mode 100644 index 54a5988..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/generators.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -g1,solar,1,solar_cf,0,0.01,0,10,100,100,0 -g2,coal,1,no_capacity_factor,0,5,0,5,100,100,10 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/lines.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/lines.csv deleted file mode 100644 index 4adaead..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/lines.csv +++ /dev/null @@ -1,6 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,100,FALSE,0,0.01,0,0,-360,360 -2,2,4,200,FALSE,0,0.01,0,0,-360,360 -3,1,3,200,FALSE,0,0.02,0,0,-360,360 -4,3,4,100,FALSE,0,0.02,0,0,-360,360 -5,2,3,50,FALSE,0,0.02,0,0,-360,360 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/loads.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/loads.csv deleted file mode 100644 index 6729161..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/loads.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_MW -4,1,1,100 -4,1,2,200 -4,1,3,100 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/scenarios.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/scenarios.csv deleted file mode 100644 index ad1b9ef..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -1,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/timepoints.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/timepoints.csv deleted file mode 100644 index efad3f9..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -1,winter -2,winter -3,winter \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/inputs/timeseries.csv b/examples/kron_reduction/4bus_in_series _crossed/inputs/timeseries.csv deleted file mode 100644 index 7442139..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,3,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 72aebea..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251700.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,251700.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index d759a3c..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1700.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,1700.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 97fc731..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,100.0 -g2,2,50.0 -g2,3,20.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index 983e70a..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,16 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,1,1,0.0,-0.3819718634205489,66.66666666666667,0.0 -1,1,2,1,2,0.0,-0.5729577951308232,100.0,0.0 -1,1,2,1,3,0.0,-0.3819718634205489,66.66666666666667,0.0 -3,1,3,1,1,0.0,-0.3819718634205489,33.333333333333336,0.0 -5,2,3,1,1,-0.3819718634205489,-0.3819718634205489,0.0,0.0 -3,1,3,1,2,0.0,-0.5729577951308232,50.0,0.0 -5,2,3,1,2,-0.5729577951308232,-0.5729577951308232,0.0,0.0 -3,1,3,1,3,0.0,-0.3819718634205489,33.333333333333336,0.0 -5,2,3,1,3,-0.3819718634205489,-0.3819718634205489,0.0,0.0 -2,2,4,1,1,-0.3819718634205489,-0.7639437268410978,66.66666666666667,0.0 -4,3,4,1,1,-0.3819718634205489,-0.7639437268410978,33.333333333333336,0.0 -2,2,4,1,2,-0.5729577951308232,-1.1459155902616465,100.0,0.0 -4,3,4,1,2,-0.5729577951308232,-1.1459155902616465,50.0,0.0 -2,2,4,1,3,-0.3819718634205489,-0.7639437268410978,66.66666666666667,0.0 -4,3,4,1,3,-0.3819718634205489,-0.7639437268410978,33.333333333333336,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index adebef8..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -4,1,1,0.0 -4,1,2,50.0 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 62c3839..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,250000.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 978a1f7..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,13 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,4999.999999999999 -1,1,2,10.0 -1,1,3,10.0 -2,1,1,5000.0 -2,1,2,5712.857142857143 -2,1,3,10.000000000000528 -3,1,1,5000.0 -3,1,2,3574.285714285714 -3,1,3,10.000000000000329 -4,1,1,5000.0 -4,1,2,5000.0 -4,1,3,10.00000000000046 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/costs_summary.csv deleted file mode 100644 index ce4ba70..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251699.99999999985 -CostPerPeriod_USD,0.0 -TotalCost_USD,251699.99999999985 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 68638c1..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1700.0000000000002 -CostPerPeriod_USD,0.0 -TotalCost_USD,1700.0000000000002 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 74f359c..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,100.0 -g2,2,50.00000000000003 -g2,3,20.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_flows.csv deleted file mode 100644 index 1ddb93f..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -Y_kron_f1-t4,1,4,1,1,0.0,-0.7639437268410978,99.99999999999999,0.0 -Y_kron_f1-t4,1,4,1,2,0.0,-1.1459155902616467,150.0,0.0 -Y_kron_f1-t4,1,4,1,3,0.0,-0.7639437268410978,99.99999999999999,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding.csv deleted file mode 100644 index 561900e..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -4,1,1,0.0 -4,1,2,49.99999999999997 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 3bf2e98..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,249999.99999999985 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index a37c567..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.0 -1,1,2,10.0 -1,1,3,10.0 -4,1,1,10.0 -4,1,2,5000.0 -4,1,3,10.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv deleted file mode 100644 index e13b528..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv +++ /dev/null @@ -1,2 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,4,100.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_optimization.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_optimization.csv deleted file mode 100644 index d92ccdc..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_line_capacity_via_optimization.csv +++ /dev/null @@ -1,2 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,4,150.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_removable_buses.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_removable_buses.csv deleted file mode 100644 index f7e4e4b..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/kron_removable_buses.csv +++ /dev/null @@ -1,3 +0,0 @@ -bus -3 -2 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv deleted file mode 100644 index 6ccbe17..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,150.0,0.0,100.0,50.0 -4,0.0,150.0,100.0,50.0 -2,100.0,100.0,250.0,50.0 -3,50.0,50.0,50.0,150.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_conductance_matrix.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_conductance_matrix.csv deleted file mode 100644 index 9d36148..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_conductance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,0.0,0.0,0.0,0.0 -4,0.0,0.0,0.0,0.0 -2,0.0,0.0,0.0,0.0 -3,0.0,0.0,0.0,0.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_susceptance_matrix.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_susceptance_matrix.csv deleted file mode 100644 index 3fc5a4f..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/original_system_susceptance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,-150.0,0.0,100.0,50.0 -4,0.0,-150.0,100.0,50.0 -2,100.0,100.0,-250.0,50.0 -3,50.0,50.0,50.0,-150.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/reduced_susceptance_matrix.csv b/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/reduced_susceptance_matrix.csv deleted file mode 100644 index 54f7510..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_reduction/reduced_susceptance_matrix.csv +++ /dev/null @@ -1,3 +0,0 @@ -Index,1,4 -1,-75.0,75.0 -4,75.0,-75.0 diff --git a/examples/kron_reduction/4bus_in_series _crossed/sting_log.txt b/examples/kron_reduction/4bus_in_series _crossed/sting_log.txt deleted file mode 100644 index 59679cc..0000000 --- a/examples/kron_reduction/4bus_in_series _crossed/sting_log.txt +++ /dev/null @@ -1,10322 +0,0 @@ -2026-01-17 22:14:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-17 22:15:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:16:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:18:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:22:00 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:23:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:27:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:31:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:32:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:45:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:50:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 23:00:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-17 23:00:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-18 13:10:07 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:10:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:15:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:21:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:21:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:22:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:23:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:29:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.05 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.06 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.08 seconds. - -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 12 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 15 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 29 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 45 after factor : 45 -Factor - dense dim. : 0 flops : 4.15e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.0e+02 3.8e-01 1.2e+02 0.00e+00 1.106254337e+02 9.492374029e+00 1.9e+01 0.00 -1 6.0e+00 2.2e-02 7.1e+00 2.09e+00 4.993115811e+00 4.357260622e+00 1.1e+00 0.00 -2 1.0e+00 3.8e-03 1.2e+00 1.23e+00 1.296252721e+00 1.031076816e+00 1.9e-01 0.00 -3 1.3e-01 4.8e-04 1.5e-01 1.08e+00 9.775917171e-02 5.570435934e-02 2.4e-02 0.00 -4 5.3e-02 2.0e-04 6.3e-02 1.13e+00 4.100495078e-02 2.407491765e-02 1.0e-02 0.00 -5 3.2e-02 1.2e-04 3.7e-02 -8.11e-01 6.824357426e-02 5.983282534e-02 6.0e-03 0.00 -6 1.4e-02 5.4e-05 1.7e-02 -3.03e-01 1.364775088e-01 1.380849812e-01 2.7e-03 0.00 -7 1.4e-03 5.3e-06 1.7e-03 8.68e-01 1.957348704e-01 1.934974515e-01 2.7e-04 0.00 -8 2.0e-04 7.4e-07 2.3e-04 9.52e-01 2.010571389e-01 2.007449130e-01 3.7e-05 0.00 -9 2.4e-05 8.9e-08 2.8e-05 9.94e-01 2.018146099e-01 2.017772919e-01 4.5e-06 0.00 -10 2.7e-07 1.0e-09 3.2e-07 1.00e+00 2.017988971e-01 2.017985456e-01 5.1e-08 0.00 -11 2.7e-11 1.0e-13 3.2e-11 1.00e+00 2.017999999e-01 2.017999999e-01 5.1e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0179999989e-01 nrm: 2e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 2.0179999982e-01 nrm: 6e-03 Viol. con: 1e-13 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0180000000e-01 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0180000006e-01 nrm: 6e-03 Viol. con: 2e-13 var: 2e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 201800.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:30:42 -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:30:42 -2026-01-18 13:30:42 -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 20 - Scalar variables : 20 - Scalar variables : 20 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 12 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 15 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 29 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 45 after factor : 45 -Factor - dense dim. : 0 flops : 4.15e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.0e+02 3.8e-01 1.2e+02 0.00e+00 1.106254337e+02 9.492374029e+00 1.9e+01 0.00 -1 6.0e+00 2.2e-02 7.1e+00 2.09e+00 4.993115811e+00 4.357260622e+00 1.1e+00 0.00 -2 1.0e+00 3.8e-03 1.2e+00 1.23e+00 1.296252721e+00 1.031076816e+00 1.9e-01 0.00 -3 1.3e-01 4.8e-04 1.5e-01 1.08e+00 9.775917171e-02 5.570435934e-02 2.4e-02 0.00 -4 5.3e-02 2.0e-04 6.3e-02 1.13e+00 4.100495078e-02 2.407491765e-02 1.0e-02 0.00 -5 3.2e-02 1.2e-04 3.7e-02 -8.11e-01 6.824357426e-02 5.983282534e-02 6.0e-03 0.00 -6 1.4e-02 5.4e-05 1.7e-02 -3.03e-01 1.364775088e-01 1.380849812e-01 2.7e-03 0.00 -7 1.4e-03 5.3e-06 1.7e-03 8.68e-01 1.957348704e-01 1.934974515e-01 2.7e-04 0.00 -8 2.0e-04 7.4e-07 2.3e-04 9.52e-01 2.010571389e-01 2.007449130e-01 3.7e-05 0.00 -9 2.4e-05 8.9e-08 2.8e-05 9.94e-01 2.018146099e-01 2.017772919e-01 4.5e-06 0.00 -10 2.7e-07 1.0e-09 3.2e-07 1.00e+00 2.017988971e-01 2.017985456e-01 5.1e-08 0.00 -11 2.7e-11 1.0e-13 3.2e-11 1.00e+00 2.017999999e-01 2.017999999e-01 5.1e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0179999989e-01 nrm: 2e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 2.0179999982e-01 nrm: 6e-03 Viol. con: 1e-13 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0180000000e-01 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0180000006e-01 nrm: 6e-03 Viol. con: 2e-13 var: 2e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 201800.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:30:45 -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:30:45 -2026-01-18 13:30:45 -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 20 - Scalar variables : 20 - Scalar variables : 20 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:53:03 -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:53:03 -2026-01-18 13:53:03 -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 13:53:14 -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:53:14 -2026-01-18 13:53:14 -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.05 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 13:55:05 -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:55:05 -2026-01-18 13:55:05 -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:12:10 -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 14:12:10 -2026-01-18 14:12:10 -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 17 - Scalar variables : 17 - Scalar variables : 17 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 15:16:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 15:16:50 -2026-01-18 15:16:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 17:06:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 17:06:38 -2026-01-18 17:06:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.13 seconds. - -2026-01-18 17:06:45 -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 17:06:45 -2026-01-18 17:06:45 -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 17 - Scalar variables : 17 - Scalar variables : 17 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 17:50:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... - - 'lines.csv' ... - Added 5 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 15 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 33 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 3e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 3e-14 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:50:51 -2026-01-18 17:50:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 5 'line_pi' components. - Added 5 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 5 lines. - - Original system has 4 buses and 5 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 5 constraints. - Size: 5 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 17:50:51 -2026-01-18 17:50:51 -2026-01-18 17:50:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 5 'line_pi' components. - Added 5 'line_pi' components. - Added 5 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 5 lines. - - Original system has 4 buses and 5 lines. - - Original system has 4 buses and 5 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 5 constraints. - Size: 5 constraints. - Size: 5 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 8 - Constraints : 8 - Constraints : 8 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 - Dual. obj: 1.5000000000e+02 nrm: 1e+00 Viol. con: 2e-16 var: 4e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 21 - Constraints : 21 - Constraints : 21 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 17 - Scalar variables : 17 - Scalar variables : 17 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 9e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series _crossed/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - diff --git a/examples/kron_reduction/4bus_in_series/inputs/buses.csv b/examples/kron_reduction/4bus_in_series/inputs/buses.csv deleted file mode 100644 index c2ab77b..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/buses.csv +++ /dev/null @@ -1,5 +0,0 @@ -name,bus_type -1,slack -2,PQ -3,PQ -4,PQ \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/capacity_factors.csv b/examples/kron_reduction/4bus_in_series/inputs/capacity_factors.csv deleted file mode 100644 index efcc040..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/capacity_factors.csv +++ /dev/null @@ -1,4 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -solar_cf,1,1,solar,0 -solar_cf,1,2,solar,1 -solar_cf,1,3,solar,0.8 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/generators.csv b/examples/kron_reduction/4bus_in_series/inputs/generators.csv deleted file mode 100644 index 54a5988..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/generators.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -g1,solar,1,solar_cf,0,0.01,0,10,100,100,0 -g2,coal,1,no_capacity_factor,0,5,0,5,100,100,10 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/lines.csv b/examples/kron_reduction/4bus_in_series/inputs/lines.csv deleted file mode 100644 index 7d118c0..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/lines.csv +++ /dev/null @@ -1,5 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,100,FALSE,0,0.01,0,0,-360,360 -2,2,4,200,FALSE,0,0.01,0,0,-360,360 -3,1,3,200,FALSE,0,0.02,0,0,-360,360 -4,3,4,100,FALSE,0,0.02,0,0,-360,360 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/loads.csv b/examples/kron_reduction/4bus_in_series/inputs/loads.csv deleted file mode 100644 index 6729161..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/loads.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_MW -4,1,1,100 -4,1,2,200 -4,1,3,100 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/scenarios.csv b/examples/kron_reduction/4bus_in_series/inputs/scenarios.csv deleted file mode 100644 index ad1b9ef..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -1,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/timepoints.csv b/examples/kron_reduction/4bus_in_series/inputs/timepoints.csv deleted file mode 100644 index efad3f9..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -1,winter -2,winter -3,winter \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/inputs/timeseries.csv b/examples/kron_reduction/4bus_in_series/inputs/timeseries.csv deleted file mode 100644 index 7442139..0000000 --- a/examples/kron_reduction/4bus_in_series/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,3,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 72aebea..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251700.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,251700.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index d759a3c..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1700.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,1700.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 97fc731..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,100.0 -g2,2,50.0 -g2,3,20.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index c02de7e..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,13 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,1,1,0.0,-0.3819718634205489,66.66666666666667,0.0 -1,1,2,1,2,0.0,-0.5729577951308232,100.0,0.0 -1,1,2,1,3,0.0,-0.3819718634205489,66.66666666666667,0.0 -3,1,3,1,1,0.0,-0.3819718634205489,33.333333333333336,0.0 -3,1,3,1,2,0.0,-0.5729577951308232,50.0,0.0 -3,1,3,1,3,0.0,-0.3819718634205489,33.333333333333336,0.0 -2,2,4,1,1,-0.3819718634205489,-0.7639437268410978,66.66666666666667,0.0 -4,3,4,1,1,-0.3819718634205489,-0.7639437268410978,33.333333333333336,0.0 -2,2,4,1,2,-0.5729577951308232,-1.1459155902616465,100.0,0.0 -4,3,4,1,2,-0.5729577951308232,-1.1459155902616465,50.0,0.0 -2,2,4,1,3,-0.3819718634205489,-0.7639437268410978,66.66666666666667,0.0 -4,3,4,1,3,-0.3819718634205489,-0.7639437268410978,33.333333333333336,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index adebef8..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -4,1,1,0.0 -4,1,2,50.0 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 62c3839..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,250000.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 345fafd..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,13 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.0 -1,1,2,10.0 -1,1,3,10.0 -2,1,1,10.00000000000023 -2,1,2,6247.5 -2,1,3,10.00000000000023 -3,1,1,10.00000000000023 -3,1,2,2505.0000000000005 -3,1,3,10.00000000000023 -4,1,1,10.00000000000046 -4,1,2,5000.0 -4,1,3,10.00000000000046 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv deleted file mode 100644 index ce4ba70..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,251699.99999999985 -CostPerPeriod_USD,0.0 -TotalCost_USD,251699.99999999985 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 68638c1..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,1700.0000000000002 -CostPerPeriod_USD,0.0 -TotalCost_USD,1700.0000000000002 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 74f359c..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,100.0 -g2,2,50.00000000000003 -g2,3,20.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_flows.csv deleted file mode 100644 index 1ddb93f..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -Y_kron_f1-t4,1,4,1,1,0.0,-0.7639437268410978,99.99999999999999,0.0 -Y_kron_f1-t4,1,4,1,2,0.0,-1.1459155902616467,150.0,0.0 -Y_kron_f1-t4,1,4,1,3,0.0,-0.7639437268410978,99.99999999999999,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv deleted file mode 100644 index 561900e..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,4 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -4,1,1,0.0 -4,1,2,49.99999999999997 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 3bf2e98..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,249999.99999999985 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index a37c567..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.0 -1,1,2,10.0 -1,1,3,10.0 -4,1,1,10.0 -4,1,2,5000.0 -4,1,3,10.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 6370423..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,100.0 -g1,1,3,80.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv deleted file mode 100644 index e13b528..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv +++ /dev/null @@ -1,2 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,4,100.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv deleted file mode 100644 index d92ccdc..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_line_capacity_via_optimization.csv +++ /dev/null @@ -1,2 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,4,150.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_removable_buses.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_removable_buses.csv deleted file mode 100644 index f0c7862..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/kron_removable_buses.csv +++ /dev/null @@ -1,3 +0,0 @@ -bus -2 -3 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv deleted file mode 100644 index 7bf2341..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,150.0,0.0,100.0,50.0 -4,0.0,150.0,100.0,50.0 -2,100.0,100.0,200.0,0.0 -3,50.0,50.0,0.0,100.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv deleted file mode 100644 index 9d36148..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_conductance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,0.0,0.0,0.0,0.0 -4,0.0,0.0,0.0,0.0 -2,0.0,0.0,0.0,0.0 -3,0.0,0.0,0.0,0.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv deleted file mode 100644 index 368252c..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/original_system_susceptance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,4,2,3 -1,-150.0,0.0,100.0,50.0 -4,0.0,-150.0,100.0,50.0 -2,100.0,100.0,-200.0,0.0 -3,50.0,50.0,0.0,-100.0 diff --git a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv b/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv deleted file mode 100644 index 54f7510..0000000 --- a/examples/kron_reduction/4bus_in_series/outputs/kron_reduction/reduced_susceptance_matrix.csv +++ /dev/null @@ -1,3 +0,0 @@ -Index,1,4 -1,-75.0,75.0 -4,75.0,-75.0 diff --git a/examples/kron_reduction/4bus_in_series/sting_log.txt b/examples/kron_reduction/4bus_in_series/sting_log.txt deleted file mode 100644 index 21ca46e..0000000 --- a/examples/kron_reduction/4bus_in_series/sting_log.txt +++ /dev/null @@ -1,9210 +0,0 @@ -2026-01-17 22:14:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-17 22:15:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:16:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:18:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:22:00 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:23:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:27:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:31:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:32:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:45:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:50:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 23:00:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-17 23:00:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-18 13:10:07 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:10:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:15:43 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:21:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:21:48 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:22:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:23:12 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-18 13:29:32 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.05 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.06 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.08 seconds. - -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 12 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 15 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 29 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 45 after factor : 45 -Factor - dense dim. : 0 flops : 4.15e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.0e+02 3.8e-01 1.2e+02 0.00e+00 1.106254337e+02 9.492374029e+00 1.9e+01 0.00 -1 6.0e+00 2.2e-02 7.1e+00 2.09e+00 4.993115811e+00 4.357260622e+00 1.1e+00 0.00 -2 1.0e+00 3.8e-03 1.2e+00 1.23e+00 1.296252721e+00 1.031076816e+00 1.9e-01 0.00 -3 1.3e-01 4.8e-04 1.5e-01 1.08e+00 9.775917171e-02 5.570435934e-02 2.4e-02 0.00 -4 5.3e-02 2.0e-04 6.3e-02 1.13e+00 4.100495078e-02 2.407491765e-02 1.0e-02 0.00 -5 3.2e-02 1.2e-04 3.7e-02 -8.11e-01 6.824357426e-02 5.983282534e-02 6.0e-03 0.00 -6 1.4e-02 5.4e-05 1.7e-02 -3.03e-01 1.364775088e-01 1.380849812e-01 2.7e-03 0.00 -7 1.4e-03 5.3e-06 1.7e-03 8.68e-01 1.957348704e-01 1.934974515e-01 2.7e-04 0.00 -8 2.0e-04 7.4e-07 2.3e-04 9.52e-01 2.010571389e-01 2.007449130e-01 3.7e-05 0.00 -9 2.4e-05 8.9e-08 2.8e-05 9.94e-01 2.018146099e-01 2.017772919e-01 4.5e-06 0.00 -10 2.7e-07 1.0e-09 3.2e-07 1.00e+00 2.017988971e-01 2.017985456e-01 5.1e-08 0.00 -11 2.7e-11 1.0e-13 3.2e-11 1.00e+00 2.017999999e-01 2.017999999e-01 5.1e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0179999989e-01 nrm: 2e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 2.0179999982e-01 nrm: 6e-03 Viol. con: 1e-13 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0180000000e-01 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0180000006e-01 nrm: 6e-03 Viol. con: 2e-13 var: 2e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 201800.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:30:42 -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:30:42 -2026-01-18 13:30:42 -2026-01-18 13:30:42 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 20 - Scalar variables : 20 - Scalar variables : 20 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Decision variables of load shedding - Size: 12 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Load shedding cost expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - Constraints : 15 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 29 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 45 after factor : 45 -Factor - dense dim. : 0 flops : 4.15e+02 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.0e+02 3.8e-01 1.2e+02 0.00e+00 1.106254337e+02 9.492374029e+00 1.9e+01 0.00 -1 6.0e+00 2.2e-02 7.1e+00 2.09e+00 4.993115811e+00 4.357260622e+00 1.1e+00 0.00 -2 1.0e+00 3.8e-03 1.2e+00 1.23e+00 1.296252721e+00 1.031076816e+00 1.9e-01 0.00 -3 1.3e-01 4.8e-04 1.5e-01 1.08e+00 9.775917171e-02 5.570435934e-02 2.4e-02 0.00 -4 5.3e-02 2.0e-04 6.3e-02 1.13e+00 4.100495078e-02 2.407491765e-02 1.0e-02 0.00 -5 3.2e-02 1.2e-04 3.7e-02 -8.11e-01 6.824357426e-02 5.983282534e-02 6.0e-03 0.00 -6 1.4e-02 5.4e-05 1.7e-02 -3.03e-01 1.364775088e-01 1.380849812e-01 2.7e-03 0.00 -7 1.4e-03 5.3e-06 1.7e-03 8.68e-01 1.957348704e-01 1.934974515e-01 2.7e-04 0.00 -8 2.0e-04 7.4e-07 2.3e-04 9.52e-01 2.010571389e-01 2.007449130e-01 3.7e-05 0.00 -9 2.4e-05 8.9e-08 2.8e-05 9.94e-01 2.018146099e-01 2.017772919e-01 4.5e-06 0.00 -10 2.7e-07 1.0e-09 3.2e-07 1.00e+00 2.017988971e-01 2.017985456e-01 5.1e-08 0.00 -11 2.7e-11 1.0e-13 3.2e-11 1.00e+00 2.017999999e-01 2.017999999e-01 5.1e-12 0.00 -Basis identification started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 1 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0179999989e-01 nrm: 2e+02 Viol. con: 6e-08 var: 0e+00 - Dual. obj: 2.0179999982e-01 nrm: 6e-03 Viol. con: 1e-13 var: 5e-14 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0180000000e-01 nrm: 2e+02 Viol. con: 4e-14 var: 0e+00 - Dual. obj: 2.0180000006e-01 nrm: 6e-03 Viol. con: 2e-13 var: 2e-09 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 201800.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:30:45 -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 13:30:45 -2026-01-18 13:30:45 -2026-01-18 13:30:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 20 - Scalar variables : 20 - Scalar variables : 20 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 13:53:03 -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:53:03 -2026-01-18 13:53:03 -2026-01-18 13:53:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 13:53:14 -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:53:14 -2026-01-18 13:53:14 -2026-01-18 13:53:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - Size: 12 variables - - Decision variables of load shedding - Size: 12 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 32 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 10 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -Loading a SolverResults object with a warning status into model.name="unknown"; - - termination condition: infeasible - - message from solver: Problem is primal infeasible. The solution is a certificate of primal infeasibility. - -Basic solution summary - Problem status : PRIMAL_INFEASIBLE - Solution status : PRIMAL_INFEASIBLE_CER - Dual. obj: 2.6666666667e-03 nrm: 8e-05 Viol. con: 0e+00 var: 2e-16 -> Time spent by solver: 0.06 seconds. -> Solver finished with status: warning, termination condition: infeasible. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.05 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.15 seconds. - -2026-01-18 13:55:05 -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - - ->> Run completed in 0.01 seconds. - -2026-01-18 13:55:05 -2026-01-18 13:55:05 -2026-01-18 13:55:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Buses with either generation, load or storage: 1 - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. - - Kron reduction will remove 3 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. - - Kron system has 1 buses and 0 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Decision variables - - Decision variables - - Decision variables - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 14 - Scalar variables : 14 - Scalar variables : 14 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e-05 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Objective value: 0.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:12:10 -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 14:12:10 -2026-01-18 14:12:10 -2026-01-18 14:12:10 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 17 - Scalar variables : 17 - Scalar variables : 17 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 15:16:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 15:16:50 -2026-01-18 15:16:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 17:06:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 17:06:38 -2026-01-18 17:06:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 3 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 12 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 30 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 23 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Eliminator started. -Freed constraints in eliminator : 16 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 1e-14 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.13 seconds. - -2026-01-18 17:06:45 -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - - ->> Run completed in 0.02 seconds. - -2026-01-18 17:06:45 -2026-01-18 17:06:45 -2026-01-18 17:06:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Added 4 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 3 'load' components. - Added 3 'load' components. - Added 3 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 4 constraints. - Size: 4 constraints. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - Size: 2 constraints. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 7 - Constraints : 7 - Constraints : 7 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Objective value: 150.00. -> Objective value: 150.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 6 expressions - Size: 6 expressions - Size: 6 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 3 variables - Size: 3 variables - Size: 3 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 6 constraints - Size: 6 constraints - Size: 6 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 15 - Constraints : 15 - Constraints : 15 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 17 - Scalar variables : 17 - Scalar variables : 17 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Eliminator - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - tries : 0 time : 0.00 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - primal attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 2.5170000000e-01 nrm: 2e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 - Dual. obj: 2.5170000000e-01 nrm: 5e-03 Viol. con: 0e+00 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Objective value: 251700.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_in_series/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - - ->> Run completed in 0.05 seconds. - diff --git a/examples/kron_reduction/4bus_star/inputs/buses.csv b/examples/kron_reduction/4bus_star/inputs/buses.csv deleted file mode 100644 index c2ab77b..0000000 --- a/examples/kron_reduction/4bus_star/inputs/buses.csv +++ /dev/null @@ -1,5 +0,0 @@ -name,bus_type -1,slack -2,PQ -3,PQ -4,PQ \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/capacity_factors.csv b/examples/kron_reduction/4bus_star/inputs/capacity_factors.csv deleted file mode 100644 index efcc040..0000000 --- a/examples/kron_reduction/4bus_star/inputs/capacity_factors.csv +++ /dev/null @@ -1,4 +0,0 @@ -site,scenario,timepoint,technology,capacity_factor -solar_cf,1,1,solar,0 -solar_cf,1,2,solar,1 -solar_cf,1,3,solar,0.8 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/generators.csv b/examples/kron_reduction/4bus_star/inputs/generators.csv deleted file mode 100644 index 887e223..0000000 --- a/examples/kron_reduction/4bus_star/inputs/generators.csv +++ /dev/null @@ -1,3 +0,0 @@ -name,technology,bus,site,c2_USDperMWh2,c1_USDperMWh,c0_USD,cost_fixed_power_USDperkW,cap_existing_power_MW,cap_max_power_MW,cost_variable_USDperMWh -g1,solar,1,solar_cf,0,0.01,0,10,100,100,0.01 -g2,coal,1,no_capacity_factor,0,5,0,5,100,100,10 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/lines.csv b/examples/kron_reduction/4bus_star/inputs/lines.csv deleted file mode 100644 index 55247a8..0000000 --- a/examples/kron_reduction/4bus_star/inputs/lines.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,from_bus,to_bus,cap_existing_power_MW,expand_capacity,r_pu,x_pu,g_pu,b_pu,angle_min_deg,angle_max_deg -1,1,2,60,FALSE,0,0.01,0,0,-360,360 -2,2,3,40,FALSE,0,0.02,0,0,-360,360 -3,2,4,60,FALSE,0,0.01,0,0,-360,360 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/loads.csv b/examples/kron_reduction/4bus_star/inputs/loads.csv deleted file mode 100644 index 2717243..0000000 --- a/examples/kron_reduction/4bus_star/inputs/loads.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,load_MW -3,1,1,10 -3,1,2,20 -3,1,3,10 -4,1,1,50 -4,1,2,50 -4,1,3,50 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/scenarios.csv b/examples/kron_reduction/4bus_star/inputs/scenarios.csv deleted file mode 100644 index ad1b9ef..0000000 --- a/examples/kron_reduction/4bus_star/inputs/scenarios.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,probability -1,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/timepoints.csv b/examples/kron_reduction/4bus_star/inputs/timepoints.csv deleted file mode 100644 index efad3f9..0000000 --- a/examples/kron_reduction/4bus_star/inputs/timepoints.csv +++ /dev/null @@ -1,4 +0,0 @@ -name,timeseries -1,winter -2,winter -3,winter \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/inputs/timeseries.csv b/examples/kron_reduction/4bus_star/inputs/timeseries.csv deleted file mode 100644 index 7442139..0000000 --- a/examples/kron_reduction/4bus_star/inputs/timeseries.csv +++ /dev/null @@ -1,2 +0,0 @@ -name,timepoint_duration_hr,number_of_timepoints,timeseries_scale_to_period -winter,1,3,1 \ No newline at end of file diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index f9b51f7..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,50601.2 -CostPerPeriod_USD,0.0 -TotalCost_USD,50601.2 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 77c5a08..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,601.2 -CostPerPeriod_USD,0.0 -TotalCost_USD,601.2 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 6fd2f81..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,60.0 -g2,2,0.0 -g2,3,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_flows.csv deleted file mode 100644 index 10acd5a..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/line_flows.csv +++ /dev/null @@ -1,10 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -1,1,2,1,1,0.0,-0.34377467707849396,60.0,0.0 -1,1,2,1,2,0.0,-0.34377467707849396,60.0,0.0 -1,1,2,1,3,0.0,-0.34377467707849396,60.0,0.0 -2,2,3,1,1,-0.34377467707849396,-0.4583662361046587,10.000000000000009,0.0 -2,2,3,1,2,-0.34377467707849396,-0.5729577951308232,20.0,0.0 -2,2,3,1,3,-0.34377467707849396,-0.4583662361046587,10.000000000000009,0.0 -3,2,4,1,1,-0.34377467707849396,-0.6302535746439055,49.99999999999999,0.0 -3,2,4,1,2,-0.34377467707849396,-0.5729577951308232,40.0,0.0 -3,2,4,1,3,-0.34377467707849396,-0.6302535746439055,49.99999999999999,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding.csv deleted file mode 100644 index 2c0a8d6..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -3,1,1,0.0 -3,1,2,0.0 -3,1,3,0.0 -4,1,1,0.0 -4,1,2,10.0 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 1e51a83..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,50000.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 3efa390..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,13 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.0 -1,1,2,0.01 -1,1,3,0.01 -2,1,1,10.0 -2,1,2,5000.0 -2,1,3,0.01 -3,1,1,9.999999999999593 -3,1,2,5000.0 -3,1,3,0.01 -4,1,1,9.999999999999593 -4,1,2,5000.0 -4,1,3,0.009999999999940612 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index a1d6f6a..0000000 --- a/examples/kron_reduction/4bus_star/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,60.0 -g1,1,3,60.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/costs_summary.csv deleted file mode 100644 index f9b51f7..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,50601.2 -CostPerPeriod_USD,0.0 -TotalCost_USD,50601.2 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_capacity.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_capacity.csv deleted file mode 100644 index 3a8d785..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,Capacity_MW -g2,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_costs_summary.csv deleted file mode 100644 index 77c5a08..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,601.2 -CostPerPeriod_USD,0.0 -TotalCost_USD,601.2 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_dispatch.csv deleted file mode 100644 index 6fd2f81..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,timepoint,Dispatch_MW -g2,1,60.0 -g2,2,0.0 -g2,3,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_built_capacity.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_built_capacity.csv deleted file mode 100644 index dc3cc82..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_built_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -line,capacity_MW diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_costs_summary.csv deleted file mode 100644 index 741e2ea..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -CostPerPeriod_USD,0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_flows.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_flows.csv deleted file mode 100644 index 151f07c..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/line_flows.csv +++ /dev/null @@ -1,10 +0,0 @@ -name,from_bus,to_bus,scenario,timepoint,from_bus_angle_deg,to_bus_angle_deg,DCflow_MW,losses_MW -Y_kron_f1-t3,1,3,1,1,0.0,-0.4583662361046586,15.999999999999996,0.0 -Y_kron_f1-t3,1,3,1,2,0.0,-0.4583662361046586,15.999999999999996,0.0 -Y_kron_f1-t3,1,3,1,3,0.0,-0.4583662361046586,15.999999999999996,0.0 -Y_kron_f1-t4,1,4,1,1,0.0,-0.6302535746439055,43.999999999999986,0.0 -Y_kron_f3-t4,3,4,1,1,-0.4583662361046586,-0.6302535746439055,5.999999999999997,0.0 -Y_kron_f1-t4,1,4,1,2,0.0,-0.6302535746439055,43.999999999999986,0.0 -Y_kron_f3-t4,3,4,1,2,-0.4583662361046586,-0.6302535746439055,5.999999999999997,0.0 -Y_kron_f1-t4,1,4,1,3,0.0,-0.6302535746439055,43.999999999999986,0.0 -Y_kron_f3-t4,3,4,1,3,-0.4583662361046586,-0.6302535746439055,5.999999999999997,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding.csv deleted file mode 100644 index 5f6fab3..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding.csv +++ /dev/null @@ -1,7 +0,0 @@ -bus,scenario,timepoint,load_shedding_MW -3,1,1,0.0 -3,1,2,10.0 -3,1,3,0.0 -4,1,1,0.0 -4,1,2,0.0 -4,1,3,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv deleted file mode 100644 index 1e51a83..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/load_shedding_costs_summary.csv +++ /dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,50000.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 4af37bb..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,10 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,1,10.0 -1,1,2,0.01 -1,1,3,0.01 -3,1,1,10.0 -3,1,2,5000.0 -3,1,3,0.01 -4,1,1,9.999999999999593 -4,1,2,5000.0 -4,1,3,0.009999999999940612 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index a680c2b..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 7c23394..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_capacity.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_capacity.csv deleted file mode 100644 index 8758a78..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_capacity.csv +++ /dev/null @@ -1,2 +0,0 @@ -generator,scenario,Capacity_MW -g1,1,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index a1d6f6a..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,4 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -g1,1,1,0.0 -g1,1,2,60.0 -g1,1,3,60.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv deleted file mode 100644 index 362b01d..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_algorithm.csv +++ /dev/null @@ -1,4 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,3,100.0 -1,4,100.0 -3,4,100.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_optimization.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_optimization.csv deleted file mode 100644 index e1f2272..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_line_capacity_via_optimization.csv +++ /dev/null @@ -1,4 +0,0 @@ -from_bus,to_bus,calculated_capacity_MW -1,3,28.0 -1,4,48.0 -3,4,28.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_removable_buses.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_removable_buses.csv deleted file mode 100644 index aa67fed..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/kron_removable_buses.csv +++ /dev/null @@ -1,2 +0,0 @@ -bus -2 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv deleted file mode 100644 index 1891958..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_absolute_admittance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,2 -1,100.0,0.0,0.0,100.0 -3,0.0,50.0,0.0,50.0 -4,0.0,0.0,100.0,100.0 -2,100.0,50.0,100.0,250.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_conductance_matrix.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_conductance_matrix.csv deleted file mode 100644 index 6fec192..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_conductance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,2 -1,0.0,0.0,0.0,0.0 -3,0.0,0.0,0.0,0.0 -4,0.0,0.0,0.0,0.0 -2,0.0,0.0,0.0,0.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_susceptance_matrix.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_susceptance_matrix.csv deleted file mode 100644 index 2ff708a..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/original_system_susceptance_matrix.csv +++ /dev/null @@ -1,5 +0,0 @@ -Index,1,3,4,2 -1,-100.0,0.0,0.0,100.0 -3,0.0,-50.0,0.0,50.0 -4,0.0,0.0,-100.0,100.0 -2,100.0,50.0,100.0,-250.0 diff --git a/examples/kron_reduction/4bus_star/outputs/kron_reduction/reduced_susceptance_matrix.csv b/examples/kron_reduction/4bus_star/outputs/kron_reduction/reduced_susceptance_matrix.csv deleted file mode 100644 index ae08fda..0000000 --- a/examples/kron_reduction/4bus_star/outputs/kron_reduction/reduced_susceptance_matrix.csv +++ /dev/null @@ -1,4 +0,0 @@ -Index,1,3,4 -1,-60.0,20.0,40.0 -3,20.0,-40.0,20.0 -4,40.0,20.0,-60.0 diff --git a/examples/kron_reduction/4bus_star/sting_log.txt b/examples/kron_reduction/4bus_star/sting_log.txt deleted file mode 100644 index dd24fec..0000000 --- a/examples/kron_reduction/4bus_star/sting_log.txt +++ /dev/null @@ -1,29055 +0,0 @@ -2026-01-17 22:14:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 6 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.0000000000e+02 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.0000000000e+02 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 100.00. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-17 22:15:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:16:38 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:18:20 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:22:00 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:23:19 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:27:16 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:29:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 0.0000000000e+00 nrm: 1e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 0.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:31:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. -2026-01-17 22:32:50 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:45:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 22:50:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 2.0000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.0000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 200.00. -> Time spent by solver: 0.04 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.05 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-17 23:00:27 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-17 23:00:33 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus/inputs ... - - 'lines.csv' ... - Added 4 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 2 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 2 - - Kron reduction will remove 2 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 4 lines. - - Kron system has 2 buses and 1 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 4 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 2 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 7 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 4 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 1.5000000000e+02 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 1.5000000000e+02 nrm: 2e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 150.00. -> Time spent by solver: 0.02 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.02 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.03 seconds. - -2026-01-17 23:07:39 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. -2026-01-17 23:08:45 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. -2026-01-17 23:15:47 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. -2026-01-17 23:15:57 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.04 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.04 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.06 seconds. - -> Completed in 0.07 seconds. - - ->> Run completed in 0.08 seconds. - -2026-01-17 23:17:04 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/paul/Documents/STING/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 3 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'all'} -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via algorithm ... - - Exported line capacities calculated via algorithm as CSV. -> Completed in 0.00 seconds. - -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.02 seconds. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Decision variables of bus angles. - Size: 5 variables. - - Constraints of angle differences for original system. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -Problem - Name : - Objective sense : maximize - Type : LO (linear optimization problem) - Constraints : 5 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 6 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:18:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 11 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0000000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0000000000e-04 nrm: 5e-03 Viol. con: 5e-22 var: 5e-18 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0000000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0000000000e-04 nrm: 5e-03 Viol. con: 5e-22 var: 5e-18 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 600.00 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:18:37 -2026-01-18 14:18:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:18:37 -2026-01-18 14:18:37 -2026-01-18 14:18:37 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842839954e+00 9.547063453e+00 3.0e+01 0.00 -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842839954e+00 9.547063453e+00 3.0e+01 0.00 -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842839954e+00 9.547063453e+00 3.0e+01 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090042988e-01 9.837221337e+00 5.2e+00 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090042988e-01 9.837221337e+00 5.2e+00 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090042988e-01 9.837221337e+00 5.2e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718811413e-01 2.408503205e+00 1.1e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718811413e-01 2.408503205e+00 1.1e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718811413e-01 2.408503205e+00 1.1e+00 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085776296e-02 3.883725932e-01 2.1e-01 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085776296e-02 3.883725932e-01 2.1e-01 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085776296e-02 3.883725932e-01 2.1e-01 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.558030734e-03 2.571280282e-03 1.0e-03 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.558030734e-03 2.571280282e-03 1.0e-03 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.558030734e-03 2.571280282e-03 1.0e-03 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.000959504e-04 6.001972140e-04 1.0e-07 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.000959504e-04 6.001972140e-04 1.0e-07 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.000959504e-04 6.001972140e-04 1.0e-07 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.000000096e-04 6.000000197e-04 1.0e-11 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.000000096e-04 6.000000197e-04 1.0e-11 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.000000096e-04 6.000000197e-04 1.0e-11 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0000000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Primal. obj: 6.0000000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Primal. obj: 6.0000000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Dual. obj: 6.0000001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - Dual. obj: 6.0000001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - Dual. obj: 6.0000001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0000000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0000000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0000000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0000000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 - Dual. obj: 6.0000000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 - Dual. obj: 6.0000000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 600.00 USD. -> Objective value: 600.00 USD. -> Objective value: 600.00 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 14:20:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 11 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0130000000e-04 nrm: 5e-03 Viol. con: 6e-20 var: 8e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0130000000e-04 nrm: 5e-03 Viol. con: 6e-20 var: 8e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:20:58 -2026-01-18 14:20:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:20:58 -2026-01-18 14:20:58 -2026-01-18 14:20:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 6e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 6.6666666667e+01 nrm: 1e+02 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 6.6666666667e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 66.67. -> Objective value: 66.67. -> Objective value: 66.67. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842841259e+00 9.547064490e+00 3.0e+01 0.00 -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842841259e+00 9.547064490e+00 3.0e+01 0.00 -0 2.0e+02 5.1e-01 2.2e+01 0.00e+00 1.842841259e+00 9.547064490e+00 3.0e+01 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090048244e-01 9.837221842e+00 5.2e+00 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090048244e-01 9.837221842e+00 5.2e+00 0.00 -1 3.5e+01 8.9e-02 3.9e+00 3.36e+00 7.090048244e-01 9.837221842e+00 5.2e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718821136e-01 2.408502737e+00 1.1e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718821136e-01 2.408502737e+00 1.1e+00 0.00 -2 7.6e+00 1.9e-02 8.3e-01 1.03e+00 4.718821136e-01 2.408502737e+00 1.1e+00 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085893766e-02 3.883732617e-01 2.1e-01 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085893766e-02 3.883732617e-01 2.1e-01 0.00 -3 1.4e+00 3.5e-03 1.5e-01 9.84e-01 7.085893766e-02 3.883732617e-01 2.1e-01 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.559329079e-03 2.572572681e-03 1.0e-03 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.559329079e-03 2.572572681e-03 1.0e-03 0.00 -4 7.0e-03 1.8e-05 7.8e-04 1.01e+00 1.559329079e-03 2.572572681e-03 1.0e-03 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.013959502e-04 6.014972132e-04 1.0e-07 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.013959502e-04 6.014972132e-04 1.0e-07 0.00 -5 7.0e-07 1.8e-09 7.8e-08 1.00e+00 6.013959502e-04 6.014972132e-04 1.0e-07 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.013000096e-04 6.013000197e-04 1.0e-11 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.013000096e-04 6.013000197e-04 1.0e-11 0.00 -6 7.1e-11 1.8e-13 7.8e-12 1.00e+00 6.013000096e-04 6.013000197e-04 1.0e-11 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Primal. obj: 6.0130000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Primal. obj: 6.0130000960e-04 nrm: 7e+01 Viol. con: 2e-11 var: 0e+00 - Dual. obj: 6.0130001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - Dual. obj: 6.0130001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - Dual. obj: 6.0130001403e-04 nrm: 5e-03 Viol. con: 6e-14 var: 2e-14 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0130000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 - Dual. obj: 6.0130000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 - Dual. obj: 6.0130000302e-04 nrm: 5e-03 Viol. con: 5e-14 var: 1e-14 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 14:22:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:22:05 -2026-01-18 14:22:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:22:05 -2026-01-18 14:22:05 -2026-01-18 14:22:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 14:23:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:23:14 -2026-01-18 14:23:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:23:14 -2026-01-18 14:23:14 -2026-01-18 14:23:14 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 14:50:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.05 seconds. - -2026-01-18 14:50:02 -2026-01-18 14:50:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 14:50:02 -2026-01-18 14:50:02 -2026-01-18 14:50:02 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 9 - Constraints : 9 - Constraints : 9 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Freed constraints in eliminator : 5 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 14:51:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.14 seconds. - -2026-01-18 14:51:28 -2026-01-18 14:51:28 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 15:13:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.08 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.01 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.05 seconds. - -> Completed in 0.06 seconds. - - ->> Run completed in 0.17 seconds. - -2026-01-18 15:13:22 -2026-01-18 15:13:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. -2026-01-18 15:13:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.05 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.04 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.05 seconds. - - ->> Run completed in 0.13 seconds. - -2026-01-18 15:13:31 -2026-01-18 15:13:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 15:13:31 -2026-01-18 15:13:31 -2026-01-18 15:13:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:12:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:12:01 -2026-01-18 17:12:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:12:01 -2026-01-18 17:12:01 -2026-01-18 17:12:01 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - threads : 24 -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - solved problem : the primal -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Constraints : 6 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Cones : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Scalar variables : 12 conic : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Optimizer - Semi-definite variables: 0 scalarized : 0 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - setup time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - dense det. time : 0.00 GP order time : 0.00 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - nonzeros before factor : 9 after factor : 9 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -Factor - dense dim. : 0 flops : 6.30e+01 -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -0 1.1e+02 5.6e-01 1.2e+01 0.00e+00 1.639220132e+00 7.257431779e+00 1.7e+01 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -1 1.6e+01 8.0e-02 1.7e+00 3.12e+00 6.850341932e-01 5.897864479e+00 2.5e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -2 1.4e+01 6.6e-02 1.4e+00 8.31e-01 4.748985043e-01 5.150683550e+00 2.1e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -3 1.1e+01 5.5e-02 1.2e+00 9.51e-01 6.696424306e-01 3.938581358e+00 1.7e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -4 6.6e+00 3.2e-02 6.8e-01 9.37e-01 5.217653417e-01 2.412435513e+00 1.0e+00 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -5 5.7e+00 2.8e-02 5.8e-01 8.06e-01 2.148793085e-01 1.974160045e+00 8.6e-01 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -6 3.3e-01 1.6e-03 3.4e-02 1.02e+00 5.326947667e-02 1.254743691e-01 5.0e-02 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -7 2.8e-04 1.4e-06 2.9e-05 1.02e+00 6.482139218e-04 6.440933792e-04 4.2e-05 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -8 2.8e-08 1.4e-10 2.9e-09 1.00e+00 6.013046916e-04 6.013042795e-04 4.2e-09 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -9 2.9e-12 1.4e-14 2.9e-13 1.00e+00 6.013000005e-04 6.013000004e-04 4.2e-13 0.00 -Basis identification started. -Basis identification started. -Basis identification started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization started. -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Basis identification initialization terminated. Time: 0.00 -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase started. -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Primal basis identification phase terminated. Time: 0.00 -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase started. -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Dual basis identification phase terminated. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Initialization. Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Primal. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Dual. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Optimization. Iterations: 0 Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Basis identification terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Primal. obj: 6.0130000047e-04 nrm: 7e+01 Viol. con: 1e-12 var: 0e+00 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - Dual. obj: 6.0130000029e-04 nrm: 5e-03 Viol. con: 5e-15 var: 1e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 6.0130000000e-04 nrm: 7e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 - Dual. obj: 6.0129999997e-04 nrm: 5e-03 Viol. con: 6e-15 var: 2e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Objective value: 601.30 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:28:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:28:22 -2026-01-18 17:28:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:28:22 -2026-01-18 17:28:22 -2026-01-18 17:28:22 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -2026-01-18 17:28:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:28:51 -2026-01-18 17:28:51 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:28:52 -2026-01-18 17:28:52 -2026-01-18 17:28:52 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 3.3171189900e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 3.3171189900e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 33171.19 USD. -> Objective value: 33171.19 USD. -> Objective value: 33171.19 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:30:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:30:30 -2026-01-18 17:30:30 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:30:31 -2026-01-18 17:30:31 -2026-01-18 17:30:31 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:36:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.02 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:36:54 -2026-01-18 17:36:54 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:36:55 -2026-01-18 17:36:55 -2026-01-18 17:36:55 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 25616.24 USD. -> Objective value: 25616.24 USD. -> Objective value: 25616.24 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:37:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:37:03 -2026-01-18 17:37:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:37:03 -2026-01-18 17:37:03 -2026-01-18 17:37:03 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Freed constraints in eliminator : 3 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Primal. obj: 2.5616239980e-02 nrm: 6e+01 Viol. con: 2e-15 var: 0e+00 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 - Dual. obj: 2.5616239980e-02 nrm: 7e-03 Viol. con: 0e+00 var: 4e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 25616.24 USD. -> Objective value: 25616.24 USD. -> Objective value: 25616.24 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:40:46 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:40:46 -2026-01-18 17:40:46 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:40:46 -2026-01-18 17:40:46 -2026-01-18 17:40:46 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 24 - Constraints : 24 - Constraints : 24 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 12 -Freed constraints in eliminator : 12 -Freed constraints in eliminator : 12 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 8e-19 var: 5e-15 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:41:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:41:58 -2026-01-18 17:41:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.04 seconds. - -> Completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:41:58 -2026-01-18 17:41:58 -2026-01-18 17:41:58 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:42:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 1e-19 var: 6e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:42:05 -2026-01-18 17:42:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:42:05 -2026-01-18 17:42:05 -2026-01-18 17:42:05 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 4e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 4.0000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 - Dual. obj: 4.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 7e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 40.00. -> Objective value: 40.00. -> Objective value: 40.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 5e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 7e-18 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - -> Completed in 0.01 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - - ->> Run completed in 0.07 seconds. - -2026-01-18 17:44:35 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Completed in 0.00 seconds. - - 'buses.csv' ... - Added 4 'bus' components. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - Added 1 'ts' components. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - Added 3 'tp' components. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - Added 1 'sc' components. - Completed in 0.00 seconds. - - 'loads.csv' ... - Added 6 'load' components. - Completed in 0.00 seconds. - - 'generators.csv' ... - Added 2 'gen' components. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': False, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - Size: 8 variables - - Maximum built capacity constraints - Size: 0 constraints - - Maximum dispatch constraints - Size: 3 constraints - - Capacity factor constraints - Size: 3 constraints - - Dispatch at bus expressions - Size: 12 expressions - - Generation cost per timepoint expressions - Size: 3 expressions - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - Size: 0 variables - - Energy capacity constraints - Size: 0 constraints - - Power capacity constraints - Size: 0 constraints - - Maximum charge and discharge constraints - Size: 0 constraints - - Maximum state of charge constraints - Size: 0 constraints - - State of charge constraints - Size: 12 constraints - - Storage cost per timepoint expressions - Size: 3 expressions - - Storage cost per period expression - Size: 1 expressions -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Decision variables of bus angles - Size: 12 variables - - Decision variables of load shedding - Size: 6 variables - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - Size: 0 variables - - Maximum and minimum flow constraints per line - Size: 9 constraints - - Line cost per period expression - - Angle difference limit constraints per line - Size: 0 constraints - - Power balance at each bus - Size: 12 constraints - - Load shedding cost expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.01 seconds. - -> Solving capacity expansion model... -Problem - Name : - Objective sense : minimize - Type : LO (linear optimization problem) - Constraints : 27 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Scalar variables : 26 - Matrix variables : 0 - Integer variables : 0 - -Optimizer started. -Presolve started. -Linear dependency checker started. -Linear dependency checker terminated. -Eliminator started. -Freed constraints in eliminator : 9 -Eliminator terminated. -Eliminator started. -Freed constraints in eliminator : 0 -Eliminator terminated. -Eliminator - tries : 2 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 9e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 2e-15 - -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 9e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 2e-15 -> Time spent by solver: 0.03 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/capacity_expansion -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Completed in 0.01 seconds. - -> Completed in 0.02 seconds. - - ->> Run completed in 0.06 seconds. - -2026-01-18 17:44:35 -2026-01-18 17:44:35 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.01 seconds. - -> Completed in: 0.01 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 28.00. -> Objective value: 28.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 48.00. -> Objective value: 48.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - - -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - - -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 28.00. -> Objective value: 28.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Run completed in 0.04 seconds. - - ->> Run completed in 0.04 seconds. - -2026-01-18 17:44:35 -2026-01-18 17:44:35 -2026-01-18 17:44:35 - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - - ______ __ - / __/ /__/ /_ _____ _ - _\ \/ __/ _// \/ / _ `/ -/___/__/// /_/\_/\_, / - / /___/ - -Version: 0.1.0 (2025-11-12) -======================================== - -> Initializing system ... -> Initializing system ... -> Initializing system ... - Completed - Completed - Completed -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... -> Loading system from CSV files from /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/inputs ... - - 'lines.csv' ... - - 'lines.csv' ... - - 'lines.csv' ... - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Added 3 'line_pi' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'buses.csv' ... - - 'buses.csv' ... - - 'buses.csv' ... - Added 4 'bus' components. - Added 4 'bus' components. - Added 4 'bus' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timeseries.csv' ... - - 'timeseries.csv' ... - - 'timeseries.csv' ... - Added 1 'ts' components. - Added 1 'ts' components. - Added 1 'ts' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'timepoints.csv' ... - - 'timepoints.csv' ... - - 'timepoints.csv' ... - Added 3 'tp' components. - Added 3 'tp' components. - Added 3 'tp' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'scenarios.csv' ... - - 'scenarios.csv' ... - - 'scenarios.csv' ... - Added 1 'sc' components. - Added 1 'sc' components. - Added 1 'sc' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'loads.csv' ... - - 'loads.csv' ... - - 'loads.csv' ... - Added 6 'load' components. - Added 6 'load' components. - Added 6 'load' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'generators.csv' ... - - 'generators.csv' ... - - 'generators.csv' ... - Added 2 'gen' components. - Added 2 'gen' components. - Added 2 'gen' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - - 'capacity_factors.csv' ... - Added 3 'cf' components. - Added 3 'cf' components. - Added 3 'cf' components. - Completed in 0.00 seconds. - Completed in 0.00 seconds. - Completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Post system initialization completed in 0.00 seconds. -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - -> Completed in: 0.00 seconds. - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - - ->> Starting Kron reduction ... - -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -{'bus_neighbor_limit': None, 'tolerance': 0.0, 'find_kron_removable_buses': True, 'consider_kron_removable_bus_attribute': False, 'expand_line_capacity': False, 'cost_fixed_power_USDperkW': 1, 'line_capacity_method': 'optimization'} -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... -> Initializing identify removable buses for Kron reduction ... - - Total number of buses: 4 - - Total number of buses: 4 - - Total number of buses: 4 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Buses with either generation, load or storage: 3 - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. - - Kron reduction will remove 1 buses out of 4 total buses. -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... -> Initializing reduction of the system via Kron reduction ... - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Original system has 4 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. - - Kron system has 3 buses and 3 lines. -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -> Initializing estimation of line capacities for the Kron system via optimization ... -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -SolverSettings(solver_name='mosek_direct', tee=True, solver_options={'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}) -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. -> Estimating capacity for line from bus 1 to bus 3. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 28.00. -> Objective value: 28.00. -> Objective value: 28.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. -> Estimating capacity for line from bus 1 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Primal. obj: 4.8000000000e+01 nrm: 6e+01 Viol. con: 3e-15 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 - Dual. obj: 4.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 48.00. -> Objective value: 48.00. -> Objective value: 48.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. -> Estimating capacity for line from bus 3 to bus 4. - - Building optimization model ... - - Building optimization model ... - - Building optimization model ... - - Decision variables of bus angles. - - Decision variables of bus angles. - - Decision variables of bus angles. - Size: 5 variables. - Size: 5 variables. - Size: 5 variables. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - - Constraints of angle differences for original system. - Size: 3 constraints. - Size: 3 constraints. - Size: 3 constraints. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - - Constraint of angle difference for a line in the Kron system. - Size: 1 constraints. - Size: 1 constraints. - Size: 1 constraints. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. - - Objective function to maximize the angle difference bound. -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -> Solving optimization model to find maximum angle difference bound... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : maximize - Objective sense : maximize - Objective sense : maximize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 5 - Constraints : 5 - Constraints : 5 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 6 - Scalar variables : 6 - Scalar variables : 6 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Freed constraints in eliminator : 2 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Primal. obj: 2.8000000000e+01 nrm: 6e+01 Viol. con: 1e-15 var: 0e+00 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 - Dual. obj: 2.8000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 3e-13 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 28.00. -> Objective value: 28.00. -> Objective value: 28.00. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. - - Exported line capacities calculated via optimization as CSV. -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - -> Completed in 0.03 seconds. - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - - ->> Starting capacity expansion... - -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Solver settings: {'solver_name': 'mosek_direct', 'tee': True, 'solver_options': {'MSK_DPAR_INTPNT_TOL_PFEAS': '1e-5'}} -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -Model settings: {'gen_costs': 'linear', 'consider_shedding': True, 'consider_single_storage_injection': False, 'consider_line_capacity': True, 'consider_bus_max_flow': True, 'consider_angle_limits': True, 'policies': []} - -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of the optimization model for capacity expansion ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... -> Initializing construction of generator variables, constraints, and costs ... - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Sets of generators for first-stage and second-stage decisions - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - - Decision variables of dispatch and capacity - Size: 8 variables - Size: 8 variables - Size: 8 variables - - Maximum built capacity constraints - - Maximum built capacity constraints - - Maximum built capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - - Maximum dispatch constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Capacity factor constraints - - Capacity factor constraints - - Capacity factor constraints - Size: 3 constraints - Size: 3 constraints - Size: 3 constraints - - Dispatch at bus expressions - - Dispatch at bus expressions - - Dispatch at bus expressions - Size: 9 expressions - Size: 9 expressions - Size: 9 expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - - Generation cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Generation cost per period expression - - Generation cost per period expression - - Generation cost per period expression -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... -> Initializing construction of storage variables, constraints, and costs ... - - Decision variables - - Decision variables - - Decision variables - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Energy capacity constraints - - Energy capacity constraints - - Energy capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power capacity constraints - - Power capacity constraints - - Power capacity constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - - Maximum charge and discharge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - - Maximum state of charge constraints - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - State of charge constraints - - State of charge constraints - - State of charge constraints - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - - Storage cost per timepoint expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions - - Storage cost per period expression - - Storage cost per period expression - - Storage cost per period expression - Size: 1 expressions - Size: 1 expressions - Size: 1 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... -> Initializing construction of transmission variables, constraints, and costs for capacity expansion model ... - - Load data lookup - - Load data lookup - - Load data lookup - - Decision variables of bus angles - - Decision variables of bus angles - - Decision variables of bus angles - Size: 9 variables - Size: 9 variables - Size: 9 variables - - Decision variables of load shedding - - Decision variables of load shedding - - Decision variables of load shedding - Size: 6 variables - Size: 6 variables - Size: 6 variables - - Power flow per bus expressions - - Power flow per bus expressions - - Power flow per bus expressions - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Set of expandable and non-expandable lines - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - - Decision variables of line capacity expansion - Size: 0 variables - Size: 0 variables - Size: 0 variables - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - - Maximum and minimum flow constraints per line - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Line cost per period expression - - Line cost per period expression - - Line cost per period expression - - Maximum flow constraints per bus - - Maximum flow constraints per bus - - Maximum flow constraints per bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Angle difference limit constraints per line - - Angle difference limit constraints per line - - Angle difference limit constraints per line - Size: 0 constraints - Size: 0 constraints - Size: 0 constraints - - Power balance at each bus - - Power balance at each bus - - Power balance at each bus - Size: 9 constraints - Size: 9 constraints - Size: 9 constraints - - Load shedding cost expressions - - Load shedding cost expressions - - Load shedding cost expressions - Size: 3 expressions - Size: 3 expressions - Size: 3 expressions -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Initializing construction of objective function ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Solving capacity expansion model... -> Solving capacity expansion model... -> Solving capacity expansion model... -Problem -Problem -Problem - Name : - Name : - Name : - Objective sense : minimize - Objective sense : minimize - Objective sense : minimize - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Type : LO (linear optimization problem) - Constraints : 33 - Constraints : 33 - Constraints : 33 - Affine conic cons. : 0 - Affine conic cons. : 0 - Affine conic cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Disjunctive cons. : 0 - Cones : 0 - Cones : 0 - Cones : 0 - Scalar variables : 23 - Scalar variables : 23 - Scalar variables : 23 - Matrix variables : 0 - Matrix variables : 0 - Matrix variables : 0 - Integer variables : 0 - Integer variables : 0 - Integer variables : 0 - - - -Optimizer started. -Optimizer started. -Optimizer started. -Presolve started. -Presolve started. -Presolve started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker started. -Linear dependency checker terminated. -Linear dependency checker terminated. -Linear dependency checker terminated. -Eliminator started. -Eliminator started. -Eliminator started. -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Freed constraints in eliminator : 6 -Eliminator terminated. -Eliminator terminated. -Eliminator terminated. -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Eliminator - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - tries : 1 time : 0.00 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - primal attempts : 1 successes : 1 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - dual attempts : 0 successes : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Lin. dep. - primal deps. : 0 dual deps. : 0 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Presolve terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 -Optimizer terminated. Time: 0.00 - - - - - - -Interior-point solution summary -Interior-point solution summary -Interior-point solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 - - - -Basic solution summary -Basic solution summary -Basic solution summary - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Problem status : PRIMAL_AND_DUAL_FEASIBLE - Solution status : OPTIMAL - Solution status : OPTIMAL - Solution status : OPTIMAL - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Primal. obj: 5.0601200000e-02 nrm: 6e+01 Viol. con: 7e-15 var: 0e+00 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 - Dual. obj: 5.0601200000e-02 nrm: 5e-03 Viol. con: 4e-19 var: 3e-21 -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Time spent by solver: 0.01 seconds. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Solver finished with status: ok, termination condition: optimal. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Objective value: 50601.20 USD. -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -> Initializing export all results to CSV files ... -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -- Directory: /Users/psernatorre/Documents/sting/examples/kron_reduction/4bus_star/outputs/kron_capacity_expansion -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Initializing generator results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Initializing storage results to CSV files ... -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Completed in 0.00 seconds. - -> Initializing transmission results to CSV files ... -> Initializing transmission results to CSV files ... -> 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-scenario,timepoint,site,capacity_factor -1,2035-01-01T00:00:00.000000-0800,pvu9,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu16,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu17,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu19,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu43,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu51,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu57,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu71,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu78,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu88,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu99,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu101,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu108,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu109,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu111,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu113,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu114,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu116,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu121,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu127,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu131,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu137,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu138,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu143,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu144,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu145,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu147,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu149,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu155,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu171,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu181,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu182,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu200,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu204,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu207,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu209,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu217,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu219,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu226,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu227,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu229,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu231,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu235,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu240,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu241,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu250,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu258,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu259,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu260,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu268,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu273,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu276,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu288,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu289,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu295,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu296,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu308,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu309,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu316,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu317,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu318,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu319,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu322,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu326,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu342,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu344,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu347,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu348,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu377,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu385,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu393,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu401,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu407,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu444,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu446,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu448,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu449,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu452,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu456,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu471,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu475,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu478,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu481,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu487,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu491,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu503,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu523,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu528,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu543,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu562,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu565,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu567,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu570,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu573,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu576,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu577,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu582,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu603,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu610,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu611,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu613,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu618,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu619,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu649,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu694,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu775,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu779,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu781,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu782,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu796,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu801,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu803,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu806,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu811,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu812,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu814,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu816,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu818,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu822,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu838,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu839,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu859,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu877,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu879,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu883,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu893,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu898,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu909,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu915,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu917,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu945,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu957,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu974,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu975,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu984,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu987,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu990,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu993,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu995,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu998,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu999,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1000,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1002,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1006,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1013,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1016,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1023,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1025,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1031,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1033,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1035,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1037,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1038,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1041,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1051,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1053,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1059,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1061,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1080,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1084,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1085,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1090,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1096,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1110,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1114,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1118,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1143,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1146,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1168,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1172,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1176,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1178,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1180,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1183,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1188,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1194,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1206,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1241,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1247,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1251,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1264,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1268,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1284,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1320,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1326,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1330,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1336,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1338,0.0 -1,2035-01-01T00:00:00.000000-0800,pvu1344,0.0 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-1,2035-01-01T00:00:00.000000-0800,wto2407,0.0 -1,2035-01-01T00:00:00.000000-0800,wto7830,0.0 -1,2035-01-01T00:00:00.000000-0800,wto7938,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8403,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8456,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8507,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8534,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8535,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8593,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8680,0.0 -1,2035-01-01T00:00:00.000000-0800,wto8712,0.253 diff --git a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_constraints.csv b/examples/kron_reduction/one_hour_kron/inputs/energy_budget_constraints.csv deleted file mode 100644 index ad9802c..0000000 --- a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_constraints.csv +++ /dev/null @@ -1,6 +0,0 @@ -budget_term,budget_region,budget_constraint_GWh -base_2018_hydro_month_1,LADWP,55.1638567 -base_2018_hydro_month_1,NCNC,229.6131656 -base_2018_hydro_month_1,PACW,382.663 -base_2018_hydro_month_1,PGE,863.5482292 -base_2018_hydro_month_1,SCE,247.8367868 diff --git a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_regions.csv b/examples/kron_reduction/one_hour_kron/inputs/energy_budget_regions.csv deleted file mode 100644 index b39105c..0000000 --- a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_regions.csv +++ /dev/null @@ -1,205 +0,0 @@ -generator,budget_region -cats_5,SCE -cats_6,PGE -cats_7,LADWP -cats_8,LADWP -cats_9,PGE -cats_10,PGE -cats_11,PGE -cats_12,PGE -cats_13,PACW -cats_14,PGE -cats_15,NCNC -cats_16,PACW -cats_17,NCNC -cats_18,NCNC -cats_19,PGE -cats_20,NCNC -cats_21,NCNC -cats_22,PGE -cats_23,SCE -cats_24,SCE -cats_25,PGE -cats_26,PGE -cats_27,PGE -cats_28,LADWP -cats_29,SCE -cats_30,PGE -cats_31,PGE -cats_32,PGE -cats_33,PGE -cats_34,PGE -cats_35,PGE -cats_36,LADWP -cats_37,PGE -cats_38,PGE -cats_39,PGE -cats_40,PGE -cats_41,PGE -cats_42,PGE -cats_43,PGE -cats_44,PGE -cats_45,PGE -cats_46,PGE -cats_47,SCE -cats_48,SCE -cats_49,SCE -cats_50,SCE -cats_51,SCE -cats_52,SCE -cats_53,SCE -cats_54,SCE -cats_55,SCE -cats_56,PGE -cats_57,PGE -cats_58,PGE -cats_59,PGE -cats_60,SCE -cats_61,PGE -cats_62,LADWP -cats_63,PGE -cats_64,PGE -cats_65,PGE -cats_66,PGE -cats_67,SCE -cats_68,PGE -cats_69,PGE -cats_70,NCNC -cats_71,SCE -cats_72,SCE -cats_73,LADWP -cats_74,LADWP -cats_75,LADWP -cats_76,LADWP -cats_77,PACW -cats_78,PACW -cats_79,PGE -cats_80,PGE -cats_81,PGE -cats_82,PACW -cats_83,PACW -cats_84,PACW -cats_85,PACW -cats_86,NCNC -cats_87,PGE -cats_88,PGE -cats_89,PGE -cats_90,PGE -cats_91,PGE -cats_92,PGE -cats_93,PGE -cats_94,PGE -cats_95,PGE -cats_96,PGE -cats_97,PGE -cats_98,PGE -cats_99,PGE -cats_100,SCE -cats_101,SCE -cats_102,SCE -cats_103,SCE -cats_104,SCE -cats_105,PGE -cats_106,PGE -cats_107,PGE -cats_108,PGE -cats_109,PGE -cats_110,PGE -cats_111,PGE -cats_112,PGE -cats_113,PGE -cats_114,NCNC -cats_115,LADWP -cats_116,LADWP -cats_117,SCE -cats_118,PGE -cats_119,SCE -cats_120,LADWP -cats_121,SCE -cats_122,PGE -cats_123,PGE -cats_124,PGE -cats_125,PGE -cats_126,PGE -cats_127,PGE -cats_128,SCE -cats_129,PGE -cats_130,SCE -cats_131,SCE -cats_132,NCNC -cats_133,SCE -cats_134,SCE -cats_135,SCE -cats_136,PGE -cats_137,PGE -cats_138,PGE -cats_139,SCE -cats_140,SCE -cats_141,PGE -cats_142,PGE -cats_143,PGE -cats_144,PGE -cats_145,PGE -cats_146,SCE -cats_147,SCE -cats_148,SCE -cats_149,PGE -cats_150,PGE -cats_151,PGE -cats_152,PGE -cats_153,PGE -cats_154,PGE -cats_155,PGE -cats_156,SCE -cats_157,PGE -cats_158,PGE -cats_159,PGE -cats_160,PGE -cats_161,SCE -cats_162,SCE -cats_163,PGE -cats_164,PGE -cats_165,PGE -cats_166,PGE -cats_167,PGE -cats_168,PGE -cats_169,PGE -cats_170,PGE -cats_171,PGE -cats_172,PGE -cats_173,PGE -cats_174,PGE -cats_175,SCE -cats_176,PGE -cats_177,PGE -cats_178,PACW -cats_179,PACW -cats_180,PGE -cats_181,PGE -cats_182,SCE -cats_183,PGE -cats_184,PGE -cats_185,PGE -cats_186,PGE -cats_187,PGE -cats_188,PGE -cats_189,PGE -cats_190,PGE -cats_191,PGE -cats_192,PGE -cats_193,PGE -cats_194,PGE -cats_195,PGE -cats_196,PGE -cats_197,NCNC -cats_198,PGE -cats_199,PGE -cats_200,PGE -cats_201,PGE -cats_202,SCE -cats_203,LADWP -cats_204,LADWP -cats_205,PGE -cats_206,PGE -cats_207,PGE -cats_208,SCE diff --git a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_terms.csv b/examples/kron_reduction/one_hour_kron/inputs/energy_budget_terms.csv deleted file mode 100644 index d2838fb..0000000 --- a/examples/kron_reduction/one_hour_kron/inputs/energy_budget_terms.csv +++ /dev/null @@ -1,2 +0,0 @@ -budget_term,timepoint -base_2018_hydro_month_1,2035-01-01T00:00:00.000000-0800 diff --git a/examples/kron_reduction/one_hour_kron/inputs/generators.csv b/examples/kron_reduction/one_hour_kron/inputs/generators.csv deleted file mode 100644 index 6a44b4d..0000000 --- a/examples/kron_reduction/one_hour_kron/inputs/generators.csv +++ /dev/null @@ -1,1509 +0,0 @@ -name,bus,site,technology,expand_capacity,c0_USD,c1_USDperMWh,c2_USDperMWh2,cap_existing_power_MW,cap_max_power_MW,cost_fixed_power_USDperkW,cost_variable_USDperMWh -cats_1,1793,no_capacity_factor,all other,false,102.705607,15.604003,0.058760544,4.0,4.0,0.0,0.0 -cats_2,2117,no_capacity_factor,all other,false,102.705607,15.604003,0.058760544,8.0,8.0,0.0,0.0 -cats_3,714,no_capacity_factor,all other,false,554.685123,22.409643000000003,0.094703922,1.0,1.0,0.0,0.0 -cats_4,8774,no_capacity_factor,all other,false,110.850758,15.5533405,0.046668863,31.9,31.9,0.0,0.0 -cats_5,1005,no_capacity_factor,conventional hydroelectric,false,66.7386997,14.8788144,0.041,276.2,276.2,0.0,0.0 -cats_6,103,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,12.7,12.7,0.0,0.0 -cats_7,1045,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.4,1.4,0.0,0.0 -cats_8,1046,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,5.9,5.9,0.0,0.0 -cats_9,105,no_capacity_factor,conventional hydroelectric,false,36.540858,14.8788144,0.074347899,10.0,10.0,0.0,0.0 -cats_10,106,no_capacity_factor,conventional hydroelectric,false,22.3377955,14.8788144,0.120339515,10.0,10.0,0.0,0.0 -cats_11,125,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,37.5,37.5,0.0,0.0 -cats_12,1286,no_capacity_factor,conventional hydroelectric,false,36.540858,14.8788144,0.074347899,10.0,10.0,0.0,0.0 -cats_13,1292,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,4.2,4.2,0.0,0.0 -cats_14,1294,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,10.0,10.0,0.0,0.0 -cats_15,1296,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,3.6,3.6,0.0,0.0 -cats_16,1299,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,5.0,5.0,0.0,0.0 -cats_17,1350,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,4.4,4.4,0.0,0.0 -cats_18,1360,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.0,1.0,0.0,0.0 -cats_19,1381,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,5.3,5.3,0.0,0.0 -cats_20,1408,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,5.0,5.0,0.0,0.0 -cats_21,1409,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,2.0,2.0,0.0,0.0 -cats_22,141,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,1.3,1.3,0.0,0.0 -cats_23,1425,no_capacity_factor,conventional hydroelectric,false,23.3042834,14.8788144,0.11614112700000001,20.1,20.1,0.0,0.0 -cats_24,1438,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,1.8,1.8,0.0,0.0 -cats_25,1446,no_capacity_factor,conventional hydroelectric,false,86.1224701,14.8788144,0.031561893,156.8,156.8,0.0,0.0 -cats_26,1446,no_capacity_factor,conventional hydroelectric,false,43.9716516,14.8788144,0.062200000000000005,115.5,115.5,0.0,0.0 -cats_27,1448,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,1.6,1.6,0.0,0.0 -cats_28,1457,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.2,1.2,0.0,0.0 -cats_29,1458,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.0,1.0,0.0,0.0 -cats_30,1487,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,11.5,11.5,0.0,0.0 -cats_31,1489,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,41.9,41.9,0.0,0.0 -cats_32,1489,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,67.2,67.2,0.0,0.0 -cats_33,1498,no_capacity_factor,conventional hydroelectric,false,161.930945,14.8788141,0.017017665000000005,714.0,714.0,0.0,0.0 -cats_34,1500,no_capacity_factor,conventional hydroelectric,false,73.1903316,14.8788144,0.037223309,15.3,15.3,0.0,0.0 -cats_35,1502,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,6.0,6.0,0.0,0.0 -cats_36,1528,no_capacity_factor,conventional hydroelectric,false,37.2572181,14.8788144,0.073726559,33.0,33.0,0.0,0.0 -cats_37,1572,no_capacity_factor,conventional hydroelectric,false,32.2246755,14.8788144,0.084603464,29.9,29.9,0.0,0.0 -cats_38,158,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,5.0,5.0,0.0,0.0 -cats_39,1580,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,6.1,6.1,0.0,0.0 -cats_40,1582,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,12.1,12.1,0.0,0.0 -cats_41,1584,no_capacity_factor,conventional hydroelectric,false,82.9372199,14.8788144,0.032880744,74.1,74.1,0.0,0.0 -cats_42,1585,no_capacity_factor,conventional hydroelectric,false,28.5667366,14.8788144,0.098441376,25.5,25.5,0.0,0.0 -cats_43,1586,no_capacity_factor,conventional hydroelectric,false,87.6069929,14.8788144,0.03131569,157.8,157.8,0.0,0.0 -cats_44,1586,no_capacity_factor,conventional hydroelectric,false,90.9183037,14.8788144,0.029785941000000003,161.6,161.6,0.0,0.0 -cats_45,1587,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.4,1.4,0.0,0.0 -cats_46,1593,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,29.9,29.9,0.0,0.0 -cats_47,1602,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,11.3,11.3,0.0,0.0 -cats_48,1606,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,37.5,37.5,0.0,0.0 -cats_49,1606,no_capacity_factor,conventional hydroelectric,false,42.0372347,14.8788144,0.065976133,37.5,37.5,0.0,0.0 -cats_50,1606,no_capacity_factor,conventional hydroelectric,false,42.121352,14.8788144,0.065687132,37.5,37.5,0.0,0.0 -cats_51,1629,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,8.2,8.2,0.0,0.0 -cats_52,1631,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,7.3,7.3,0.0,0.0 -cats_53,1632,no_capacity_factor,conventional hydroelectric,false,73.1903316,14.8788144,0.037223309,66.6,66.6,0.0,0.0 -cats_54,1633,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,88.4,88.4,0.0,0.0 -cats_55,1633,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,10.8,10.8,0.0,0.0 -cats_56,1634,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,31.0,31.0,0.0,0.0 -cats_57,1634,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,97.2,97.2,0.0,0.0 -cats_58,1634,no_capacity_factor,conventional hydroelectric,false,75.8585367,14.8788144,0.036962208,135.0,135.0,0.0,0.0 -cats_59,1634,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,48.6,48.6,0.0,0.0 -cats_60,1635,no_capacity_factor,conventional hydroelectric,false,32.3543419,14.8788144,0.084180748,30.0,30.0,0.0,0.0 -cats_61,1636,no_capacity_factor,conventional hydroelectric,false,105.8405,14.8788144,0.025798991000000004,190.0,190.0,0.0,0.0 -cats_62,1639,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,3.2,3.2,0.0,0.0 -cats_63,164,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.5,1.5,0.0,0.0 -cats_64,1643,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,12.8,12.8,0.0,0.0 -cats_65,1643,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,100.0,100.0,0.0,0.0 -cats_66,1644,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,2.8,2.8,0.0,0.0 -cats_67,1644,no_capacity_factor,conventional hydroelectric,false,37.8341532,14.8788144,0.071691417,140.5,140.5,0.0,0.0 -cats_68,1645,no_capacity_factor,conventional hydroelectric,false,155.128416,14.878814,0.017626567,139.5,139.5,0.0,0.0 -cats_69,1646,no_capacity_factor,conventional hydroelectric,false,62.8694967,14.8788144,0.04471446,165.0,165.0,0.0,0.0 -cats_70,166,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.3,1.3,0.0,0.0 -cats_71,1662,no_capacity_factor,conventional hydroelectric,false,29.1025112,14.8788144,0.092849808,26.4,26.4,0.0,0.0 -cats_72,1663,no_capacity_factor,conventional hydroelectric,false,23.7075931,14.8788144,0.11494648400000002,40.3,40.3,0.0,0.0 -cats_73,1718,no_capacity_factor,conventional hydroelectric,false,36.540858,14.8788144,0.074347899,19.6,19.6,0.0,0.0 -cats_74,1719,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,9.2,9.2,0.0,0.0 -cats_75,1720,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,4.4,4.4,0.0,0.0 -cats_76,1722,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,4.0,4.0,0.0,0.0 -cats_77,1723,no_capacity_factor,conventional hydroelectric,false,23.3042834,14.8788144,0.11614112700000001,18.0,18.0,0.0,0.0 -cats_78,1724,no_capacity_factor,conventional hydroelectric,false,22.8253546,14.8788144,0.11698962300000001,20.0,20.0,0.0,0.0 -cats_79,1727,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,80.1,80.1,0.0,0.0 -cats_80,1727,no_capacity_factor,conventional hydroelectric,false,58.4255407,14.8788144,0.046889973,103.4,103.4,0.0,0.0 -cats_81,1727,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,1.2,1.2,0.0,0.0 -cats_82,1728,no_capacity_factor,conventional hydroelectric,false,93.6100229,14.8788144,0.028656809,168.6,168.6,0.0,0.0 -cats_83,1729,no_capacity_factor,conventional hydroelectric,false,44.2065545,14.8788144,0.061662881,79.2,79.2,0.0,0.0 -cats_84,1729,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,2.0,2.0,0.0,0.0 -cats_85,1730,no_capacity_factor,conventional hydroelectric,false,42.9634433,14.8788144,0.064820939,141.60000000000002,141.60000000000002,0.0,0.0 -cats_86,1731,no_capacity_factor,conventional hydroelectric,false,78.1222241,14.8788144,0.035001326,140.0,140.0,0.0,0.0 -cats_87,1732,no_capacity_factor,conventional hydroelectric,false,26.2074855,14.8788144,0.104841048,3.5,3.5,0.0,0.0 -cats_88,1733,no_capacity_factor,conventional 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-cats_202,8724,no_capacity_factor,conventional hydroelectric,false,32.4200547,14.8788144,0.084144494,120.0,120.0,0.0,0.0 -cats_203,8832,no_capacity_factor,conventional hydroelectric,false,36.540858,14.8788144,0.074347899,8.8,8.8,0.0,0.0 -cats_204,8832,no_capacity_factor,conventional hydroelectric,false,32.0494007,14.8788144,0.085772205,2.8,2.8,0.0,0.0 -cats_205,99,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,8.3,8.3,0.0,0.0 -cats_206,99,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,268.7,268.7,0.0,0.0 -cats_207,99,no_capacity_factor,conventional hydroelectric,false,46.4995731,14.8788144,0.059172355,3.0,3.0,0.0,0.0 -cats_208,990,no_capacity_factor,conventional hydroelectric,false,34.6467874,14.8788144,0.078724432,3.0,3.0,0.0,0.0 -cats_209,1019,no_capacity_factor,conventional steam coal,false,79.9977839,16.01,0.03994707,55.0,55.0,0.0,133.83816000000002 -cats_210,1620,no_capacity_factor,geothermal,false,0.0,0.0,0.0,15.0,15.0,0.0,0.0 -cats_211,1620,no_capacity_factor,geothermal,false,0.0,0.0,0.0,15.0,15.0,0.0,0.0 -cats_212,1621,no_capacity_factor,geothermal,false,0.0,0.0,0.0,10.0,10.0,0.0,0.0 -cats_213,1621,no_capacity_factor,geothermal,false,0.0,0.0,0.0,44.4,44.4,0.0,0.0 -cats_214,1656,no_capacity_factor,geothermal,false,0.0,0.0,0.0,92.2,92.2,0.0,0.0 -cats_215,1657,no_capacity_factor,geothermal,false,0.0,0.0,0.0,90.0,90.0,0.0,0.0 -cats_216,1659,no_capacity_factor,geothermal,false,0.0,0.0,0.0,90.0,90.0,0.0,0.0 -cats_217,1706,no_capacity_factor,geothermal,false,0.0,0.0,0.0,10.0,10.0,0.0,0.0 -cats_218,1706,no_capacity_factor,geothermal,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_219,1707,no_capacity_factor,geothermal,false,0.0,0.0,0.0,47.5,47.5,0.0,0.0 -cats_220,1708,no_capacity_factor,geothermal,false,0.0,0.0,0.0,53.9,53.9,0.0,0.0 -cats_221,1709,no_capacity_factor,geothermal,false,0.0,0.0,0.0,39.6,39.6,0.0,0.0 -cats_222,1710,no_capacity_factor,geothermal,false,0.0,0.0,0.0,45.5,45.5,0.0,0.0 -cats_223,1711,no_capacity_factor,geothermal,false,0.0,0.0,0.0,45.5,45.5,0.0,0.0 -cats_224,1712,no_capacity_factor,geothermal,false,0.0,0.0,0.0,45.5,45.5,0.0,0.0 -cats_225,1721,no_capacity_factor,geothermal,false,0.0,0.0,0.0,81.5,81.5,0.0,0.0 -cats_226,1760,no_capacity_factor,geothermal,false,0.0,0.0,0.0,1163.0,1163.0,0.0,0.0 -cats_227,1760,no_capacity_factor,geothermal,false,0.0,0.0,0.0,78.0,78.0,0.0,0.0 -cats_228,1760,no_capacity_factor,geothermal,false,0.0,0.0,0.0,176.4,176.4,0.0,0.0 -cats_229,1762,no_capacity_factor,geothermal,false,0.0,0.0,0.0,110.0,110.0,0.0,0.0 -cats_230,1762,no_capacity_factor,geothermal,false,0.0,0.0,0.0,55.0,55.0,0.0,0.0 -cats_231,181,no_capacity_factor,geothermal,false,0.0,0.0,0.0,80.0,80.0,0.0,0.0 -cats_232,2044,no_capacity_factor,geothermal,false,0.0,0.0,0.0,58.3,58.3,0.0,0.0 -cats_233,2332,no_capacity_factor,geothermal,false,0.0,0.0,0.0,11.5,11.5,0.0,0.0 -cats_234,2405,no_capacity_factor,geothermal,false,0.0,0.0,0.0,55.0,55.0,0.0,0.0 -cats_235,8303,no_capacity_factor,geothermal,false,0.0,0.0,0.0,74.5,74.5,0.0,0.0 -cats_236,8376,no_capacity_factor,geothermal,false,0.0,0.0,0.0,25.0,25.0,0.0,0.0 -cats_237,1293,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_238,1898,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_239,2734,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_240,2740,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_241,2756,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_242,2758,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_243,2760,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_244,6690,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_245,8191,no_capacity_factor,import nw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_246,2261,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_247,2733,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_248,2776,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_249,4707,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_250,4715,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_251,4787,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_252,6676,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_253,6761,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_254,6774,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_255,6775,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_256,6780,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_257,6996,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_258,7562,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_259,7583,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_260,7604,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_261,8031,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_262,8179,no_capacity_factor,import sw,false,0.0,31.4,0.0,200.0,200.0,0.0,31.4 -cats_263,1057,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,5.4,5.4,0.0,5.246639999999999 -cats_264,1086,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,6.4,6.4,0.0,5.246639999999999 -cats_265,1199,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,11.399999999999999,11.399999999999999,0.0,5.246639999999999 -cats_266,1213,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.4,1.4,0.0,5.246639999999999 -cats_267,1264,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.0,4.0,0.0,5.246639999999999 -cats_268,1269,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.6,1.6,0.0,5.246639999999999 -cats_269,1333,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,8.0,8.0,0.0,5.246639999999999 -cats_270,1336,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.2,3.2,0.0,5.246639999999999 -cats_271,1336,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.2,3.2,0.0,5.246639999999999 -cats_272,1600,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.0,3.0,0.0,5.246639999999999 -cats_273,1607,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.4,4.4,0.0,5.246639999999999 -cats_274,1822,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.0,3.0,0.0,5.246639999999999 -cats_275,1832,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.1,1.1,0.0,5.246639999999999 -cats_276,1884,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.5,3.5,0.0,5.246639999999999 -cats_277,1904,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.6,1.6,0.0,5.246639999999999 -cats_278,1942,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.1,1.1,0.0,5.246639999999999 -cats_279,2212,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,9.2,9.2,0.0,5.246639999999999 -cats_280,46,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,2.3,2.3,0.0,5.246639999999999 -cats_281,461,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,9.2,9.2,0.0,5.246639999999999 -cats_282,465,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,6.8,6.8,0.0,5.246639999999999 -cats_283,468,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,2.2,2.2,0.0,5.246639999999999 -cats_284,582,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.0,4.0,0.0,5.246639999999999 -cats_285,638,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.4,1.4,0.0,5.246639999999999 -cats_286,692,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,23.8,23.8,0.0,5.246639999999999 -cats_287,698,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,35.7,35.7,0.0,5.246639999999999 -cats_288,761,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.800000000000001,4.800000000000001,0.0,5.246639999999999 -cats_289,7649,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.0,3.0,0.0,5.246639999999999 -cats_290,7850,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.4,4.4,0.0,5.246639999999999 -cats_291,8018,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.0,3.0,0.0,5.246639999999999 -cats_292,8148,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,3.8,3.8,0.0,5.246639999999999 -cats_293,8196,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,5.1,5.1,0.0,5.246639999999999 -cats_294,8830,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,4.4,4.4,0.0,5.246639999999999 -cats_295,8832,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,23.0,23.0,0.0,5.246639999999999 -cats_296,8843,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,1.5,1.5,0.0,5.246639999999999 -cats_297,910,no_capacity_factor,landfill gas,false,173.53,58.907,0.25325,9.0,9.0,0.0,5.246639999999999 -cats_298,1384,no_capacity_factor,municipal solid waste,false,173.53,58.907,0.25325,24.0,24.0,0.0,5.246639999999999 -cats_299,388,no_capacity_factor,municipal solid waste,false,173.53,58.907,0.25325,35.6,35.6,0.0,5.246639999999999 -cats_300,1118,no_capacity_factor,natural gas fired combined cycle,false,1547.8861,15.236961,0.016096182000000004,14.299999999999999,14.299999999999999,0.0,122.638285 -cats_301,1239,no_capacity_factor,natural gas fired combined cycle,false,985.970697,9.4610491,0.023999937000000002,154.0,154.0,0.0,81.87518499999999 -cats_302,1389,no_capacity_factor,natural gas fired combined cycle,false,800.556711,13.918461,0.027579692000000003,636.0,636.0,0.0,76.42200999999999 -cats_303,1455,no_capacity_factor,natural gas fired combined cycle,false,247.166078,8.51894613,0.169468784,31.1,31.1,0.0,89.011195 -cats_304,1499,no_capacity_factor,natural gas fired combined cycle,false,273.739392,16.3717118,0.09454125,109.3,109.3,0.0,89.67541309999999 -cats_305,1519,no_capacity_factor,natural gas fired combined cycle,false,572.947107,8.86336251,0.095998499,51.400000000000006,51.400000000000006,0.0,88.448605 -cats_306,1533,no_capacity_factor,natural gas fired combined cycle,false,365.028494,9.17539209,0.057836312,32.0,32.0,0.0,89.67541309999999 -cats_307,1589,no_capacity_factor,natural gas fired combined cycle,false,2323.40845,12.4652175,0.028192924,678.3,678.3,0.0,74.33944 -cats_308,1592,no_capacity_factor,natural gas fired combined cycle,false,460.953869,7.95071277,0.12511162000000003,80.0,80.0,0.0,89.67541309999999 -cats_309,1595,no_capacity_factor,natural gas fired combined cycle,false,1512.3587,10.956217500000001,0.027419538,619.7,619.7,0.0,73.268545 -cats_310,1599,no_capacity_factor,natural gas fired combined cycle,false,1110.30224,9.34812416,0.014862244000000002,155.6,155.6,0.0,155.50538499999996 -cats_311,1653,no_capacity_factor,natural gas fired combined cycle,false,222.512216,8.40984319,0.195165562,36.2,36.2,0.0,103.96424499999999 -cats_312,1660,no_capacity_factor,natural gas fired combined cycle,false,1565.83201,9.79517349,0.025323319,133.2,133.2,0.0,86.839795 -cats_313,1671,no_capacity_factor,natural gas fired combined cycle,false,2499.46439,12.5488628,0.027655331000000002,623.0,623.0,0.0,72.409855 -cats_314,1693,no_capacity_factor,natural gas fired combined cycle,false,230.144388,16.3717119,0.11955343,120.5,120.5,0.0,135.92823999999996 -cats_315,1694,no_capacity_factor,natural gas fired combined cycle,false,2412.81753,12.5075294,0.027768316,387.6,387.6,0.0,89.67541309999999 -cats_316,1699,no_capacity_factor,natural gas fired combined cycle,false,772.625301,8.94241382,0.087384278,180.1,180.1,0.0,115.295005 -cats_317,1775,no_capacity_factor,natural gas fired combined cycle,false,968.448887,9.40230679,0.047207877,149.39999999999998,149.39999999999998,0.0,89.88962499999998 -cats_318,1778,no_capacity_factor,natural gas fired combined cycle,false,878.874372,13.4742144,0.022715841,556.8,556.8,0.0,70.92442 -cats_319,1787,no_capacity_factor,natural gas fired combined cycle,false,708.274969,13.5748531,0.028668281000000004,288.9,288.9,0.0,73.04647 -cats_320,1797,no_capacity_factor,natural gas fired combined cycle,false,2334.13617,9.86947683,0.009868153,336.1,336.1,0.0,85.65046 -cats_321,1801,no_capacity_factor,natural gas fired combined cycle,false,438.904604,16.3717118,0.061066146,98.2,98.2,0.0,89.96364999999999 -cats_322,1806,no_capacity_factor,natural gas fired combined cycle,false,1214.01557,9.36133114,0.05419084,300.6,300.6,0.0,79.36327 -cats_323,1820,no_capacity_factor,natural gas fired combined cycle,false,2297.80403,12.4436279,0.027652759,635.0,635.0,0.0,75.57319 -cats_324,1821,no_capacity_factor,natural gas fired combined cycle,false,1683.4498,9.8240635,0.007277085,130.0,130.0,0.0,90.79272999999999 -cats_325,1834,no_capacity_factor,natural gas fired combined cycle,false,1941.15289,9.89195883,0.016403498,852.0,852.0,0.0,74.87241999999999 -cats_326,1847,no_capacity_factor,natural gas fired combined cycle,false,240.823874,8.45575669,0.191234446,30.8,30.8,0.0,90.087025 -cats_327,1879,no_capacity_factor,natural gas fired combined cycle,false,401.19412,16.3717118,0.067573963,33.0,33.0,0.0,89.67541309999999 -cats_328,1937,no_capacity_factor,natural gas fired combined cycle,false,1006.75797,13.5099476,0.019216809,685.2,685.2,0.0,89.67541309999999 -cats_329,2022,no_capacity_factor,natural gas fired combined cycle,false,563.76042,8.56486783,0.102797947,49.0,49.0,0.0,88.97171499999999 -cats_330,2107,no_capacity_factor,natural gas fired combined cycle,false,1269.56348,10.0233692,0.030706901,712.4,712.4,0.0,73.26361 -cats_331,2117,no_capacity_factor,natural gas fired combined cycle,false,572.658144,13.314779700000003,0.007556471,247.4,247.4,0.0,91.37999499999998 -cats_332,2121,no_capacity_factor,natural gas fired combined cycle,false,878.874372,13.4742144,0.022715841,943.5,943.5,0.0,74.46775 -cats_333,2136,no_capacity_factor,natural gas fired combined cycle,false,167.188707,7.93857786,0.22901104900000002,28.5,28.5,0.0,120.98999499999998 -cats_334,220,no_capacity_factor,natural gas fired combined cycle,false,2334.13617,9.86947683,0.009868153,779.0,779.0,0.0,71.66960499999999 -cats_335,2223,no_capacity_factor,natural gas fired combined cycle,false,878.874372,13.4742144,0.022715841,165.0,165.0,0.0,80.80429 -cats_336,2300,no_capacity_factor,natural gas fired combined cycle,false,874.243191,13.471932000000002,0.023001417000000003,306.1,306.1,0.0,88.68548499999999 -cats_337,2324,no_capacity_factor,natural gas fired combined cycle,false,1547.8861,15.236961,0.016096182000000004,13.399999999999999,13.399999999999999,0.0,89.67541309999999 -cats_338,2384,no_capacity_factor,natural gas fired combined cycle,false,966.27283,9.22003628,0.051003293,61.5,61.5,0.0,85.44812499999999 -cats_339,2401,no_capacity_factor,natural gas fired combined cycle,false,1415.75836,10.436742900000002,0.030006828000000003,629.9000000000001,629.9000000000001,0.0,82.793095 -cats_340,2401,no_capacity_factor,natural gas fired combined cycle,false,878.874372,13.4742144,0.022715841,678.0,678.0,0.0,89.67541309999999 -cats_341,282,no_capacity_factor,natural gas fired combined cycle,false,749.289673,13.8353416,0.000678007,1156.0,1156.0,0.0,73.75711 -cats_342,346,no_capacity_factor,natural gas fired combined cycle,false,1399.03018,8.49648297,0.045648313,245.6,245.6,0.0,89.67541309999999 -cats_343,363,no_capacity_factor,natural gas fired combined cycle,false,340.343109,7.67744915,0.091411024,405.0,405.0,0.0,119.84507499999998 -cats_344,384,no_capacity_factor,natural gas fired combined cycle,false,907.718723,8.16964701,0.070011402,107.39999999999999,107.39999999999999,0.0,89.67541309999999 -cats_345,426,no_capacity_factor,natural gas fired combined cycle,false,848.043789,15.9947772,0.032401462,87.0,87.0,0.0,116.67186999999998 -cats_346,426,no_capacity_factor,natural gas fired combined cycle,false,878.874372,13.4742144,0.022715841,13.0,13.0,0.0,89.67541309999999 -cats_347,519,no_capacity_factor,natural gas fired combined cycle,false,479.744314,16.3717118,0.052303032,43.0,43.0,0.0,89.67541309999999 -cats_348,552,no_capacity_factor,natural gas fired combined cycle,false,476.575454,8.15261569,0.11243294700000002,130.0,130.0,0.0,130.91428 -cats_349,7751,no_capacity_factor,natural gas fired combined cycle,false,411.887105,16.3717118,0.066698734,276.70000000000005,276.70000000000005,0.0,98.328475 -cats_350,7773,no_capacity_factor,natural gas fired combined 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gas fired combustion turbine,false,1427.41303,44.9151794,0.082991653,4.4,4.4,0.0,127.33919499999998 -cats_372,1326,no_capacity_factor,natural gas fired combustion turbine,false,284.095812,14.5098437,0.056610378,49.9,49.9,0.0,127.6073893556701 -cats_373,1330,no_capacity_factor,natural gas fired combustion turbine,false,284.310681,14.2690889,0.051498059000000006,47.0,47.0,0.0,113.93573499999998 -cats_374,1389,no_capacity_factor,natural gas fired combustion turbine,false,1427.41303,44.9151794,0.082991653,69.8,69.8,0.0,81.19200999999998 -cats_375,1418,no_capacity_factor,natural gas fired combustion turbine,false,278.09026,15.0260079,0.046209611,60.5,60.5,0.0,119.91201999999998 -cats_376,1443,no_capacity_factor,natural gas fired combustion turbine,false,315.964182,13.502241700000003,0.051140815,3.5,3.5,0.0,127.6073893556701 -cats_377,1481,no_capacity_factor,natural gas fired combustion turbine,false,283.415806,14.512150300000002,0.05553775,49.8,49.8,0.0,110.49604 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fired combustion turbine,false,300.659481,14.2331099,0.064041704,60.5,60.5,0.0,107.19945999999999 -cats_412,1855,no_capacity_factor,natural gas fired combustion turbine,false,428.748492,15.1584724,0.035004509,800.0,800.0,0.0,127.6073893556701 -cats_413,1858,no_capacity_factor,natural gas fired combustion turbine,false,282.759749,14.5490693,0.054250157,149.7,149.7,0.0,111.50277999999999 -cats_414,1859,no_capacity_factor,natural gas fired combustion turbine,false,315.964182,13.502241700000003,0.051140815,40.0,40.0,0.0,141.10290999999998 -cats_415,1861,no_capacity_factor,natural gas fired combustion turbine,false,283.415806,14.512150300000002,0.05553775,196.0,196.0,0.0,103.31067999999999 -cats_416,1872,no_capacity_factor,natural gas fired combustion turbine,false,139.009799,16.2591415,0.17644402400000003,92.4,92.4,0.0,167.490355 -cats_417,1878,no_capacity_factor,natural gas fired combustion turbine,false,284.095812,14.5098437,0.056610378,106.0,106.0,0.0,127.6073893556701 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turbine,false,315.964182,13.502241700000003,0.051140815,13.6,13.6,0.0,127.6073893556701 -cats_425,1924,no_capacity_factor,natural gas fired combustion turbine,false,141.739131,16.0912893,0.196394076,48.8,48.8,0.0,120.834865 -cats_426,1937,no_capacity_factor,natural gas fired combustion turbine,false,315.964182,13.502241700000003,0.051140815,6.0,6.0,0.0,235.69205499999998 -cats_427,1975,no_capacity_factor,natural gas fired combustion turbine,false,301.625885,13.6908428,0.062218840000000004,92.2,92.2,0.0,115.82583999999999 -cats_428,198,no_capacity_factor,natural gas fired combustion turbine,false,301.04705,14.1903896,0.064737135,121.0,121.0,0.0,127.6073893556701 -cats_429,1997,no_capacity_factor,natural gas fired combustion turbine,false,282.657965,14.5884532,0.053668806,49.8,49.8,0.0,123.74157999999998 -cats_430,2017,no_capacity_factor,natural gas fired combustion turbine,false,1427.41303,44.9151794,0.082991653,16.4,16.4,0.0,127.6073893556701 -cats_431,2030,no_capacity_factor,natural 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biomass,false,554.685123,22.409643000000003,0.094703922,1.7999999999999998,1.7999999999999998,0.0,5.246639999999999 -cats_743,68,no_capacity_factor,other waste biomass,false,127.93,34.988,0.11593,29.1,29.1,0.0,5.246639999999999 -cats_744,68,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,4.0,4.0,0.0,5.246639999999999 -cats_745,713,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,7.5,7.5,0.0,5.246639999999999 -cats_746,714,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,15.0,15.0,0.0,5.246639999999999 -cats_747,7823,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,1.1,1.1,0.0,5.246639999999999 -cats_748,8000,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,1.5,1.5,0.0,5.246639999999999 -cats_749,8730,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,33.0,33.0,0.0,5.246639999999999 -cats_750,8856,no_capacity_factor,other waste biomass,false,554.685123,22.409643000000003,0.094703922,1.4,1.4,0.0,5.246639999999999 -cats_751,1804,no_capacity_factor,petroleum liquids,false,1427.41303,44.9151794,0.082991653,71.2,71.2,0.0,421.38855 -cats_752,463,no_capacity_factor,petroleum liquids,false,1427.41303,44.9151794,0.082991653,11.3,11.3,0.0,252.66911999999996 -cats_753,8199,no_capacity_factor,petroleum liquids,false,57.6,25.05,0.29833333300000003,4.5,4.5,0.0,370.82661 -cats_754,8495,no_capacity_factor,petroleum liquids,false,546.49488,48.2276671,0.8973301690000001,24.9,24.9,0.0,270.71021999999994 -cats_755,1000,pvu1000,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_756,1000,pvu1000,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_757,1002,pvu1002,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_758,1006,pvu1006,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_759,101,pvu101,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_760,1013,pvu1013,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_761,1013,pvu1013,solar photovoltaic,false,0.0,0.0,0.0,12.0,12.0,0.0,0.0 -cats_762,1013,pvu1013,solar photovoltaic,false,0.0,0.0,0.0,18.5,18.5,0.0,0.0 -cats_763,1016,pvu1016,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_764,1023,pvu1023,solar photovoltaic,false,0.0,0.0,0.0,0.9,0.9,0.0,0.0 -cats_765,1025,pvu1025,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_766,1025,pvu1025,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_767,1025,pvu1025,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_768,1025,pvu1025,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_769,1025,pvu1025,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_770,1031,pvu1031,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_771,1033,pvu1033,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_772,1035,pvu1035,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_773,1037,pvu1037,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_774,1038,pvu1038,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_775,1041,pvu1041,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_776,1051,pvu1051,solar photovoltaic,false,0.0,0.0,0.0,26.0,26.0,0.0,0.0 -cats_777,1051,pvu1051,solar photovoltaic,false,0.0,0.0,0.0,6.3,6.3,0.0,0.0 -cats_778,1053,pvu1053,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_779,1059,pvu1059,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_780,1061,pvu1061,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_781,1061,pvu1061,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_782,1061,pvu1061,solar photovoltaic,false,0.0,0.0,0.0,4.3,4.3,0.0,0.0 -cats_783,108,pvu108,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_784,108,pvu108,solar photovoltaic,false,0.0,0.0,0.0,2.4,2.4,0.0,0.0 -cats_785,108,pvu108,solar photovoltaic,false,0.0,0.0,0.0,1.6,1.6,0.0,0.0 -cats_786,1080,pvu1080,solar photovoltaic,false,0.0,0.0,0.0,1.7,1.7,0.0,0.0 -cats_787,1084,pvu1084,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_788,1085,pvu1085,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_789,1085,pvu1085,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 -cats_790,1085,pvu1085,solar photovoltaic,false,0.0,0.0,0.0,1.4,1.4,0.0,0.0 -cats_791,109,pvu109,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_792,1090,pvu1090,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_793,1096,pvu1096,solar photovoltaic,false,0.0,0.0,0.0,2.9,2.9,0.0,0.0 -cats_794,111,pvu111,solar photovoltaic,false,0.0,0.0,0.0,140.0,140.0,0.0,0.0 -cats_795,1110,pvu1110,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_796,1114,pvu1114,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_797,1118,pvu1118,solar photovoltaic,false,0.0,0.0,0.0,0.7999999999999999,0.7999999999999999,0.0,0.0 -cats_798,113,pvu113,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_799,114,pvu114,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_800,114,pvu114,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_801,1143,pvu1143,solar photovoltaic,false,0.0,0.0,0.0,4.5,4.5,0.0,0.0 -cats_802,1146,pvu1146,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_803,116,pvu116,solar photovoltaic,false,0.0,0.0,0.0,19.0,19.0,0.0,0.0 -cats_804,116,pvu116,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_805,116,pvu116,solar photovoltaic,false,0.0,0.0,0.0,9.0,9.0,0.0,0.0 -cats_806,116,pvu116,solar photovoltaic,false,0.0,0.0,0.0,205.3,205.3,0.0,0.0 -cats_807,116,pvu116,solar photovoltaic,false,0.0,0.0,0.0,202.5,202.5,0.0,0.0 -cats_808,1168,pvu1168,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_809,1172,pvu1172,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_810,1176,pvu1176,solar photovoltaic,false,0.0,0.0,0.0,249.8,249.8,0.0,0.0 -cats_811,1176,pvu1176,solar photovoltaic,false,0.0,0.0,0.0,585.9,585.9,0.0,0.0 -cats_812,1178,pvu1178,solar photovoltaic,false,0.0,0.0,0.0,130.0,130.0,0.0,0.0 -cats_813,1178,pvu1178,solar photovoltaic,false,0.0,0.0,0.0,150.0,150.0,0.0,0.0 -cats_814,1180,pvu1180,solar photovoltaic,false,0.0,0.0,0.0,4.5,4.5,0.0,0.0 -cats_815,1183,pvu1183,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_816,1183,pvu1183,solar photovoltaic,false,0.0,0.0,0.0,1.6,1.6,0.0,0.0 -cats_817,1188,pvu1188,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_818,1194,pvu1194,solar photovoltaic,false,0.0,0.0,0.0,3.4,3.4,0.0,0.0 -cats_819,1206,pvu1206,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_820,121,pvu121,solar photovoltaic,false,0.0,0.0,0.0,10.0,10.0,0.0,0.0 -cats_821,121,pvu121,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_822,1241,pvu1241,solar photovoltaic,false,0.0,0.0,0.0,1.7,1.7,0.0,0.0 -cats_823,1247,pvu1247,solar photovoltaic,false,0.0,0.0,0.0,1.4,1.4,0.0,0.0 -cats_824,1251,pvu1251,solar photovoltaic,false,0.0,0.0,0.0,1.7,1.7,0.0,0.0 -cats_825,1264,pvu1264,solar photovoltaic,false,0.0,0.0,0.0,14.4,14.4,0.0,0.0 -cats_826,1268,pvu1268,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 -cats_827,127,pvu127,solar photovoltaic,false,0.0,0.0,0.0,2.6,2.6,0.0,0.0 -cats_828,127,pvu127,solar photovoltaic,false,0.0,0.0,0.0,1.4,1.4,0.0,0.0 -cats_829,127,pvu127,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_830,1284,pvu1284,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_831,131,pvu131,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_832,131,pvu131,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_833,1320,pvu1320,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_834,1326,pvu1326,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_835,1330,pvu1330,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_836,1336,pvu1336,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_837,1338,pvu1338,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_838,1338,pvu1338,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_839,1344,pvu1344,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_840,1354,pvu1354,solar photovoltaic,false,0.0,0.0,0.0,25.0,25.0,0.0,0.0 -cats_841,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,61.6,61.6,0.0,0.0 -cats_842,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_843,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,40.0,40.0,0.0,0.0 -cats_844,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_845,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,50.0,50.0,0.0,0.0 -cats_846,137,pvu137,solar photovoltaic,false,0.0,0.0,0.0,50.0,50.0,0.0,0.0 -cats_847,138,pvu138,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_848,1382,pvu1382,solar photovoltaic,false,0.0,0.0,0.0,40.0,40.0,0.0,0.0 -cats_849,1384,pvu1384,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_850,1391,pvu1391,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_851,1402,pvu1402,solar photovoltaic,false,0.0,0.0,0.0,8.4,8.4,0.0,0.0 -cats_852,1412,pvu1412,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_853,1412,pvu1412,solar photovoltaic,false,0.0,0.0,0.0,50.0,50.0,0.0,0.0 -cats_854,1412,pvu1412,solar photovoltaic,false,0.0,0.0,0.0,20.2,20.2,0.0,0.0 -cats_855,1412,pvu1412,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_856,1413,pvu1413,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_857,1418,pvu1418,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_858,1418,pvu1418,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_859,1419,pvu1419,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_860,1421,pvu1421,solar photovoltaic,false,0.0,0.0,0.0,3.4,3.4,0.0,0.0 -cats_861,1423,pvu1423,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_862,1426,pvu1426,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_863,1429,pvu1429,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_864,1429,pvu1429,solar photovoltaic,false,0.0,0.0,0.0,4.5,4.5,0.0,0.0 -cats_865,143,pvu143,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_866,1431,pvu1431,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 -cats_867,1435,pvu1435,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_868,1435,pvu1435,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_869,1435,pvu1435,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_870,144,pvu144,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_871,144,pvu144,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_872,1442,pvu1442,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_873,1447,pvu1447,solar photovoltaic,false,0.0,0.0,0.0,3.6,3.6,0.0,0.0 -cats_874,145,pvu145,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_875,145,pvu145,solar photovoltaic,false,0.0,0.0,0.0,2.4,2.4,0.0,0.0 -cats_876,1451,pvu1451,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_877,1455,pvu1455,solar photovoltaic,false,0.0,0.0,0.0,3.7,3.7,0.0,0.0 -cats_878,1461,pvu1461,solar photovoltaic,false,0.0,0.0,0.0,2.9,2.9,0.0,0.0 -cats_879,1464,pvu1464,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_880,147,pvu147,solar photovoltaic,false,0.0,0.0,0.0,2.8,2.8,0.0,0.0 -cats_881,1470,pvu1470,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_882,1487,pvu1487,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_883,1487,pvu1487,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_884,149,pvu149,solar photovoltaic,false,0.0,0.0,0.0,60.0,60.0,0.0,0.0 -cats_885,1505,pvu1505,solar photovoltaic,false,0.0,0.0,0.0,19.2,19.2,0.0,0.0 -cats_886,1506,pvu1506,solar photovoltaic,false,0.0,0.0,0.0,40.0,40.0,0.0,0.0 -cats_887,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,6.8,6.8,0.0,0.0 -cats_888,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_889,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_890,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_891,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_892,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_893,1508,pvu1508,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_894,1521,pvu1521,solar photovoltaic,false,0.0,0.0,0.0,2.9,2.9,0.0,0.0 -cats_895,1521,pvu1521,solar photovoltaic,false,0.0,0.0,0.0,1.9,1.9,0.0,0.0 -cats_896,1523,pvu1523,solar photovoltaic,false,0.0,0.0,0.0,6.0,6.0,0.0,0.0 -cats_897,1541,pvu1541,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_898,1541,pvu1541,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_899,1541,pvu1541,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_900,155,pvu155,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_901,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,37.8,37.8,0.0,0.0 -cats_902,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,47.3,47.3,0.0,0.0 -cats_903,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,56.0,56.0,0.0,0.0 -cats_904,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,56.0,56.0,0.0,0.0 -cats_905,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,50.0,50.0,0.0,0.0 -cats_906,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,105.0,105.0,0.0,0.0 -cats_907,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,155.0,155.0,0.0,0.0 -cats_908,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,60.0,60.0,0.0,0.0 -cats_909,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,90.0,90.0,0.0,0.0 -cats_910,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_911,1553,pvu1553,solar photovoltaic,false,0.0,0.0,0.0,1.9,1.9,0.0,0.0 -cats_912,1567,pvu1567,solar photovoltaic,false,0.0,0.0,0.0,7.6,7.6,0.0,0.0 -cats_913,1577,pvu1577,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_914,1578,pvu1578,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_915,16,pvu16,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_916,1601,pvu1601,solar photovoltaic,false,0.0,0.0,0.0,10.5,10.5,0.0,0.0 -cats_917,1603,pvu1603,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_918,1623,pvu1623,solar photovoltaic,false,0.0,0.0,0.0,3.3,3.3,0.0,0.0 -cats_919,1640,pvu1640,solar photovoltaic,false,0.0,0.0,0.0,200.0,200.0,0.0,0.0 -cats_920,1650,pvu1650,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_921,1661,pvu1661,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_922,1666,pvu1666,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_923,1674,pvu1674,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_924,1676,pvu1676,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_925,17,pvu17,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_926,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_927,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,2.9,2.9,0.0,0.0 -cats_928,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_929,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_930,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,2.2,2.2,0.0,0.0 -cats_931,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 -cats_932,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,2.9,2.9,0.0,0.0 -cats_933,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_934,1703,pvu1703,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_935,171,pvu171,solar photovoltaic,false,0.0,0.0,0.0,2.2,2.2,0.0,0.0 -cats_936,1712,pvu1712,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_937,1712,pvu1712,solar photovoltaic,false,0.0,0.0,0.0,30.0,30.0,0.0,0.0 -cats_938,1712,pvu1712,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_939,1712,pvu1712,solar photovoltaic,false,0.0,0.0,0.0,50.0,50.0,0.0,0.0 -cats_940,1713,pvu1713,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_941,1763,pvu1763,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_942,1776,pvu1776,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_943,1776,pvu1776,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_944,1778,pvu1778,solar photovoltaic,false,0.0,0.0,0.0,10.8,10.8,0.0,0.0 -cats_945,1778,pvu1778,solar photovoltaic,false,0.0,0.0,0.0,160.0,160.0,0.0,0.0 -cats_946,1796,pvu1796,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_947,1809,pvu1809,solar photovoltaic,false,0.0,0.0,0.0,1.6,1.6,0.0,0.0 -cats_948,181,pvu181,solar photovoltaic,false,0.0,0.0,0.0,5.7,5.7,0.0,0.0 -cats_949,181,pvu181,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_950,1813,pvu1813,solar photovoltaic,false,0.0,0.0,0.0,2.2,2.2,0.0,0.0 -cats_951,182,pvu182,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_952,182,pvu182,solar photovoltaic,false,0.0,0.0,0.0,30.0,30.0,0.0,0.0 -cats_953,182,pvu182,solar photovoltaic,false,0.0,0.0,0.0,70.0,70.0,0.0,0.0 -cats_954,1833,pvu1833,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_955,1833,pvu1833,solar photovoltaic,false,0.0,0.0,0.0,13.8,13.8,0.0,0.0 -cats_956,1834,pvu1834,solar photovoltaic,false,0.0,0.0,0.0,100.0,100.0,0.0,0.0 -cats_957,1835,pvu1835,solar photovoltaic,false,0.0,0.0,0.0,25.3,25.3,0.0,0.0 -cats_958,1844,pvu1844,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_959,1844,pvu1844,solar photovoltaic,false,0.0,0.0,0.0,2.6,2.6,0.0,0.0 -cats_960,1846,pvu1846,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_961,1846,pvu1846,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_962,1846,pvu1846,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_963,1846,pvu1846,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_964,1853,pvu1853,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_965,1858,pvu1858,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_966,1858,pvu1858,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_967,1875,pvu1875,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_968,1876,pvu1876,solar photovoltaic,false,0.0,0.0,0.0,1.6,1.6,0.0,0.0 -cats_969,1879,pvu1879,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_970,1885,pvu1885,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_971,1885,pvu1885,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_972,1885,pvu1885,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_973,19,pvu19,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_974,1902,pvu1902,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_975,1910,pvu1910,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_976,1923,pvu1923,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_977,1923,pvu1923,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_978,1923,pvu1923,solar photovoltaic,false,0.0,0.0,0.0,2.3,2.3,0.0,0.0 -cats_979,1926,pvu1926,solar photovoltaic,false,0.0,0.0,0.0,1.4,1.4,0.0,0.0 -cats_980,1945,pvu1945,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_981,1952,pvu1952,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_982,1952,pvu1952,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_983,1952,pvu1952,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_984,1953,pvu1953,solar photovoltaic,false,0.0,0.0,0.0,7.0,7.0,0.0,0.0 -cats_985,1953,pvu1953,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_986,1955,pvu1955,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_987,1960,pvu1960,solar photovoltaic,false,0.0,0.0,0.0,4.4,4.4,0.0,0.0 -cats_988,1969,pvu1969,solar photovoltaic,false,0.0,0.0,0.0,21.3,21.3,0.0,0.0 -cats_989,1970,pvu1970,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_990,1970,pvu1970,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_991,1973,pvu1973,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_992,1979,pvu1979,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_993,1985,pvu1985,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_994,1993,pvu1993,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_995,1993,pvu1993,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_996,1993,pvu1993,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_997,1993,pvu1993,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_998,1993,pvu1993,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_999,1998,pvu1998,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_1000,200,pvu200,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1001,200,pvu200,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1002,2000,pvu2000,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1003,2001,pvu2001,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 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photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_1017,2063,pvu2063,solar photovoltaic,false,0.0,0.0,0.0,1.9,1.9,0.0,0.0 -cats_1018,2065,pvu2065,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1019,2068,pvu2068,solar photovoltaic,false,0.0,0.0,0.0,7.4,7.4,0.0,0.0 -cats_1020,207,pvu207,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_1021,2077,pvu2077,solar photovoltaic,false,0.0,0.0,0.0,1.7,1.7,0.0,0.0 -cats_1022,2080,pvu2080,solar photovoltaic,false,0.0,0.0,0.0,1.9,1.9,0.0,0.0 -cats_1023,2084,pvu2084,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1024,209,pvu209,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_1025,209,pvu209,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1026,2091,pvu2091,solar photovoltaic,false,0.0,0.0,0.0,1.6,1.6,0.0,0.0 -cats_1027,2110,pvu2110,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_1028,2113,pvu2113,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_1029,2116,pvu2116,solar 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photovoltaic,false,0.0,0.0,0.0,2.2,2.2,0.0,0.0 -cats_1043,219,pvu219,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_1044,2196,pvu2196,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_1045,2199,pvu2199,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1046,2202,pvu2202,solar photovoltaic,false,0.0,0.0,0.0,60.0,60.0,0.0,0.0 -cats_1047,2202,pvu2202,solar photovoltaic,false,0.0,0.0,0.0,16.6,16.6,0.0,0.0 -cats_1048,2202,pvu2202,solar photovoltaic,false,0.0,0.0,0.0,15.0,15.0,0.0,0.0 -cats_1049,2202,pvu2202,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1050,2210,pvu2210,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 -cats_1051,2235,pvu2235,solar photovoltaic,false,0.0,0.0,0.0,313.7,313.7,0.0,0.0 -cats_1052,2235,pvu2235,solar photovoltaic,false,0.0,0.0,0.0,249.7,249.7,0.0,0.0 -cats_1053,2235,pvu2235,solar photovoltaic,false,0.0,0.0,0.0,80.0,80.0,0.0,0.0 -cats_1054,2235,pvu2235,solar photovoltaic,false,0.0,0.0,0.0,125.0,125.0,0.0,0.0 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photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1068,2264,pvu2264,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1069,2267,pvu2267,solar photovoltaic,false,0.0,0.0,0.0,1.2,1.2,0.0,0.0 -cats_1070,2268,pvu2268,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1071,2268,pvu2268,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1072,227,pvu227,solar photovoltaic,false,0.0,0.0,0.0,27.0,27.0,0.0,0.0 -cats_1073,2275,pvu2275,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1074,2276,pvu2276,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1075,2276,pvu2276,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1076,2276,pvu2276,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1077,2277,pvu2277,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1078,2280,pvu2280,solar photovoltaic,false,0.0,0.0,0.0,11.1,11.1,0.0,0.0 -cats_1079,2283,pvu2283,solar photovoltaic,false,0.0,0.0,0.0,1.8,1.8,0.0,0.0 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photovoltaic,false,0.0,0.0,0.0,151.1,151.1,0.0,0.0 -cats_1093,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,100.0,100.0,0.0,0.0 -cats_1094,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,75.0,75.0,0.0,0.0 -cats_1095,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1096,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,107.9,107.9,0.0,0.0 -cats_1097,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,54.0,54.0,0.0,0.0 -cats_1098,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,54.0,54.0,0.0,0.0 -cats_1099,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,111.2,111.2,0.0,0.0 -cats_1100,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,192.0,192.0,0.0,0.0 -cats_1101,2314,pvu2314,solar photovoltaic,false,0.0,0.0,0.0,128.0,128.0,0.0,0.0 -cats_1102,2315,pvu2315,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1103,2324,pvu2324,solar photovoltaic,false,0.0,0.0,0.0,4.5,4.5,0.0,0.0 -cats_1104,2325,pvu2325,solar photovoltaic,false,0.0,0.0,0.0,23.0,23.0,0.0,0.0 -cats_1105,2325,pvu2325,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1106,2325,pvu2325,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1107,2329,pvu2329,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1108,2332,pvu2332,solar photovoltaic,false,0.0,0.0,0.0,6.0,6.0,0.0,0.0 -cats_1109,2334,pvu2334,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_1110,2334,pvu2334,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_1111,235,pvu235,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1112,235,pvu235,solar photovoltaic,false,0.0,0.0,0.0,10.0,10.0,0.0,0.0 -cats_1113,2351,pvu2351,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1114,2351,pvu2351,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1115,2351,pvu2351,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1116,2353,pvu2353,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 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photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1425,8673,pvu8673,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1426,8690,pvu8690,solar photovoltaic,false,0.0,0.0,0.0,15.0,15.0,0.0,0.0 -cats_1427,8690,pvu8690,solar photovoltaic,false,0.0,0.0,0.0,19.5,19.5,0.0,0.0 -cats_1428,8691,pvu8691,solar photovoltaic,false,0.0,0.0,0.0,12.0,12.0,0.0,0.0 -cats_1429,8704,pvu8704,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1430,8739,pvu8739,solar photovoltaic,false,0.0,0.0,0.0,3.1,3.1,0.0,0.0 -cats_1431,8766,pvu8766,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1432,877,pvu877,solar photovoltaic,false,0.0,0.0,0.0,17.0,17.0,0.0,0.0 -cats_1433,877,pvu877,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1434,877,pvu877,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1435,877,pvu877,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1436,8775,pvu8775,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1437,879,pvu879,solar photovoltaic,false,0.0,0.0,0.0,1.3,1.3,0.0,0.0 -cats_1438,88,pvu88,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_1439,883,pvu883,solar photovoltaic,false,0.0,0.0,0.0,2.7,2.7,0.0,0.0 -cats_1440,8830,pvu8830,solar photovoltaic,false,0.0,0.0,0.0,1.1,1.1,0.0,0.0 -cats_1441,8833,pvu8833,solar photovoltaic,false,0.0,0.0,0.0,0.6000000000000001,0.6000000000000001,0.0,0.0 -cats_1442,8833,pvu8833,solar photovoltaic,false,0.0,0.0,0.0,3.2,3.2,0.0,0.0 -cats_1443,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,19.8,19.8,0.0,0.0 -cats_1444,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,14.0,14.0,0.0,0.0 -cats_1445,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1446,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1447,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,20.0,20.0,0.0,0.0 -cats_1448,8865,pvu8865,solar photovoltaic,false,0.0,0.0,0.0,15.0,15.0,0.0,0.0 -cats_1449,8865,pvu8865,solar 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photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1463,945,pvu945,solar photovoltaic,false,0.0,0.0,0.0,7.0,7.0,0.0,0.0 -cats_1464,957,pvu957,solar photovoltaic,false,0.0,0.0,0.0,3.5,3.5,0.0,0.0 -cats_1465,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1466,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1467,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1468,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1469,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1470,974,pvu974,solar photovoltaic,false,0.0,0.0,0.0,5.0,5.0,0.0,0.0 -cats_1471,975,pvu975,solar photovoltaic,false,0.0,0.0,0.0,3.0,3.0,0.0,0.0 -cats_1472,984,pvu984,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1473,987,pvu987,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1474,987,pvu987,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1475,99,pvu99,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1476,990,pvu990,solar photovoltaic,false,0.0,0.0,0.0,6.0,6.0,0.0,0.0 -cats_1477,990,pvu990,solar photovoltaic,false,0.0,0.0,0.0,2.0,2.0,0.0,0.0 -cats_1478,990,pvu990,solar photovoltaic,false,0.0,0.0,0.0,4.2,4.2,0.0,0.0 -cats_1479,993,pvu993,solar photovoltaic,false,0.0,0.0,0.0,1.5,1.5,0.0,0.0 -cats_1480,995,pvu995,solar photovoltaic,false,0.0,0.0,0.0,4.0,4.0,0.0,0.0 -cats_1481,998,pvu998,solar photovoltaic,false,0.0,0.0,0.0,2.5,2.5,0.0,0.0 -cats_1482,999,pvu999,solar photovoltaic,false,0.0,0.0,0.0,1.0,1.0,0.0,0.0 -cats_1483,7911,pvu7911,solar thermal without energy storage,false,0.0,0.0,0.0,92.0,92.0,0.0,3.95766 -cats_1484,7911,pvu7911,solar thermal without energy storage,false,0.0,0.0,0.0,280.0,280.0,0.0,3.95766 -cats_1485,7919,pvu7919,solar thermal without energy storage,false,0.0,0.0,0.0,133.4,133.4,0.0,3.95766 -cats_1486,7919,pvu7919,solar thermal without energy storage,false,0.0,0.0,0.0,133.4,133.4,0.0,3.95766 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-name,start,end,timepoint_duration_hr,timeseries_scale_to_period,timepoint_selection_method,number_of_timepoints -winter,2035-01-01T00:00:00.000000-0800,2035-01-01T01:00:00.000000-0800,1,4,all,1 \ No newline at end of file diff --git a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/costs_summary.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/costs_summary.csv deleted file mode 100644 index 2bc5b50..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,3743305.8303562854 -CostPerPeriod_USD,0.0 -TotalCost_USD,3743305.8303562854 diff --git a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/generator_capacity.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/generator_capacity.csv deleted file mode 100644 index 5684aaa..0000000 --- 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file mode 100644 index f3a0b51..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/solver_status.csv +++ /dev/null @@ -1,5 +0,0 @@ -attribute,value -SolverName,mosek_direct -SolverStatus,ok -TerminationCondition,optimal -TimeSpent_seconds,1.1520068645477295 diff --git a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_capacity.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_capacity.csv deleted file mode 100644 index 6f9c68d..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,119 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -cats_1,1,0.0,0.0 -cats_2,1,0.0,0.0 -cats_3,1,0.0,0.0 -cats_4,1,0.0,0.0 -cats_5,1,0.0,0.0 -cats_6,1,0.0,0.0 -cats_7,1,0.0,0.0 -cats_8,1,0.0,0.0 -cats_9,1,0.0,0.0 -cats_10,1,0.0,0.0 -cats_11,1,0.0,0.0 -cats_12,1,0.0,0.0 -cats_13,1,0.0,0.0 -cats_14,1,0.0,0.0 -cats_15,1,0.0,0.0 -cats_16,1,0.0,0.0 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a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_costs_summary.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_dispatch.csv deleted file mode 100644 index aa6e9a6..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,119 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,1,2035-01-01T00:00:00.000000-0800,0.0,0.0,0.0 -cats_2,1,2035-01-01T00:00:00.000000-0800,0.0,0.0,0.0 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a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/variable_generator_dispatch.csv b/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/variable_generator_dispatch.csv deleted file mode 100644 index 52180be..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/capacity_expansion/variable_generator_dispatch.csv +++ /dev/null @@ -1,840 +0,0 @@ -generator,scenario,timepoint,Dispatch_MW -cats_528,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_529,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_530,1,2035-01-01T00:00:00.000000-0800,0.079 -cats_531,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_532,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_533,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_534,1,2035-01-01T00:00:00.000000-0800,0.22 -cats_535,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_536,1,2035-01-01T00:00:00.000000-0800,0.3 -cats_537,1,2035-01-01T00:00:00.000000-0800,0.006000000000000005 -cats_538,1,2035-01-01T00:00:00.000000-0800,0.0 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/dev/null @@ -1,2 +0,0 @@ -component,cost -TotalCost_USD,12661886.861860562 diff --git a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/local_marginal_prices.csv b/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/local_marginal_prices.csv deleted file mode 100644 index 49edce3..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/local_marginal_prices.csv +++ /dev/null @@ -1,3199 +0,0 @@ -bus,scenario,timepoint,local_marginal_price_USDperMWh -1,1,2035-01-01T00:00:00.000000-0800,75.50274197284023 -2,1,2035-01-01T00:00:00.000000-0800,75.55074083512129 -3,1,2035-01-01T00:00:00.000000-0800,75.54545135170308 -4,1,2035-01-01T00:00:00.000000-0800,75.52051277610789 -5,1,2035-01-01T00:00:00.000000-0800,75.54757120397447 -6,1,2035-01-01T00:00:00.000000-0800,8.348097052763352 -7,1,2035-01-01T00:00:00.000000-0800,75.53579755404246 -8,1,2035-01-01T00:00:00.000000-0800,75.50501565162736 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-attribute,value -SolverName,mosek_direct -SolverStatus,ok -TerminationCondition,optimal -TimeSpent_seconds,6.034795045852661 diff --git a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_capacity.csv b/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_capacity.csv deleted file mode 100644 index 6f9c68d..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_capacity.csv +++ /dev/null @@ -1,119 +0,0 @@ -storage,scenario,power_capacity_MW,energy_capacity_MWh -cats_1,1,0.0,0.0 -cats_2,1,0.0,0.0 -cats_3,1,0.0,0.0 -cats_4,1,0.0,0.0 -cats_5,1,0.0,0.0 -cats_6,1,0.0,0.0 -cats_7,1,0.0,0.0 -cats_8,1,0.0,0.0 -cats_9,1,0.0,0.0 -cats_10,1,0.0,0.0 -cats_11,1,0.0,0.0 -cats_12,1,0.0,0.0 -cats_13,1,0.0,0.0 -cats_14,1,0.0,0.0 -cats_15,1,0.0,0.0 -cats_16,1,0.0,0.0 -cats_17,1,0.0,0.0 -cats_18,1,0.0,0.0 -cats_19,1,0.0,0.0 -cats_20,1,0.0,0.0 -cats_21,1,0.0,0.0 -cats_22,1,0.0,0.0 -cats_23,1,0.0,0.0 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b/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_costs_summary.csv deleted file mode 100644 index b9d5fad..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_costs_summary.csv +++ /dev/null @@ -1,4 +0,0 @@ -component,cost -CostPerTimepoint_USD,0.0 -CostPerPeriod_USD,0.0 -TotalCost_USD,0.0 diff --git a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_dispatch.csv b/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_dispatch.csv deleted file mode 100644 index 61b7b01..0000000 --- a/examples/kron_reduction/one_hour_kron/outputs/kron_capacity_expansion/storage_dispatch.csv +++ /dev/null @@ -1,119 +0,0 @@ -storage,scenario,timepoint,discharge_MW,charge_MW,state_of_charge_MWh -cats_1,1,2035-01-01T00:00:00.000000-0800,0.0,0.0,0.0 -cats_2,1,2035-01-01T00:00:00.000000-0800,0.0,0.0,0.0 -cats_3,1,2035-01-01T00:00:00.000000-0800,0.0,0.0,0.0 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-cats_1478,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1479,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1480,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1481,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1482,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1483,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1484,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1485,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1486,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1487,1,2035-01-01T00:00:00.000000-0800,0.0 -cats_1488,1,2035-01-01T00:00:00.000000-0800,0.0 diff --git a/examples/small_signal_and_emt/2-bus-src-gfli_e/run.py b/examples/small_signal_and_emt/2-bus-src-gfli_e/run.py new file mode 100644 index 0000000..b3d0bdf --- /dev/null +++ b/examples/small_signal_and_emt/2-bus-src-gfli_e/run.py @@ -0,0 +1,38 @@ +""" +Simulates an infinite source and GFLI_e connected via a transmission line. + +""" +# Import Python standard and third-party packages +from pathlib import Path + +# Import sting package +from sting import main + +# Step-change input to applied to the system +def step1(t): + return 0.3 if t >= 0.1 else 0.0 + +def step2(t): + return 0.0 + +inputs = { + 'infinite_sources_0': { + 'v_ref_d': step1 + }, + 'gfli_e_0': { + 'i_load_ref': step2 + } + } + +t_max = 2.0 # Simulation length (in seconds) + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +_, ssm = main.run_ssm(case_directory=case_dir) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation +main.run_emt(case_directory=case_dir, inputs=inputs, t_max=t_max) + +print('\nok') \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_analysis.py b/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_analysis.py new file mode 100644 index 0000000..d7b8887 --- /dev/null +++ b/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_analysis.py @@ -0,0 +1,202 @@ +""" + +Analysis of EMT response of GFMI_E v INF bus system to a grid disturbance under different P/Q and different Pref/Pload relationships + +In progress - April 3 (Ruth) + +""" + +# Import Python standard and third-party packages +from pathlib import Path +import numpy as np +import seaborn as sns +import matplotlib.pyplot as plt + +# Import sting package +from sting.system.core import System +from sting.system.operations import SystemModifier +from sting.modules.power_flow.core import ACPowerFlow +from sting.modules.simulation_emt.core import SimulationEMT +from sting.modules.small_signal_modeling.core import SmallSignalModel + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +def step1(t): + return 0.3 if t >= 0.5 else 0.0 + +def step2(t): + return 0.0 + +def step3(t): + return 0.1 if t > 1.0 else 0.0 + +inputs = {'infinite_sources_0': {'v_ref_d': step1}, + 'gfmi_e_0': {'p_ref': step2, + 'q_ref': step2, + 'v_ref': step2, + 'v_dc_ref': step2, + 'v_s': step2, + 'i_load_ref': step2}} + +t_max = 2.0 + +# Load system from CSV files +sys = System.from_csv(case_directory=case_dir) + +n = 3 +Prange = np.linspace(100,0,n) +Qrange = np.linspace(-50,50,n) + +Sbase = 100 # MVA +vdc_ref = 1.05 # pu + +tps = np.linspace(0, t_max, 500) +dt = tps[1] - tps[0] + +def run_sim(sys, P, Q, Sbase, vdc_ref, factor): + sys.gfmi_e[0].minimum_active_power_MW = -P*factor + sys.gfmi_e[0].maximum_active_power_MW = -P*factor + sys.gfmi_e[0].minimum_reactive_power_MVAR = Q + sys.gfmi_e[0].maximum_reactive_power_MVAR = Q + sys.gfmi_e[0].i_load_ref = P/Sbase/vdc_ref + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + emt_sc = SimulationEMT(system=sys) + emt_sc.sim(t_max, inputs) + return emt_sc + + +# Case 1: Pref = Pload +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 1.0) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_e[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results +fig, axes = plt.subplots(nrows=2,ncols=3, figsize=(30,15)) + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,1], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,1].set_xlabel("Q_sh") +axes[0,1].set_ylabel("P_load") +axes[0,1].set_title("Pref = Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,1], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,1].set_xlabel("Q_sh") +axes[1,1].set_ylabel("P_load") +axes[1,1].set_title("Pref = Pload") + + +# Case 2: Pref < Pload (Pref=0.8*Pload) + +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 0.8) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_e[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,0], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,0].set_xlabel("Q_sh") +axes[0,0].set_ylabel("P_load") +axes[0,0].set_title("Pref = 0.8*Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,0], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,0].set_xlabel("Q_sh") +axes[1,0].set_ylabel("P_load") +axes[1,0].set_title("Pref = 0.8*Pload") + + +# Case 3: Pref > Pload (Pref=1.2*Pload) + +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 1.2) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_e[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,2], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,2].set_xlabel("Q_sh") +axes[0,2].set_ylabel("P_load") +axes[0,2].set_title("Pref = 1.2*Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,2], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,2].set_xlabel("Q_sh") +axes[1,2].set_ylabel("P_load") +axes[1,2].set_title("Pref = 1.2*Pload") + +plt.show() +plt.savefig(str(case_dir)+"/emt_heatmaps.png") + +print('ok') \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_heatmaps.png b/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_heatmaps.png new file mode 100644 index 0000000..3855df0 Binary files /dev/null and b/examples/small_signal_and_emt/2-bus-src-gfmi_e/emt_heatmaps.png differ diff --git a/examples/small_signal_and_emt/2-bus-src-gfmi_e/run_compare_ssm_emt.py b/examples/small_signal_and_emt/2-bus-src-gfmi_e/run_compare_ssm_emt.py new file mode 100644 index 0000000..5ea78ad --- /dev/null +++ b/examples/small_signal_and_emt/2-bus-src-gfmi_e/run_compare_ssm_emt.py @@ -0,0 +1,459 @@ +""" +In progress (March 6, 2026 - Ruth) + +Simulates a a GFMIe connected to an infinite source via a transmission line. + +1. Computes and simulates the small-signal model using STING. + +2. Runs EMT using sting. + +3. Compares corresponding SSM and EMT states in plots. + +""" + +# Import Python standard and third-party packages +import os +import numpy as np +import plotly.graph_objects as go +from plotly.subplots import make_subplots +from pathlib import Path +from typing import Callable +from scipy import signal + +# Import sting package +from sting import main +from sting.utils.transformations import dq02abc, abc2dq0 +from sting.modules.small_signal_modeling.core import SmallSignalModel +from sting.system.core import System +from sting.system.component import Component +from sting.system.operations import SystemModifier +from sting.modules.power_flow.core import ACPowerFlow +from sting.modules.simulation_emt.core import SimulationEMT + + +# Define additional functions that return required data in order to compare SSM and EMT + +def simulate_ssm_ruth(ssm: SmallSignalModel, t_max: float, inputs: dict[str, dict[str, Callable[[float], float]]] = None, settings={'dense_output': True, 'method': 'Radau', 'max_step': 0.001}): + """Simulate the small-signal model under a given input profile.""" + + x0 = np.zeros_like(ssm.model.x.init) + tps, solution = ssm.model.simulate(t_max=t_max, inputs=inputs, x0=x0, settings=settings, output_directory=ssm.output_directory, plot=False) + + # Add the initial conditions back to the solution (for plotting purposes) + for i in range(len(ssm.model.x.init)): + solution[i] = solution[i] + ssm.model.x.init[i] + + components_to_plot = np.unique(ssm.model.x.component) # Get the components in the same order as solution vector + i = 0 # Initialize counter + + name_list = [] + component_list = [] + # Make a html file for each component. Each file plots the states corresponding to each component. + for component in components_to_plot: + number_of_states = sum(ssm.model.x.component == component) + nrows = int(np.ceil(number_of_states / 2)) + ncols = 2 if number_of_states > 1 else 1 + #fig = make_subplots(rows=nrows, cols=ncols) + for j in range(number_of_states): + row = j // ncols + 1 + col = j % ncols + 1 + #fig.add_trace(go.Scatter(x=tps, y=solution[i]), row=row, col=col) + #fig.update_xaxes(title_text='Time [s]', row=row, col=col) + #fig.update_yaxes(title_text=ssm.model.x.name[i], row=row, col=col) + name_list.append(ssm.model.x.name[i]) # added + component_list.append(component) + i += 1 + + + #fig.update_layout(title_text = component, title_x=0.5, showlegend = False) + #fig.write_html(os.path.join(ssm.output_directory, f"{component}.html")) + + return tps, solution, name_list, component_list + +def run_emt_ruth(sys, t_max, inputs, case_directory=os.getcwd(), model_settings=None, solver_settings=None): + """ + Routine to simulate the EMT dynamics of the system from a case study directory. + """ + + # Load system from CSV files + sys = System.from_csv(case_directory=case_directory) + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=model_settings, solver_settings=solver_settings) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + emt_sc = SimulationEMT(system=sys) + emt_sc.sim(t_max, inputs) + + return sys, emt_sc + + +def reconstruct_input_timeseries(fcn_name, tps, init_cond): + output = np.zeros_like(tps) + i = 0 + for t in tps: + output[i] = fcn_name(t) + i += 1 + return output + init_cond # add back initial condition + + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +def step1(t): + return 0.1 if t >= 0.5 else 0.0 + +def no_step(t): + return 0.0 + +def step3(t): + return 0.1 if t > 1.0 else 0.0 + +def noisy_i_load_ref(t): + avg = 0.1*np.sin(2*np.pi*1*t)/2 # 1 Hz + fast = 0.05*np.sin(2*np.pi*20*t)/2 # 20 Hz + return avg + fast + +def p_ref(t): + return -0.1*np.sin(2*np.pi*1*t) if t < 1 else 0 #1 Hz oscillation + +def slow_small_oscillation(t): + return 0.1*np.sin(2*np.pi*1*t) if t < 1 else 0 #1 Hz oscillation + + +def square_oscillation(t): + osc = 0.1*signal.square(2 * np.pi * 14 * t) + return osc + +# Specify inputs to excite - any constant input does not need to be specified +# NB: input is a perturbation from the nominal value +inputs = {'infinite_sources_0': {'v_ref_d': no_step}, + 'gfmi_e_0': {'p_ref': no_step, + 'q_ref': no_step, + 'v_ref': no_step, + 'v_dc_ref': no_step, + 'v_s': no_step, + 'i_load_ref': square_oscillation}} + +t_max = 4.0 + +# Load system from CSV files +sys = System.from_csv(case_directory=case_dir) + +# Run power flow +pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) +pf.solve() + +# Build and perturb small-signal model +sys, ssm = main.run_ssm(case_directory=case_dir) +tps, sol, ssm_state_names, component_name = simulate_ssm_ruth(ssm, t_max=t_max, inputs=inputs) + +# Retrieve state traces +i_bus_d_inf = sol[0,:] # infinite source +i_bus_q_inf = sol[1,:] # infinite source +angle_pc = sol[2,:] +w_pc = sol[3,:] +p_pc = sol[4,:] +q_pc = sol[5,:] +pi_vc = sol[6,:] +i_vsc_d = sol[7,:] +i_vsc_q = sol[8,:] +i_bus_d = sol[9,:] # gfmie +i_bus_q = sol[10,:] # gfmie +v_sh_d = sol[11,:] +v_sh_q = sol[12,:] +iLf = sol[13,:] +vdcf = sol[14,:] +idcf = sol[15,:] +iloadf = sol[16,:] +x1 = sol[17,:] +x2 = sol[18,:] +iL = sol[19,:] +vdc = sol[20,:] +i_load = sol[21,:] +v_bus_D_rc0 = sol[22,:] # RC0 +v_bus_Q_rc0 = sol[23,:] # RC0 +v_bus_D_rc1 = sol[24,:] #RC1 +v_bus_Q_rc1 = sol[25,:] #RC1 +i_br_D_br0 = sol[26,:] #BR0 +i_br_Q_br0 = sol[27,:] #BR0 + +# Run EMT + +emt_sc = SimulationEMT(system=sys) +emt_sc.sim(t_max, inputs) + +emt_state_names = emt_sc.variables.x.name +# Define timepoints that will be used to evaluate the solution of the ODEs +tps = np.linspace(0, t_max, 500) +n_tps = len(tps) + +# Extract solutions directly from each component +gfm = emt_sc.system.gfmi_e[0].variables_emt.x.value +gfm_names = emt_sc.system.gfmi_e[0].variables_emt.x.name + +angle_pc_emt = gfm[0,:] +w_pc_emt = gfm[1,:] +p_pc_emt = gfm[2,:] +q_pc_emt = gfm[3,:] +gamma_emt = gfm[4,:] +i_vsc_a = gfm[5,:] +i_vsc_b = gfm[6,:] +i_vsc_c = gfm[7,:] +v_sh_a = gfm[8,:] +v_sh_b = gfm[9,:] +v_sh_c = gfm[10,:] +i_bus_a = gfm[11,:] +i_bus_b = gfm[12,:] +i_bus_c = gfm[13,:] +iLf_emt = gfm[14,:] +vdcf_emt = gfm[15,:] +idcf_emt = gfm[16,:] +iloadf_emt = gfm[17,:] +x1_emt = gfm[18,:] +x2_emt = gfm[19,:] +iL_emt = gfm[20,:] +vdc_emt = gfm[21,:] +i_load_emt = gfm[22,:] + +inf_src = emt_sc.system.infinite_sources[0].variables_emt.x.value + +# convert abc to dq for plotting comparison +angle_pc_emt_init = sys.gfmi_e[0].emt_init.angle_ref * np.pi / 180 + +i_bus_d_emt, i_bus_q_emt, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, angle_pc_emt)]) #? what angle to use here + +i_vsc_d_emt, i_vsc_q_emt, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_vsc_a, i_vsc_b, i_vsc_c, angle_pc_emt)]) + +v_sh_d_emt, v_sh_q_emt, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, angle_pc_emt)]) + +fig = make_subplots( + rows=14, cols=2, + horizontal_spacing=0.15, + vertical_spacing=0.05, +) + +r, c = 1,1 # define row, column for convenience +# plot inf source voltages? +fig.add_trace(go.Scatter(x=tps, y=angle_pc_emt, name="angle_pc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=angle_pc, name="angle_pc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='angle_pc', row=r, col=c) + +r, c = 1,2 +fig.add_trace(go.Scatter(x=tps, y=angle_pc_emt, name="angle_pc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=angle_pc, name="angle_pc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='angle_pc', row=r, col=c) + + +r, c = 2,1 +fig.add_trace(go.Scatter(x=tps, y=gamma_emt, name="gamma (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=pi_vc, name="gamma (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='gamma', row=r, col=c) + +r, c = 2, 2 +fig.add_trace(go.Scatter(x=tps, y=w_pc_emt, name="w_pc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=w_pc, name="w_pc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) + +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='w_pc', row=r, col=c) + +r, c = 3,1 +fig.add_trace(go.Scatter(x=tps, y=p_pc_emt, name="p_pc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=p_pc, name="p_pc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) + +pref = reconstruct_input_timeseries(inputs['gfmi_e_0']['p_ref'], tps, sys.gfmi_e[0].emt_init.p_ref) +fig.add_trace(go.Scatter(x=tps, y=pref, name="p_ref", mode='lines', line=dict(color='green', dash='dot'), legendgroup=str(r)), row=r, col=c) + +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p_pc', row=r, col=c) + +r, c = 3,2 +fig.add_trace(go.Scatter(x=tps, y=q_pc_emt, name="q_pc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=q_pc, name="q_pc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +qref = reconstruct_input_timeseries(inputs['gfmi_e_0']['q_ref'], tps, sys.gfmi_e[0].emt_init.q_ref) +fig.add_trace(go.Scatter(x=tps, y=qref, name="q_ref", mode='lines', line=dict(color='green', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='q_pc', row=r, col=c) + +r, c = 4,1 +fig.add_trace(go.Scatter(x=tps, y=i_vsc_d_emt, name="i_vsc_d (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_vsc_d, name="i_vsc_d (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_vsc_d', row=r, col=c) + +r, c = 4,2 +fig.add_trace(go.Scatter(x=tps, y=i_vsc_q_emt, name="i_vsc_q (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_vsc_q, name="i_vsc_q (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_vsc_q', row=r, col=c) + + +r, c = 5,1 +fig.add_trace(go.Scatter(x=tps, y=v_sh_d_emt, name="v_sh_d (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=v_sh_d, name="v_sh_d (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='v_sh_d', row=r, col=c) + + +r, c = 5,2 +fig.add_trace(go.Scatter(x=tps, y=v_sh_q_emt, name="v_sh_q (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=v_sh_q, name="v_sh_q (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='v_sh_q', row=r, col=c) + +r, c = 6,1 +fig.add_trace(go.Scatter(x=tps, y=i_bus_d_emt, name="i_bus_d (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_bus_d, name="i_bus_d (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_bus_d', row=r, col=c) + +r, c = 6,2 +fig.add_trace(go.Scatter(x=tps, y=i_bus_q_emt, name="i_bus_q (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_bus_q, name="i_bus_q (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_bus_q', row=r, col=c) + +r, c = 7,1 +fig.add_trace(go.Scatter(x=tps, y=iLf_emt, name="iLf (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=iLf, name="iLf (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='iLf', row=r, col=c) + + +r, c = 7,2 +fig.add_trace(go.Scatter(x=tps, y=vdcf_emt, name="vdcf (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=vdcf, name="vdcf (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='vdcf', row=r, col=c) + +r, c = 8,1 +fig.add_trace(go.Scatter(x=tps, y=idcf_emt, name="idcf (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=idcf, name="idcf (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='idcf', row=r, col=c) + +r, c = 8,2 +fig.add_trace(go.Scatter(x=tps, y=iloadf_emt, name="iloadf (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=iloadf, name="iloadf (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='iloadf', row=r, col=c) + +r, c = 9,1 +fig.add_trace(go.Scatter(x=tps, y=x1_emt, name="x1 (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=x1, name="x1 (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='x1', row=r, col=c) + +r, c = 9,2 +fig.add_trace(go.Scatter(x=tps, y=x2_emt, name="x2 (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=x2, name="x2 (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='x2', row=r, col=c) + + +r, c = 10,1 +fig.add_trace(go.Scatter(x=tps, y=iL_emt, name="iL (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=iL, name="iL (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='iL', row=r, col=c) + +r, c = 10,2 +fig.add_trace(go.Scatter(x=tps, y=vdc_emt, name="vdc (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=vdc, name="vdc (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +vdc_ref = reconstruct_input_timeseries(inputs['gfmi_e_0']['v_dc_ref'], tps, sys.gfmi_e[0].emt_init.v_dc) +fig.add_trace(go.Scatter(x=tps, y=vdc_ref, name="vdc_ref", mode='lines', line=dict(color='green', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='vdc', row=r, col=c) + +r, c = 11,1 +fig.add_trace(go.Scatter(x=tps, y=i_load_emt, name="iload (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_load, name="iload (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +iload_ref = reconstruct_input_timeseries(inputs['gfmi_e_0']['i_load_ref'], tps, sys.gfmi_e[0].emt_init.i_load) +fig.add_trace(go.Scatter(x=tps, y=iload_ref, name="i_load_ref", mode='lines', line=dict(color='green', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='iload', row=r, col=c) + +r, c = 11, 2 +pload_emt = i_load_emt*vdc_emt +pload = i_load*vdc + +fig.add_trace(go.Scatter(x=tps, y=pload_emt, name="pload (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=pload, name="pload (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='pload (calculated)', row=r, col=c) + +r, c = 12, 1 + +pbattery_emt = iL_emt*sys.gfmi_e[0].v_s # needs fixing if we perturb v_s +pbattery = iL*sys.gfmi_e[0].v_s # needs fixing if we perturb v_s + +fig.add_trace(go.Scatter(x=tps, y=pbattery_emt, name="p_battery (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=pbattery, name="p_battery (ssm)", mode='lines', line=dict(color='blue', dash='dot'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p_battery (calculated)', row=r, col=c) + +r, c = 13, 1 + +# power comparisons +g = sys.gfmi_e[0] +v_vsc_d_emt = v_sh_d_emt + np.multiply(g.rf1_pu, i_vsc_d_emt) - np.multiply(g.xf1_pu, i_vsc_q_emt) +v_vsc_q_emt = v_sh_q_emt + np.multiply(g.rf1_pu, i_vsc_q_emt) + np.multiply(g.xf1_pu, i_vsc_d_emt) + +p_ac_emt = np.multiply(i_vsc_d_emt,v_vsc_d_emt) + np.multiply(i_vsc_q_emt,v_vsc_q_emt) +idc_emt = p_ac_emt/vdc_emt + +duty_cycle_emt = g.kp_i_L*(g.kp_v_dc*(g.v_dc_ref - vdcf_emt) + x1_emt - iLf_emt + g.Kff_idc*idcf_emt + g.Kff_iload*iloadf_emt) + x2_emt + +i_cap = -idc_emt - i_load + (1-duty_cycle_emt)*iL_emt + +p_capacitor_emt = vdc_emt*i_cap +p_bat_inductor = (sys.gfmi_e[0].v_s - (1-duty_cycle_emt)*vdc_emt)*iL_emt + +fig.add_trace(go.Scatter(x=tps, y=pbattery_emt, name="p_battery (emt)", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=np.multiply(pload_emt, -1.0), name="p_load (emt)", mode='lines', line=dict(color='blue', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=p_ac_emt, name="p_ac (emt)", mode='lines', line=dict(color='green', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p (calculated)', row=r, col=c) + +power_sum = pload_emt - np.multiply(p_ac_emt, -1.0) + p_capacitor_emt +r, c = 13,2 +fig.add_trace(go.Scatter(x=tps, y=p_capacitor_emt, name="p_capacitor", mode='lines', line=dict(color='pink', dash='dash'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p capacitor', row=r, col=c) + +r, c = 14,1 +fig.add_trace(go.Scatter(x=tps, y=p_bat_inductor, name="battery inductor power", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p inductor', row=r, col=c) + +r, c = 14, 1 + +# p_sh_emt = np.multiply(i_bus_d_emt,v_sh_d_emt) + np.multiply(i_bus_q_emt,v_sh_q_emt) +# #ptracking = -0.1 -0.1*np.sin(2*np.pi*0.1*tps) + +# fig.add_trace(go.Scatter(x=tps, y=p_pc_emt, name="p_pc", mode='lines', line=dict(color='red', dash='solid'), legendgroup=str(r)), row=r, col=c) +# #fig.add_trace(go.Scatter(x=tps, y=p_sh_emt, name="p_actual", mode='lines', line=dict(color='blue', dash='dash'), legendgroup=str(r)), row=r, col=c) +# #fig.add_trace(go.Scatter(x=tps, y=ptracking, name="p_ref", mode='lines', line=dict(color='green', dash='dot'), legendgroup=str(r)), row=r, col=c) + +# fig.update_xaxes(title_text='Time [s]', row=r, col=c) +# fig.update_yaxes(title_text='p (calculated)', row=r, col=c) + +fig.update_layout(height=1200*4, + width=800*2, + legend_tracegroupgap=400, + margin={'t': 0, 'l': 0, 'b': 0, 'r': 0}) +fig.show() +fig.write_html("examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_emt_comparison.html") +print('ok') diff --git a/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_analysis.py b/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_analysis.py new file mode 100644 index 0000000..c6442b3 --- /dev/null +++ b/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_analysis.py @@ -0,0 +1,129 @@ +""" + +Small signal analysis of GFMIE v INF source under variation in Pload, Pref, and Qref. + +""" + +# Import Python standard and third-party packages +from pathlib import Path +import numpy as np +import seaborn as sns +import matplotlib.pyplot as plt + +# Import sting package +from sting.system.core import System +from sting.system.operations import SystemModifier +from sting.modules.power_flow.core import ACPowerFlow +from sting.modules.small_signal_modeling.core import SmallSignalModel + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model + +inputs = {} +t_max = 2.0 + +# Load system from CSV files +sys = System.from_csv(case_directory=case_dir) + +# Define range of P and Q to vary over +n = 11 +Prange = np.linspace(100,0,n) +Qrange = np.linspace(-50,50,n) + +Sbase = 100 # MVA +vdc_ref = 1.05 # pu + +def run_sim(sys, P, Q, Sbase, vdc_ref, factor): + sys.gfmi_e[0].minimum_active_power_MW = -P*factor + sys.gfmi_e[0].maximum_active_power_MW = -P*factor + sys.gfmi_e[0].minimum_reactive_power_MVAR = Q + sys.gfmi_e[0].maximum_reactive_power_MVAR = Q + sys.gfmi_e[0].i_load_ref = P/Sbase/vdc_ref + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + return ssm + +# Case 1: Pref = Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + ssm = run_sim(sys, P, Q, Sbase, vdc_ref, 1.0) + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + +# Plot results +fig, axes = plt.subplots(nrows=1,ncols=3, figsize=(30,10)) + +# Colorbar - use the same range for each +vmin = -6 +vmax = 0 +# Plot small-signal stability heatmap +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1], vmin=vmin, vmax=vmax, cbar=False, cbar_kws = {'label': 'maximum eig. real part'}) +axes[1].set_xlabel("Q_sh (MVAR)") +axes[1].set_ylabel("P_load (MW)") +axes[1].set_title("Pref = Pload") + +## Case 2: Pref = 0.5*Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + ssm = run_sim(sys, P, Q, Sbase, vdc_ref, 0.5) + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + + +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0], vmin=vmin, vmax=vmax, cbar=False, cbar_kws = {'label': 'maximum eig. real part'}) +axes[0].set_xlabel("Q_sh (MVAR)") +axes[0].set_ylabel("P_load (MW)") +axes[0].set_title("Pref = 0.5*Pload") + +## Case 3: Pref = 1.5*Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + ssm = run_sim(sys, P, Q, Sbase, vdc_ref, 1.5) + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5,ax=axes[2], vmin=vmin, vmax=vmax, cbar=True, cbar_kws = {'label': 'maximum eig. real part'}) +axes[2].set_xlabel("Q_sh (MVAR)") +axes[2].set_ylabel("P_load (MW)") +axes[2].set_title("Pref = 1.5*Pload") +fig.suptitle("Effect of Pref v Pload across P & Q space") + +plt.show() +plt.savefig(str(case_dir)+"/ssm_heatmaps.png") + +print('ok') + \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_heatmaps.png b/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_heatmaps.png new file mode 100644 index 0000000..1df2492 Binary files /dev/null and b/examples/small_signal_and_emt/2-bus-src-gfmi_e/ssm_heatmaps.png differ diff --git a/examples/small_signal_and_emt/2-bus_src-gfli_d/run.py b/examples/small_signal_and_emt/2-bus_src-gfli_d/run.py new file mode 100644 index 0000000..ad5a469 --- /dev/null +++ b/examples/small_signal_and_emt/2-bus_src-gfli_d/run.py @@ -0,0 +1,36 @@ +""" +Simulates an infinite source and GFLI_d connected via a transmission line. + +""" +# Import Python standard and third-party packages +from pathlib import Path + +# Import sting package +from sting import main + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Step function to simulate +def step1(t): + return 0.3 if t >= 0.1 else 0.0 + +def step2(t): + return 0.0 + +inputs = { + 'infinite_sources_0': { + 'v_ref_d': step1 + }, + 'gfli_d_0': { + 'i_load_ref': step2} + } +t_max = 2.0 # Simulation length + +# Construct system and small-signal model +_, ssm = main.run_ssm(case_directory=case_dir) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation +main.run_emt(case_directory=case_dir, inputs=inputs, t_max=t_max) + +print('\nok') \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus_src-gfm/emt_analysis.py b/examples/small_signal_and_emt/2-bus_src-gfm/emt_analysis.py new file mode 100644 index 0000000..c3a806c --- /dev/null +++ b/examples/small_signal_and_emt/2-bus_src-gfm/emt_analysis.py @@ -0,0 +1,201 @@ +""" + +Analysis of EMT response of gfmi_c v INF bus system to a grid disturbance under different P/Q and different Pref/Pload relationships + +In progress - April 3 (Ruth) + +""" + +# Import Python standard and third-party packages +from pathlib import Path +import numpy as np +import seaborn as sns +import matplotlib.pyplot as plt + +# Import sting package +from sting.system.core import System +from sting.system.operations import SystemModifier +from sting.modules.power_flow.core import ACPowerFlow +from sting.modules.simulation_emt.core import SimulationEMT +from sting.modules.small_signal_modeling.core import SmallSignalModel + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +def step1(t): + return 0.3 if t >= 0.5 else 0.0 + +def step2(t): + return 0.0 + +def step3(t): + return 0.1 if t > 1.0 else 0.0 + +inputs = {'infinite_sources_0': {'v_ref_d': step1}, + 'gfmi_c_0': {'p_ref': step2, + 'q_ref': step2, + 'v_ref': step2, + 'v_dc_ref': step2, + 'v_s': step2, + 'i_load_ref': step2}} + +t_max = 2.0 + +# Load system from CSV files +sys = System.from_csv(case_directory=case_dir) + +n = 3 +Prange = np.linspace(100,0,n) +Qrange = np.linspace(-50,50,n) + +Sbase = 100 # MVA +vdc_ref = 1.05 # pu + +tps = np.linspace(0, t_max, 500) +dt = tps[1] - tps[0] + +def run_sim(sys, P, Q, Sbase, vdc_ref, factor): + sys.gfmi_c[0].minimum_active_power_MW = -P*factor + sys.gfmi_c[0].maximum_active_power_MW = -P*factor + sys.gfmi_c[0].minimum_reactive_power_MVAR = Q + sys.gfmi_c[0].maximum_reactive_power_MVAR = Q + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + emt_sc = SimulationEMT(system=sys) + emt_sc.sim(t_max, inputs) + return emt_sc + + +# Case 1: Pref = Pload +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 1.0) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_c[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results +fig, axes = plt.subplots(nrows=2,ncols=3, figsize=(30,15)) + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,1], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,1].set_xlabel("Q_sh") +axes[0,1].set_ylabel("P_load") +axes[0,1].set_title("Pref = Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,1], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,1].set_xlabel("Q_sh") +axes[1,1].set_ylabel("P_load") +axes[1,1].set_title("Pref = Pload") + + +# Case 2: Pref < Pload (Pref=0.8*Pload) + +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 0.8) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_c[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,0], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,0].set_xlabel("Q_sh") +axes[0,0].set_ylabel("P_load") +axes[0,0].set_title("Pref = 0.8*Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,0], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,0].set_xlabel("Q_sh") +axes[1,0].set_ylabel("P_load") +axes[1,0].set_title("Pref = 0.8*Pload") + + +# Case 3: Pref > Pload (Pref=1.2*Pload) + +results_rocof = np.zeros([Prange.shape[0],Qrange.shape[0]]) +results_nadir = np.zeros([Prange.shape[0],Qrange.shape[0]]) + +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + emt_sc = run_sim(sys, P, Q, Sbase, vdc_ref, 1.2) + + # Measure some performance metrics - frequency ROCOF and nadir and steady state error ? + gfm = emt_sc.system.gfmi_c[0].variables_emt.x.value + w_pc = gfm[1,:] + # nadir + nadir = np.min(w_pc) + results_nadir[i,j] = nadir + # rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) + df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof + df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) + rocof = np.max(df_dt_ma) + + results_rocof[i,j] = rocof + j += 1 + i += 1 + +# Plot results + +sns.heatmap(results_nadir, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0,2], cbar=True, cbar_kws = {'label': 'nadir'}) +axes[0,2].set_xlabel("Q_sh") +axes[0,2].set_ylabel("P_load") +axes[0,2].set_title("Pref = 1.2*Pload") + +sns.heatmap(results_rocof, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1,2], cbar=True, cbar_kws = {'label': 'rocof'}) +axes[1,2].set_xlabel("Q_sh") +axes[1,2].set_ylabel("P_load") +axes[1,2].set_title("Pref = 1.2*Pload") + +plt.show() +plt.savefig(str(case_dir)+"/emt_heatmaps.png") + +print('ok') \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus_src-gfm/emt_heatmaps.png b/examples/small_signal_and_emt/2-bus_src-gfm/emt_heatmaps.png new file mode 100644 index 0000000..72c694a Binary files /dev/null and b/examples/small_signal_and_emt/2-bus_src-gfm/emt_heatmaps.png differ diff --git a/examples/small_signal_and_emt/2-bus_src-gfm/run.py b/examples/small_signal_and_emt/2-bus_src-gfm/run.py new file mode 100644 index 0000000..5cb7e36 --- /dev/null +++ b/examples/small_signal_and_emt/2-bus_src-gfm/run.py @@ -0,0 +1,59 @@ +""" +Simulates an infinite source and GFMI_c connected via a transmission line. + +You should obtain the following eigenvalues: +shape: (19, 5) +┌───────────┬───────────┬──────────────────────┬──────────────────┬───────────────────────┐ +│ real ┆ imag ┆ natural_frequency_hz ┆ damping_ratio_pu ┆ time_constant_seconds │ +│ --- ┆ --- ┆ --- ┆ --- ┆ --- │ +│ f64 ┆ f64 ┆ f64 ┆ f64 ┆ f64 │ +╞═══════════╪═══════════╪══════════════════════╪══════════════════╪═══════════════════════╡ +│ -4.321 ┆ 0.698 ┆ 0.697 ┆ 0.987 ┆ 0.2314 │ +│ -4.321 ┆ -0.698 ┆ 0.697 ┆ 0.987 ┆ 0.2314 │ +│ -19.414 ┆ 376.269 ┆ 59.965 ┆ 0.052 ┆ 0.0515 │ +│ -19.414 ┆ -376.269 ┆ 59.965 ┆ 0.052 ┆ 0.0515 │ +│ -65.905 ┆ 0.0 ┆ 10.489 ┆ 1.0 ┆ 0.0152 │ +│ … ┆ … ┆ … ┆ … ┆ … │ +│ -1000.0 ┆ 0.0 ┆ 159.155 ┆ 1.0 ┆ 0.001 │ +│ -1271.429 ┆ 4404.988 ┆ 729.695 ┆ 0.277 ┆ 0.0008 │ +│ -1271.429 ┆ -4404.988 ┆ 729.695 ┆ 0.277 ┆ 0.0008 │ +│ -1653.37 ┆ 5937.579 ┆ 980.948 ┆ 0.268 ┆ 0.0006 │ +│ -1653.37 ┆ -5937.579 ┆ 980.948 ┆ 0.268 ┆ 0.0006 │ +└───────────┴───────────┴──────────────────────┴──────────────────┴───────────────────────┘ +""" + +# Import Python standard and third-party packages +from pathlib import Path +# Import sting package +from sting import main +from sting.system.core import System + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +sys = System.from_csv(case_directory=case_dir) + +# Step function to simulate +def step1(t): + return 0.1 if t >= 0.5 else 0.0 + +def step2(t): + return 0.0 + +inputs = { + 'infinite_sources_0': { + 'v_ref_d': step2 + }, + 'gfmi_c_0': { + 'p_ref': step2} + } +t_max = 2.0 # Simulation length + +# Construct system and small-signal model +sys, ssm = main.run_ssm(case_directory=case_dir) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation +main.run_emt(case_directory=case_dir, inputs=inputs, t_max=t_max) + +print('\nok') \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus_src-gfm/ssm_analysis.py b/examples/small_signal_and_emt/2-bus_src-gfm/ssm_analysis.py new file mode 100644 index 0000000..2a08991 --- /dev/null +++ b/examples/small_signal_and_emt/2-bus_src-gfm/ssm_analysis.py @@ -0,0 +1,157 @@ +""" + +Small signal analysis of GFMI_E v INF source under variation in Pload, Pref, and Qref. + +""" + +# Import Python standard and third-party packages +from pathlib import Path +import numpy as np +import seaborn as sns +import matplotlib.pyplot as plt + +# Import sting package +from sting.system.core import System +from sting.system.operations import SystemModifier +from sting.modules.power_flow.core import ACPowerFlow +from sting.modules.small_signal_modeling.core import SmallSignalModel + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model + +inputs = {} +t_max = 2.0 + +# Load system from CSV files +sys = System.from_csv(case_directory=case_dir) + + +# Define range of P and Q to vary over +n = 11 +Prange = np.linspace(-100,0,n) +Qrange = Prange + +Sbase = 100 # MVA +vdc_ref = 1.05 # pu + +# Case 1: Pref = Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + sys.gfmi_c[0].minimum_active_power_MW = P + sys.gfmi_c[0].maximum_active_power_MW = P + sys.gfmi_c[0].minimum_reactive_power_MVAR = Q + sys.gfmi_c[0].maximum_reactive_power_MVAR = Q + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + +# Plot results +fig, axes = plt.subplots(nrows=1,ncols=3, figsize=(30,10)) + +# Colorbar - use the same range for each +vmin = -6 +vmax = 0 +# Plot small-signal stability heatmap +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[1], vmin=vmin, vmax=vmax, cbar=False, cbar_kws = {'label': 'maximum eig. real part'}) +axes[1].set_xlabel("Q_sh (MVAR)") +axes[1].set_ylabel("P_load (MW)") +axes[1].set_title("Pref = Pload") + +## Case 2: Pref = 0.5*Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + sys.gfmi_c[0].minimum_active_power_MW = P/2 + sys.gfmi_c[0].maximum_active_power_MW = P/2 + sys.gfmi_c[0].minimum_reactive_power_MVAR = Q + sys.gfmi_c[0].maximum_reactive_power_MVAR = Q + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + + +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5, ax=axes[0], vmin=vmin, vmax=vmax, cbar=False, cbar_kws = {'label': 'maximum eig. real part'}) +axes[0].set_xlabel("Q_sh (MVAR)") +axes[0].set_ylabel("P_load (MW)") +axes[0].set_title("Pref = 0.5*Pload") + +## Case 3: Pref = 1.5*Pload +results = np.zeros([n,n]) +i = 0 +for P in Prange: + j = 0 + for Q in Qrange: + sys.gfmi_c[0].minimum_active_power_MW = P*1.5 + sys.gfmi_c[0].maximum_active_power_MW = P*1.5 + sys.gfmi_c[0].minimum_reactive_power_MVAR = Q + sys.gfmi_c[0].maximum_reactive_power_MVAR = Q + + # Run power flow + pf = ACPowerFlow(system=sys, model_settings=None, solver_settings=None) + pf.solve() + + # Break down lines into branches and shunts for small-signal modeling + sys_modifier = SystemModifier(system=sys) + sys_modifier.decompose_lines() + sys_modifier.combine_shunts() + + # Construct small-signal model + ssm = SmallSignalModel(system=sys) + ssm.construct_system_ssm() + + max_eig = np.max(np.linalg.eigvals(ssm.model.A).real) + + results[i,j] = max_eig + j += 1 + i += 1 + +sns.heatmap(results, xticklabels=Qrange, yticklabels=Prange, linewidth=0.5,ax=axes[2], vmin=vmin, vmax=vmax, cbar=True, cbar_kws = {'label': 'maximum eig. real part'}) +axes[2].set_xlabel("Q_sh (MVAR)") +axes[2].set_ylabel("P_load (MW)") +axes[2].set_title("Pref = 1.5*Pload") +fig.suptitle("Effect of Pref v Pload across P & Q space") + +plt.show() +plt.savefig(str(case_dir)+"/ssm_heatmaps.png") + +print('ok') + \ No newline at end of file diff --git a/examples/small_signal_and_emt/2-bus_src-gfm/ssm_heatmaps.png b/examples/small_signal_and_emt/2-bus_src-gfm/ssm_heatmaps.png new file mode 100644 index 0000000..1df2492 Binary files /dev/null and b/examples/small_signal_and_emt/2-bus_src-gfm/ssm_heatmaps.png differ diff --git a/examples/small_signal_and_emt/gfmi_e_v_gfmi_c.py b/examples/small_signal_and_emt/gfmi_e_v_gfmi_c.py new file mode 100644 index 0000000..8f5cb0d --- /dev/null +++ b/examples/small_signal_and_emt/gfmi_e_v_gfmi_c.py @@ -0,0 +1,275 @@ +""" +Compares the EMT and small signal response of the GFMI_C, which does not model the DC side of the converter, +the GFMI_E which models a battery and current-source load on the DC side. + +In progress - March 31 - Ruth +""" + +# Import Python standard and third-party packages +from pathlib import Path +import os +import numpy as np +import pandas as pd +import plotly.graph_objects as go +from plotly.subplots import make_subplots +from scipy.linalg import eig, inv +import seaborn as sns +import matplotlib.pyplot as plt +from sting.utils.transformations import dq02abc, abc2dq0 +from scipy import signal + + +# Import sting package +from sting import main +from sting.system.core import System + +# Specify path of the case study directory + +case_dir_gfmc = os.path.join(Path(__file__).resolve().parent,"2-bus_src-gfm") +case_dir_gfme = os.path.join(Path(__file__).resolve().parent,"2-bus-src-gfmi_e") + +# Define inputs +def step1(t): + return 0.3 if t >= 0.5 else 0.0 + +def step2(t): + return 0.0 + +# Combine inputs for gfmi_c and gfmi_e +inputs = {'infinite_sources_0': {'v_ref_d': step1}, + 'gfmi_e_0': {'p_ref': step2, + 'q_ref': step2, + 'v_ref': step2, + 'v_dc_ref': step2, + 'v_s': step2, + 'i_load_ref': step2}, + 'gfmi_c_0': {'p_ref': step2, + 'q_ref': step2, + 'v_ref': step2}} + +t_max = 2.0 + +# Run GFMI_C +_, ssm_c = main.run_ssm(case_directory=case_dir_gfmc) # Construct system and small-signal model +ssm_c.simulate_ssm(t_max=t_max, inputs=inputs) +sys_c, emt_sc_c = main.run_emt(case_directory=case_dir_gfmc, inputs=inputs, t_max=t_max) # Run EMT simulation + +# Run GFMI_E +_, ssm_e = main.run_ssm(case_directory=case_dir_gfme) # Construct system and small-signal model +ssm_e.simulate_ssm(t_max=t_max, inputs=inputs) +sys_e, emt_sc_e = main.run_emt(case_directory=case_dir_gfme, inputs=inputs, t_max=t_max) # Run EMT simulation + + +# # Compare eigenvalues of A matrix +# gfmic_A = pd.read_csv(case_dir_gfmc+"/outputs/small_signal_model/A.csv") +# gfmie_A = pd.read_csv(case_dir_gfme+"/outputs/small_signal_model/A.csv") + +# gfmie_eigs = np.linalg.eigvals(gfmie_A.iloc[:,1:].to_numpy()) +# gfmic_eigs = np.linalg.eigvals(gfmic_A.iloc[:,1:].to_numpy()) + +# # Plot eigenvalues +# fig = make_subplots( +# rows=1, cols=1, +# horizontal_spacing=0.15, +# vertical_spacing=0.05, +# ) + +# fig.add_trace(go.Scatter(x=gfmie_eigs.real, y=gfmie_eigs.imag, name="GFMI_E", mode="markers", marker=dict(size=12, opacity=1.0, symbol="circle", line=dict(color="black", width=1)))) +# fig.add_trace(go.Scatter(x=gfmic_eigs.real, y=gfmic_eigs.imag, name="GFMI_C", mode="markers", marker=dict(size=12, opacity=0.5, symbol="square", line=dict(color="black", width=1)))) +# fig.show() +# fig.write_html("examples/small_signal_and_emt/2-bus-scr-gfm_comparison/eig_comparison.html") + +# Compare EMT traces +gfmi_c = pd.read_csv(case_dir_gfmc+"/outputs/simulation_emt/gfmi_c_0_states.csv") +gfmi_e = pd.read_csv(case_dir_gfme+"/outputs/simulation_emt/gfmi_e_0_states.csv") + +fig = make_subplots( + rows=9, cols=2, + horizontal_spacing=0.15, + vertical_spacing=0.05, +) + +tps = gfmi_c["time"] + +# converting abc to dq +# GFMI_E +i_bus_de, i_bus_qe, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_e["i_bus_a"], gfmi_e["i_bus_b"], gfmi_e["i_bus_c"], gfmi_e["angle_pc"])]) +i_vsc_de, i_vsc_qe, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_e["i_vsc_a"], gfmi_e["i_vsc_b"], gfmi_e["i_vsc_c"], gfmi_e["angle_pc"])]) +v_sh_de, v_sh_qe, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_e["v_sh_a"], gfmi_e["v_sh_b"], gfmi_e["v_sh_c"], gfmi_e["angle_pc"])]) + +# GFMI_c +i_bus_dc, i_bus_qc, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_c["i_bus_a"], gfmi_c["i_bus_b"], gfmi_c["i_bus_c"], gfmi_c["angle_pc"])]) +i_vsc_dc, i_vsc_qc, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_c["i_vsc_a"], gfmi_c["i_vsc_b"], gfmi_c["i_vsc_c"], gfmi_c["angle_pc"])]) +v_sh_dc, v_sh_qc, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(gfmi_c["v_sh_a"], gfmi_c["v_sh_b"], gfmi_c["v_sh_c"], gfmi_c["angle_pc"])]) + +r, c = 1,1 +fig.add_trace(go.Scatter(x=tps, y=gfmi_c["angle_pc"], name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["angle_pc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='angle_pc', row=r, col=c) + +r, c = 1,2 +fig.add_trace(go.Scatter(x=tps, y=gfmi_c["w_pc"], name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["w_pc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='w_pc', row=r, col=c) + +r, c = 2,1 +fig.add_trace(go.Scatter(x=tps, y=gfmi_c["p_pc"], name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["p_pc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p_pc', row=r, col=c) + +r, c = 2,2 +fig.add_trace(go.Scatter(x=tps, y=gfmi_c["q_pc"], name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["q_pc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='q_pc', row=r, col=c) + +r, c = 3,1 +fig.add_trace(go.Scatter(x=tps, y=gfmi_c["gamma"], name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["gamma"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='gamma', row=r, col=c) + +r, c = 4,1 +fig.add_trace(go.Scatter(x=tps, y=i_vsc_dc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_vsc_de, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_vsc_d', row=r, col=c) + +r, c = 4,2 +fig.add_trace(go.Scatter(x=tps, y=i_vsc_qc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_vsc_qe, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_vsc_q', row=r, col=c) + +r, c = 5,1 +fig.add_trace(go.Scatter(x=tps, y=v_sh_dc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=v_sh_de, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='v_sh_d', row=r, col=c) + +r, c = 5,2 +fig.add_trace(go.Scatter(x=tps, y=v_sh_qc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=v_sh_qe, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='v_sh_q', row=r, col=c) + +r, c = 6,1 +fig.add_trace(go.Scatter(x=tps, y=i_bus_dc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_bus_de, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_bus_d', row=r, col=c) + +r, c = 6,2 +fig.add_trace(go.Scatter(x=tps, y=i_bus_qc, name="GFMI_C", mode='lines', line=dict(color='red', dash='solid'), legendgroup='1'), row=r, col=c) +fig.add_trace(go.Scatter(x=tps, y=i_bus_qe, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_bus_q', row=r, col=c) + +r, c = 7,1 +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["i_L"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_L', row=r, col=c) + +r, c = 7,2 +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["v_dc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='v_dc', row=r, col=c) + +r, c = 8,1 +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["i_load"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='i_load', row=r, col=c) + +r, c = 8,2 +fig.add_trace(go.Scatter(x=tps, y=gfmi_e["soc"], name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='soc', row=r, col=c) + +r, c = 9,1 +p_load = np.multiply(gfmi_e["i_load"],gfmi_e["v_dc"]) +fig.add_trace(go.Scatter(x=tps, y=p_load, name="GFMI_E", mode='lines', line=dict(color='blue', dash='dot'), legendgroup='1'), row=r, col=c) +fig.update_xaxes(title_text='Time [s]', row=r, col=c) +fig.update_yaxes(title_text='p_load', row=r, col=c) + + + +# r, c = 9, 1 +# duty_cycle = self.kp_i_L*(self.kp_v_dc*(v_dc_ref - v_dcf) + x1 - i_Lf + self.Kff_idc*i_dcf + self.Kff_iload*i_loadf) + x2 +# duty_cycle = np.clip(duty_cycle, 0.0, 1.0) +# fig.add_trace(go.Scatter(x=tps, y=duty_cycle, name="duty cycle", mode='lines', line=dict(color='blue', dash='dot')), +# row=r, col=c) +# fig.update_xaxes(title_text='Time [s]', row=r, col=c) +# fig.update_yaxes(title_text='duty cycle [p.u.]', row=r, col=c) + + + +fig.update_layout(height=1200*2, + width=800*2, + legend_tracegroupgap=400, + showlegend=False, + margin={'t': 0, 'l': 0, 'b': 0, 'r': 0}) + + + +fig.show() +fig.write_html("examples/small_signal_and_emt/gfmi_e_vs_gfmi_c_emt_traces.html") + + +## Print nadir/rocof + +# Measure some performance metrics - frequency ROCOF and nadir and steady state error ? +gfm = emt_sc_c.system.gfmi_c[0].variables_emt.x.value +w_pc = gfm[1,:] +# nadir +nadir_c = np.min(w_pc) +tps = np.linspace(0, t_max, 500) +dt = tps[1] - tps[0] + +# rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) +df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof +df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) +rocof_c = np.max(df_dt_ma) + +gfm = emt_sc_e.system.gfmi_e[0].variables_emt.x.value +w_pc = gfm[1,:] +# nadir +nadir_e = np.min(w_pc) +tps = np.linspace(0, t_max, 500) +dt = tps[1] - tps[0] + +# rocof - calculate as a moving average of duration 100ms (~25 timesteps for us) +df_dt = np.abs(np.diff(w_pc)/dt) # calculate raw rocof +df_dt_ma = np.convolve(df_dt,np.ones(25)/25) # get moving averages over 25 time steps (~100ms) +rocof_e = np.max(df_dt_ma) + + + +# participation factor analysis - can turn this into a function / method for SSM class + +# def participation_factor_plot(ssm): +# w,vr = eig(ssm.model.A) +# vl = inv(vr) # ensures normalization + +# p = np.zeros_like(vl) +# for i in range(len(w)): +# for k in range(len(w)): +# # use correct formula for complex eigenvalues +# p[k, i] = (vl[i,k].real)**2/(np.dot(vl[i,:].real,vl[i,:].real)) # participation of k-th state (row) in i-th mode (column) + +# pf_df = pd.DataFrame(p.real, index=ssm.model.x.name) +# ax = sns.heatmap(pf_df, yticklabels=pf_df.index, xticklabels=w.real>0, linewidths=1, linecolor='white') +# ax.set_yticklabels(ax.get_yticklabels(), fontsize=8) +# ax.set_xticklabels(ax.get_xticklabels(), fontsize=8) +# plt.show() +# plt.savefig("ssm.png") + + +# participation_factor_plot(ssm_c) +# participation_factor_plot(ssm_e) + + + +print('ok') diff --git a/run_template.py b/run_template.py new file mode 100644 index 0000000..96332a7 --- /dev/null +++ b/run_template.py @@ -0,0 +1,74 @@ +""" +Simulates an infinite source and GFLI_d connected via a transmission line. + +""" +# Import Python standard and third-party packages +from pathlib import Path +import sys +sys.path.append("/Users/ruthkravis/Documents/STING") + +import numpy as np +import pandas as pd +from scipy.linalg import eig, inv +import seaborn as sns +import matplotlib.pyplot as plt +from scipy import signal + +# Import sting package +from sting import main +from sting.system.core import System + +# Specify path of the case study directory +case_dir = Path(__file__).resolve().parent + +# Construct system and small-signal model +sys = System.from_csv(case_directory=case_dir) + +# Step function to simulate +def step1(t): + return 0.3 if t >= 0.1 else 0.0 + +def step2(t): + return 0.0 + +def square_oscillation(t): + return 0.01*signal.square(2*np.pi*5*t) if t > 0.1 else 0.0 + +inputs = { + 'infinite_sources_0': { + 'v_ref_d': step2 + }, + 'gfli_d_0': { + 'i_load_ref': square_oscillation} + } +t_max = 2.0 # Simulation length + +# Construct system and small-signal model +_, ssm = main.run_ssm(case_directory=case_dir) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation (not implemented yet for gfli_a) +main.run_emt(case_directory=case_dir, inputs=inputs, t_max=t_max) + +# def participation_factor_plot(ssm): +# w,vr = eig(ssm.model.A) +# vl = inv(vr) # ensures normalization + +# p = np.zeros_like(vl) +# for i in range(len(w)): +# for k in range(len(w)): +# # use correct formula for complex eigenvalues +# p[k, i] = (vl[i,k].real)**2/(np.dot(vl[i,:].real,vl[i,:].real)) # participation of k-th state (row) in i-th mode (column) + +# pf_df = pd.DataFrame(p.real, index=ssm.model.x.name) +# fig = plt.figure(figsize=(12,8)) +# ax = sns.heatmap(pf_df, yticklabels=pf_df.index, xticklabels=np.round(w.real,3), linewidths=1, linecolor='white') +# ax.set_yticklabels(ax.get_yticklabels(), fontsize=8) +# ax.set_xticklabels(ax.get_xticklabels(), fontsize=8) +# plt.show() +# plt.savefig("ssm.png") + + +# participation_factor_plot(ssm) + + +print('\nok') \ No newline at end of file diff --git a/ssm.png b/ssm.png new file mode 100644 index 0000000..c26ef79 Binary files /dev/null and b/ssm.png differ diff --git a/sting/components/__init__.py b/sting/components/__init__.py index e8a54c4..b69580a 100644 --- a/sting/components/__init__.py +++ b/sting/components/__init__.py @@ -1,5 +1,7 @@ from .active_power_pi_1a import ActivePowerPI1A from .dc_circuit_2a import DCCircuit2A +from .dc_circuit_1a import DCCircuit1A +from .dc_voltage_controller_1a import DCVoltageController1A from .dc_controller_6a import DCController6A from .dc_load_1a import DCLoad1A from .excitation_system_4a import ExcitationSystem4A diff --git a/sting/components/dc_circuit_1a.py b/sting/components/dc_circuit_1a.py new file mode 100644 index 0000000..5fa3ed2 --- /dev/null +++ b/sting/components/dc_circuit_1a.py @@ -0,0 +1,132 @@ +from dataclasses import dataclass, field +from typing import NamedTuple +import numpy as np +from sting.utils.dynamical_systems import DynamicalVariables, StateSpaceModel + +# ------------------------------------ +# Sub-classes +# ------------------------------------ +class InitialConditionsEMT(NamedTuple): + """Initial conditions for EMT simulation.""" + v_dc: float + i_dc: float + i_load: float + +# ------------------------------------ +# Main class +# ------------------------------------ +@dataclass(slots=True) +class DCCircuit1A: + """DC side circuit 1A model.""" + + c_dc: float + r_dc: float + wbase: float + + emt_init: InitialConditionsEMT = field(init=False) + + def get_steady_state(self, p: float, v_dc: float): + + # DC-side initial conditions + i_dc = p / v_dc + i_load = -v_dc/self.r_dc - i_dc + self.emt_init = InitialConditionsEMT( + v_dc = v_dc, + i_dc = i_dc, + i_load = i_load + ) + + def get_small_signal_model(self, i_load: float, i_dc: float, v_dc: float) -> StateSpaceModel: + """ + Returns the small-signal state-space model of the DC circuit 1A. + + Inputs: + - i_load: load current + - i_dc: ac-side current + + State-space representation in tableau form: + + │ Δx │ Δu + ──────────────────────── + dΔx/dt │ A │ B + ──────────────────────── + Δy │ C │ D + + Define the state vector, input vector, and output vector are: + Δx = [Δv_dc] + Δu = [Δi_load, Δi_dc] + Δy = [Δv_dc] + + Then, the state-space matrices are defined as follows: + + │ Δv_dc │ Δi_load Δi_dc + ───────────────────────────────────────────────────────────────────────────────────────────── + dΔv_dc/dt │ -ωb/(c_dc*r_dc) │ -ωb/c_dc -ωb/c_dc + ───────────────────────────────────────────────────────────────────────────────────────────── + v_dc │ 1 │ 0 0 + + + """ + # Parameters + wbase = self.wbase + c_dc = self.c_dc + r_dc = self.r_dc + + model = StateSpaceModel( + A = wbase * np.array([[-1/(c_dc*r_dc)]]), + B = wbase * np.array([[-1/c_dc, -1/c_dc]]), + C = np.array([[1]]), + D = np.array([[0, 0]]), + u = DynamicalVariables(name=['i_load', 'i_dc'], + init=[i_load, i_dc]), + y = DynamicalVariables(name=['v_dc'], + init=[v_dc]), + x = DynamicalVariables(name = ['v_dc'], + init = [v_dc]) + ) + + return model + + def define_variables_emt_dc(self): + + x = DynamicalVariables( + name = ['v_dc'], + component = f"{self.__class__.__name__}", + init = [self.emt_init.v_dc] + ) + + u = DynamicalVariables( + name=["i_load", "i_dc"], + component=f"{self.__class__.__name__}", + init=[self.emt_init.i_load, self.emt_init.i_dc] + + ) + + y = DynamicalVariables( + name=["v_dc"], + component=f"{self.__class__.__name__}", + init=[self.emt_init.v_dc] + ) + + return [x, u, y] + + def get_derivatives_step_emt_dc(self, i_load: float, i_dc: float, v_dc: float): + """ + Compute the derivatives of the state variables for the DC circuit 1A model. + Differential equations: + dv_dc/dt = (ωb/c_dc) * (-i_dc - i_load + v_dc/r_dc) + + Inputs: + - i_load: Load current [pu] + - i_dc: DC current [pu] + + Returns: + - List of derivatives [dv_dc/dt] + """ + wb = self.wbase + c_dc = self.c_dc + r_dc = self.r_dc + + d_v_dc = (wb/c_dc) * (-i_dc - i_load - v_dc/r_dc) + + return [d_v_dc] \ No newline at end of file diff --git a/sting/components/dc_voltage_controller_1a.py b/sting/components/dc_voltage_controller_1a.py new file mode 100644 index 0000000..0e4dbcc --- /dev/null +++ b/sting/components/dc_voltage_controller_1a.py @@ -0,0 +1,91 @@ +from dataclasses import dataclass, field +from typing import NamedTuple +import numpy as np +from sting.utils.dynamical_systems import DynamicalVariables, StateSpaceModel + +# ------------------------------------ +# Sub-classes +# ------------------------------------ +class InitialConditionsEMT(NamedTuple): + """Initial conditions for EMT simulation.""" + x_oc: float + i_d: float + v_dc: float + +# ------------------------------------ +# Main class +# ------------------------------------ +@dataclass(slots=True) +class DCVoltageController1A: + + kp_vdc_pu: float + ki_vdc_puHz: float + v_dc_ref: float + + emt_init: InitialConditionsEMT = field(init=False) + + def get_steady_state(self, v_dc: float, i_d: float): + + self.emt_init = InitialConditionsEMT( + x_oc = i_d, + i_d = i_d, + v_dc = v_dc, + ) + + def get_small_signal_model(self, v_dc: float, i_d: float) -> StateSpaceModel: + + # Parameters + kp_vdc = self.kp_vdc_pu + ki_vdc = self.ki_vdc_puHz + + controller = StateSpaceModel( + A = np.array([[0]]), + B = np.array([[-ki_vdc, ki_vdc]]), + C = np.array([[1]]), + D = np.array([[-kp_vdc, kp_vdc]]), + u = DynamicalVariables(name=['v_dc_ref', 'v_dc'], + init=[v_dc, v_dc]), + y = DynamicalVariables(name=['i_d_ref'], + init=[i_d]), + x = DynamicalVariables( + name = ['x_oc'], + init = [v_dc] + ) + ) + return controller + + def define_variables_emt_dc(self): + + x = DynamicalVariables( + name = ["x_oc"], + component = f"{self.__class__.__name__}", + init = [self.emt_init.x_oc] + ) + + u = DynamicalVariables( + name=["v_dc_ref", "v_dc"], + component=f"{self.__class__.__name__}", + init=[self.emt_init.v_dc, self.emt_init.v_dc] + + ) + + y = DynamicalVariables( + name=["i_d_ref"], + component=f"{self.__class__.__name__}", + init=[self.emt_init.i_d] + ) + + return [x, u, y] + + def get_derivatives_step_emt_dc(self, v_dc_ref: float, v_dc: float): + + d_x_oc = self.ki_vdc_puHz*(-v_dc_ref + v_dc) + + return [d_x_oc] + + def get_algebraics_step_emt_dc(self, x_oc: float, v_dc_ref: float, v_dc: float): + + i_d_ref = self.kp_vdc_pu*(-v_dc_ref + v_dc) + x_oc + + return i_d_ref + \ No newline at end of file diff --git a/sting/generator/__init__.py b/sting/generator/__init__.py index f3276a8..acb2803 100644 --- a/sting/generator/__init__.py +++ b/sting/generator/__init__.py @@ -5,6 +5,8 @@ from .gfmi_18b import GFMI18B from .gfmi_18p import GFMI18P from .gfmi_25a import GFMI25A +from .gfli_23a import GFLI23A +from .gfli_16c import GFLI16C from .voltage_source_4a import VoltageSource4A from .voltage_source_5a import VoltageSource5A from .synchronous_generator_14a import SynchronousGenerator14A diff --git a/sting/generator/gfli_16c.py b/sting/generator/gfli_16c.py new file mode 100644 index 0000000..d13b808 --- /dev/null +++ b/sting/generator/gfli_16c.py @@ -0,0 +1,450 @@ +""" +This module implements a 16-th order Grid-Following Inverter comprised of: +- 6th order LCL filter: Two Series RL branches (one branch is the transformer) and one Parallel RC shunt. +- 1st order outer loop control: outer loop DC voltage PI controller +- 1st order DC circuit: DC-side capacitor dynamics with resistor +- 1st order load: filtered current source +- Current controller: A dq-based frame PI controller +- PLL: Tracks the phase of the grid voltage. + +""" +# ---------------------- +# Import python packages +# ---------------------- +import numpy as np +from dataclasses import dataclass, field + +# ------------------ +# Import sting code +# ------------------ +from sting.generator.core import Generator +from sting.utils.dynamical_systems import StateSpaceModel, DynamicalVariables +from sting.modules.simulation_emt.utils import VariablesEMT +from sting.utils.transformations import R_DQ2dq, R_dq2DQ, d_DQ2dq_dangle, d_dq2DQ_dangle, abc2dq0, dq02abc +from sting.components import ( + DCCircuit1A, + DCLoad1A, + InnerCurrentController2A, + PhaseLockedLoop2A, + LCLFilter9A, + DCVoltageController1A + ) + +@dataclass(slots=True, kw_only=True, eq=False) +class GFLI16C(Generator): + # LCL filter parameters + rf1_pu: float + xf1_pu: float + rsh_pu: float + csh_pu: float + txr_power_MVA: float + txr_voltage1_kV: float + txr_voltage2_kV: float + txr_r1_pu: float + txr_x1_pu: float + txr_r2_pu: float + txr_x2_pu: float + # Current controller parameters + kff_cc: float + kp_cc_pu: float + ki_cc_puHz: float + # Phase-locked loop parameters + kp_pll_rad_s: float + ki_pll_rad2_s2: float + # DC circuit parameters + v_dc_ref: float + c_dc_pu: float + r_dc_pu: float + # Outer control parameters + kp_oc_pu: float + ki_oc_puHz: float + # Load parameters + Tload_s: float + + # Components + lcl_filter: LCLFilter9A = field(init=False) + current_controller: InnerCurrentController2A = field(init=False) + phase_locked_loop: PhaseLockedLoop2A = field(init=False) + dc_circuit: DCCircuit1A = field(init=False) + dc_load: DCLoad1A = field(init=False) + outer_control: DCVoltageController1A = field(init=False) + + def __post_init__(self): + self.lcl_filter = LCLFilter9A(self.rf1_pu, self.xf1_pu, self.rsh_pu, self.csh_pu, self.rf2_pu, self.xf2_pu, self.wbase) + self.phase_locked_loop = PhaseLockedLoop2A(self.kp_pll_rad_s, self.ki_pll_rad2_s2, self.wbase) + self.current_controller = InnerCurrentController2A(self.kp_cc_pu, self.ki_cc_puHz, self.kff_cc, self.xf1_pu + self.xf2_pu) + self.dc_circuit = DCCircuit1A(self.c_dc_pu, self.r_dc_pu, self.wbase) + self.dc_load = DCLoad1A(self.Tload_s) + self.outer_control = DCVoltageController1A(self.kp_oc_pu, self.ki_oc_puHz, self.v_dc_ref) + + + @property + def rf2_pu(self): + return (self.txr_r1_pu + self.txr_r2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def xf2_pu(self): + return (self.txr_x1_pu + self.txr_x2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def wbase(self): + return 2 * np.pi * self.base_frequency_Hz + + + def _build_small_signal_model(self): + # Unpack OPF solutions + v_mag, phase_deg = self.power_flow_variables.vmag_bus, self.power_flow_variables.vphase_bus + # Initial conditions in the LCL filter + i_bus_d, i_bus_q = self.lcl_filter.emt_init.i_bus_d, self.lcl_filter.emt_init.i_bus_q + i_vsc_d, i_vsc_q = self.lcl_filter.emt_init.i_vsc_d, self.lcl_filter.emt_init.i_vsc_q + v_sh_d, v_sh_q = self.lcl_filter.emt_init.v_sh_d, self.lcl_filter.emt_init.v_sh_q + v_bus_d, v_bus_q = self.lcl_filter.emt_init.v_bus_d, self.lcl_filter.emt_init.v_bus_q + + z_cc_d, z_cc_q = self.current_controller.emt_init.z_cc_d, self.current_controller.emt_init.z_cc_q + + # Create each components small-signal model + pll_ssm = self.phase_locked_loop.get_small_signal_model( + v_bus_mag=v_mag, relative_phase_deg=phase_deg) + + cc_ssm = self.current_controller.get_small_signal_model( + z_cc_d=z_cc_d, z_cc_q=z_cc_q, i_d=i_bus_d, i_q=i_bus_q, v_d=v_bus_d, v_q=v_bus_q, w=1) + + lcl_ssm = self.lcl_filter.get_small_signal_model( + i_vsc_d=i_vsc_d, i_vsc_q=i_vsc_q, i_bus_d=i_bus_d, i_bus_q=i_bus_q, v_sh_d=v_sh_d, v_sh_q=v_sh_q) + + dc_load_ssm = self.dc_load.get_small_signal_model(self.dc_load.emt_init.i_load) + + dc_circuit_ssm = self.dc_circuit.get_small_signal_model( + self.dc_load.emt_init.i_load, + self.dc_circuit.emt_init.i_dc, + self.dc_circuit.emt_init.v_dc) + + oc_ssm = self.outer_control.get_small_signal_model( + self.dc_circuit.emt_init.v_dc, + self.lcl_filter.emt_init.i_bus_d) + + # Inputs and outputs + v_bus_D, v_bus_Q = self.lcl_filter.emt_init.v_bus_D, self.lcl_filter.emt_init.v_bus_Q + i_bus_D, i_bus_Q = self.lcl_filter.emt_init.i_bus_D, self.lcl_filter.emt_init.i_bus_Q + + u = DynamicalVariables( + name = ["v_dc_ref", "i_load_ref", "i_ref_q", "v_bus_D", "v_bus_Q"], + type = ["device", "device", "device", "grid", "grid"], + init = [self.dc_circuit.emt_init.v_dc, + self.dc_load.emt_init.i_load, + self.lcl_filter.emt_init.i_bus_q, + self.lcl_filter.emt_init.v_bus_D, + self.lcl_filter.emt_init.v_bus_Q + ] + ) + + y = DynamicalVariables( + name=['i_bus_D', 'i_bus_Q'], + init=[i_bus_D, i_bus_Q]) + + # Generate small-signal model + components = [pll_ssm, cc_ssm, lcl_ssm, oc_ssm, dc_load_ssm, dc_circuit_ssm] + + connections = self.get_interconnection_ssm(v_bus_D, v_bus_Q, i_bus_d, i_bus_q, phase_deg, + self.lcl_filter.emt_init.v_vsc_d, + self.lcl_filter.emt_init.v_vsc_q, + self.lcl_filter.emt_init.i_vsc_d, + self.lcl_filter.emt_init.i_vsc_q, + self.dc_circuit.emt_init.v_dc, + self.dc_circuit.emt_init.i_dc) + + + self.ssm = StateSpaceModel.from_interconnected(components, connections, u, y, component_label=f"{self.type_}_{self.id}") + + return self.ssm + + + def get_interconnection_ssm(self, v_bus_D, v_bus_Q, i_bus_d, i_bus_q, relative_phase_deg, v_vsc_d, v_vsc_q, i_vsc_d, i_vsc_q, v_dc, i_dc): + + """ + Construct the interconnection matrices F, H, G, and L that satisfies: + u_stack = F * y_stack + G * u_sys + y_sys = H * y_stack + L * u_sys + + Given the tableau form: + + │ y_stack │ u_sys + ─────────────────────────────────────────────── + u_stack │ F │ G + ─────────────────────────────────────────────── + y_sys │ H │ L + + where: + u_stack = [u_pll, u_inner_current_controller, u_lcl_filter, u_outer_control, u_dc_load, u_dc_circuit] + y_stack = [y_pll, y_inner_current_controller, y_lcl_filter, y_outer_control, y_dc_load, y_dc_circuit] + y_sys = [Δi_bus_D, Δi_bus_Q] + u_sys = [Δv_dc_ref, Δi_load_ref, Δi_q_ref, Δv_bus_D, Δv_bus_Q] + + note that: + u_pll = [Δv_bus_D, Δv_bus_Q] (2 inputs) + u_inner_current_controller = [Δi_ref_dq, Δi_vsc_dq, Δv_sh_dq, Δω] (7 inputs) + u_lcl_filter = [Δv_vsc_dq, Δv_bus_dq, Δω] (5 inputs) + u_outer_control = [Δv_dc_ref, Δv_dc] (2 inputs) + u_dc_load = [Δi_load_ref] (1 input) + u_dc_circuit = [Δi_load, Δi_dc] (2 inputs) + + y_pll = [Δϕ, Δω] (2 outputs) + y_inner_current_controller = [Δv_ref_dq] (2 outputs) + y_lcl_filter = [Δi_vsc_dq, Δi_bus_dq, Δv_sh_dq] (6 outputs) + y_outer_control = [Δi_ref_d] (1 output) + y_dc_load = [Δi_load] (1 output) + y_dc_circuit = [Δv_dc] (1 output) + + thus: + u_stack has 2 + 7 + 5 + 2 + 1 + 2 = 19 inputs + y_stack has 2 + 2 + 6 + 1 + 1 + 1 = 13 outputs + y_sys has 2 outputs + u_sys has 5 inputs. + + Interconnection matrices + ------------------------ + Recall that to linearize the transformation from DQ to dq (and vice versa) + Δv_dq = Uᵀ*(v_DQ)ₒ*Δϕ + Rᵀ*Δv_DQ + Δi_DQ = U *(i_dq)ₒ*Δϕ + R *Δi_dq + where + R = [ cosϕₒ -sinϕₒ ] + [ sinϕₒ cosϕₒ ] + U = d/dϕₒ R + and we will define + a := Uᵀ*(v_DQ)ₒ + b := U *(i_dq)ₒ + + + ┌ component ──▶ │ PLL ┆ ICC ┆ LCL ┆ OC ┆ DC Load ┆ DC circuit │ Grid inputs + │ ┌ index ──▶ │ 0 1 ┆ 2,3 ┆ 4,5 6,7 8,9 │ 10 ┆ 11 ┆ 12 │ 0 1 2 3,4 + ▼ ▼ │ Δϕ Δω ┆ Δv_vsc_dq ┆ Δi_vsc_dq Δi_bus_dq Δv_sh_dq │ Δi_ref_d ┆ Δi_load ┆ Δv_dc │ Δv_dc_ref, Δi_load_ref, Δi_ref_q Δv_bus_DQ + ──────────────────────────┼────────┴───────────┴──────────────────────────────────────────────────────────────────────┼────────────────────────── + PLL 0,1 Δv_bus_DQ │ 0 0 0 0 0 0 0 I₂ + ICC 2 Δi_ref_d │ 0 0 0 0 0 0 0 0 + 3 Δi_ref_q │ 0 0 0 0 0 0 1 0 + 4,5 Δi_bus_dq │ 0 0 0 0 I₂ 0 0 0 + 6,7 Δv_bus_dq │ a 0 0 0 0 0 0 Rᵀ + 8 Δw │ 0 1 0 0 0 0 0 0 + LCL 9,10 Δv_vsc_dq │ 0 0 I₂ 0 0 0 0 0 + 11,12 Δv_bus_dq │ a 0 0 0 0 0 0 Rᵀ + 13 Δw │ 0 1 0 0 0 0 0 0 + OC 14 Δv_dc_ref | + 15 Δv_dc | + DC load 16 Δi_load_ref| + DC circ.17 Δi_load | + 18 Δi_dc | + ──────────────────────────┼──────────────────────────────────────────────────────────────────────────────────────────┼────────────────────── + Grid 0,1 Δi_bus_DQ │ b 0 0 0 R 0 0 0 + outputs + """ + + #┼ + #┴ + + angle = relative_phase_deg * np.pi / 180 + R = R_dq2DQ(angle) + I = np.eye(2) + + a = d_DQ2dq_dangle(v_bus_D, v_bus_Q, angle).reshape(2,1) + b = d_dq2DQ_dangle(i_bus_d, i_bus_q, angle).reshape(2,1) + + F = np.zeros((19, 13)) + G = np.zeros((19, 5)) + H = np.zeros((2, 13)) + L = np.zeros((2, 5)) + + a1 = v_vsc_d/v_dc + a2 = i_vsc_d/v_dc + a3 = v_vsc_q/v_dc + a4 = i_vsc_q/v_dc + a5 = -i_dc/v_dc + + # Entries in F and G entered as tuples: (row_idx, col_idx, values) + idx_F =[ + ([4,5], [6, 7], I), ([6,7], [0], a), ([8], [1], 1), ([9,10], [2,3], I), ([11,12], [1], a), ([13], [1], 1), + ([2], [10], 1), ([15], [12], 1), ([17], [11], 1), ([18], [2], a2), ([18], [3], a4), ([18], [4], a1), ([18], [5], a3), ([18], [12], a5) + ] + for rows, cols, value in idx_F: + F[np.ix_(rows, cols)] = value + + idx_G = [ + ([3], [2], 1), ([0,1], [3,4], I), + ([6,7], [3,4], R.T), ([11,12], [3,4], R.T), + ([14],[0], 1), ([16], [1], 1) + ] + for rows, cols, value in idx_G: + G[np.ix_(rows, cols)] = value + # Add values to H + H[:,[0]] = b + H[np.ix_([0,1],[6,7])] = R + + return (F,G,H,L) + + + def _calculate_emt_initial_conditions(self): + + lcl_init = self.lcl_filter.get_steady_state( + v_bus_mag = self.power_flow_variables.vmag_bus, + relative_phase_deg = self.power_flow_variables.vphase_bus, + p_bus = self.power_flow_variables.p_bus, + q_bus = self.power_flow_variables.q_bus, + reference_node = 'bus' + ) + + self.current_controller.get_steady_state( + v_out_d=lcl_init.v_vsc_d, + v_out_q=lcl_init.v_vsc_q, + v_d=lcl_init.v_bus_d, + v_q=lcl_init.v_bus_q, + i_d=lcl_init.i_bus_d, + i_q=lcl_init.i_bus_q, + w = 1 + ) + + self.phase_locked_loop.get_steady_state( + v_mag = self.power_flow_variables.vmag_bus, + relative_phase_deg = self.power_flow_variables.vphase_bus + ) + + self.dc_circuit.get_steady_state( + p = lcl_init.v_vsc_d * lcl_init.i_vsc_d + lcl_init.v_vsc_q * lcl_init.i_vsc_q, + v_dc = self.v_dc_ref + ) + + self.dc_load.get_steady_state( + i_load = self.dc_circuit.emt_init.i_load + ) + + self.outer_control.get_steady_state( + v_dc = self.v_dc_ref, + i_d = lcl_init.i_bus_d + ) + + + def define_variables_emt(self): + + + # States + x = DynamicalVariables( + name = ["z_cc_d", "z_cc_q", "theta_pll", "gamma_pll", "i_vsc_a", "i_vsc_b", "i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c", "i_load", "x_oc", "v_dc"], + component = f"{self.type_}_{self.id}", + init = [self.current_controller.emt_init.z_cc_d, + self.current_controller.emt_init.z_cc_q, + self.phase_locked_loop.emt_init.theta_pll, + self.phase_locked_loop.emt_init.z_pll, + self.lcl_filter.emt_init.i_vsc_a, self.lcl_filter.emt_init.i_vsc_b, self.lcl_filter.emt_init.i_vsc_c, + self.lcl_filter.emt_init.v_sh_a, self.lcl_filter.emt_init.v_sh_b, self.lcl_filter.emt_init.v_sh_c, + self.lcl_filter.emt_init.i_bus_a, self.lcl_filter.emt_init.i_bus_b, self.lcl_filter.emt_init.i_bus_c, + self.dc_load.emt_init.i_load, self.outer_control.emt_init.x_oc, self.dc_circuit.emt_init.v_dc] + ) + + # Inputs + u = DynamicalVariables( + name=["v_dc_ref", "i_load_ref", "i_ref_q", "v_bus_a", "v_bus_b", "v_bus_c"], + component=f"{self.type_}_{self.id}", + type=["device", "device", "device", "grid", "grid", "grid"], + init=[self.dc_circuit.emt_init.v_dc, + self.dc_load.emt_init.i_load, + self.lcl_filter.emt_init.i_bus_q, + self.lcl_filter.emt_init.v_bus_a, + self.lcl_filter.emt_init.v_bus_b, + self.lcl_filter.emt_init.v_bus_c] + ) + + # Outputs + y = DynamicalVariables( + name=["i_bus_a", "i_bus_b", "i_bus_c"], + component=f"{self.type_}_{self.id}", + init=[self.lcl_filter.emt_init.i_bus_a, + self.lcl_filter.emt_init.i_bus_b, + self.lcl_filter.emt_init.i_bus_c] + ) + + self.variables_emt = VariablesEMT(x=x,u=u,y=y) + + def get_derivative_state_emt(self, x: np.ndarray, u: np.ndarray) -> np.ndarray: + """ + It returns a vector with the differential equations that describe the dynamics of the GFLI. + """ + + # Get state values + z_cc_d, z_cc_q, theta_pll, z_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_load, x_oc, v_dc = x + + # Get input values (external inputs) + v_dc_ref, i_load_ref, i_ref_q, v_bus_a, v_bus_b, v_bus_c = u + + # convert relevant quantities to dq (reference frame of the IBR) + v_bus_d, v_bus_q, _ = abc2dq0(v_bus_a, v_bus_b, v_bus_c, theta_pll) + i_bus_d, i_bus_q, _ = abc2dq0(i_bus_a, i_bus_b, i_bus_c, theta_pll) + i_vsc_d, i_vsc_q, _ = abc2dq0(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll) + + + # Compute time derivatives of PLL + d_x_pll = self.phase_locked_loop.get_derivatives_step_emt_abc(theta_pll, z_pll, # states in PLL + v_bus_a, v_bus_b, v_bus_c # inputs to PLL + ) + + # Compute frequency estimated by PLL + w_pll = d_x_pll[0]/self.wbase + + + # Compute current reference from outer loop voltage controller + i_ref_d = self.outer_control.get_algebraics_step_emt_dc(x_oc, v_dc_ref, v_dc) + + # Compute the voltage references from the inner current controller. No delay assumed in VSC. + v_vsc_d, v_vsc_q = self.current_controller.get_algebraics_step_emt_dq0(z_cc_d, z_cc_q, # states in current controller + i_ref_d, i_ref_q, i_bus_d, i_bus_q, v_bus_d, v_bus_q, w_pll # inputs to current controller + ) + + # Compute the time derivatives of the current controller + d_x_cc = self.current_controller.get_derivatives_step_emt_dq0(i_ref_d, i_ref_q, i_bus_d, i_bus_q) # inputs to current controller + + # Convert to abc to feed into filter dynamics + v_vsc_a, v_vsc_b, v_vsc_c = dq02abc(v_vsc_d, v_vsc_q, 0, theta_pll) + + # DC/AC power balance + i_dc = (v_vsc_d*i_vsc_d + v_vsc_q*i_vsc_q)/v_dc + + # Compute the time derivatives of the LCL filter + d_x_lcl = self.lcl_filter.get_derivatives_step_emt_abc( + i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, # states in LCL filter + v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c # inputs to LCL filter + ) + + # Compute time derivative of load + d_dc_load = self.dc_load.get_derivatives_step_emt_dc(i_load, i_load_ref) + + # Compute time derivative of outer loop control + d_outer_control = self.outer_control.get_derivatives_step_emt_dc(v_dc_ref, v_dc) + + # Compute time derivative of dc circuit + d_dc_circuit = self.dc_circuit.get_derivatives_step_emt_dc(i_load, i_dc, v_dc) + + return d_x_cc + d_x_pll + d_x_lcl + d_dc_load + d_outer_control + d_dc_circuit + + def get_output_emt(self, x: np.ndarray) -> np.ndarray: + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_load, x_oc, v_dc = x + + return [i_bus_a, i_bus_b, i_bus_c] + + def plot_results_emt(self) -> DynamicalVariables: + """ + Plot EMT simulation results + """ + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_load, x_oc, v_dc = self.variables_emt.x.value + tps = self.variables_emt.x.time + + # Transform abc to dq0 + i_vsc_d, i_vsc_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll)]) + v_sh_d, v_sh_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, theta_pll)]) + i_bus_d, i_bus_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, theta_pll)]) + + results = DynamicalVariables( + name=['pi_cc_d', 'pi_cc_q', 'theta_pll', 'gamma_pll', 'i_vsc_d', 'i_vsc_q', 'v_sh_d', 'v_sh_q', 'i_bus_d', 'i_bus_q', 'i_load', 'x_oc', 'v_dc'], + component=f"{self.type_}_{self.id}", + value=[pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_d, i_vsc_q, v_sh_d, v_sh_q, i_bus_d, i_bus_q, i_load, x_oc, v_dc], + time=tps + ) + return results \ No newline at end of file diff --git a/sting/generator/gfli_23a.py b/sting/generator/gfli_23a.py new file mode 100644 index 0000000..8b81c58 --- /dev/null +++ b/sting/generator/gfli_23a.py @@ -0,0 +1,417 @@ +""" +This module implements a GFLI that incorporates: +- LCL filter: Two Series RL branches (one branch is the transformer) and one Parallel RC shunt. +- Current controller: A dq-based frame PI controller +- PLL: It that tracks the phase of the grid voltage. The PLL has a proportional and integral gain. +- DC-DC converter for controlling Vdc +- DC side circuit with load modeled as current source +""" +# ---------------------- +# Import python packages +# ---------------------- +import numpy as np +from dataclasses import dataclass, field + +# ------------------ +# Import sting code +# ------------------ +from sting.generator.core import Generator +from sting.utils.dynamical_systems import StateSpaceModel, DynamicalVariables +from sting.modules.simulation_emt.utils import VariablesEMT +from sting.utils.transformations import dq02abc, abc2dq0 +from sting.components import ( + DCCircuit2A, + DCController6A, + DCLoad1A, + InnerCurrentController2A, + LCLFilter9A, + PhaseLockedLoop2A + ) +from sting.utils.transformations import R_dq2DQ, d_DQ2dq_dangle, d_dq2DQ_dangle + +@dataclass(slots=True, kw_only=True, eq=False) +class GFLI23A(Generator): + # LCL filter parameters + rf1_pu: float + xf1_pu: float + csh_pu: float + rsh_pu: float + txr_power_MVA: float + txr_voltage1_kV: float + txr_voltage2_kV: float + txr_r1_pu: float + txr_x1_pu: float + txr_r2_pu: float + txr_x2_pu: float + # PLL + kp_pll_rad_s: float + ki_pll_rad2_s2: float + # CC + kp_cc_pu: float + ki_cc_puHz: float + kff_cc: float + # DC controller and circuit and load + kp_vdc_pu: float # DC voltage regulator P gain + ki_vdc_puHz: float # DC voltage regulator I gain [1/s] + kp_iL_pu: float # DC current regulator P gain + ki_iL_puHz: float # DC current regulator I gain [1/s] + l_dc_pu: float # DC/DC converter inductance, [pu] + c_dc_pu: float # DC link capacitance, [pu] + v_dc_ref: float # DC bus reference voltage, [pu] + v_s_pu: float # DC voltage source voltage, [pu] + Ti_L_s: float # measurement filter time constants [s] + Tv_dc_s: float + Ti_dc_s: float + kff_idc: float + kff_iload: float + i_load_ref: float + Ti_load_s: float # for DC/DC controller - measurement filter + Tload_s: float # time constant for xactuation of load current change + + # Components + lcl_filter: LCLFilter9A = field(init=False) + current_controller: InnerCurrentController2A = field(init=False) + phase_locked_loop: PhaseLockedLoop2A = field(init=False) + dc_controller: DCController6A = field(init=False) + dc_circuit: DCCircuit2A = field(init=False) + dc_load: DCLoad1A = field(init=False) + + @property + def rf2_pu(self): + return (self.txr_r1_pu + self.txr_r2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def xf2_pu(self): + return (self.txr_x1_pu + self.txr_x2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def wbase(self): + return 2 * np.pi * self.base_frequency_Hz + + def __post_init__(self): + self.lcl_filter = LCLFilter9A(self.rf1_pu, self.xf1_pu, self.rsh_pu, self.csh_pu, self.rf2_pu, self.xf2_pu, self.wbase) + self.phase_locked_loop = PhaseLockedLoop2A(self.kp_pll_rad_s, self.ki_pll_rad2_s2, self.wbase) + self.current_controller = InnerCurrentController2A(self.kp_cc_pu, self.ki_cc_puHz, self.kff_cc, self.xf1_pu + self.xf2_pu) + self.dc_controller = DCController6A(self.Ti_L_s, self.Tv_dc_s, self.Ti_dc_s, self.Ti_load_s, self.kp_vdc_pu, self.ki_vdc_puHz, self.kp_iL_pu, self.ki_iL_puHz, self.kff_idc, self.kff_iload) + self.dc_circuit = DCCircuit2A(self.v_s_pu, self.l_dc_pu, self.c_dc_pu, self.wbase) + self.dc_load = DCLoad1A(self.Tload_s) + + def _calculate_emt_initial_conditions(self): + + lcl_init = self.lcl_filter.get_steady_state( + v_bus_mag = self.power_flow_variables.vmag_bus, + relative_phase_deg = self.power_flow_variables.vphase_bus, + p_bus = self.power_flow_variables.p_bus, + q_bus = self.power_flow_variables.q_bus, + reference_node = 'bus' + ) + + self.current_controller.get_steady_state( + v_out_d=lcl_init.v_vsc_d, + v_out_q=lcl_init.v_vsc_q, + v_d=lcl_init.v_bus_d, + v_q=lcl_init.v_bus_q, + i_d=lcl_init.i_bus_d, + i_q=lcl_init.i_bus_q, + w = 1 + ) + + self.phase_locked_loop.get_steady_state( + v_mag = self.power_flow_variables.vmag_bus, + relative_phase_deg = self.power_flow_variables.vphase_bus + ) + + self.dc_circuit.get_steady_state( + p = lcl_init.v_vsc_d * lcl_init.i_vsc_d + lcl_init.v_vsc_q * lcl_init.i_vsc_q, + v_dc = self.v_dc_ref, + i_load = self.i_load_ref + ) + + self.dc_controller.get_steady_state( + i_L = self.dc_circuit.emt_init.i_L, + i_dc = self.dc_circuit.emt_init.i_dc, + i_load = self.i_load_ref, + d = self.dc_circuit.emt_init.d, + v_dc = self.v_dc_ref + ) + + self.dc_load.get_steady_state( + i_load = self.i_load_ref + ) + + + + def _build_small_signal_model(self): + # Unpack OPF solutions + v_mag, phase_deg = self.power_flow_variables.vmag_bus, self.power_flow_variables.vphase_bus + # Initial conditions in the LCL filter + i_bus_d, i_bus_q = self.lcl_filter.emt_init.i_bus_d, self.lcl_filter.emt_init.i_bus_q + i_vsc_d, i_vsc_q = self.lcl_filter.emt_init.i_vsc_d, self.lcl_filter.emt_init.i_vsc_q + v_sh_d, v_sh_q = self.lcl_filter.emt_init.v_sh_d, self.lcl_filter.emt_init.v_sh_q + v_bus_d, v_bus_q = self.lcl_filter.emt_init.v_bus_d, self.lcl_filter.emt_init.v_bus_q + + z_cc_d, z_cc_q = self.current_controller.emt_init.z_cc_d, self.current_controller.emt_init.z_cc_q + + # Create each components small-signal model + pll_ssm = self.phase_locked_loop.get_small_signal_model( + v_bus_mag=v_mag, relative_phase_deg=phase_deg) + cc_ssm = self.current_controller.get_small_signal_model( + z_cc_d=z_cc_d, z_cc_q=z_cc_q, i_d=i_bus_d, i_q=i_bus_q, v_d=v_bus_d, v_q=v_bus_q, w=1) + lcl_ssm = self.lcl_filter.get_small_signal_model( + i_vsc_d=i_vsc_d, i_vsc_q=i_vsc_q, i_bus_d=i_bus_d, i_bus_q=i_bus_q, v_sh_d=v_sh_d, v_sh_q=v_sh_q) + + dc_controller_ssm = self.dc_controller.get_small_signal_model( + i_dc = self.dc_circuit.emt_init.i_dc, + i_L = self.dc_circuit.emt_init.i_L, + v_dc = self.dc_circuit.emt_init.v_dc, + i_load = self.i_load_ref, + x_1 = self.dc_controller.emt_init.x_1, + x_2 = self.dc_controller.emt_init.x_2, + d = self.dc_circuit.emt_init.d + ) + + dc_circuit_ssm = self.dc_circuit.get_small_signal_model( + d = self.dc_circuit.emt_init.d, + i_L = self.dc_circuit.emt_init.i_L, + v_dc = self.dc_circuit.emt_init.v_dc) + + dc_load_ssm = self.dc_load.get_small_signal_model( + i_load = self.dc_load.emt_init.i_load) + + # Inverter level inputs and outputs + v_bus_D, v_bus_Q = self.lcl_filter.emt_init.v_bus_D, self.lcl_filter.emt_init.v_bus_Q + i_bus_D, i_bus_Q = self.lcl_filter.emt_init.i_bus_D, self.lcl_filter.emt_init.i_bus_Q + # Inputs and outputs + u = DynamicalVariables( + name=["i_ref_d", "i_ref_q", "v_dc_ref", "v_s", "i_load_ref", "v_bus_D", "v_bus_Q"], + type=["device", "device", "device","device","device", "grid", "grid"], + init=[i_bus_d, i_bus_q, self.v_dc_ref, self.v_s_pu, self.i_load_ref, v_bus_D, v_bus_Q]) + + y = DynamicalVariables( + name=['i_bus_D', 'i_bus_Q'], + init=[i_bus_D, i_bus_Q]) + + # Generate small-signal model + components = [pll_ssm, cc_ssm, lcl_ssm, dc_controller_ssm, dc_circuit_ssm, dc_load_ssm] + connections = self.get_interconnections_ssm(v_bus_D, v_bus_Q, i_bus_d, i_bus_q, phase_deg,self.lcl_filter.emt_init.v_vsc_d, + self.lcl_filter.emt_init.v_vsc_q, + self.lcl_filter.emt_init.i_vsc_d, + self.lcl_filter.emt_init.i_vsc_q, + self.dc_circuit.emt_init.v_dc, + self.dc_circuit.emt_init.i_dc) + self.ssm = StateSpaceModel.from_interconnected(components, connections, u, y, component_label=f"{self.type_}_{self.id}") + + return self.ssm + + def get_interconnections_ssm(self, v_bus_D, v_bus_Q, i_bus_d, i_bus_q, relative_phase_deg, v_vsc_d, v_vsc_q, i_vsc_d, i_vsc_q, v_dc, i_dc): + """ + Construct the interconnection matrices F, H, G, and L that satisfies: + u_stack = F * y_stack + H * u_sys + y_sys = G * y_stack + L * u_sys + + Given the tableau form: + + │ y_stack │ u_sys + ─────────────────────────────────────────────── + u_stack │ F │ G + ─────────────────────────────────────────────── + y_sys │ H │ L + + where: + u_stack = [u_pll, u_inner_current_controller, u_lcl_filter, u_dc_controller, u_dc_circuit, u_dc_load] + y_stack = [y_pll, y_inner_current_controller, y_lcl_filter, y_dc_controller, y_dc_circuit,y_dc_load] + y_sys = [Δi_bus_D, Δi_bus_Q] + u_sys = [Δi_d_ref, Δi_q_ref, Δv_dc_ref, Δv_s, Δi_load_ref, Δv_bus_D, Δv_bus_Q] + + note that: + u_pll = [Δv_bus_D, Δv_bus_Q] (2 inputs) + u_inner_current_controller = [Δi_ref_dq, Δi_vsc_dq, Δv_sh_dq, Δω] (7 inputs) + u_lcl_filter = [Δv_vsc_dq, Δv_bus_dq, Δω] (5 inputs) + u_dc_controller = [Δi_L, Δv_dc, Δi_dc, Δi_load, Δv_dc_ref] (5 inputs) + u_dc_circuit = [Δv_s, Δd, Δi_dc, Δi_load] (4 inputs) + u_dc_load = [Δi_load_ref] (1 input) + + y_pll = [Δϕ, Δω] (2 outputs) + y_inner_current_controller = [Δv_ref_dq] (2 outputs) + y_lcl_filter = [Δi_vsc_dq, Δi_bus_dq, Δv_sh_dq] (6 outputs) + y_dc_controller = [Δd] (1 output) + y_dc_circuit = [Δi_L, Δv_dc] (2 outputs) + y_dc_load = [Δi_load] (1 output) + + thus: + u_stack has 2 + 7 + 5 + 5 + 4 + 1 = 24 inputs + y_stack has 2 + 2 + 6 + 1 + 2 + 1 = 14 outputs + y_sys has 2 outputs + u_sys has 7 inputs + + """ + + angle = relative_phase_deg * np.pi / 180 + R = R_dq2DQ(angle) + I = np.eye(2) + + a = d_DQ2dq_dangle(v_bus_D, v_bus_Q, angle).reshape(2,1) + b = d_dq2DQ_dangle(i_bus_d, i_bus_q, angle).reshape(2,1) + + F = np.zeros((24, 14)) + G = np.zeros((24, 7)) + H = np.zeros((2, 14)) + L = np.zeros((2, 7)) + + a1 = v_vsc_d/v_dc + a2 = i_vsc_d/v_dc + a3 = v_vsc_q/v_dc + a4 = i_vsc_q/v_dc + a5 = -i_dc/v_dc + + # Entries in F and G entered as tuples: (row_idx, col_idx, values) + idx_F =[ + ([4,5], [6, 7], I), ([6,7], [0], a), ([8], [1], 1), ([9,10], [2,3], I), ([11,12], [1], a), ([13], [1], 1), + ([14],[11], 1), ([15], [12], 1), ([16], [2],a2), ([16],[3], a4), ([16], [4], a1), ([16], [5], a3), ([16], [12], a5), + ([21], [2],a2), ([21],[3], a4), ([21], [4], a1), ([21], [5], a3), ([21], [12], a5), + ([17],[13], 1), ([20], [10], 1), ([22],[13], 1) + ] + for rows, cols, value in idx_F: + F[np.ix_(rows, cols)] = value + + idx_G = [ + ([2], [0], 1), ([3], [1], 1), ([0,1], [5,6], I), + ([6,7], [5,6], R.T), ([11,12], [5,6], R.T), + ([18],[2], 1), ([19], [3], 1), ([23], [4], 1) + ] + for rows, cols, value in idx_G: + G[np.ix_(rows, cols)] = value + # Add values to H + H[:,[0]] = b + H[np.ix_([0,1],[6,7])] = R + + return (F,G,H,L) + + def define_variables_emt(self): + + # States + x = DynamicalVariables( + name = ["z_cc_d", "z_cc_q", "theta_pll", "gamma_pll", "i_vsc_a", "i_vsc_b", "i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c", "i_L_f", "v_dc_f", "i_dc_f", "i_load_f","x_1", "x_2", "i_L", "v_dc", "i_load"], + component = f"{self.type_}_{self.id}", + init = [self.current_controller.emt_init.z_cc_d, + self.current_controller.emt_init.z_cc_q, + self.phase_locked_loop.emt_init.theta_pll, + self.phase_locked_loop.emt_init.z_pll, + self.lcl_filter.emt_init.i_vsc_a, self.lcl_filter.emt_init.i_vsc_b, self.lcl_filter.emt_init.i_vsc_c, + self.lcl_filter.emt_init.v_sh_a, self.lcl_filter.emt_init.v_sh_b, self.lcl_filter.emt_init.v_sh_c, + self.lcl_filter.emt_init.i_bus_a, self.lcl_filter.emt_init.i_bus_b, self.lcl_filter.emt_init.i_bus_c, + self.dc_controller.emt_init.i_L_f, + self.dc_controller.emt_init.v_dc_f, + self.dc_controller.emt_init.i_dc_f, + self.dc_controller.emt_init.i_load_f, + self.dc_controller.emt_init.x_1, + self.dc_controller.emt_init.x_2, + self.dc_circuit.emt_init.i_L, + self.dc_circuit.emt_init.v_dc, + self.dc_load.emt_init.i_load] + ) + + # Inputs + u = DynamicalVariables( + name=["i_ref_d", "i_ref_q", "v_dc_ref", "v_s", "i_load_ref","v_bus_a", "v_bus_b", "v_bus_c"], + component=f"{self.type_}_{self.id}", + type=["device", "device", "device", "device", "device", "grid", "grid", "grid"], + init=[ self.lcl_filter.emt_init.i_bus_d, + self.lcl_filter.emt_init.i_bus_q, + self.v_dc_ref, + self.v_s_pu, + self.i_load_ref, + self.lcl_filter.emt_init.v_bus_a, + self.lcl_filter.emt_init.v_bus_b, + self.lcl_filter.emt_init.v_bus_c] + ) + + # Outputs + y = DynamicalVariables( + name=["i_bus_a", "i_bus_b", "i_bus_c"], + component=f"{self.type_}_{self.id}", + init=[self.lcl_filter.emt_init.i_bus_a, + self.lcl_filter.emt_init.i_bus_b, + self.lcl_filter.emt_init.i_bus_c] + ) + + self.variables_emt = VariablesEMT(x=x,u=u,y=y) + + def get_derivative_state_emt(self, x: np.ndarray, u: np.ndarray) -> np.ndarray: + + # Get state values + z_cc_d, z_cc_q, theta_pll, z_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, i_L, v_dc, i_load = x + + # Get input values (external inputs) + i_ref_d, i_ref_q, v_dc_ref, v_s, i_load_ref, v_bus_a, v_bus_b, v_bus_c = u + + # convert relevant quantities to dq (reference frame of the IBR) + v_bus_d, v_bus_q, _ = abc2dq0(v_bus_a, v_bus_b, v_bus_c, theta_pll) + i_bus_d, i_bus_q, _ = abc2dq0(i_bus_a, i_bus_b, i_bus_c, theta_pll) + i_vsc_d, i_vsc_q, _ = abc2dq0(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll) + + # Compute time derivatives of PLL + d_x_pll = self.phase_locked_loop.get_derivatives_step_emt_abc(theta_pll, z_pll, # states in PLL + v_bus_a, v_bus_b, v_bus_c # inputs to PLL + ) + + # Compute frequency estimated by PLL + w_pll = d_x_pll[0]/self.wbase + + # Compute the voltage references from the inner current controller. No delay assumed in VSC. + v_vsc_d, v_vsc_q = self.current_controller.get_algebraics_step_emt_dq0(z_cc_d, z_cc_q, # states in current controller + i_ref_d, i_ref_q, i_bus_d, i_bus_q, v_bus_d, v_bus_q, w_pll # inputs to current controller + ) + + # Compute the time derivatives of the current controller + d_x_cc = self.current_controller.get_derivatives_step_emt_dq0(i_ref_d, i_ref_q, i_bus_d, i_bus_q) # inputs to current controller + + # Convert to abc to feed into filter dynamics + v_vsc_a, v_vsc_b, v_vsc_c = dq02abc(v_vsc_d, v_vsc_q, 0, theta_pll) + + # DC/AC power balance + i_dc = (v_vsc_d*i_vsc_d + v_vsc_q*i_vsc_q)/v_dc + + # Compute duty cycle for DC/DC converter + d = self.dc_controller.get_algebraics_step_emt_dc(i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, v_dc_ref) + + # Compute the time derivatives of the LCL filter + d_x_lcl = self.lcl_filter.get_derivatives_step_emt_abc( + i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, # states in LCL filter + v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c # inputs to LCL filter + ) + d_dc_controller = self.dc_controller.get_derivatives_step_emt_dc(i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, i_L, v_dc, i_dc, i_load_ref, v_dc_ref) + d_dc_circuit = self.dc_circuit.get_derivatives_step_emt_dc(i_L, v_dc, v_s, d, i_load, i_dc) + d_dc_load = self.dc_load.get_derivatives_step_emt_dc(i_load, i_load_ref) + + return d_x_cc + d_x_pll + d_x_lcl + d_dc_controller + d_dc_circuit + d_dc_load + + def get_output_emt(self, x: np.ndarray) -> np.ndarray: + + # Output is i_bus_abc + z_cc_d, z_cc_q, theta_pll, z_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, i_L, v_dc, i_load = x + + return [i_bus_a, i_bus_b, i_bus_c] + + def plot_results_emt(self): + + """ + Plot EMT simulation results + """ + + z_cc_d, z_cc_q, theta_pll, z_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, i_L, v_dc, i_load = self.variables_emt.x.value + tps = self.variables_emt.x.time + + # Transform abc to dq0 + i_vsc_d, i_vsc_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll)]) + v_sh_d, v_sh_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, theta_pll)]) + i_bus_d, i_bus_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, theta_pll)]) + + results = DynamicalVariables( + name=["z_cc_d", "z_cc_q", "theta_pll", "gamma_pll", "i_vsc_d", "i_vsc_q", "v_sh_d", "v_sh_q", "i_bus_d", "i_bus_q", "i_L_f", "v_dc_f", "i_dc_f", "i_load_f","x_1", "x_2", "i_L", "v_dc", "i_load"], + component=f"{self.type_}_{self.id}", + value=[z_cc_d, z_cc_q, theta_pll, z_pll, i_vsc_d, i_vsc_q, v_sh_d, v_sh_q, i_bus_d, i_bus_q, i_L_f, v_dc_f, i_dc_f, i_load_f, x_1, x_2, i_L, v_dc, i_load], + time=tps + ) + return results + diff --git a/sting/generator/gfli_d.py b/sting/generator/gfli_d.py new file mode 100644 index 0000000..c703690 --- /dev/null +++ b/sting/generator/gfli_d.py @@ -0,0 +1,635 @@ +""" +This module implements a GFLI that incorporates: +- LCL filter: Two Series RL branches (one branch is the transformer) and one Parallel RC shunt. +- Current controller: A dq-based frame PI controller +- PLL: It that tracks the phase of the grid voltage. The PLL has a proportional and integral gain. +- DC-DC converter for controlling Vdc +- DC side circuit with load modeled as current source +""" +# ---------------------- +# Import python packages +# ---------------------- +import numpy as np +from dataclasses import dataclass +from typing import NamedTuple, Optional +from sting.generator.core import Generator + +# ------------------ +# Import sting code +# ------------------ +from sting.utils.dynamical_systems import StateSpaceModel, DynamicalVariables +from sting.modules.simulation_emt.utils import VariablesEMT +from sting.utils.transformations import dq02abc, abc2dq0 + +# ----------- +# Sub-classes +# ----------- +class InitialConditionsEMT(NamedTuple): + vmag_bus: float + vphase_bus: float + p_bus: float + q_bus: float + angle_ref: float + pi_cc_d: float + pi_cc_q: float + i_vsc_d: float + i_vsc_q: float + i_bus_d: float + i_bus_q: float + v_lcl_sh_d: float + v_lcl_sh_q: float + i_bus_D: float + i_bus_Q: float + v_bus_D: float + v_bus_Q: float + v_vsc_mag: float + v_vsc_DQ_phase: float + v_vsc_d: float + v_vsc_q: float + v_dc: float # DC bus voltage + d: float # DC/DC converter duty cycle + i_dc: float # current into/out of inverter + i_L: float # DC/DC converter inductor current + x_1: float # DC voltage regulator integrator + x_2: float # DC current regulator integrator + i_load: float + p_vsc: float + +# ----------- +# Main class +# ----------- +@dataclass(slots=True, kw_only=True, eq=False) +class GFLId(Generator): + rf1_pu: float + xf1_pu: float + csh_pu: float + rsh_pu: float + txr_power_MVA: float + txr_voltage1_kV: float + txr_voltage2_kV: float + txr_r1_pu: float + txr_x1_pu: float + txr_r2_pu: float + txr_x2_pu: float + beta: float + kp_pll_pu: float + ki_pll_puHz: float + kp_cc_pu: float + ki_cc_puHz: float + kp_v_dc: float # DC voltage regulator P gain + ki_v_dc: float # DC voltage regulator I gain [1/s] + kp_i_L: float # DC current regulator P gain + ki_i_L: float # DC current regulator I gain [1/s] + l_dc: float # DC/DC converter inductance, [pu] + c_dc: float # DC link capacitance, [pu] + v_dc_ref: float # DC bus reference voltage, [pu] + v_s: float # DC voltage source voltage, [pu] + Ti_L: float # measurement filter time constants [s] + Tv_dc: float + Ti_dc: float + Kff_idc: float + Kff_iload: float + i_load_ref: float + SOC_init_pu: float # initial battery state of charge (pu) + Ti_load: float # for DC/DC controller - measurement filter + Tload: float # time constant for actuation of load current change + emt_init: Optional[InitialConditionsEMT] = None + + @property + def rf2_pu(self): + return (self.txr_r1_pu + self.txr_r2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def xf2_pu(self): + return (self.txr_x1_pu + self.txr_x2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def wbase(self): + return 2 * np.pi * self.base_frequency_Hz + + def _build_small_signal_model(self): + + # Current PI controller + kp_cc, ki_cc = self.kp_cc_pu, self.ki_cc_puHz + pi_cc_d, pi_cc_q = self.emt_init.pi_cc_d, self.emt_init.pi_cc_q + + pi_controller = StateSpaceModel( A = np.zeros((2,2)), + B = ki_cc*np.hstack((np.eye(2), -np.eye(2))), + C = np.eye(2), + D = kp_cc*np.hstack((np.eye(2), -np.eye(2))), + u = DynamicalVariables(name=['i_bus_d_ref', 'i_bus_q_ref', 'i_bus_d', 'i_bus_q']), + y = DynamicalVariables(name=['e_d', 'e_q']), + x = DynamicalVariables( name=['pi_cc_d', 'pi_cc_q'], + init= [pi_cc_d, pi_cc_q]) ) + + # LCL filter + rf1, lf1, rf2, lf2, rsh, csh = self.rf1_pu, self.xf1_pu, self.rf2_pu, self.xf2_pu, self.rsh_pu, self.csh_pu + wb = self.wbase + i_vsc_d, i_vsc_q = self.emt_init.i_vsc_d, self.emt_init.i_vsc_q + i_bus_d, i_bus_q = self.emt_init.i_bus_d, self.emt_init.i_bus_q + v_lcl_sh_d, v_lcl_sh_q = self.emt_init.v_lcl_sh_d, self.emt_init.v_lcl_sh_q + + lcl_filter = StateSpaceModel( + A = wb*np.array([[-rf1/lf1 , 1 , 0 , 0 , -1/lf1 , 0], + [-1 , -rf1/lf1, 0 , 0 , 0 , -1/lf1], + [0 , 0 , -rf2/lf2 , 1 , 1/lf2 , 0], + [0 , 0 , -1 , -rf2/lf2, 0 , 1/lf2], + [1/csh , 0 , -1/csh , 0 , -1/(rsh*csh), 1], + [0 , 1/csh , 0 , -1/csh , -1 , -1/(rsh*csh)]]), + B = wb*np.array([[1/lf1 , 0 , 0 , 0 , i_vsc_q], + [0 , 1/lf1 , 0 , 0 , -i_vsc_d], + [0 , 0 , -1/lf2 , 0 , i_bus_q], + [0 , 0 , 0 , -1/lf2 , -i_bus_d], + [0 , 0 , 0 , 0 , v_lcl_sh_q], + [0 , 0 , 0 , 0 , -v_lcl_sh_d]]), + C = np.hstack((np.eye(4), np.zeros((4,2)))), + D = np.zeros((4,5)), + x = DynamicalVariables(name=["i_vsc_d", "i_vsc_q", "i_bus_d", "i_bus_q", "v_lcl_sh_d", "v_lcl_sh_q"], + init=[i_vsc_d, i_vsc_q, i_bus_d, i_bus_q, v_lcl_sh_d, v_lcl_sh_q]), + u = DynamicalVariables(name=['v_vsc_d', 'v_vsc_q', 'v_bus_d', 'v_bus_q', 'w']), + y = DynamicalVariables(name=["i_vsc_d", "i_vsc_q", "i_bus_d", "i_bus_q"])) + + # Phase-locked loop + kp_pll, ki_pll = self.kp_pll_pu, self.ki_pll_puHz + beta = self.beta + vmag_bus = self.emt_init.vmag_bus + sinphi = np.sin(self.emt_init.angle_ref*np.pi/180) + cosphi = np.cos(self.emt_init.angle_ref*np.pi/180) + int_pll = 0 + phase_pll = self.emt_init.angle_ref*np.pi/180 + + pll = StateSpaceModel( A = np.array([ [ 0 , -vmag_bus*ki_pll], + [1 , -1*vmag_bus*kp_pll]]), + B = np.array([ [-sinphi*ki_pll , +cosphi*ki_pll], + [-1*kp_pll*sinphi, 1*kp_pll*cosphi]]), + C = np.array([ [0 , 1], + [1/wb , -1/wb * vmag_bus*kp_pll]]), + D = np.array([ [0 , 0], + [-1/wb * kp_pll * sinphi , 1/wb * kp_pll * cosphi]]), + u = DynamicalVariables(name=['v_bus_D', 'v_bus_Q']), + y = DynamicalVariables(name=['phase', 'w']), + x = DynamicalVariables(name=["int_pll", "phase_pll"], + init=[int_pll, phase_pll] ) ) + + # DC-DC controller + # Parameters + l_dc, c_dc, TiL, Tvdc, Tidc, Kp_vdc, Ki_vdc, Kp_iL, Ki_iL, Kff_idc, Kff_iload, Ti_load, Tload = self.l_dc, self.c_dc, self.Ti_L, self.Tv_dc, self.Ti_dc, self.kp_v_dc, self.ki_v_dc, self.kp_i_L, self.ki_i_L, self.Kff_idc, self.Kff_iload, self.Ti_load, self.Tload + + # Initial conditions + v_dc, duty_cycle, i_dc, i_L, x1, x2, i_load = self.emt_init.v_dc, self.emt_init.d, self.emt_init.i_dc, self.emt_init.i_L, self.emt_init.x_1, self.emt_init.x_2, self.emt_init.i_load + + + # DC control + dc_dc_controller = StateSpaceModel( + A = np.array([ + [-1/TiL, 0, 0, 0, 0, 0], + [0,-1/Tvdc, 0, 0, 0, 0], + [0, 0, -1/Tidc, 0, 0, 0], + [0, 0, 0, -1/Ti_load, 0, 0], + [0, -Ki_vdc, 0, 0, 0, 0], + [-Ki_iL, -Kp_vdc*Ki_iL, Kff_idc*Ki_iL, Kff_iload*Ki_iL, Ki_iL, 0]]), + B = np.array([ + [1/TiL, 0, 0, 0, 0], + [0, 1/Tvdc, 0, 0, 0], + [0, 0, 1/Tidc, 0, 0], + [0, 0, 0, 1/Ti_load, 0], + [0, 0, 0, 0, Ki_vdc], + [0, 0, 0, 0, Ki_iL*Kp_vdc]]), + + C = np.array([[-Kp_iL, -Kp_iL*Kp_vdc, Kp_iL*Kff_idc, Kp_iL*Kff_iload, Kp_iL, 1]]), + D = np.array([[0, 0, 0, 0, Kp_iL*Kp_vdc]]), + u = DynamicalVariables(name=['i_L', 'v_dc', 'i_dc', 'i_load', 'v_dc_ref']), + y = DynamicalVariables(name=['d']), + x = DynamicalVariables( + name = ['i_l_f', 'v_dc_f', 'i_dc_f', 'i_load_f','x_1', 'x_2'], + init = [i_L, v_dc, i_dc, i_load, x1, x2] + ) + ) + + # DC circuit - includes capacitor, inductor, and load dynamics + dc_circuit = StateSpaceModel( + A = wb*np.array([[0, (duty_cycle-1)/l_dc, 0, 0], + [(1-duty_cycle)/c_dc, 0, -1/c_dc, 0], + [0, 0, -1/(wb*Tload), 0], + [1, 0, 0, 0]]), + B = wb*np.array([[1/l_dc, v_dc/l_dc, 0, 0], + [0, -i_L/c_dc, -1/c_dc, 0], + [0, 0, 0, 1/(wb*Tload)], + [0, 0, 0, 0]]), + C = np.hstack((np.eye(3),np.zeros((3,1)))), + D = np.zeros((3,4)), + u = DynamicalVariables(name=['v_s', 'd', 'i_dc','i_load_ref']), + y = DynamicalVariables(name=['i_L','v_dc', 'i_load']), + x = DynamicalVariables( + name = ['i_L', 'v_dc', 'iload', 'soc'], + init = [i_L, v_dc, i_load, self.SOC_init_pu] + ) + ) + + # Construction of CCM matrices + + # dc power balance linearization coefficients + v_dc = self.emt_init.v_dc + + b1 = self.emt_init.v_vsc_d/v_dc # i1d + b2 = self.emt_init.i_vsc_d/v_dc #e1d + b3 = - (self.emt_init.i_vsc_d/v_dc)*(self.xf1_pu+self.xf2_pu) #i2q + b4 = self.emt_init.v_vsc_q/v_dc # i1q + b5 = self.emt_init.i_vsc_q/v_dc # e1q + b6 = (self.emt_init.i_vsc_q/v_dc)*(self.xf1_pu+self.xf2_pu) #i2d + b7 = - self.emt_init.i_dc/v_dc #vdc + b8 = -(self.emt_init.i_vsc_q/v_dc)*self.beta*vmag_bus # phi + + Fccm = np.vstack( ( np.zeros((12, )) ,# i2ref_d + np.zeros((12, )) , # i2ref_q + np.hstack((np.zeros((2,4)), np.eye(2) ,np.zeros((2,6)))), # i2c_dq + [1, 0 , 0, 0, 0 , -(lf1+lf2) , 0 , 0, 0, 0, 0, 0], # v1c_d + [0, 1 , 0, 0, (lf1+lf2) , 0 , -beta*vmag_bus , 0, 0, 0, 0, 0], # v1c_q + np.zeros((12, )) , # v2c_d + np.append( np.zeros((1,6)) , [-vmag_bus, 0, 0, 0, 0, 0] ), # v2c_q + np.append( np.zeros((1,7)) , [1, 0, 0, 0, 0] ), # w + np.zeros((2,12)),# v2c_dq + np.hstack((np.zeros(9,), [1, 0, 0])), #iL + np.hstack((np.zeros(9,), [0, 1, 0])), #vdc + [b2, b5, b1, b4, b6, b3, b8, 0, 0, 0, b7, 0], #idc + np.hstack((np.zeros(11,), [1])), #iload + np.zeros((2,12)), #vdc_ref, v_s + np.hstack((np.zeros(8,), [1, 0, 0, 0])), #d + [b2, b5, b1, b4, b6, b3, b8, 0, 0, 0, b7, 0], #idc + np.zeros(12,) # iload_ref + )) + + Gccm = np.vstack(( [1, 0, 0, 0, 0, 0, 0], # i2ref_d + [0, 1, 0, 0, 0, 0, 0], # i2ref_q + np.zeros((2,7)), # i2c_dq + [0, 0, 0, 0, 0, beta*cosphi , beta*sinphi], # v1c_d + [0, 0, 0, 0, 0, -beta*sinphi, beta*cosphi], # v1c_q + [0, 0, 0, 0, 0, cosphi ,sinphi], # v2c_d + [0, 0, 0, 0, 0, -sinphi ,cosphi], # v2c_q + np.zeros((7, )), # w + np.hstack( (np.zeros((2,5)), np.eye(2) ) ),# v2_dq + np.zeros((4,7)), #iL, vdc, idc, iload + [0, 0, 1, 0, 0, 0, 0], #vdc_ref + [0, 0, 0, 1, 0, 0, 0], #vs + np.zeros((2,7)), #d, idc + [0, 0, 0, 0, 1, 0, 0] #i_load_ref + ) ) + + Hccm = np.vstack(( [ 0, 0 , 0, 0, cosphi , -sinphi, -sinphi*i_bus_d-cosphi*i_bus_q, 0, 0, 0, 0, 0], + [0, 0, 0, 0, sinphi , cosphi , cosphi*i_bus_d-sinphi*i_bus_q, 0, 0, 0, 0, 0] )) + + Lccm = np.zeros((2, 7)) + + components = [pi_controller, lcl_filter, pll, dc_dc_controller, dc_circuit] + connections = [Fccm, Gccm, Hccm, Lccm] + + # Inputs and outputs + v_bus_D, v_bus_Q= self.emt_init.v_bus_D, self.emt_init.v_bus_Q + u = DynamicalVariables( + name=["i_bus_d_ref", "i_bus_q_ref", "v_dc_ref", "v_s", "i_load_ref", "v_bus_D", "v_bus_Q"], + type=["device", "device", "device", "device", "device", "grid", "grid"], + init=[i_bus_d, i_bus_q, v_dc, self.v_s, i_load, v_bus_D, v_bus_Q]) + + i_bus_D, i_bus_Q= self.emt_init.i_bus_D, self.emt_init.i_bus_Q + y = DynamicalVariables( + name=['i_bus_D', 'i_bus_Q'], + init=[i_bus_D, i_bus_Q]) + + # Generate small-signal model + self.ssm = StateSpaceModel.from_interconnected(components, connections, u, y, component_label=f"{self.type_}_{self.id}") + + def _calculate_emt_initial_conditions(self): + + # Extract power flow solution + vmag_bus = self.power_flow_variables.vmag_bus + vphase_bus = self.power_flow_variables.vphase_bus + p_bus = self.power_flow_variables.p_bus + q_bus = self.power_flow_variables.q_bus + + # Voltage in the end of the LCL filter + v_bus_DQ = vmag_bus * np.exp(vphase_bus * np.pi / 180 * 1j) + angle_ref = np.angle(v_bus_DQ, deg=True) + + # Current sent from the end of the LCL filter + i_bus_DQ = (p_bus - q_bus * 1j) / np.conjugate(v_bus_DQ) + + # Voltage across the shunt element in the LCL filter + v_lcl_sh_DQ = v_bus_DQ + (self.rf2_pu + self.xf2_pu * 1j) * i_bus_DQ + + # Current flowing through shunt element of LCL filter + i_lcl_sh_DQ = v_lcl_sh_DQ * (self.csh_pu * 1j) + v_lcl_sh_DQ / self.rsh_pu + + # Current sent from the beginning of the LCL filter + i_vsc_DQ = i_bus_DQ + i_lcl_sh_DQ + v_vsc_DQ = v_lcl_sh_DQ + (self.rf1_pu + self.xf1_pu * 1j) * i_vsc_DQ + + # We refer the voltage and currents to the synchronous frames of the + # inverter + v_vsc_dq = v_vsc_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + i_vsc_dq = i_vsc_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + v_bus_dq = v_bus_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + i_bus_dq = i_bus_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + v_lcl_sh_dq = v_lcl_sh_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + # Initial conditions for the integral controller + pi_cc_dq = ( + v_vsc_dq - self.beta * v_bus_dq - 1j * (self.xf1_pu + self.xf2_pu) * i_bus_dq + ) + + # DC side + # DC-side initial conditions + v_dc = self.v_dc_ref + p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real # power at converter terminals + i_dc = p_vsc/v_dc + i_load = self.i_load_ref + duty_cycle = (v_dc - self.v_s)/v_dc + i_L = (i_load+i_dc)/(1-duty_cycle) + x_1 = i_L - self.Kff_idc*i_dc - self.Kff_iload*i_load + x_2 = duty_cycle - self.kp_i_L*(x_1 - i_L + self.Kff_idc*i_dc + self.Kff_iload*i_load) + + + self.emt_init = InitialConditionsEMT( + vmag_bus=vmag_bus, + vphase_bus=vphase_bus, + p_bus=p_bus, + q_bus=q_bus, + angle_ref=angle_ref, + pi_cc_d=pi_cc_dq.real, + pi_cc_q=pi_cc_dq.imag, + i_vsc_d=i_vsc_dq.real, + i_vsc_q=i_vsc_dq.imag, + i_bus_d=i_bus_dq.real, + i_bus_q=i_bus_dq.imag, + v_lcl_sh_d=v_lcl_sh_dq.real, + v_lcl_sh_q=v_lcl_sh_dq.imag, + i_bus_D=i_bus_DQ.real, + i_bus_Q=i_bus_DQ.imag, + v_bus_D=v_bus_DQ.real, + v_bus_Q=v_bus_DQ.imag, + v_vsc_mag = abs(v_vsc_DQ), + v_vsc_DQ_phase = np.angle(v_vsc_DQ, deg=True), + v_vsc_d=v_vsc_dq.real, + v_vsc_q=v_vsc_dq.imag, + v_dc=v_dc, + p_vsc=p_vsc, + i_dc=i_dc, + i_load=i_load, + d = duty_cycle, + i_L = i_L, + x_1 = x_1, + x_2 = x_2 + ) + + def define_variables_emt(self): + # States + # ------ + + # Initial conditions + angle_ref = self.emt_init.angle_ref + pi_cc_d, pi_cc_q = self.emt_init.pi_cc_d, self.emt_init.pi_cc_q + + # these quantities are already in the converter ref frame (defined by angle_ref) + i_bus_d, i_bus_q = self.emt_init.i_bus_d, self.emt_init.i_bus_q + i_vsc_d, i_vsc_q = self.emt_init.i_vsc_d, self.emt_init.i_vsc_q + v_sh_d, v_sh_q = self.emt_init.v_lcl_sh_d, self.emt_init.v_lcl_sh_q + + # convert to abc + i_bus_a, i_bus_b, i_bus_c = dq02abc(i_bus_d, i_bus_q, 0, angle_ref*np.pi/180) + i_vsc_a, i_vsc_b, i_vsc_c = dq02abc(i_vsc_d, i_vsc_q, 0, angle_ref*np.pi/180) + v_sh_a, v_sh_b, v_sh_c = dq02abc(v_sh_d, v_sh_q, 0, angle_ref*np.pi/180) + + # DC side + v_dc, i_dc, i_L, x1, x2, i_load = self.emt_init.v_dc, self.emt_init.i_dc, self.emt_init.i_L, self.emt_init.x_1, self.emt_init.x_2, self.emt_init.i_load + + + x = DynamicalVariables( + name = ['pi_cc_d', 'pi_cc_q', 'theta_pll', 'gamma_pll', "i_vsc_a", "i_vsc_b", "i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c",'i_l_f', 'v_dc_f', 'i_dc_f', 'i_load_f','x_1', 'x_2', 'i_L', 'v_dc', 'i_load', 'soc'], + component = f"{self.type_}_{self.id}", + init = [pi_cc_d, pi_cc_q, angle_ref * np.pi/180, 0, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c,i_L, v_dc, i_dc, i_load, x1, x2, i_L, v_dc, i_load, self.SOC_init_pu] + ) + + # Inputs + # ------ + + # Initial conditions + v_bus_D, v_bus_Q = self.emt_init.v_bus_D, self.emt_init.v_bus_Q + v_bus_a, v_bus_b, v_bus_c = dq02abc(v_bus_D, v_bus_Q, 0, 0) + + u = DynamicalVariables( + name=["i_bus_d_ref", "i_bus_q_ref", "v_dc_ref", "v_s", "i_load_ref", "v_bus_a", "v_bus_b", "v_bus_c"], + component=f"{self.type_}_{self.id}", + type=["device", "device", "device", "device", "device", "grid", "grid", "grid"], + init=[i_bus_d, i_bus_q, v_dc, self.v_s, i_load, v_bus_a, v_bus_b, v_bus_c] + ) + + # Outputs + # ------- + + y = DynamicalVariables( + name=["i_bus_a", "i_bus_b", "i_bus_c"], + component=f"{self.type_}_{self.id}", + init=[i_bus_a, i_bus_b, i_bus_c] + ) + + self.variables_emt = VariablesEMT(x=x,u=u,y=y) + + def get_derivative_state_emt(self): + """ + It returns a vector with the differential equations that describe the dynamics of the GFLI. + This model includes: pi controller, pll, and LCL filter. + """ + # Get state values # here in progress + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc = self.variables_emt.x.value + + # Get input values (external inputs) + i_bus_d_ref, i_bus_q_ref, v_dc_ref, v_s, i_load_ref, v_bus_a, v_bus_b, v_bus_c = self.variables_emt.u.value + + # convert relevant quantities to dq + v_bus_d, v_bus_q, _ = abc2dq0(v_bus_a, v_bus_b, v_bus_c, theta_pll) + i_bus_d, i_bus_q, _ = abc2dq0(i_bus_a, i_bus_b, i_bus_c, theta_pll) + + # Update algebraic states + e_d = pi_cc_d + self.kp_cc_pu * (i_bus_d_ref - i_bus_d) + e_q = pi_cc_q + self.kp_cc_pu * (i_bus_q_ref - i_bus_q) + + v_vsc_d = e_d + self.beta * v_bus_d - (self.xf1_pu + self.xf2_pu) * i_bus_q + v_vsc_q = e_q + self.beta * v_bus_q + (self.xf1_pu + self.xf2_pu) * i_bus_d + + # convert to abc to feed into filter dynamics + v_vsc_a, v_vsc_b, v_vsc_c = dq02abc(v_vsc_d, v_vsc_q, 0, theta_pll) + + # DC/AC power balance + i_vsc_d, i_vsc_q, _ = abc2dq0(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll) + i_dc = (v_vsc_d*i_vsc_d + v_vsc_q*i_vsc_q)/v_dc + + def current_controller_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the current controller. + The current controller has: virtual inertia, filter for active and reactive power. + """ + + # Definition of states for the ODEs of the current controller + pi_cc_d, pi_cc_q = y[0], y[1] + + # Extract the list of parameters + kp_cc = self.kp_cc_pu # proportional gain of current controller + ki_cc = self.ki_cc_puHz # integral gain of current controller + + # Define internal inputs for the current controller at timepoint "t" + i_bus_d_ref, i_bus_q_ref, i_bus_d, i_bus_q = internal_inputs + + # Define ODEs that describe the dynamics of the current controller + d_pi_cc_d = ki_cc * (i_bus_d_ref - i_bus_d) + d_pi_cc_q = ki_cc * (i_bus_q_ref - i_bus_q) + + return [d_pi_cc_d, d_pi_cc_q] + + def pll_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the PLL. + The PLL tracks the phase of the grid voltage. + """ + # Definition of states for the ODEs of the pll + theta_pll, gamma_pll = y[0], y[1] + + # Extract the list of parameters + kp_pll = self.kp_pll_pu # proportional gain of PLL + ki_pll = self.ki_pll_puHz # integral gain of PLL + w_base = self.wbase # base frequency of the system + + # Define voltage at bus + v_bus_q = internal_inputs + + # Define ODEs that describe the dynamics of the PLL + d_theta_pll = kp_pll * v_bus_q + gamma_pll + w_base + d_gamma_pll = ki_pll * v_bus_q + + return [d_theta_pll, d_gamma_pll] + + def lcl_filter_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the LCL filter. + The LCL filter connects the VSC to the grid. It has three branches: the first branch (RL) connects + the VSC to the shunt element, the second branch is the shunt element (RC), and the third branch (RL) + connects the shunt element to the grid. + """ + + # Definition of states for the ODEs of the LCL filter + i_vsc_a , i_vsc_b, i_vsc_c = y[0], y[1], y[2] # currents flowing out of VSC + v_sh_a, v_sh_b, v_sh_c = y[3], y[4], y[5] # currents flowing through paralell RC shunt + i_bus_a, i_bus_b, i_bus_c = y[6], y[7], y[8] # currents flowing to bus + + # Extract the list of parameters + r1 = self.rf1_pu # resistance [p.u.] of first branch of filter + l1 = self.xf1_pu # inductance [p.u.] of first branch of filter + r2 = self.rf2_pu # resistance [p.u.] of second branch of filter + l2 = self.xf2_pu # inductance [p.u.] of second branch of filter + rsh = self.rsh_pu # resistance [p.u.] of series RC shunt + csh = self.csh_pu # capacitance [p.u.] of series RC shunt + wb = self.wbase # nominal frequency of the system + + # Define voltage at vsc at timepoint "t" + v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c = internal_inputs + + # Define ODEs that describe the dynamics of the LCL filter + di_vsc_a = wb/l1 *(v_vsc_a - v_sh_a - r1 * i_vsc_a) + di_vsc_b = wb/l1 *(v_vsc_b - v_sh_b - r1 * i_vsc_b) + di_vsc_c = wb/l1 *(v_vsc_c - v_sh_c - r1 * i_vsc_c) + + dv_sh_a = wb/csh * (-v_sh_a/rsh + i_vsc_a - i_bus_a) + dv_sh_b = wb/csh * (-v_sh_b/rsh + i_vsc_b - i_bus_b) + dv_sh_c = wb/csh * (-v_sh_c/rsh + i_vsc_c - i_bus_c) + + di_bus_a = wb/l2 *(v_sh_a - v_bus_a - r2 * i_bus_a) + di_bus_b = wb/l2 *(v_sh_b - v_bus_b - r2 * i_bus_b) + di_bus_c = wb/l2 *(v_sh_c - v_bus_c - r2 * i_bus_c) + + return [di_vsc_a, di_vsc_b, di_vsc_c, dv_sh_a, dv_sh_b, dv_sh_c, di_bus_a, di_bus_b, di_bus_c] + + def dc_side(y, internal_inputs): + """ + DC-DC controller + circuit + load control + """ + # Define states + i_Lf, v_dcf, i_dcf, i_loadf, x_1, x_2, i_L, v_dc, i_load, soc = y[0], y[1], y[2], y[3], y[4], y[5], y[6], y[7], y[8], y[9] + + # Inputs + i_dc, i_load_ref, v_dc_ref, v_s = internal_inputs + + # Parameters + l_dc, c_dc, TiL, Tvdc, Tidc, Kp_vdc, Ki_vdc, Kp_iL, Ki_iL, Kff_idc, Kff_iload, Ti_load, Tload = self.l_dc, self.c_dc, self.Ti_L, self.Tv_dc, self.Ti_dc, self.kp_v_dc, self.ki_v_dc, self.kp_i_L, self.ki_i_L, self.Kff_idc, self.Kff_iload, self.Ti_load, self.Tload + wb = self.wbase + + # ODEs + + # DC-DC controller + d_i_Lf = (1/TiL)*(i_L - i_Lf) + d_v_dcf = (1/Tvdc)*(v_dc - v_dcf) + d_i_dcf = (1/Tidc)*(i_dc - i_dcf) + d_i_load_f = (1/Ti_load)*(i_load - i_loadf) + d_x_1 = Ki_vdc*(v_dc_ref - v_dcf) + d_x_2 = Ki_iL*(Kp_vdc*(v_dc_ref - v_dcf) + x_1 - i_Lf + Kff_idc*i_dcf + Kff_iload*i_loadf) + duty_cycle = Kp_iL*(Kp_vdc*(v_dc_ref - v_dcf) + x_1 - i_Lf + Kff_idc*i_dcf + Kff_iload*i_loadf) + x_2 + + # Circuit equations + d_v_dc = (wb/c_dc)*(-i_dc - i_load + (1-duty_cycle)*i_L) + d_i_L = (wb/l_dc)*(v_s - (1-duty_cycle)*v_dc) + + # Load control + d_i_load = (1/Tload)*(i_load_ref - i_load) + + # SOC + d_soc = i_L + + return [d_i_Lf, d_v_dcf, d_i_dcf, d_i_load_f, d_x_1, d_x_2, d_i_L, d_v_dc, d_i_load, d_soc] + + d_cc= current_controller_dynamics([pi_cc_d, pi_cc_q], [i_bus_d_ref, i_bus_q_ref, i_bus_d, i_bus_q]) + + d_pll = pll_dynamics([theta_pll, gamma_pll], v_bus_q) + + d_lcl = lcl_filter_dynamics([i_vsc_a , i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c], [v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c]) + + d_dc = dc_side([i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc], [i_dc, i_load_ref, v_dc_ref, v_s]) + + return np.hstack([d_cc, d_pll, d_lcl, d_dc]) + + def get_output_emt(self): + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load,soc = self.variables_emt.x.value + + return [i_bus_a, i_bus_b, i_bus_c] + + def plot_results_emt(self): + """ + Plot EMT simulation results + """ + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load,soc = self.variables_emt.x.value + tps = self.variables_emt.x.time + + # Transform abc to dq0 + i_vsc_d, i_vsc_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll)]) + v_sh_d, v_sh_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, theta_pll)]) + i_bus_d, i_bus_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, theta_pll)]) + + # Additional quantities to plot + v_sh_dq = v_sh_d + np.multiply(v_sh_q, 1j) + i_vsc_dq = i_vsc_d + np.multiply(i_vsc_q, 1j) + i_bus_dq = i_bus_d + np.multiply(i_bus_q, 1j) + v_vsc_dq = v_sh_dq + np.multiply((self.rf1_pu + self.xf1_pu * 1j), i_vsc_dq) + p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real + + p_sh = (v_sh_dq*np.conjugate(i_bus_dq)).real + q_sh = (v_sh_dq*np.conjugate(i_bus_dq)).imag + + p_load = v_dc*i_load + + results = DynamicalVariables( + name=['pi_cc_d', 'pi_cc_q', 'theta_pll', 'gamma_pll', 'i_vsc_d', 'i_vsc_q', 'v_sh_d', 'v_sh_q', 'i_bus_d', 'i_bus_q', 'i_l_f', 'v_dc_f', 'i_dc_f', 'i_load_f','x_1', 'x_2', 'i_L', 'v_dc', 'i_load', 'soc', 'p_vsc', 'p_sh', 'pload', 'q_sh'], + component=f"{self.type_}_{self.id}", + value=[pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_d, i_vsc_q, v_sh_d, v_sh_q, i_bus_d, i_bus_q, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc, p_vsc, p_sh, p_load, q_sh], + time=tps + ) + return results \ No newline at end of file diff --git a/sting/generator/gfli_e.py b/sting/generator/gfli_e.py new file mode 100644 index 0000000..7e7f8ea --- /dev/null +++ b/sting/generator/gfli_e.py @@ -0,0 +1,577 @@ +""" +This module implements a GFLI that incorporates: +- LCL filter: Two Series RL branches (one branch is the transformer) and one Parallel RC shunt. +- Outer loop DC voltage PI controller +- DC-side capacitor dynamics with resistor and current source representing a load +- Current controller: A dq-based frame PI controller +- PLL: A basic implementation + +""" +# ---------------------- +# Import python packages +# ---------------------- +import numpy as np +from dataclasses import dataclass, field +from typing import NamedTuple, Optional + +# ------------------ +# Import sting code +# ------------------ +from sting.utils.dynamical_systems import StateSpaceModel, DynamicalVariables +from sting.utils.transformations import dq02abc, abc2dq0 +from sting.generator.core import Generator + +# ----------- +# Sub-classes +# ----------- +class PowerFlowVariables(NamedTuple): + p_bus: float + q_bus: float + vmag_bus: float + vphase_bus: float + + +class InitialConditionsEMT(NamedTuple): + vmag_bus: float + vphase_bus: float + p_bus: float + q_bus: float + angle_ref: float + pi_cc_d: float + pi_cc_q: float + i_vsc_d: float + i_vsc_q: float + i_bus_d: float + i_bus_q: float + v_lcl_sh_d: float + v_lcl_sh_q: float + i_bus_D: float + i_bus_Q: float + v_bus_D: float + v_bus_Q: float + v_vsc_mag: float + v_vsc_DQ_phase: float + v_vsc_d: float + v_vsc_q: float + p_vsc: float + v_dc: float + int_vdc: float + i_dc: float + i_load_ref: float + + +class VariablesEMT(NamedTuple): + x: DynamicalVariables + u: DynamicalVariables + y: DynamicalVariables + +# ----------- +# Main class +# ----------- +@dataclass(slots=True, kw_only=True, eq=False) +class GFLIe(Generator): + rf1_pu: float + xf1_pu: float + rsh_pu: float + csh_pu: float + txr_power_MVA: float + txr_voltage1_kV: float + txr_voltage2_kV: float + txr_r1_pu: float + txr_x1_pu: float + txr_r2_pu: float + txr_x2_pu: float + beta: float + kp_pll_pu: float + ki_pll_puHz: float + kp_cc_pu: float + ki_cc_puHz: float + v_dc_ref: float # added + c_dc: float # added + kp_oc_pu: float # added + ki_oc_puHz: float # added + Tload: float # added + r_dc: float # added + x_pll_rescale: np.ndarray = field(default_factory=lambda: np.array([[100, 0], [0, 1]])) + name: str = field(default_factory=str) + emt_init: Optional[InitialConditionsEMT] = None + ssm: Optional[StateSpaceModel] = None + + @property + def rf2_pu(self): + return (self.txr_r1_pu + self.txr_r2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def xf2_pu(self): + return (self.txr_x1_pu + self.txr_x2_pu) * self.base_power_MVA / self.txr_power_MVA + + @property + def wbase(self): + return 2 * np.pi * self.base_frequency_Hz + + def _build_small_signal_model(self): + + # Current PI controller + kp_cc, ki_cc = self.kp_cc_pu, self.ki_cc_puHz + pi_cc_d, pi_cc_q = self.emt_init.pi_cc_d, self.emt_init.pi_cc_q + + pi_controller = StateSpaceModel( A = np.zeros((2,2)), + B = ki_cc*np.hstack((np.eye(2), -np.eye(2))), + C = np.eye(2), + D = kp_cc*np.hstack((np.eye(2), -np.eye(2))), + u = DynamicalVariables(name=['i_bus_d_ref', 'i_bus_q_ref', 'i_bus_d', 'i_bus_q']), + y = DynamicalVariables(name=['e_d', 'e_q']), + x = DynamicalVariables( name=['pi_cc_d', 'pi_cc_q'], + init= [pi_cc_d, pi_cc_q]) ) + + # LCL filter + rf1, xf1, rf2, xf2, rsh, csh = self.rf1_pu, self.xf1_pu, self.rf2_pu, self.xf2_pu, self.rsh_pu, self.csh_pu + wb = self.wbase + i_vsc_d, i_vsc_q = self.emt_init.i_vsc_d, self.emt_init.i_vsc_q + i_bus_d, i_bus_q = self.emt_init.i_bus_d, self.emt_init.i_bus_q + v_lcl_sh_d, v_lcl_sh_q = self.emt_init.v_lcl_sh_d, self.emt_init.v_lcl_sh_q + + lcl_filter = StateSpaceModel( + A = wb*np.array([[-rf1/xf1 , 1 , 0 , 0 , -1/xf1 , 0], + [-1 , -rf1/xf1, 0 , 0 , 0 , -1/xf1], + [0 , 0 , -rf2/xf2 , 1 , 1/xf2 , 0], + [0 , 0 , -1 , -rf2/xf2, 0 , 1/xf2], + [1/csh , 0 , -1/csh , 0 , -1/(rsh*csh), 1], + [0 , 1/csh , 0 , -1/csh , -1 , -1/(rsh*csh)]]), + B = wb*np.array([[1/xf1 , 0 , 0 , 0 , i_vsc_q], + [0 , 1/xf1 , 0 , 0 , -i_vsc_d], + [0 , 0 , -1/xf2 , 0 , i_bus_q], + [0 , 0 , 0 , -1/xf2 , -i_bus_d], + [0 , 0 , 0 , 0 , v_lcl_sh_q], + [0 , 0 , 0 , 0 , -v_lcl_sh_d]]), + C = np.hstack((np.eye(4,4), np.zeros((4,2)))), + D = np.zeros((4,5)), + x = DynamicalVariables(name=["i_vsc_d", "i_vsc_q", "i_bus_d", "i_bus_q", "v_lcl_sh_d", "v_lcl_sh_q"], + init=[i_vsc_d, i_vsc_q, i_bus_d, i_bus_q, v_lcl_sh_d, v_lcl_sh_q]), + u = DynamicalVariables(name=['v_vsc_d', 'v_vsc_q', 'v_bus_d', 'v_bus_q', 'w']), + y = DynamicalVariables(name=["i_vsc_d", "i_vsc_q", "i_bus_d", "i_bus_q"])) + + # Phase-locked loop + kp_pll, ki_pll = self.kp_pll_pu, self.ki_pll_puHz + beta = self.beta + vmag_bus = self.emt_init.vmag_bus + sinphi = np.sin(self.emt_init.angle_ref*np.pi/180) + cosphi = np.cos(self.emt_init.angle_ref*np.pi/180) + int_pll = 0 + phase_pll = self.emt_init.angle_ref*np.pi/180 + + pll = StateSpaceModel( A = np.array([ [ 0 , -vmag_bus*ki_pll], + [1 , -1*vmag_bus*kp_pll]]), + B = np.array([ [-sinphi*ki_pll , +cosphi*ki_pll], + [-1*kp_pll*sinphi, 1*kp_pll*cosphi]]), + C = np.array([ [0 , 1], + [1/wb , -1/wb * vmag_bus*kp_pll]]), + D = np.array([ [0 , 0], + [-1/wb * kp_pll * sinphi , 1/wb * kp_pll * cosphi]]), + u = DynamicalVariables(name=['v_bus_D', 'v_bus_Q']), + y = DynamicalVariables(name=['phase', 'w']), + x = DynamicalVariables(name=["int_pll", "phase_pll"], + init=[int_pll, phase_pll] ) ) + + # Re-scale the states so that they are not very small numbers compared to + # other states. It was tested in EMT simulation. + #pll.A = self.x_pll_rescale @ pll.A @ scipy.linalg.inv(self.x_pll_rescale) + #pll.B = self.x_pll_rescale @ pll.B + #pll.C = pll.C @ scipy.linalg.inv(self.x_pll_rescale) + + # Outer control + DC capacitor dynamics + Kp, Ki, Cdc, Tload, r_dc = self.kp_oc_pu, self.ki_oc_puHz, self.c_dc, self.Tload, self.r_dc + outer_control = StateSpaceModel(A = np.array([[0, Ki, 0], + [0, -1/r_dc, -wb/Cdc], + [0, 0, -1/Tload]]), + B = np.array([[-Ki, 0, 0], + [0, 0, -wb/Cdc], + [0, 1/Tload, 0]]), + C = np.array([[1, Kp, 0], + [0, 1, 0]]), + D = np.array([[-Kp, 0, 0], + [0, 0, 0]]), + u = DynamicalVariables(name=["v_dc_ref", "i_load_ref", "idc"]), + y = DynamicalVariables(name=["i_bus_d_ref", "v_dc"]), + x = DynamicalVariables(name=["int_vdc", "v_dc", "i_load"], + init=[self.emt_init.int_vdc, self.emt_init.v_dc, self.emt_init.i_load_ref])) + + # Construction of CCM matrices + # ustack = F*ystack + G*u + + # ustack = i2dq_ref, i2dq_c, v1dq_c, v2dq_c, w, v2dq, vdcref, iload_ref, idc (14) + # y_stack = e1d, e1q, i1d_c, i1q_c, i2d_c, i2q_c, theta, w, i2d_ref, vdc (12) + # u = vdc_ref, iload_ref, i2q_ref, v2d, v2q + # y = i2dq + + # dc power balance linearization + v_dc = self.emt_init.v_dc + + b1 = self.emt_init.v_vsc_d/v_dc # i1d + b2 = self.emt_init.i_vsc_d/v_dc #e1d + b3 = - (self.emt_init.i_vsc_d/v_dc)*(self.xf1_pu+self.xf2_pu) #i2q + b4 = self.emt_init.v_vsc_q/v_dc # i1q + b5 = self.emt_init.i_vsc_q/v_dc # e1q + b6 = (self.emt_init.i_vsc_q/v_dc)*(self.xf1_pu+self.xf2_pu) #i2d + b7 = - self.emt_init.i_dc/v_dc #vdc + b8 = -(self.emt_init.i_vsc_q/v_dc)*self.beta*vmag_bus # theta + + # Construction of CCM matrices + Fccm = np.vstack( ( np.hstack((np.zeros((8, )), 1, 0)) ,# i2d_ref + np.zeros((10,)), # i2q_ref + np.hstack((np.zeros((2,4)), np.eye(2) ,np.zeros((2,4)))), # i2dq_c + [1, 0, 0, 0, 0, -(xf1+xf2), 0, 0, 0, 0], # v1d_c + [0, 1, 0, 0, (xf1+xf2), 0, -beta*vmag_bus, 0, 0, 0], # v1q_c + np.zeros((10, )) , # v2d_c + np.append( np.zeros((6,)) , [-vmag_bus, 0, 0, 0] ), # v2q_c + np.append( np.zeros((7,)) , [1, 0, 0] ), # w + np.zeros((2, 10)), # v2_dq + np.zeros((2, 10)), #vdc_ref, iload_ref + [b2, b5, b1, b4, b6, b3, b8, 0, 0, b7] #idc + ) + ) + + + Gccm = np.vstack(( np.zeros(5,), # i2ref_d, + [0, 0, 1, 0, 0], #i2q_ref + np.zeros((2,5)), #i2dq_c, + [0, 0, 0, beta*cosphi , beta*sinphi], # v1d_c + [0, 0, 0, -beta*sinphi, beta*cosphi], # v1q_c + [0, 0, 0, cosphi ,sinphi], # v2d_c + [0, 0, 0, -sinphi ,cosphi], # v2q_c + np.zeros((5, )), # w + np.hstack((np.zeros((2,3)), np.eye(2) ) ), # v2dq + [1, 0, 0, 0, 0], #vdc_ref + [0, 1, 0, 0, 0], #iload_ref + np.zeros((1,5)) # idc + ) + ) + + Hccm = np.vstack(( [ 0, 0 , 0, 0, cosphi , -sinphi, -sinphi*i_bus_d-cosphi*i_bus_q, 0, 0, 0], + [0, 0, 0, 0, sinphi , cosphi , cosphi*i_bus_d-sinphi*i_bus_q, 0, 0, 0] )) + + Lccm = np.zeros((2, 5)) + + components = [pi_controller, lcl_filter, pll, outer_control] + connections = [Fccm, Gccm, Hccm, Lccm] + + # Inputs and outputs + v_bus_D, v_bus_Q= self.emt_init.v_bus_D, self.emt_init.v_bus_Q + u = DynamicalVariables( + name=["v_dc_ref", "i_load_ref", "i_bus_q_ref", "v_bus_D", "v_bus_Q"], + type=["device", "device", "device", "grid", "grid"], + init=[self.emt_init.v_dc, self.emt_init.i_load_ref, self.emt_init.i_bus_q, v_bus_D, v_bus_Q]) + + i_bus_D, i_bus_Q= self.emt_init.i_bus_D, self.emt_init.i_bus_Q + y = DynamicalVariables( + name=['i_bus_D', 'i_bus_Q'], + init=[i_bus_D, i_bus_Q]) + + # Generate small-signal model + ssm = StateSpaceModel.from_interconnected(components, connections, u, y, component_label=f"{self.type_}_{self.id}") + + self.ssm = ssm + + def _calculate_emt_initial_conditions(self): + + + # Extract power flow solution + vmag_bus = self.power_flow_variables.vmag_bus + vphase_bus = self.power_flow_variables.vphase_bus + p_bus = self.power_flow_variables.p_bus + q_bus = self.power_flow_variables.q_bus + + # Voltage in the end of the LCL filter + v_bus_DQ = vmag_bus * np.exp(vphase_bus * np.pi / 180 * 1j) + angle_ref = np.angle(v_bus_DQ, deg=True) + + # Current sent from the end of the LCL filter + i_bus_DQ = (p_bus - q_bus * 1j) / np.conjugate(v_bus_DQ) + + # Voltage across the shunt element in the LCL filter + v_lcl_sh_DQ = v_bus_DQ + (self.rf2_pu + self.xf2_pu * 1j) * i_bus_DQ + + # Current flowing through shunt element of LCL filter + i_lcl_sh_DQ = v_lcl_sh_DQ * (self.csh_pu * 1j) + v_lcl_sh_DQ / self.rsh_pu + + # Current sent from the beginning of the LCL filter + i_vsc_DQ = i_bus_DQ + i_lcl_sh_DQ + v_vsc_DQ = v_lcl_sh_DQ + (self.rf1_pu + self.xf1_pu * 1j) * i_vsc_DQ + + # We refer the voltage and currents to the synchronous frames of the + # inverter + v_vsc_dq = v_vsc_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + i_vsc_dq = i_vsc_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + v_bus_dq = v_bus_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + i_bus_dq = i_bus_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + v_lcl_sh_dq = v_lcl_sh_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) + + # Initial conditions for the current controller + pi_cc_dq = ( + v_vsc_dq - self.beta * v_bus_dq - 1j * (self.xf1_pu + self.xf2_pu) * i_bus_dq + ) + + # DC-side initial conditions + v_dc = self.v_dc_ref + p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real # power at converter terminals + i_dc = p_vsc/v_dc + i_load = -v_dc/self.r_dc - i_dc + + self.emt_init = InitialConditionsEMT( + vmag_bus=vmag_bus, + vphase_bus=vphase_bus, + p_bus=p_bus, + q_bus=q_bus, + angle_ref=angle_ref, + pi_cc_d=pi_cc_dq.real, + pi_cc_q=pi_cc_dq.imag, + i_vsc_d=i_vsc_dq.real, + i_vsc_q=i_vsc_dq.imag, + i_bus_d=i_bus_dq.real, + i_bus_q=i_bus_dq.imag, + v_lcl_sh_d=v_lcl_sh_dq.real, + v_lcl_sh_q=v_lcl_sh_dq.imag, + i_bus_D=i_bus_DQ.real, + i_bus_Q=i_bus_DQ.imag, + v_bus_D=v_bus_DQ.real, + v_bus_Q=v_bus_DQ.imag, + v_vsc_mag = abs(v_vsc_DQ), + v_vsc_DQ_phase = np.angle(v_vsc_DQ, deg=True), + v_dc=v_dc, + p_vsc=p_vsc, + i_dc=i_dc, + int_vdc=i_bus_dq.real, + i_load_ref=i_load, + v_vsc_d=v_vsc_dq.real, + v_vsc_q=v_vsc_dq.imag + ) + + def define_variables_emt(self): + # States + # ------ + + # Initial conditions + angle_ref = self.emt_init.angle_ref + pi_cc_d, pi_cc_q = self.emt_init.pi_cc_d, self.emt_init.pi_cc_q + + # these quantities are already in the converter ref frame (defined by angle_ref) + i_bus_d, i_bus_q = self.emt_init.i_bus_d, self.emt_init.i_bus_q + i_vsc_d, i_vsc_q = self.emt_init.i_vsc_d, self.emt_init.i_vsc_q + v_sh_d, v_sh_q = self.emt_init.v_lcl_sh_d, self.emt_init.v_lcl_sh_q + + # convert to abc + i_bus_a, i_bus_b, i_bus_c = dq02abc(i_bus_d, i_bus_q, 0, angle_ref*np.pi/180) + i_vsc_a, i_vsc_b, i_vsc_c = dq02abc(i_vsc_d, i_vsc_q, 0, angle_ref*np.pi/180) + v_sh_a, v_sh_b, v_sh_c = dq02abc(v_sh_d, v_sh_q, 0, angle_ref*np.pi/180) + + x = DynamicalVariables( + name = ['pi_cc_d', 'pi_cc_q', 'theta_pll', 'gamma_pll', "i_vsc_a", "i_vsc_b", "i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c", "int_vdc", "v_dc", "i_load"], + component = f"{self.type_}_{self.id}", + init = [pi_cc_d, pi_cc_q, angle_ref * np.pi/180, 0, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, self.emt_init.int_vdc, self.emt_init.v_dc, self.emt_init.i_load_ref] + ) + + # Inputs + # ------ + + # Initial conditions + v_bus_D, v_bus_Q = self.emt_init.v_bus_D, self.emt_init.v_bus_Q + v_bus_a, v_bus_b, v_bus_c = dq02abc(v_bus_D, v_bus_Q, 0, 0) + + u = DynamicalVariables( + name=["v_dc_ref", "i_load_ref", "i_bus_q_ref", "v_bus_a", "v_bus_b", "v_bus_c"], + component=f"{self.type_}_{self.id}", + type=["device", "device", "device", "grid", "grid", "grid"], + init=[self.emt_init.v_dc, self.emt_init.i_load_ref, self.emt_init.i_bus_q, v_bus_a, v_bus_b, v_bus_c] + ) + + # Outputs + # ------- + + y = DynamicalVariables( + name=["i_bus_a", "i_bus_b", "i_bus_c"], + component=f"{self.type_}_{self.id}", + init=[i_bus_a, i_bus_b, i_bus_c] + ) + + self.variables_emt = VariablesEMT(x=x,u=u,y=y) + + def get_derivative_state_emt(self): + """ + It returns a vector with the differential equations that describe the dynamics of the GFLI. + This model includes: pi controller, pll, and LCL filter. + """ + # Get state values # here in progress + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, int_vdc, v_dc, i_load = self.variables_emt.x.value + + # Get input values (external inputs) + v_dc_ref, i_load_ref, i_bus_q_ref, v_bus_a, v_bus_b, v_bus_c = self.variables_emt.u.value + + # convert relevant quantities to dq + v_bus_d, v_bus_q, _ = abc2dq0(v_bus_a, v_bus_b, v_bus_c, theta_pll) + i_bus_d, i_bus_q, _ = abc2dq0(i_bus_a, i_bus_b, i_bus_c, theta_pll) + + # Update algebraic states + + # outer loop Vdc control + i_bus_d_ref = self.kp_oc_pu*(-v_dc_ref + v_dc) + int_vdc + + # current controller output + e_d = pi_cc_d + self.kp_cc_pu * (i_bus_d_ref - i_bus_d) + e_q = pi_cc_q + self.kp_cc_pu * (i_bus_q_ref - i_bus_q) + + v_vsc_d = e_d + self.beta * v_bus_d - (self.xf1_pu + self.xf2_pu) * i_bus_q + v_vsc_q = e_q + self.beta * v_bus_q + (self.xf1_pu + self.xf2_pu) * i_bus_d + + # calculate idc + i_vsc_d, i_vsc_q, _ = abc2dq0(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll) + i_dc = (v_vsc_d*i_vsc_d + v_vsc_q*i_vsc_q)/v_dc + + # convert to abc to feed into filter dynamics + v_vsc_a, v_vsc_b, v_vsc_c = dq02abc(v_vsc_d, v_vsc_q, 0, theta_pll) + + def current_controller_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the current controller. + The current controller has: virtual inertia, filter for active and reactive power. + """ + + # Definition of states for the ODEs of the current controller + pi_cc_d, pi_cc_q = y[0], y[1] + + # Extract the list of parameters + kp_cc = self.kp_cc_pu # proportional gain of current controller + ki_cc = self.ki_cc_puHz # integral gain of current controller + + # Define internal inputs for the current controller at timepoint "t" + i_bus_d_ref, i_bus_q_ref, i_bus_d, i_bus_q = internal_inputs + + # Define ODEs that describe the dynamics of the current controller + d_pi_cc_d = ki_cc * (i_bus_d_ref - i_bus_d) + d_pi_cc_q = ki_cc * (i_bus_q_ref - i_bus_q) + + return [d_pi_cc_d, d_pi_cc_q] + + def pll_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the PLL. + The PLL tracks the phase of the grid voltage. + """ + # Definition of states for the ODEs of the pll + theta_pll, gamma_pll = y[0], y[1] + + # Extract the list of parameters + kp_pll = self.kp_pll_pu # proportional gain of PLL + ki_pll = self.ki_pll_puHz # integral gain of PLL + w_base = self.wbase # base frequency of the system + + # Define voltage at bus + v_bus_q = internal_inputs + + # Define ODEs that describe the dynamics of the PLL + d_theta_pll = kp_pll * v_bus_q + gamma_pll + w_base + d_gamma_pll = ki_pll * v_bus_q + + return [d_theta_pll, d_gamma_pll] + + def lcl_filter_dynamics(y, internal_inputs): + """ + It returns the differential equations that describe the dynamics of the LCL filter. + The LCL filter connects the VSC to the grid. It has three branches: the first branch (RL) connects the VSC to the shunt element, the second branch is the shunt element (RC), and the third branch (RL) connects the shunt element to the grid. + """ + + # Definition of states for the ODEs of the LCL filter + i_vsc_a , i_vsc_b, i_vsc_c = y[0], y[1], y[2] # currents flowing out of VSC + v_sh_a, v_sh_b, v_sh_c = y[3], y[4], y[5] # currents flowing through paralell RC shunt + i_bus_a, i_bus_b, i_bus_c = y[6], y[7], y[8] # currents flowing to bus + + # Extract the list of parameters + r1 = self.rf1_pu # resistance [p.u.] of first branch of filter + l1 = self.xf1_pu # inductance [p.u.] of first branch of filter + r2 = self.rf2_pu # resistance [p.u.] of second branch of filter + l2 = self.xf2_pu # inductance [p.u.] of second branch of filter + rsh = self.rsh_pu # resistance [p.u.] of series RC shunt + csh = self.csh_pu # capacitance [p.u.] of series RC shunt + wb = self.wbase # nominal frequency of the system + + # Define voltage at vsc at timepoint "t" + v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c = internal_inputs + + # Define ODEs that describe the dynamics of the LCL filter + di_vsc_a = wb/l1 *(v_vsc_a - v_sh_a - r1 * i_vsc_a) + di_vsc_b = wb/l1 *(v_vsc_b - v_sh_b - r1 * i_vsc_b) + di_vsc_c = wb/l1 *(v_vsc_c - v_sh_c - r1 * i_vsc_c) + + dv_sh_a = wb/csh * (-v_sh_a/rsh + i_vsc_a - i_bus_a) + dv_sh_b = wb/csh * (-v_sh_b/rsh + i_vsc_b - i_bus_b) + dv_sh_c = wb/csh * (-v_sh_c/rsh + i_vsc_c - i_bus_c) + + di_bus_a = wb/l2 *(v_sh_a - v_bus_a - r2 * i_bus_a) + di_bus_b = wb/l2 *(v_sh_b - v_bus_b - r2 * i_bus_b) + di_bus_c = wb/l2 *(v_sh_c - v_bus_c - r2 * i_bus_c) + + return [di_vsc_a, di_vsc_b, di_vsc_c, dv_sh_a, dv_sh_b, dv_sh_c, di_bus_a, di_bus_b, di_bus_c] + + def outer_loop_and_dc_side(y, internal_inputs): + """ + Dynamics of PI controller (of Vdc), Vdc (capacitor dynamics based on current balance), and the load (current source). + """ + int_vdc, v_dc, i_load = y[0], y[1], y[2] + + v_dc_ref, i_load_ref, i_dc = internal_inputs + + d_int_vdc = self.ki_oc_puHz*(-v_dc_ref + v_dc) + d_vdc = (self.wbase/self.c_dc)*(-i_load - v_dc/self.r_dc - i_dc) + d_iload = 1/(self.Tload)*(i_load_ref - i_load) + + return [d_int_vdc, d_vdc, d_iload] + + d_pi_cc_d, d_pi_cc_q = current_controller_dynamics([pi_cc_d, pi_cc_q], [i_bus_d_ref, i_bus_q_ref, i_bus_d, i_bus_q]) + + d_theta_pll, d_gamma_pll = pll_dynamics([theta_pll, gamma_pll], v_bus_q) + + di_vsc_a, di_vsc_b, di_vsc_c, dv_sh_a, dv_sh_b, dv_sh_c, di_bus_a, di_bus_b, di_bus_c = lcl_filter_dynamics([i_vsc_a , i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c], [v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c]) + + d_int_vdc, d_vdc, d_iload = outer_loop_and_dc_side([int_vdc, v_dc, i_load], [v_dc_ref, i_load_ref, i_dc]) + + return [d_pi_cc_d, d_pi_cc_q, d_theta_pll, d_gamma_pll, di_vsc_a, di_vsc_b, di_vsc_c, dv_sh_a, dv_sh_b, dv_sh_c, di_bus_a, di_bus_b, di_bus_c, d_int_vdc, d_vdc, d_iload] + + def get_output_emt(self): + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, int_vdc, v_dc, i_load = self.variables_emt.x.value + return [i_bus_a, i_bus_b, i_bus_c] + + def plot_results_emt(self) -> DynamicalVariables: + """ + Plot EMT simulation results + """ + + pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, int_vdc, v_dc, i_load = self.variables_emt.x.value + + tps = self.variables_emt.x.time + + # Transform abc to dq0 + i_vsc_d, i_vsc_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_vsc_a, i_vsc_b, i_vsc_c, theta_pll)]) + v_sh_d, v_sh_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, theta_pll)]) + i_bus_d, i_bus_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, theta_pll)]) + + # Additional quantities to plot + v_sh_dq = v_sh_d + np.multiply(v_sh_q, 1j) + i_vsc_dq = i_vsc_d + np.multiply(i_vsc_q, 1j) + i_bus_dq = i_bus_d + np.multiply(i_bus_q, 1j) + v_vsc_dq = v_sh_dq + np.multiply((self.rf1_pu + self.xf1_pu * 1j), i_vsc_dq) + p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real + + p_sh = (v_sh_dq*np.conjugate(i_bus_dq)).real + q_sh = (v_sh_dq*np.conjugate(i_bus_dq)).imag + + p_load = v_dc*i_load + + results = DynamicalVariables( + name=['pi_cc_d', 'pi_cc_q', 'theta_pll', 'gamma_pll', 'i_vsc_d', 'i_vsc_q', 'v_sh_d', 'v_sh_q', 'i_bus_d', 'i_bus_q', 'int_vdc', 'v_dc', 'i_load', 'p_vsc', 'p_sh', 'pload', 'q_sh'], + component=f"{self.type_}_{self.id}", + value=[pi_cc_d, pi_cc_q, theta_pll, gamma_pll, i_vsc_d, i_vsc_q, v_sh_d, v_sh_q, i_bus_d, i_bus_q, int_vdc, v_dc, i_load, p_vsc, p_sh, p_load, q_sh], + time=tps + ) + return results \ No newline at end of file diff --git a/sting/generator/gfmi_e.py b/sting/generator/gfmi_e.py index 99cb9db..9212d55 100644 --- a/sting/generator/gfmi_e.py +++ b/sting/generator/gfmi_e.py @@ -8,6 +8,7 @@ - Voltage magnitude controller - DC-side DC-DC converter circuit and controller - DC-side load with controller +- does not model any battery resistance / lossless DC-DC converter """ # ---------------------- @@ -113,12 +114,12 @@ class GFMIe(Generator): Ti_load: float # for DC/DC controller - measurement filter Tload: float # time constant for actuation of load current change i_load_ref: float - #bus_id: int = None + Pbat_max_pu: float # maximum power capacity of battery (pu by S) + SOC_max_pu: float # maximum energy capacity of battery (pu by S) + SOC_init_pu: float # initial battery state of charge (pu) name: str = field(default_factory=str) - #pf: Optional[Power_flow_variables] = None emt_init: Optional[InitialConditionsEMT] = None ssm: Optional[StateSpaceModel] = None - #tags: ClassVar[list[str]] = ["generator"] @property def rf2_pu(self): @@ -292,7 +293,7 @@ def _build_small_signal_model(self): # DC circuit a1 = v_vsc_d/v_dc a2 = i_vsc_d/v_dc - a3 = self.emt_init.v_vsc_q/v_dc # is this just 0 ? + a3 = self.emt_init.v_vsc_q/v_dc a4 = i_vsc_q/v_dc a5 = -i_dc/v_dc @@ -402,11 +403,11 @@ def _calculate_emt_initial_conditions(self): v_lcl_sh_dq = v_lcl_sh_DQ * np.exp(-angle_ref * np.pi / 180 * 1j) # DC-side initial conditions - v_dc = self.v_dc_ref - duty_cycle = (v_dc - self.v_s)/v_dc + v_dc = self.v_dc_ref p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real # power at converter terminals i_dc = p_vsc/v_dc i_load = self.i_load_ref + duty_cycle = (v_dc - self.v_s)/v_dc i_L = (i_load+i_dc)/(1-duty_cycle) x_1 = i_L - self.Kff_idc*i_dc - self.Kff_iload*i_load x_2 = duty_cycle - self.kp_i_L*(x_1 - i_L + self.Kff_idc*i_dc + self.Kff_iload*i_load) @@ -422,7 +423,7 @@ def _calculate_emt_initial_conditions(self): v_ref=v_ref, angle_ref=angle_ref, v_vsc_d=v_vsc_dq.real, - v_vsc_q=v_vsc_dq.imag, # added + v_vsc_q=v_vsc_dq.imag, i_vsc_d=i_vsc_dq.real, i_vsc_q=i_vsc_dq.imag, i_bus_d=i_bus_dq.real, @@ -470,9 +471,9 @@ def define_variables_emt(self): v_dc, i_dc, i_L, x1, x2, i_load = self.emt_init.v_dc, self.emt_init.i_dc, self.emt_init.i_L, self.emt_init.x_1, self.emt_init.x_2, self.emt_init.i_load x = DynamicalVariables( - name = ['angle_pc', 'w_pc', 'p_pc', 'q_pc', 'gamma',"i_vsc_a", "i_vsc_b","i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c", 'i_l_f', 'v_dc_f', 'i_dc_f', 'i_load_f','x_1', 'x_2', 'i_L', 'v_dc', 'i_load'], + name = ['angle_pc', 'w_pc', 'p_pc', 'q_pc', 'gamma',"i_vsc_a", "i_vsc_b","i_vsc_c", "v_sh_a", "v_sh_b","v_sh_c", "i_bus_a", "i_bus_b", "i_bus_c", 'i_l_f', 'v_dc_f', 'i_dc_f', 'i_load_f','x_1', 'x_2', 'i_L', 'v_dc', 'i_load', 'soc'], component = f"{self.type_}_{self.id}", - init=[angle_ref*np.pi/180, 1.0, p_ref, q_ref, v_vsc_d, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_L, v_dc, i_dc, i_load, x1, x2, i_L, v_dc, i_load] + init=[angle_ref*np.pi/180, 1.0, p_ref, q_ref, v_vsc_d, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_L, v_dc, i_dc, i_load, x1, x2, i_L, v_dc, i_load, self.SOC_init_pu] ) # Inputs @@ -504,7 +505,7 @@ def define_variables_emt(self): def get_derivative_state_emt(self): # Get state values - angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load = self.variables_emt.x.value + angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc = self.variables_emt.x.value # Get input values (external inputs) p_ref, q_ref, v_ref, v_dc_ref, v_s, i_load_ref, v_bus_a, v_bus_b, v_bus_c = self.variables_emt.u.value @@ -515,21 +516,19 @@ def get_derivative_state_emt(self): i_vsc_d, i_vsc_q, _ = abc2dq0(i_vsc_a, i_vsc_b, i_vsc_c, angle_pc) # Do Q-V droop - v_sh_mag_ref = v_ref - self.droop_q_pu*(q_pc - q_ref) # droop on error from ref + v_sh_mag_ref = v_ref - self.droop_q_pu*(q_pc - q_ref) # adjusting voltage reference based on reactive power error (measured at capacitor) - # NB updating algebraic states! + # Updating converter terminal voltages v_vsc_d = gamma + self.kp_vc_pu*(v_sh_mag_ref - (v_sh_d**2 + v_sh_q**2)**0.5) # update v_vsc_q = 0.0 # update # convert to abc to feed into filter dynamics v_vsc_a, v_vsc_b, v_vsc_c = dq02abc(v_vsc_d, v_vsc_q, 0, angle_pc) # correct to use this angle? - # power balance + # DC/AC power balance i_dc = (v_vsc_d*i_vsc_d + v_vsc_q*i_vsc_q)/v_dc - # abc->dq conversions - # Differential equations # ---------------------- @@ -623,7 +622,7 @@ def dc_side(y, internal_inputs): DC-DC controller + circuit + load control """ # Define states - i_Lf, v_dcf, i_dcf, i_loadf, x_1, x_2, i_L, v_dc, i_load = y[0], y[1], y[2], y[3], y[4], y[5], y[6], y[7], y[8] + i_Lf, v_dcf, i_dcf, i_loadf, x_1, x_2, i_L, v_dc, i_load, soc = y[0], y[1], y[2], y[3], y[4], y[5], y[6], y[7], y[8], y[9] # Inputs i_dc, i_load_ref, v_dc_ref, v_s = internal_inputs @@ -643,21 +642,23 @@ def dc_side(y, internal_inputs): d_x_2 = Ki_iL*(Kp_vdc*(v_dc_ref - v_dcf) + x_1 - i_Lf + Kff_idc*i_dcf + Kff_iload*i_loadf) duty_cycle = Kp_iL*(Kp_vdc*(v_dc_ref - v_dcf) + x_1 - i_Lf + Kff_idc*i_dcf + Kff_iload*i_loadf) + x_2 - # Circuit equations + # Circuit equations d_v_dc = (wb/c_dc)*(-i_dc - i_load + (1-duty_cycle)*i_L) d_i_L = (wb/l_dc)*(v_s - (1-duty_cycle)*v_dc) # Load control - d_i_load = (1/Tload)*(i_load_ref - i_load) + d_i_load = (1/Tload)*(i_load_ref - i_load) - return [d_i_Lf, d_v_dcf, d_i_dcf, d_i_load_f, d_x_1, d_x_2, d_i_L, d_v_dc, d_i_load] - #return [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + #SOC + d_soc = i_L*v_s + + return [d_i_Lf, d_v_dcf, d_i_dcf, d_i_load_f, d_x_1, d_x_2, d_i_L, d_v_dc, d_i_load, d_soc] dy_pc = power_controller_dynamics([angle_pc, w_pc, p_pc, q_pc], [v_sh_d, v_sh_q, i_bus_d, i_bus_q, p_ref]) dy_vc = voltage_controller_dynamics([gamma], [v_sh_mag_ref, v_sh_d, v_sh_q]) dy_lcl = lcl_filter_dynamics([i_vsc_a , i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c], [v_vsc_a, v_vsc_b, v_vsc_c, v_bus_a, v_bus_b, v_bus_c]) - dy_dc_side = dc_side([i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load], [i_dc, i_load_ref, v_dc_ref, v_s]) + dy_dc_side = dc_side([i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc], [i_dc, i_load_ref, v_dc_ref, v_s]) return np.hstack([dy_pc, dy_vc, dy_lcl, dy_dc_side]) @@ -665,13 +666,13 @@ def dc_side(y, internal_inputs): def get_output_emt(self): # Output is i_bus_abc - angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load = self.variables_emt.x.value + angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc = self.variables_emt.x.value return [i_bus_a, i_bus_b, i_bus_c] - def plot_results_emt(self, output_dir): + def plot_results_emt(self) -> DynamicalVariables: - angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load = self.variables_emt.x.value + angle_pc, w_pc, p_pc, q_pc, gamma, i_vsc_a, i_vsc_b, i_vsc_c, v_sh_a, v_sh_b, v_sh_c, i_bus_a, i_bus_b, i_bus_c, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc = self.variables_emt.x.value tps = self.variables_emt.x.time @@ -680,162 +681,24 @@ def plot_results_emt(self, output_dir): v_sh_d, v_sh_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(v_sh_a, v_sh_b, v_sh_c, angle_pc)]) i_bus_d, i_bus_q, _ = zip(*[abc2dq0(a, b, c, ang) for a, b, c, ang in zip(i_bus_a, i_bus_b, i_bus_c, angle_pc)]) - # calculate v_vsc v_sh_dq = v_sh_d + np.multiply(v_sh_q, 1j) i_vsc_dq = i_vsc_d + np.multiply(i_vsc_q, 1j) + i_bus_dq = i_bus_d + np.multiply(i_bus_q, 1j) v_vsc_dq = v_sh_dq + np.multiply((self.rf1_pu + self.xf1_pu * 1j), i_vsc_dq) - - fig = make_subplots( - rows=12, cols=2, - horizontal_spacing=0.15, - vertical_spacing=0.05, - ) - - fig.add_trace(go.Scatter(x=tps, y=w_pc, mode='lines', line=dict(color='red', dash='solid')), - row=1, col=1) - fig.update_xaxes(title_text='Time [s]', row=1, col=1) - fig.update_yaxes(title_text='Frequency pc [p.u.]', row=1, col=1) - - fig.add_trace(go.Scatter(x=tps, y=angle_pc * 180 / np.pi, mode='lines', line=dict(color='red', dash='solid')), - row=1, col=2) - fig.update_xaxes(title_text='Time [s]', row=1, col=2) - fig.update_yaxes(title_text='Angle pc [deg]', row=1, col=2) - - fig.add_trace(go.Scatter(x=tps, y=p_pc, name="p_pc", mode='lines', line=dict(color='red', dash='solid')), - row=2, col=1) - fig.update_xaxes(title_text='Time [s]', row=2, col=1) - fig.update_yaxes(title_text='Active Power pc [p.u.]', row=2, col=1) - - fig.add_trace(go.Scatter(x=tps, y=q_pc, mode='lines', line=dict(color='red', dash='solid')), - row=2, col=2) - fig.update_xaxes(title_text='Time [s]', row=2, col=2) - fig.update_yaxes(title_text='Reactive Power pc [p.u.]', row=2, col=2) - - fig.add_trace(go.Scatter(x=tps, y=gamma, mode='lines', line=dict(color='red', dash='solid')), - row=3, col=1) - fig.update_xaxes(title_text='Time [s]', row=3, col=1) - fig.update_yaxes(title_text='Gamma [p.u.]', row=3, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_loadf, mode='lines', line=dict(color='red', dash='solid')), - row=3, col=2) - fig.update_xaxes(title_text='Time [s]', row=3, col=2) - fig.update_yaxes(title_text='iload_f [p.u.]', row=3, col=2) - - - - fig.add_trace(go.Scatter(x=tps, y=i_vsc_d, mode='lines', line=dict(color='red', dash='solid')), - row=4, col=1) - fig.update_xaxes(title_text='Time [s]', row=4, col=1) - fig.update_yaxes(title_text='i_vsc_d [p.u.]', row=4, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_vsc_q, mode='lines', line=dict(color='red', dash='solid')), - row=4, col=2) - fig.update_xaxes(title_text='Time [s]', row=4, col=2) - fig.update_yaxes(title_text='i_vsc_q [p.u.]', row=4, col=2) - - fig.add_trace(go.Scatter(x=tps, y=v_sh_d, mode='lines', line=dict(color='red', dash='solid')), - row=5, col=1) - fig.update_xaxes(title_text='Time [s]', row=5, col=1) - fig.update_yaxes(title_text='v_sh_d [p.u.]', row=5, col=1) - - fig.add_trace(go.Scatter(x=tps, y=v_sh_q, mode='lines', line=dict(color='red', dash='solid')), - row=5, col=2) - fig.update_xaxes(title_text='Time [s]', row=5, col=2) - fig.update_yaxes(title_text='v_sh_q [p.u.]', row=5, col=2) - - fig.add_trace(go.Scatter(x=tps, y=i_bus_d, mode='lines', line=dict(color='red', dash='solid')), - row=6, col=1) - fig.update_xaxes(title_text='Time [s]', row=6, col=1) - fig.update_yaxes(title_text='i_bus_d [p.u.]', row=6, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_bus_q, mode='lines', line=dict(color='red', dash='solid')), - row=6, col=2) - fig.update_xaxes(title_text='Time [s]', row=6, col=2) - fig.update_yaxes(title_text='i_bus_q [p.u.]', row=6, col=2) - - fig.add_trace(go.Scatter(x=tps, y=v_dc, mode='lines', line=dict(color='red', dash='solid')), - row=7, col=1) - fig.update_xaxes(title_text='Time [s]', row=7, col=1) - fig.update_yaxes(title_text='v_dc [p.u.]', row=7, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_L, mode='lines', line=dict(color='red', dash='solid')), - row=7, col=2) - fig.update_xaxes(title_text='Time [s]', row=7, col=2) - fig.update_yaxes(title_text='i_L [p.u.]', row=7, col=2) - - - fig.add_trace(go.Scatter(x=tps, y=v_dcf, mode='lines', line=dict(color='red', dash='solid')), - row=8, col=1) - fig.update_xaxes(title_text='Time [s]', row=8, col=1) - fig.update_yaxes(title_text='v_dcf [p.u.]', row=8, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_Lf, mode='lines', line=dict(color='red', dash='solid')), - row=8, col=2) - fig.update_xaxes(title_text='Time [s]', row=8, col=2) - fig.update_yaxes(title_text='i_Lf [p.u.]', row=8, col=2) - - - fig.add_trace(go.Scatter(x=tps, y=i_dcf, mode='lines', line=dict(color='red', dash='solid')), - row=9, col=1) - fig.update_xaxes(title_text='Time [s]', row=9, col=1) - fig.update_yaxes(title_text='i_dcf [p.u.]', row=9, col=1) - - fig.add_trace(go.Scatter(x=tps, y=x1, mode='lines', line=dict(color='red', dash='solid')), - row=9, col=2) - fig.update_xaxes(title_text='Time [s]', row=9, col=2) - fig.update_yaxes(title_text='x1 [p.u.]', row=9, col=2) - - fig.add_trace(go.Scatter(x=tps, y=x2, mode='lines', line=dict(color='red', dash='solid')), - row=10, col=1) - fig.update_xaxes(title_text='Time [s]', row=10, col=1) - fig.update_yaxes(title_text='x2 [p.u.]', row=10, col=1) - - fig.add_trace(go.Scatter(x=tps, y=i_load, mode='lines', line=dict(color='red', dash='solid')), - row=10, col=2) - fig.update_xaxes(title_text='Time [s]', row=10, col=2) - fig.update_yaxes(title_text='i_load [p.u.]', row=10, col=2) - - # power comparisons (calculated) p_vsc = (v_vsc_dq*np.conjugate(i_vsc_dq)).real + + p_sh = (v_sh_dq*np.conjugate(i_bus_dq)).real + p_load = i_load*v_dc - p_ref, q_ref, v_ref, v_dc_ref, v_s, i_load_ref, v_bus_a, v_bus_b, v_bus_c = self.variables_emt.u.value - p_bat = i_L*v_s - fig.add_trace(go.Scatter(x=tps, y=p_vsc, name="p_vsc", mode='lines', line=dict(color='red', dash='solid')), - row=11, col=1) - fig.add_trace(go.Scatter(x=tps, y=p_load, name="p_load", mode='lines', line=dict(color='blue', dash='solid')), - row=11, col=1) - fig.add_trace(go.Scatter(x=tps, y=p_bat, name="p_bat", mode='lines', line=dict(color='green', dash='solid')), - row=11, col=1) - - - fig.update_xaxes(title_text='Time [s]', row=11, col=1) - fig.update_yaxes(title_text='p [p.u.]', row=11, col=1) - - # v_vsc (calculated) - fig.add_trace(go.Scatter(x=tps, y=v_vsc_dq.real, mode='lines', line=dict(color='red', dash='solid')), - row=12, col=1) - fig.update_xaxes(title_text='Time [s]', row=12, col=1) - fig.update_yaxes(title_text='v_vsc_d [p.u.]', row=12, col=1) - - fig.add_trace(go.Scatter(x=tps, y=v_vsc_dq.imag, mode='lines', line=dict(color='red', dash='solid')), - row=12, col=2) - fig.update_xaxes(title_text='Time [s]', row=12, col=2) - fig.update_yaxes(title_text='v_vsc_q [p.u.]', row=12, col=2) - - - name = f"{self.type_}_{self.id}" - fig.update_layout( title_text = name, - title_x=0.5, - showlegend = False, - ) - - fig.update_layout(height=1200*2, - width=800*2, - showlegend=False, - margin={'t': 0, 'l': 0, 'b': 0, 'r': 0}) - fig.write_html(os.path.join(output_dir, name + ".html")) - - - - + results_emt = DynamicalVariables( + name = ['angle_pc', 'w_pc', 'p_pc', 'q_pc', 'gamma',"i_vsc_d", "i_vsc_q", "v_sh_d", "v_sh_q", "i_bus_d", "i_bus_q", "i_Lf", "v_dcf", "i_dcf", "i_loadf", "x1", "x2", "i_L", "v_dc", "i_load", "soc", 'p_vsc', 'p_sh', 'p_load'], + component = f"{self.type_}_{self.id}", + value=[angle_pc*np.pi/180, w_pc, p_pc, q_pc, gamma, i_vsc_d, i_vsc_q, v_sh_d, v_sh_q, i_bus_d, i_bus_q, i_Lf, v_dcf, i_dcf, i_loadf, x1, x2, i_L, v_dc, i_load, soc, p_vsc, p_sh, p_load], + time=tps + ) + + return results_emt + + + \ No newline at end of file diff --git a/sting/load/switching_load.py b/sting/load/switching_load.py index cbb1368..6972a26 100644 --- a/sting/load/switching_load.py +++ b/sting/load/switching_load.py @@ -16,6 +16,7 @@ from sting.utils.transformations import abc2dq0 from sting.generator.core import Generator from sting.modules.simulation_emt.utils import VariablesEMT +from sting.modules.power_flow.utils import ACPowerFlowSolution # ------------- # Main class @@ -118,4 +119,10 @@ def plot_results_emt(self): value=[i_bus_d, i_bus_q, p, q], time=time, ) - return results \ No newline at end of file + return results + + def load_ac_power_flow_solution(self, timepoint: str, pf_solution: ACPowerFlowSolution): + return + + def _calculate_emt_initial_conditions(self): + return \ No newline at end of file diff --git a/sting/system/core.py b/sting/system/core.py index da72d70..2ee3099 100644 --- a/sting/system/core.py +++ b/sting/system/core.py @@ -27,6 +27,8 @@ GFMI18B, GFMI18P, GFMI25A, + GFLI23A, + GFLI16C, SynchronousGenerator14A, SynchronousGenerator17A, SynchronousGenerator23A, @@ -85,6 +87,8 @@ class System: gfmi_18b: list[GFMI18B] = None gfmi_18p: list[GFMI18P] = None gfmi_25a: list[GFMI25A] = None + gfli_23a: list[GFLI23A] = None + gfli_16c: list[GFLI16C] = None synchronous_generator_14a: list[SynchronousGenerator14A] = None synchronous_generator_17a: list[SynchronousGenerator17A] = None synchronous_generator_23a: list[SynchronousGenerator23A] = None @@ -317,4 +321,4 @@ def __repr__(self): if len(getattr(self, c_type)) > 0: lines_to_display.append(f" - {c_type}: {len(getattr(self, c_type))}") - return "\n".join(lines_to_display) + return "\n".join(lines_to_display) \ No newline at end of file diff --git a/tests/emt_tests/test_gfli_16c.py b/tests/emt_tests/test_gfli_16c.py new file mode 100644 index 0000000..fb709ed --- /dev/null +++ b/tests/emt_tests/test_gfli_16c.py @@ -0,0 +1,89 @@ +import os +import sys +sys.path.append("/Users/ruthkravis/Documents/STING") + +from sting import main +from sting.system import System + +# Core components +from sting.generator import VoltageSource4A, GFLI16C +from sting.line import LinePiModel +from sting.bus import Bus +from sting.load import Load +from sting.timescales import Timepoint + +# Set up a temporary directory used by all tests +case_directory = os.path.join(os.getcwd(), "tests", "emt_tests", "tmpdir") +os.makedirs(case_directory, exist_ok=True) + +# ------------------------------------------------------- +# Construct a simple 2-bus system +# ------------------------------------------------------- +t1 = Timepoint(name="t1", weight=1) +# Buses +bus_1 = Bus(name="lima", base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, minimum_voltage_pu=1, maximum_voltage_pu=1) +bus_2 = Bus(name="santiago", base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, minimum_voltage_pu=0.95, maximum_voltage_pu=1.3) +load_1 = Load(bus="santiago", timepoint="t1", load_MW=50, load_MVAR=20) +# Transmission +line_1 = LinePiModel( + name="lima_to_santiago", from_bus="lima", to_bus="santiago", + base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, + r_pu=0.0001, x_pu=0.001, g_pu=0.0005, b_pu=0.001 + ) +# Generation +source = VoltageSource4A( + name="lima_source", bus="lima", + minimum_active_power_MW=-200, maximum_active_power_MW=200, minimum_reactive_power_MVAR=-500, maximum_reactive_power_MVAR=500, + cost_variable_USDperMWh=0, base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, + r_pu=0.001, x_pu=0.005 +) +gfli = GFLI16C( + name="santiago_gfl", bus="santiago", + # Power flow + minimum_active_power_MW=80, maximum_active_power_MW=80, minimum_reactive_power_MVAR=50, maximum_reactive_power_MVAR=51, + cost_variable_USDperMWh=10, base_power_MVA=100, base_voltage_kV=0.48, base_frequency_Hz=60, + # LCL filter + rf1_pu=0.002, xf1_pu=0.07, csh_pu=0.01, rsh_pu=1, + txr_power_MVA=100, txr_voltage1_kV=0.48, txr_voltage2_kV=230, txr_r1_pu=0.003/2, txr_x1_pu=0.08/2, txr_r2_pu=0.003/2, txr_x2_pu=0.08/2, + # Phase-locked loop (PLL) + kp_pll_rad_s=100, ki_pll_rad2_s2=2500, + # Inner current controller + kp_cc_pu=0.05, ki_cc_puHz=0.6, kff_cc=0.75, + # DC side + v_dc_ref=1.05, c_dc_pu=20.0, r_dc_pu=10, kp_oc_pu=2, ki_oc_puHz=10, Tload_s=0.001 +) + +system = System(case_directory=case_directory) + +# Build grid model +for component in [bus_1, bus_2, load_1, line_1, source, gfli, t1]: + system.add(component) + +system.apply("post_system_init", system) + +# ------------------------------------------------------- +# Run small-signal model and EMT simulations +# ------------------------------------------------------- + +# Step function inputs to simulate +def step1(t): + return 0.05 if t >= 0.1 else 0.0 + +def step2(t): + return -0.05 if t >= 100 else 0.0 + +inputs = { + 'gfli_16c_0': { + 'i_load_ref': step1, + 'v_dc_ref': step2, + } +} + +t_max = 1.5 # Simulation length in seconds + + +# Construct system and small-signal model +_, ssm = main.run_ssm(system=system, case_directory=case_directory) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation +main.run_emt(inputs=inputs, t_max=t_max, system=system, case_directory=case_directory) \ No newline at end of file diff --git a/tests/emt_tests/test_gfli_23a.py b/tests/emt_tests/test_gfli_23a.py new file mode 100644 index 0000000..05b8459 --- /dev/null +++ b/tests/emt_tests/test_gfli_23a.py @@ -0,0 +1,94 @@ +import os +import sys +sys.path.append("/Users/ruthkravis/Documents/STING") + +from sting import main, datasets +from sting.system import System + +# Core components +from sting.generator import VoltageSource4A, GFLI23A +from sting.line import LinePiModel +from sting.bus import Bus +from sting.load import Load +from sting.timescales import Timepoint + +# Set up a temporary directory used by all tests +case_directory = os.path.join(os.getcwd(), "tests", "emt_tests", "tmpdir") +os.makedirs(case_directory, exist_ok=True) + +# ------------------------------------------------------- +# Construct a simple 2-bus system +# ------------------------------------------------------- +t1 = Timepoint(name="t1", weight=1) +# Buses +bus_1 = Bus(name="lima", base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, minimum_voltage_pu=1, maximum_voltage_pu=1) +bus_2 = Bus(name="santiago", base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, minimum_voltage_pu=0.95, maximum_voltage_pu=1.3) +load_1 = Load(bus="santiago", timepoint="t1", load_MW=50, load_MVAR=20) +# Transmission +line_1 = LinePiModel( + name="lima_to_santiago", from_bus="lima", to_bus="santiago", + base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, + r_pu=0.0001, x_pu=0.001, g_pu=0.0005, b_pu=0.001 + ) +# Generation +source = VoltageSource4A( + name="lima_source", bus="lima", + minimum_active_power_MW=-200, maximum_active_power_MW=200, minimum_reactive_power_MVAR=-500, maximum_reactive_power_MVAR=500, + cost_variable_USDperMWh=0, base_power_MVA=100, base_voltage_kV=230, base_frequency_Hz=60, + r_pu=0.001, x_pu=0.005 +) + +gfli = GFLI23A( + name="santiago_gfl", bus="santiago", + # Power flow + minimum_active_power_MW=80, maximum_active_power_MW=80, minimum_reactive_power_MVAR=50, maximum_reactive_power_MVAR=51, + cost_variable_USDperMWh=10, base_power_MVA=100, base_voltage_kV=0.48, base_frequency_Hz=60, + # LCL filter + rf1_pu=0.002, xf1_pu=0.07, csh_pu=0.01, rsh_pu=1, + txr_power_MVA=100, txr_voltage1_kV=0.48, txr_voltage2_kV=230, txr_r1_pu=0.003/2, txr_x1_pu=0.08/2, txr_r2_pu=0.003/2, txr_x2_pu=0.08/2, + # Phase-locked loop (PLL) + kp_pll_rad_s=100, ki_pll_rad2_s2=2500, + # Inner current controller + kp_cc_pu=0.05, ki_cc_puHz=0.6, kff_cc=0.75, + # DC side + kp_vdc_pu=1.2, ki_vdc_puHz=20, kp_iL_pu=1, ki_iL_puHz=10, + l_dc_pu = 0.1, c_dc_pu = 20, + v_dc_ref = 1.05, v_s_pu = 0.5, + Ti_L_s = 0.01, Tv_dc_s = 0.01, Ti_dc_s = 0.01, kff_idc = 1, kff_iload = 1, Ti_load_s = 0.01, + Tload_s = 0.0001, i_load_ref = 0.3 +) + +system = System(case_directory=case_directory) + +# Build grid modelx +for component in [bus_1, bus_2, load_1, line_1, source, gfli, t1]: + system.add(component) + +system.apply("post_system_init", system) + +# ------------------------------------------------------- +# Run small-signal model and EMT simulations +# ------------------------------------------------------- + +# Step function inputs to simulate +def step1(t): + return 0.1 if t >= 0.5 else 0.0 + +def step2(t): + return -0.1 if t >= 0.5 else 0.0 + +inputs = { + 'gfli_23a_0': { + 'v_s': step1, + 'i_load_ref': step2, + } +} + +t_max = 1.5 # Simulation length in seconds + + +# Construct system and small-signal model +_, ssm = main.run_ssm(system=system, case_directory=case_directory) +ssm.simulate_ssm(t_max=t_max, inputs=inputs) +# Run EMT simulation +main.run_emt(inputs=inputs, t_max=t_max, system=system, case_directory=case_directory) \ No newline at end of file