Tutorial 7: Policy Constraints
Interactive Notebook of the tutorial
As show in previous tutorials, the settings file can be changed to adapt to a number of different systems. In Tutorial 3, we discussed how the setting Time Domain Reduction can reduce the computation time of the solver. Other settings, however, directly impact the values of the solution itself. This tutorial goes over the policy attributes in the settings and shows how implementing certain policies affects the optimal solution in GenX. To demonstrate these effects, we will be using example_systems/1_three_zones.
Table of Contents
- No Policy Constraints
- CO2 Cap
- Energy Share Requirement
- Capacity Reserve Margin
- Minimum Capacity Requirement
- All Together
No Policy Constraints
using JuMP
using HiGHS
using GenX
using CSV
using DataFrames
using Plots
using StatsPlotscase = joinpath("example_systems/1_three_zones")
genx_settings = GenX.get_settings_path(case, "genx_settings.yml");
writeoutput_settings = GenX.get_settings_path(case, "output_settings.yml")
setup = GenX.configure_settings(genx_settings,writeoutput_settings)Configuring Settings
Dict{Any, Any} with 33 entries:
"HydrogenHourlyMatching" => 0
"NetworkExpansion" => 1
"TimeDomainReductionFolder" => "TDR_results"
"WriteOutputs" => "full"
"SystemFolder" => "system"
"EnableJuMPStringNames" => 1
"Trans_Loss_Segments" => 1
"ModelingtoGenerateAlternativeSlack" => 0.1
"PoliciesFolder" => "policies"
"MultiStage" => 0
"ComputeConflicts" => 1
"OverwriteResults" => 0
"ModelingToGenerateAlternatives" => 0
"MaxCapReq" => 0
"MinCapReq" => 1
"CO2Cap" => 2
"WriteShadowPrices" => 1
"OperationalReserves" => 0
"ParameterScale" => 1
"EnergyShareRequirement" => 0
"PrintModel" => 0
"TimeDomainReduction" => 1
"DC_OPF" => 0
"CapacityReserveMargin" => 0
"MethodofMorris" => 0
⋮ => ⋮The settings we'll focus on here are , CO2Cap, EnergyShareRequirement, CapacityReserveMargin, and MinCapReq. Each of these ensures that the environmental impact of the model is taken into account, and are therefore referred to as policy settings . For more information on what each one does, see the documentation on [Emission mitigation policies].
println("MaxCapReq: ", setup["MaxCapReq"])
println("MinCapReq: ", setup["MinCapReq"])
println("CO2Cap: ", setup["CO2Cap"])
println("EnergyShareRequirement: ", setup["EnergyShareRequirement"])
println("CapacityReserveMargin: ", setup["CapacityReserveMargin"])MaxCapReq: 0
MinCapReq: 1
CO2Cap: 2
EnergyShareRequirement: 0
CapacityReserveMargin: 01_three_zones uses MinCapReq and CO2Cap. For the purpose of this tutorial, we're going to set these back to zero to start.
setup["MinCapReq"] = 0
setup["CO2Cap"] = 0;Now, we'll generate and solve the model using these results:
## Delte Previous TDR Results
if "TDR_results" in cd(readdir,case)
rm(joinpath(case,"TDR_results"), recursive=true)
end
### Create TDR_Results
TDRpath = joinpath(case, setup["TimeDomainReductionFolder"])
system_path = joinpath(case, setup["SystemFolder"])
settings_path = GenX.get_settings_path(case)
if setup["TimeDomainReduction"] == 1
GenX.prevent_doubled_timedomainreduction(system_path)
if !GenX.time_domain_reduced_files_exist(TDRpath)
println("Clustering Time Series Data (Grouped)...")
GenX.cluster_inputs(case, settings_path, setup)
else
println("Time Series Data Already Clustered.")
end
end
Clustering Time Series Data (Grouped)...
Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CSV Files Successfully Read In From example_systems/1_three_zones
Error: Geography Key 1 is invalid. Select `System' or `Zone'.
Dict{String, Any} with 9 entries:
"RMSE" => Dict("ME_NG"=>0.210014, "ME_onshore_wind_z3"=>0.310986, "D…
"OutputDF" => 1848×19 DataFrame
"ColToZoneMap" => Dict("Demand_MW_z3"=>3, "CT_battery_z2"=>2, "MA_natural_ga…
"ClusterObject" => KmeansResult{Matrix{Float64}, Float64, Int64}([-0.734116 2…
"TDRsetup" => Dict{Any, Any}("IterativelyAddPeriods"=>1, "ExtremePeriods…
"Assignments" => [1, 1, 1, 1, 2, 2, 2, 2, 2, 3 … 6, 9, 3, 10, 10, 10, 11,…
"InputDF" => 1680×52 DataFrame
"Weights" => [673.846, 1179.23, 842.308, 673.846, 1010.77, 1347.69, 134…
"Centers" => Any[4, 8, 12, 15, 20, 23, 27, 30, 44, 48, 49]OPTIMIZER = GenX.configure_solver(settings_path,HiGHS.Optimizer);
inputs = GenX.load_inputs(setup, case)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CSV Files Successfully Read In From example_systems/1_three_zones
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Dict{Any, Any} with 67 entries:
"Z" => 3
"LOSS_LINES" => [1, 2]
"STOR_HYDRO_SHORT_DURATION" => Int64[]
"RET_CAP_CHARGE" => Set{Int64}()
"pC_D_Curtail" => [50.0, 45.0, 27.5, 10.0]
"pTrans_Max_Possible" => [5.9, 4.0]
"pNet_Map" => [1.0 -1.0 0.0; 1.0 0.0 -1.0]
"omega" => 4.01099, 4.01099, 4.01099, 4.01099, 4.01099, …
"pMax_Line_Reinforcement" => [2.95, 2.0]
"RET_CAP_ENERGY" => Int64[]
"RESOURCES" => AbstractResource
"COMMIT" => [1, 2, 3]
"pMax_D_Curtail" => [1.0, 0.04, 0.024, 0.003]
"STOR_ALL" => [8, 9, 10]
"THERM_ALL" => [1, 2, 3]
"REP_PERIOD" => 11
"PWFU_Num_Segments" => 0
"STOR_LONG_DURATION" => Int64[]
"THERM_COMMIT_PWFU" => Int64[]
"STOR_SYMMETRIC" => [8, 9, 10]
"VRE" => [4, 5, 6, 7]
"RETRO" => Int64[]
"THERM_COMMIT" => [1, 2, 3]
"TRANS_LOSS_SEGS" => 1
"H" => 168
⋮ => ⋮EP = GenX.generate_model(setup,inputs,OPTIMIZER)Discharge Module
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
A JuMP Model
Minimization problem with:
Variables: 120136
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZEROGenX.solve_model(EP,setup)Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118155 rows, 81204 cols, 422835 nonzeros
110998 rows, 74047 cols, 423349 nonzeros
Presolve : Reductions: rows 110998(-42394); columns 74047(-46089); elements 423349(-47782)
Solving the presolved LP
IPX model has 110998 rows, 74047 columns and 423349 nonzeros
Input
Number of variables: 74047
Number of free variables: 3696
Number of constraints: 110998
Number of equality constraints: 16867
Number of matrix entries: 423349
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 1.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 8.62e+00 3.81e+02 3.30336414e+06 -5.31617580e+06 3.30e+03 0s
1 4.09e+00 1.06e+02 2.34353411e+05 -5.13796175e+06 1.43e+03 0s
2 3.78e+00 7.03e+01 1.87013341e+05 -1.15199236e+07 1.34e+03 0s
3 1.33e+00 4.12e+01 -3.76464137e+05 -1.37088411e+07 7.85e+02 1s
Constructing starting basis...
4 4.13e-01 1.08e+01 2.66640168e+05 -8.48314805e+06 2.43e+02 3s
5 1.12e-01 5.62e+00 3.71879810e+05 -5.58576107e+06 1.28e+02 4s
6 7.53e-03 1.62e+00 2.30531116e+05 -1.92720962e+06 3.67e+01 5s
7 9.27e-04 1.77e-01 1.30486918e+05 -3.83901614e+05 5.66e+00 6s
8 1.14e-04 4.38e-02 5.27259057e+04 -1.00386376e+05 1.48e+00 7s
9 1.52e-05 6.88e-03 2.76584248e+04 -2.19746140e+04 3.52e-01 8s
10 5.20e-06 2.59e-03 1.39025442e+04 -7.44814138e+03 1.35e-01 8s
11 2.36e-06 1.09e-03 1.02345396e+04 -1.80403130e+03 7.13e-02 10s
12 1.03e-06 3.59e-04 7.72508848e+03 1.35005473e+03 3.59e-02 12s
13 6.67e-07 1.53e-04 6.83171406e+03 2.57204744e+03 2.35e-02 15s
14 5.06e-07 7.64e-05 6.41494456e+03 3.13597410e+03 1.79e-02 18s
15 3.52e-07 4.64e-05 5.95636098e+03 3.44861286e+03 1.36e-02 21s
16 1.69e-07 2.49e-05 5.33436713e+03 3.75261594e+03 8.58e-03 24s
17 1.38e-07 2.05e-05 5.23488752e+03 3.81660239e+03 7.68e-03 26s
18 1.21e-07 1.95e-05 5.23765885e+03 3.83998603e+03 7.57e-03 28s
19 7.35e-08 1.60e-05 5.05272742e+03 3.91685812e+03 6.15e-03 30s
20 6.04e-08 1.49e-05 5.02221768e+03 3.93278446e+03 5.90e-03 33s
21 2.85e-08 1.13e-05 4.88298181e+03 4.01774654e+03 4.68e-03 35s
22 2.29e-08 6.29e-06 4.83470832e+03 4.00260600e+03 4.48e-03 37s
23 1.31e-08 3.63e-06 4.72358228e+03 4.16712858e+03 3.00e-03 38s
24 9.10e-09 2.96e-06 4.70648899e+03 4.19085995e+03 2.77e-03 40s
25 4.45e-09 1.89e-06 4.63836996e+03 4.26416898e+03 2.01e-03 41s
26 3.49e-09 1.84e-06 4.63722238e+03 4.26628187e+03 1.99e-03 42s
27 2.15e-09 1.23e-06 4.59679916e+03 4.32342389e+03 1.47e-03 43s
28 1.87e-09 1.07e-06 4.59259771e+03 4.33476451e+03 1.39e-03 46s
29 1.58e-09 1.05e-06 4.59058841e+03 4.33567604e+03 1.37e-03 48s
30 1.18e-09 8.27e-07 4.58014487e+03 4.35414040e+03 1.21e-03 49s
31 7.95e-10 4.22e-07 4.56632970e+03 4.39355672e+03 9.27e-04 51s
32 4.34e-10 3.79e-07 4.55792749e+03 4.39835388e+03 8.56e-04 51s
33 2.37e-10 2.16e-07 4.54724964e+03 4.42097386e+03 6.77e-04 52s
34 2.10e-10 2.06e-07 4.54686537e+03 4.42339252e+03 6.62e-04 53s
35 7.73e-11 1.26e-07 4.53250796e+03 4.44139125e+03 4.89e-04 54s
36 1.55e-11 1.06e-07 4.52064756e+03 4.44667475e+03 3.97e-04 55s
37 1.50e-11 1.03e-07 4.52062467e+03 4.44749533e+03 3.92e-04 55s
38 9.79e-12 1.00e-07 4.52199331e+03 4.44806728e+03 3.96e-04 56s
39 8.92e-12 6.93e-08 4.52041735e+03 4.46101031e+03 3.19e-04 56s
40 7.30e-12 5.17e-08 4.52001352e+03 4.46367984e+03 3.02e-04 57s
41 4.70e-12 3.05e-08 4.51328477e+03 4.47536516e+03 2.03e-04 57s
42 3.83e-12 2.70e-08 4.51240381e+03 4.47626904e+03 1.94e-04 58s
43 2.85e-12 2.63e-08 4.51136761e+03 4.47647929e+03 1.87e-04 59s
44 2.10e-12 1.31e-08 4.50946086e+03 4.48203628e+03 1.47e-04 59s
45 1.31e-12 4.15e-09 4.50665353e+03 4.48821996e+03 9.88e-05 60s
46 9.09e-13 3.31e-09 4.50579733e+03 4.48871202e+03 9.15e-05 61s
47 9.09e-13 3.26e-09 4.50576718e+03 4.48852664e+03 9.24e-05 61s
48 7.53e-13 2.25e-09 4.50502226e+03 4.49018328e+03 7.95e-05 62s
49 7.53e-13 2.21e-09 4.50492035e+03 4.48999997e+03 7.99e-05 62s
50 5.83e-13 1.52e-09 4.50350728e+03 4.49199895e+03 6.17e-05 63s
51 1.99e-13 1.32e-09 4.50092854e+03 4.49240806e+03 4.57e-05 63s
52 1.78e-13 1.23e-09 4.50080001e+03 4.49253227e+03 4.43e-05 64s
53 9.24e-14 7.11e-10 4.49993325e+03 4.49367022e+03 3.36e-05 64s
54 7.11e-14 5.59e-10 4.49966942e+03 4.49408670e+03 2.99e-05 65s
55 7.11e-14 5.54e-10 4.49963721e+03 4.49407202e+03 2.98e-05 65s
56 7.11e-14 5.25e-10 4.49964358e+03 4.49413082e+03 2.95e-05 66s
57 4.97e-14 3.86e-10 4.49901737e+03 4.49483758e+03 2.24e-05 66s
58 4.97e-14 3.77e-10 4.49900976e+03 4.49485417e+03 2.23e-05 66s
59 4.97e-14 3.61e-10 4.49894867e+03 4.49494477e+03 2.15e-05 67s
60 2.84e-14 2.16e-10 4.49842279e+03 4.49567956e+03 1.47e-05 67s
61 2.84e-14 1.25e-10 4.49813093e+03 4.49622420e+03 1.02e-05 67s
62 2.13e-14 9.05e-11 4.49785493e+03 4.49641576e+03 7.71e-06 68s
63 2.13e-14 2.46e-11 4.49758346e+03 4.49698685e+03 3.20e-06 68s
64 2.13e-14 1.77e-11 4.49754878e+03 4.49704995e+03 2.67e-06 68s
65 2.13e-14 3.18e-12 4.49747123e+03 4.49722789e+03 1.30e-06 69s
66 2.13e-14 1.36e-12 4.49740334e+03 4.49723907e+03 8.80e-07 69s
67 2.13e-14 1.36e-12 4.49734663e+03 4.49727135e+03 4.03e-07 70s
68 2.13e-14 9.66e-13 4.49734376e+03 4.49727731e+03 3.56e-07 70s
69 2.13e-14 5.68e-13 4.49732633e+03 4.49728530e+03 2.20e-07 70s
70 2.13e-14 4.55e-13 4.49731802e+03 4.49730841e+03 5.15e-08 71s
71 2.13e-14 4.83e-13 4.49731683e+03 4.49730985e+03 3.74e-08 71s
72 2.13e-14 1.92e-12 4.49731281e+03 4.49731141e+03 7.53e-09 72s
73 2.13e-14 5.35e-12 4.49731227e+03 4.49731210e+03 9.13e-10 72s
74* 2.13e-14 2.73e-12 4.49731219e+03 4.49731218e+03 7.21e-11 72s
75* 2.84e-14 7.65e-12 4.49731219e+03 4.49731218e+03 4.94e-12 73s
76* 3.55e-14 4.81e-12 4.49731219e+03 4.49731219e+03 4.09e-13 73s
77* 3.55e-14 7.19e-12 4.49731219e+03 4.49731219e+03 2.31e-15 73s
Running crossover as requested
Primal residual before push phase: 1.40e-09
Dual residual before push phase: 5.05e-10
Number of dual pushes required: 41031
Number of primal pushes required: 722
Summary
Runtime: 73.32s
Status interior point solve: optimal
Status crossover: optimal
objective value: 4.49731219e+03
interior solution primal residual (abs/rel): 5.48e-11 / 3.35e-12
interior solution dual residual (abs/rel): 7.19e-12 / 1.79e-14
interior solution objective gap (abs/rel): -5.22e-10 / -1.16e-13
basic solution primal infeasibility: 2.78e-17
basic solution dual infeasibility: 5.41e-16
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 77
Crossover iterations: 4712
Objective value : 4.4973121850e+03
HiGHS run time : 73.55
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120136
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 73.97517013549805)Using value.(), we can see what the total capacity is of the optimized model:
totCap_base = value.(EP[:eTotalCap])10-element Vector{Float64}:
10.41532872265646
10.085613331810192
0.0
0.0
0.0
0.0
2.026239619715743
0.0
0.0
0.16552558225070782Each element corresponds to the MW value of the node in the grid. In 1_three_zones, there are ten nodes, each of which are either natural gas, wind, solar, or battery plants. We can see which is which using RESOURCE_NAMES in the inputs dictionary:
RT = inputs["RESOURCE_NAMES"];
DataFrame([RT totCap_base],["Resource","Total Capacity"])10×2 DataFrame
| Row | Resource | Total Capacity |
|---|---|---|
| Any | Any | |
| 1 | MA_natural_gas_combined_cycle | 10.4153 |
| 2 | CT_natural_gas_combined_cycle | 10.0856 |
| 3 | ME_natural_gas_combined_cycle | 0.0 |
| 4 | MA_solar_pv | 0.0 |
| 5 | CT_onshore_wind | 0.0 |
| 6 | CT_solar_pv | 0.0 |
| 7 | ME_onshore_wind | 2.02624 |
| 8 | MA_battery | 0.0 |
| 9 | CT_battery | 0.0 |
| 10 | ME_battery | 0.165526 |
To visualize the impact of the emmissions policies, let's group the nodes together by type and plot the data.
# Group by plant type
totCapB = [totCap_base[1] + totCap_base[2] + totCap_base[3], totCap_base[4] + totCap_base[6],
totCap_base[5] + totCap_base[7], totCap_base[8] + totCap_base[9] + totCap_base[10]]
totCapB = reshape(totCapB,(:,1)) # Convert to matrix4×1 Matrix{Float64}:
20.500942054466652
0.0
2.026239619715743
0.16552558225070782colors=[:silver :yellow :deepskyblue :violetred3]
G1 = groupedbar(transpose(totCapB), bar_position = :stack, bar_width=0.1,size=(400,450),
labels=["Natural Gas" "Solar" "Wind" "Battery"],
title="No Emissions Policies \n Obj Val: $(round(objective_value(EP),digits=6))",xticks=[ ],ylabel="GW",color=colors)
As you can see, with no limit on emissions, GenX goes straight to using natural gas. Let's try changing the settings to enforce emissions constraints.
CO2 Cap
The setting CO2Cap specifies if the model should have a constraint on CO$_2$ emmissions, and, if so, what that constraint should look like. There are three types, mass, load-based, and generator-based.
Mass Cap
The first type of constraint, done by setting CO2Cap to "1", is a mass based constraint, which simply puts a limit on the total tons of CO$_2$ able to be produced per megawatt of electricty.
setup["CO2Cap"] = 1;inputs = GenX.load_inputs(setup, case)
EP2 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP2,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge ModuleThermal.csv Successfully Read. Vre.csv Successfully Read. Storage.csv Successfully Read. Resourceenergysharerequirement.csv Successfully Read. Resourcecapacityreservemargin.csv Successfully Read. Resourceminimumcapacity_requirement.csv Successfully Read.
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118158 rows, 81204 cols, 433923 nonzeros
110739 rows, 73785 cols, 435465 nonzeros
Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 435465(-46757)
Solving the presolved LP
IPX model has 110739 rows, 73785 columns and 435465 nonzeros
Input
Number of variables: 73785
Number of free variables: 3696
Number of constraints: 110739
Number of equality constraints: 16605
Number of matrix entries: 435465
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 4.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 1.16e+01 3.76e+02 3.33411424e+06 -5.16532632e+06 4.37e+03 0s
1 6.12e+00 1.19e+02 2.67580772e+05 -5.49991870e+06 2.15e+03 0s
2 5.78e+00 8.43e+01 2.63971420e+05 -1.26660532e+07 2.19e+03 1s
3 2.60e+00 5.19e+01 -6.33191198e+04 -1.58670064e+07 1.38e+03 1s
Constructing starting basis...
4 7.34e-01 1.69e+01 8.22606550e+05 -1.15977191e+07 4.66e+02 3s
5 3.33e-01 5.93e+00 6.52520930e+05 -5.60493380e+06 1.92e+02 5s
6 1.40e-01 1.86e+00 4.30003244e+05 -2.61740021e+06 7.56e+01 6s
7 7.48e-02 6.92e-01 3.17908008e+05 -1.47858711e+06 3.76e+01 7s
8 1.34e-02 2.13e-01 1.58499195e+05 -7.36966970e+05 1.06e+01 8s
9 8.58e-03 1.84e-01 1.38726156e+05 -6.77517443e+05 8.88e+00 9s
10 1.85e-03 1.25e-01 1.06997055e+05 -5.46895734e+05 6.03e+00 10s
11 9.24e-04 6.46e-02 8.86553337e+04 -3.44818602e+05 3.62e+00 11s
12 4.63e-04 4.30e-02 7.38073046e+04 -2.58650422e+05 2.62e+00 12s
13 2.59e-04 1.76e-02 5.82580398e+04 -1.15494132e+05 1.25e+00 13s
14 1.82e-04 1.25e-02 5.26785356e+04 -8.56355514e+04 9.61e-01 14s
15 8.88e-05 9.97e-03 4.58204676e+04 -6.94861851e+04 7.82e-01 15s
16 4.53e-05 6.30e-03 3.78921045e+04 -3.64421549e+04 4.86e-01 16s
17 2.06e-05 3.52e-03 3.37528536e+04 -1.59069943e+04 3.10e-01 17s
18 1.03e-05 1.99e-03 3.04164644e+04 -2.07682393e+03 1.95e-01 18s
19 8.47e-06 1.65e-03 3.00013657e+04 4.67701651e+02 1.75e-01 19s
20 7.43e-06 1.51e-03 2.96873596e+04 1.69164986e+03 1.65e-01 20s
21 4.34e-06 1.21e-03 2.86080014e+04 4.49654207e+03 1.41e-01 21s
22 3.15e-06 9.70e-04 2.84959673e+04 6.35826288e+03 1.28e-01 21s
23 8.47e-07 3.92e-04 2.73823203e+04 1.23933845e+04 8.37e-02 22s
24 2.40e-07 1.04e-04 2.61231516e+04 1.76443726e+04 4.63e-02 23s
25 2.22e-07 9.36e-05 2.60148183e+04 1.78437138e+04 4.45e-02 24s
26 1.62e-07 7.29e-05 2.55552259e+04 1.84206144e+04 3.88e-02 24s
27 1.22e-07 5.52e-05 2.50949238e+04 1.91000865e+04 3.25e-02 25s
28 1.09e-07 4.85e-05 2.50021728e+04 1.92517935e+04 3.12e-02 26s
29 8.94e-08 4.45e-05 2.47907107e+04 1.93334302e+04 2.96e-02 27s
30 8.24e-08 4.34e-05 2.47681701e+04 1.93720252e+04 2.92e-02 28s
31 7.16e-08 2.50e-05 2.46362518e+04 1.99291856e+04 2.54e-02 29s
32 4.66e-08 2.01e-05 2.42437587e+04 2.01152325e+04 2.23e-02 29s
33 4.19e-08 1.97e-05 2.42647574e+04 2.01301840e+04 2.23e-02 30s
34 2.79e-08 1.90e-05 2.40142742e+04 2.01663344e+04 2.08e-02 31s
35 2.32e-08 6.69e-06 2.39399116e+04 2.06855599e+04 1.75e-02 31s
36 1.07e-08 5.30e-06 2.34566702e+04 2.08955297e+04 1.38e-02 32s
37 9.51e-09 4.35e-06 2.33786345e+04 2.11021969e+04 1.22e-02 33s
38 8.47e-09 3.86e-06 2.33591312e+04 2.11486293e+04 1.19e-02 34s
39 4.72e-09 2.75e-06 2.31415700e+04 2.13759124e+04 9.49e-03 35s
40 4.12e-09 2.60e-06 2.31287674e+04 2.13971288e+04 9.30e-03 35s
41 4.08e-09 2.30e-06 2.31279677e+04 2.14560762e+04 8.98e-03 36s
42 2.31e-09 1.19e-06 2.29798114e+04 2.17571173e+04 6.57e-03 37s
43 2.12e-09 1.08e-06 2.29572577e+04 2.17902511e+04 6.27e-03 37s
44 1.50e-09 6.92e-07 2.28682893e+04 2.19491402e+04 4.93e-03 38s
45 1.44e-09 5.32e-07 2.28678426e+04 2.19786865e+04 4.77e-03 39s
46 7.50e-10 1.52e-07 2.27876378e+04 2.21512825e+04 3.41e-03 39s
47 6.72e-10 1.34e-07 2.27673512e+04 2.21739594e+04 3.18e-03 40s
48 4.76e-10 2.75e-08 2.27150227e+04 2.23098580e+04 2.17e-03 41s
49 3.86e-10 2.55e-08 2.26819898e+04 2.23156051e+04 1.97e-03 41s
50 3.42e-10 2.05e-08 2.26687731e+04 2.23252871e+04 1.84e-03 42s
51 3.03e-10 1.42e-08 2.26566767e+04 2.23383080e+04 1.71e-03 42s
52 1.93e-10 1.06e-08 2.26117685e+04 2.23551537e+04 1.38e-03 43s
53 1.66e-10 3.63e-09 2.25954131e+04 2.24149312e+04 9.68e-04 44s
54 8.18e-11 9.07e-10 2.25454653e+04 2.24370312e+04 5.82e-04 44s
55 5.43e-11 4.51e-10 2.25280247e+04 2.24432375e+04 4.55e-04 46s
56 5.00e-11 4.05e-10 2.25264013e+04 2.24433424e+04 4.46e-04 46s
57 4.69e-11 3.79e-10 2.25244405e+04 2.24432461e+04 4.36e-04 47s
58 4.68e-11 3.45e-10 2.25244112e+04 2.24428231e+04 4.38e-04 47s
59 4.43e-11 3.07e-10 2.25225216e+04 2.24434057e+04 4.24e-04 48s
60 4.09e-11 2.55e-11 2.25200762e+04 2.24519301e+04 3.66e-04 48s
61 3.36e-11 2.18e-11 2.25158099e+04 2.24513558e+04 3.46e-04 49s
62 2.89e-11 1.00e-11 2.25119474e+04 2.24545183e+04 3.08e-04 49s
63 1.40e-11 1.82e-12 2.24943596e+04 2.24673979e+04 1.45e-04 50s
64 7.30e-12 9.09e-13 2.24854412e+04 2.24712286e+04 7.62e-05 50s
65 6.03e-12 9.09e-13 2.24836491e+04 2.24717155e+04 6.40e-05 51s
66 3.78e-12 2.27e-13 2.24803516e+04 2.24733198e+04 3.77e-05 51s
67 1.71e-12 2.27e-13 2.24769782e+04 2.24737620e+04 1.73e-05 52s
68 3.41e-13 2.27e-13 2.24749307e+04 2.24737943e+04 6.10e-06 52s
69 2.64e-13 9.09e-13 2.24743978e+04 2.24739891e+04 2.19e-06 53s
70 1.82e-13 5.65e-13 2.24742311e+04 2.24740852e+04 7.83e-07 53s
71 2.84e-13 9.09e-13 2.24741715e+04 2.24741245e+04 2.52e-07 54s
72 8.02e-14 2.21e-12 2.24741476e+04 2.24741372e+04 5.59e-08 54s
73 1.97e-13 3.76e-12 2.24741425e+04 2.24741405e+04 1.08e-08 55s
74 2.16e-13 4.30e-12 2.24741412e+04 2.24741409e+04 1.56e-09 55s
75* 3.92e-13 4.87e-12 2.24741410e+04 2.24741410e+04 1.34e-10 56s
76* 5.84e-12 3.78e-12 2.24741410e+04 2.24741410e+04 1.00e-11 56s
77* 3.24e-12 3.33e-12 2.24741410e+04 2.24741410e+04 1.95e-12 56s
Running crossover as requested
Primal residual before push phase: 1.33e-07
Dual residual before push phase: 8.94e-07
Number of dual pushes required: 34869
Number of primal pushes required: 3818
Summary
Runtime: 56.21s
Status interior point solve: optimal
Status crossover: optimal
objective value: 2.24741410e+04
interior solution primal residual (abs/rel): 2.42e-10 / 9.32e-12
interior solution dual residual (abs/rel): 3.61e-09 / 8.97e-12
interior solution objective gap (abs/rel): 3.00e-07 / 1.33e-11
basic solution primal infeasibility: 3.53e-13
basic solution dual infeasibility: 2.56e-14
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 77
Crossover iterations: 4765
Objective value : 2.2474141017e+04
HiGHS run time : 56.47
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120139
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 56.83114790916443)totCap2 = value.(EP2[:eTotalCap])
totCapB2 = [totCap2[1] + totCap2[2] + totCap2[3], totCap2[4] + totCap2[6],
totCap2[5] + totCap2[7], totCap2[8] + totCap2[9] + totCap2[10]]
DataFrame([RT totCap2],["Resource Type","Total Capacity"])10×2 DataFrame
| Row | Resource Type | Total Capacity |
|---|---|---|
| Any | Any | |
| 1 | MA_natural_gas_combined_cycle | 0.423658 |
| 2 | CT_natural_gas_combined_cycle | 0.629033 |
| 3 | ME_natural_gas_combined_cycle | 0.35463 |
| 4 | MA_solar_pv | 42.9756 |
| 5 | CT_onshore_wind | 0.0 |
| 6 | CT_solar_pv | 67.9858 |
| 7 | ME_onshore_wind | 7.80683 |
| 8 | MA_battery | 13.262 |
| 9 | CT_battery | 29.851 |
| 10 | ME_battery | 2.62375 |
G2 = groupedbar(transpose(totCapB2), bar_position = :stack, bar_width=0.1,size=(100,450),
labels=["Natural Gas" "Solar" "Wind" "Battery"],legend = false,title="CO2 Mass Cap \n Obj Val: $(round(objective_value(EP2),digits=6))",
xticks=[ ],ylabel="GW",color=colors)
plot(G2,G1,size=(900,450),titlefontsize=8)
The model favors solar power now, but natural gas and wind are also used. One thing to note is that the objective value of this system is much higher than it was without emissions constraints. The amount of CO$_2$ allowed is determined by the input file CO2_cap.csv:
CO2Cap = CSV.read(joinpath(case,"policies/CO2_cap.csv"),DataFrame,missingstring="NA")3×11 DataFrame
| Row | Column1 | Network_zones | CO_2_Cap_Zone_1 | CO_2_Cap_Zone_2 | CO_2_Cap_Zone_3 | CO_2_Max_tons_MWh_1 | CO_2_Max_tons_MWh_2 | CO_2_Max_tons_MWh_3 | CO_2_Max_Mtons_1 | CO_2_Max_Mtons_2 | CO_2_Max_Mtons_3 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| String3 | String3 | Int64 | Int64 | Int64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | MA | z1 | 1 | 0 | 0 | 0.05 | 0.0 | 0.0 | 0.018 | 0.0 | 0.0 |
| 2 | CT | z2 | 0 | 1 | 0 | 0.0 | 0.05 | 0.0 | 0.0 | 0.025 | 0.0 |
| 3 | ME | z3 | 0 | 0 | 1 | 0.0 | 0.0 | 0.05 | 0.0 | 0.0 | 0.025 |
Tolerance
Let's try setting the CO$_2$ emissions tolerance to 0 for all nodes:
CO2Cap2 = copy(CO2Cap); # Save old tolerancesCO2Cap2[!,"CO_2_Max_tons_MWh_1"] = [0.0;0.0;0.0];
CO2Cap2[!,"CO_2_Max_tons_MWh_2"] = [0.0;0.0;0.0];
CO2Cap2[!,"CO_2_Max_tons_MWh_3"] = [0.0;0.0;0.0];
CO2Cap2[!,"CO_2_Max_Mtons_1"] = [0.0;0.0;0.0];
CO2Cap2[!,"CO_2_Max_Mtons_2"] = [0.0;0.0;0.0];
CO2Cap2[!,"CO_2_Max_Mtons_3"] = [0.0;0.0;0.0];CSV.write(joinpath(case,"policies/CO2_cap.csv"),CO2Cap2)"example_systems/1_three_zones/policies/CO2_cap.csv"inputs = GenX.load_inputs(setup, case)
EP3 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP3,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
62715 rows, 59025 cols, 206619 nonzeros
55750 rows, 52060 cols, 206345 nonzeros
Presolve : Reductions: rows 55750(-97645); columns 52060(-68079); elements 206345(-275877)
Solving the presolved LP
IPX model has 55750 rows, 52060 columns and 206345 nonzeros
Input
Number of variables: 52060
Number of free variables: 3696
Number of constraints: 55750
Number of equality constraints: 11515
Number of matrix entries: 206345
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 12
Range of scaling factors: [5.00e-01, 1.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 8.66e+00 3.74e+02 3.32626622e+06 -5.13181178e+06 3.28e+03 0s
1 4.14e+00 1.16e+02 8.23203603e+05 -4.36728593e+06 1.47e+03 0s
2 3.82e+00 7.84e+01 7.99936610e+05 -9.74711636e+06 1.47e+03 0s
3 2.29e+00 4.73e+01 6.28103564e+05 -1.28672691e+07 1.11e+03 0s
Constructing starting basis...
4 3.38e-01 1.80e+01 1.09797314e+06 -8.08041855e+06 2.88e+02 1s
5 1.83e-01 6.66e+00 7.53792907e+05 -4.07570830e+06 1.33e+02 2s
6 8.56e-02 2.91e+00 4.53047274e+05 -2.12656299e+06 6.27e+01 2s
7 4.32e-02 1.06e+00 2.95761273e+05 -9.82158558e+05 2.74e+01 3s
8 2.45e-02 4.65e-01 2.07805891e+05 -5.33311956e+05 1.42e+01 3s
9 1.41e-02 2.62e-01 1.50001050e+05 -3.47096559e+05 8.53e+00 3s
10 1.09e-02 2.01e-01 1.34054733e+05 -3.01418233e+05 7.08e+00 3s
11 3.02e-03 1.70e-01 9.84009565e+04 -2.78142992e+05 5.84e+00 4s
12 6.80e-04 1.29e-01 8.22624601e+04 -2.40603504e+05 4.88e+00 4s
13 5.19e-04 8.27e-02 7.53145221e+04 -1.68983726e+05 3.45e+00 4s
14 2.11e-04 5.30e-02 6.28457097e+04 -1.25280563e+05 2.49e+00 4s
15 8.42e-05 2.34e-02 5.29276919e+04 -7.04624346e+04 1.44e+00 5s
16 4.88e-05 1.67e-02 4.48734610e+04 -4.78632217e+04 1.05e+00 5s
17 3.17e-05 1.36e-02 4.18106416e+04 -3.79473404e+04 8.85e-01 5s
18 1.54e-05 7.88e-03 3.47578913e+04 -1.29683476e+04 5.12e-01 6s
19 5.88e-06 3.32e-03 3.06596888e+04 3.42643300e+03 2.74e-01 6s
20 3.16e-06 1.13e-03 2.91816414e+04 1.11818829e+04 1.69e-01 6s
21 2.01e-06 7.37e-04 2.80927086e+04 1.35130431e+04 1.35e-01 7s
22 1.72e-06 6.41e-04 2.77751797e+04 1.42624417e+04 1.24e-01 7s
23 1.64e-06 5.49e-04 2.77386064e+04 1.47199954e+04 1.19e-01 7s
24 7.12e-07 4.66e-04 2.64331519e+04 1.56194992e+04 9.88e-02 8s
25 2.77e-07 2.78e-04 2.60769883e+04 1.74334827e+04 7.80e-02 8s
26 2.04e-07 1.45e-04 2.59822889e+04 1.87097084e+04 6.48e-02 8s
27 7.83e-08 8.86e-05 2.50321932e+04 2.02590181e+04 4.24e-02 9s
28 6.65e-08 7.45e-05 2.50172059e+04 2.04898905e+04 4.01e-02 9s
29 5.27e-08 5.73e-05 2.49264089e+04 2.09172601e+04 3.55e-02 9s
30 3.63e-08 4.90e-05 2.48125703e+04 2.11310315e+04 3.25e-02 10s
31 2.24e-08 2.37e-05 2.46270269e+04 2.20176436e+04 2.29e-02 10s
32 1.61e-08 1.80e-05 2.44783423e+04 2.23689799e+04 1.85e-02 10s
33 1.48e-08 1.67e-05 2.44673758e+04 2.24042775e+04 1.81e-02 11s
34 1.34e-08 1.10e-05 2.44514558e+04 2.26133491e+04 1.61e-02 11s
35 5.16e-09 8.66e-06 2.42796001e+04 2.27599671e+04 1.33e-02 11s
36 3.11e-09 3.47e-06 2.42120824e+04 2.31931323e+04 8.91e-03 11s
37 5.68e-14 2.68e-06 2.40481768e+04 2.32862443e+04 6.66e-03 12s
38 5.68e-14 1.15e-06 2.39818085e+04 2.36142391e+04 3.21e-03 12s
39 5.68e-14 1.13e-06 2.39814115e+04 2.36145091e+04 3.21e-03 12s
40 5.68e-14 9.70e-07 2.39782559e+04 2.36292988e+04 3.05e-03 13s
41 6.39e-14 9.03e-07 2.39740539e+04 2.36364177e+04 2.95e-03 13s
42 8.53e-14 8.87e-07 2.39736934e+04 2.36389906e+04 2.92e-03 13s
43 8.53e-14 4.51e-07 2.39668070e+04 2.37015134e+04 2.32e-03 14s
44 5.68e-14 3.63e-07 2.39530038e+04 2.37286287e+04 1.96e-03 14s
45 6.39e-14 2.62e-07 2.39399533e+04 2.37645087e+04 1.53e-03 15s
46 7.11e-14 2.35e-07 2.39403195e+04 2.37681261e+04 1.50e-03 15s
47 5.68e-14 1.07e-07 2.39354909e+04 2.38220443e+04 9.89e-04 15s
48 5.83e-14 8.32e-08 2.39319570e+04 2.38298216e+04 8.91e-04 16s
49 6.34e-14 8.23e-08 2.39320866e+04 2.38307615e+04 8.84e-04 16s
50 5.68e-14 2.73e-08 2.39222759e+04 2.38676200e+04 4.76e-04 16s
51 5.68e-14 1.81e-08 2.39090601e+04 2.38790981e+04 2.61e-04 17s
52 5.68e-14 2.13e-09 2.39087205e+04 2.38918872e+04 1.47e-04 17s
53 5.68e-14 6.69e-10 2.39073686e+04 2.38988570e+04 7.42e-05 17s
54 5.68e-14 1.71e-10 2.39057985e+04 2.39011287e+04 4.07e-05 17s
55 5.68e-14 4.37e-11 2.39047907e+04 2.39026178e+04 1.89e-05 18s
56 5.68e-14 2.50e-11 2.39045148e+04 2.39028929e+04 1.41e-05 18s
57 5.68e-14 1.27e-11 2.39040896e+04 2.39032417e+04 7.39e-06 18s
58 5.68e-14 2.27e-12 2.39039185e+04 2.39036010e+04 2.77e-06 18s
59 5.68e-14 4.55e-13 2.39038268e+04 2.39036756e+04 1.32e-06 18s
60 5.68e-14 9.09e-13 2.39037810e+04 2.39037207e+04 5.26e-07 18s
61 5.68e-14 2.27e-13 2.39037547e+04 2.39037335e+04 1.85e-07 19s
62 5.68e-14 2.27e-13 2.39037481e+04 2.39037351e+04 1.13e-07 19s
63 5.68e-14 4.55e-13 2.39037407e+04 2.39037385e+04 1.93e-08 19s
64 5.68e-14 1.14e-13 2.39037395e+04 2.39037392e+04 2.44e-09 19s
65* 5.68e-14 2.27e-13 2.39037393e+04 2.39037393e+04 1.93e-10 19s
66* 8.53e-14 2.27e-13 2.39037393e+04 2.39037393e+04 1.22e-11 19s
67* 5.68e-14 9.09e-13 2.39037393e+04 2.39037393e+04 1.62e-12 19s
Running crossover as requested
Primal residual before push phase: 7.05e-08
Dual residual before push phase: 9.91e-07
Number of dual pushes required: 2532
Number of primal pushes required: 3866
Summary
Runtime: 19.36s
Status interior point solve: optimal
Status crossover: optimal
objective value: 2.39037393e+04
interior solution primal residual (abs/rel): 2.26e-10 / 1.38e-11
interior solution dual residual (abs/rel): 2.64e-09 / 6.57e-12
interior solution objective gap (abs/rel): 2.04e-07 / 8.51e-12
basic solution primal infeasibility: 4.44e-15
basic solution dual infeasibility: 2.08e-15
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 67
Crossover iterations: 1428
Objective value : 2.3903739324e+04
HiGHS run time : 19.55
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120139
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 19.870718002319336)totCap3 = value.(EP3[:eTotalCap])
totCapB3 = [totCap3[1] + totCap3[2] + totCap3[3], totCap3[4] + totCap3[6],
totCap3[5] + totCap3[7], totCap3[8] + totCap3[9] + totCap3[10]]
println(DataFrame([RT totCap3],["Resource Type","Total Capacity"]))
println(" ")
println("Objective Value: ", objective_value(EP3))
G3 = groupedbar(transpose(totCapB3), bar_position = :stack, bar_width=0.1,size=(400,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors,
title="CO2 Mass Cap, Zero Tolerance \n Obj Val: $(round(objective_value(EP3),digits=6))")
plot(G3,G2,size=(800,450),titlefontsize=8)10×2 DataFrame
Row│Resource Type Total Capacity
│Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 0.0
2 │ CT_natural_gas_combined_cycle 0.0
3 │ ME_natural_gas_combined_cycle 0.0
4 │ MA_solar_pv 44.2331
5 │ CT_onshore_wind 0.0
6 │ CT_solar_pv 71.8741
7 │ ME_onshore_wind 5.55301
8 │ MA_battery 15.1583
9 │ CT_battery 30.3461
10 │ ME_battery 2.16509
Objective Value: 23903.739324217397
As you can see, the use of natural gas has been eliminated compeltely. Note that the objective value increases here as well as renewable energy tends to cost more than natural gas.
CO2 Slack
Another thing we can do is, instead of demanding that the model 100% meet the CO$_2$ cap, we can add a penalty for if it violates the cap. This lets the system allow some CO$_2$ emmissions if it's determined the cost of the grid with some emmissions is low enough that it will offset the cost from the penalty variable. GenX will automatically incorporate this feature if a file by the name "CO2capslack.csv" is in the policies folder of the directory. For more information on other types of policy slack variables in GenX, see the documentation on [Policy Slack Variables].
Here, the CO$_2$ slack cap models a carbon tax of $250 per ton of emissions.
CO2Cap_slack = DataFrame(["CO_2_Cap_Zone_1" 250; "CO_2_Cap_Zone_2" 250; "CO_2_Cap_Zone_2" 250],["CO2_Cap_Constraint","PriceCap"])3×2 DataFrame
| Row | CO2_Cap_Constraint | PriceCap |
|---|---|---|
| Any | Any | |
| 1 | CO_2_Cap_Zone_1 | 250 |
| 2 | CO_2_Cap_Zone_2 | 250 |
| 3 | CO_2_Cap_Zone_2 | 250 |
CSV.write(joinpath(case,"policies/CO2_cap_slack.csv"),CO2Cap_slack)"example_systems/1_three_zones/policies/CO2_cap_slack.csv"And run it again,
inputs = GenX.load_inputs(setup, case)
EP4 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP4,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Non-served Energy Module
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118155 rows, 81204 cols, 422835 nonzeros
110998 rows, 74047 cols, 423349 nonzeros
Presolve : Reductions: rows 110998(-42397); columns 74047(-46092); elements 423349(-58873)
Solving the presolved LP
IPX model has 110998 rows, 74047 columns and 423349 nonzeros
Input
Number of variables: 74047
Number of free variables: 3696
Number of constraints: 110998
Number of equality constraints: 16867
Number of matrix entries: 423349
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 4.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 8.63e+00 3.73e+02 3.32376039e+06 -5.09189122e+06 3.23e+03 0s
1 4.16e+00 1.08e+02 3.13266750e+05 -4.82993364e+06 1.41e+03 0s
2 3.81e+00 7.25e+01 2.97980565e+05 -1.07780002e+07 1.30e+03 0s
3 1.46e+00 3.93e+01 -1.26079071e+05 -1.28105929e+07 7.47e+02 1s
Constructing starting basis...
4 3.74e-01 1.45e+01 3.73463343e+05 -8.41202259e+06 2.69e+02 3s
5 2.49e-01 2.56e+00 3.78613518e+05 -3.12923412e+06 7.93e+01 5s
6 1.75e-02 1.04e+00 2.12473288e+05 -1.52758882e+06 2.44e+01 6s
7 9.80e-04 2.35e-01 1.33331872e+05 -4.99760720e+05 6.87e+00 7s
8 2.77e-04 7.80e-02 7.82710921e+04 -1.61510326e+05 2.34e+00 9s
9 1.09e-04 2.70e-02 5.47955571e+04 -6.12119167e+04 9.57e-01 10s
10 3.77e-05 7.08e-03 4.55523212e+04 -2.90274240e+04 4.91e-01 11s
11 1.64e-05 2.18e-03 3.11621436e+04 -7.43748662e+03 2.29e-01 12s
12 7.39e-06 8.70e-04 2.26704941e+04 3.11900828e+02 1.27e-01 14s
13 3.59e-06 2.72e-04 1.86489763e+04 4.05425979e+03 8.00e-02 16s
14 1.90e-06 1.28e-04 1.56168633e+04 6.05326027e+03 5.19e-02 17s
15 1.47e-06 6.25e-05 1.47851456e+04 7.20102502e+03 4.10e-02 20s
16 1.02e-06 4.01e-05 1.38005552e+04 7.70711780e+03 3.28e-02 23s
17 5.81e-07 1.81e-05 1.24913828e+04 8.58555743e+03 2.10e-02 26s
18 3.56e-07 1.37e-05 1.18351621e+04 8.78570877e+03 1.64e-02 31s
19 2.30e-07 1.13e-05 1.14288935e+04 8.93097599e+03 1.34e-02 33s
20 1.42e-07 9.21e-06 1.12192893e+04 9.03497649e+03 1.17e-02 36s
21 1.04e-07 5.91e-06 1.11251312e+04 9.20617340e+03 1.03e-02 37s
22 6.54e-08 5.00e-06 1.09266006e+04 9.30098656e+03 8.73e-03 38s
23 3.83e-08 3.59e-06 1.07816598e+04 9.45321722e+03 7.13e-03 40s
24 3.66e-08 2.80e-06 1.07744564e+04 9.52604230e+03 6.70e-03 41s
25 1.07e-08 2.21e-06 1.06144079e+04 9.59738956e+03 5.46e-03 43s
26 5.77e-09 1.68e-06 1.05031968e+04 9.71311617e+03 4.24e-03 44s
27 4.09e-09 1.48e-06 1.04791745e+04 9.74918379e+03 3.92e-03 45s
28 2.28e-09 1.14e-06 1.04271389e+04 9.82526444e+03 3.23e-03 45s
29 1.81e-09 9.51e-07 1.04093731e+04 9.87287016e+03 2.88e-03 46s
30 1.59e-09 7.09e-07 1.04047419e+04 9.92089105e+03 2.59e-03 47s
31 1.03e-09 3.29e-07 1.03752597e+04 1.00341461e+04 1.83e-03 47s
32 6.21e-10 3.01e-07 1.03644649e+04 1.00391050e+04 1.74e-03 48s
33 3.74e-10 2.57e-07 1.03380266e+04 1.00569556e+04 1.51e-03 49s
34 1.20e-10 1.65e-07 1.03095303e+04 1.00951029e+04 1.15e-03 49s
35 8.55e-11 1.39e-07 1.03018149e+04 1.01086583e+04 1.04e-03 50s
36 5.07e-11 9.62e-08 1.02845256e+04 1.01405678e+04 7.72e-04 50s
37 4.04e-11 8.97e-08 1.02823253e+04 1.01443584e+04 7.39e-04 51s
38 2.54e-11 5.51e-08 1.02817374e+04 1.01594329e+04 6.55e-04 51s
39 1.73e-11 3.65e-08 1.02723681e+04 1.01802747e+04 4.93e-04 52s
40 1.50e-11 3.37e-08 1.02704612e+04 1.01830824e+04 4.68e-04 52s
41 2.61e-12 2.79e-08 1.02584016e+04 1.01890289e+04 3.72e-04 52s
42 2.42e-12 2.59e-08 1.02587461e+04 1.01906586e+04 3.65e-04 53s
43 2.04e-12 2.16e-08 1.02588163e+04 1.01942759e+04 3.46e-04 53s
44 1.69e-12 2.05e-08 1.02582342e+04 1.01954859e+04 3.36e-04 54s
45 1.04e-12 1.61e-08 1.02537386e+04 1.02028401e+04 2.73e-04 54s
46 9.38e-13 1.33e-08 1.02531945e+04 1.02071474e+04 2.47e-04 55s
47 3.94e-13 7.40e-09 1.02494139e+04 1.02173046e+04 1.72e-04 55s
48 2.31e-13 4.66e-09 1.02462035e+04 1.02243167e+04 1.17e-04 55s
49 1.24e-13 1.54e-09 1.02449049e+04 1.02308377e+04 7.54e-05 56s
50 9.59e-14 1.22e-09 1.02441557e+04 1.02318785e+04 6.58e-05 56s
51 8.53e-14 7.46e-10 1.02438516e+04 1.02335717e+04 5.51e-05 57s
52 1.42e-14 3.41e-10 1.02409154e+04 1.02358650e+04 2.71e-05 57s
53 1.07e-14 1.08e-10 1.02400964e+04 1.02379817e+04 1.13e-05 57s
54 1.07e-14 3.88e-11 1.02398951e+04 1.02384972e+04 7.49e-06 58s
55 1.07e-14 2.85e-11 1.02397667e+04 1.02386509e+04 5.98e-06 58s
56 1.07e-14 5.40e-12 1.02395468e+04 1.02389275e+04 3.32e-06 58s
57 1.07e-14 1.24e-12 1.02394822e+04 1.02391409e+04 1.83e-06 59s
58 1.07e-14 5.68e-13 1.02394092e+04 1.02392128e+04 1.05e-06 59s
59 1.42e-14 2.56e-13 1.02393456e+04 1.02392605e+04 4.56e-07 59s
60 1.07e-14 1.99e-13 1.02393207e+04 1.02392697e+04 2.73e-07 60s
61 1.07e-14 5.19e-13 1.02393026e+04 1.02392801e+04 1.21e-07 60s
62 1.42e-14 4.83e-13 1.02392989e+04 1.02392826e+04 8.73e-08 60s
63 1.42e-14 7.18e-13 1.02392933e+04 1.02392837e+04 5.18e-08 61s
64 1.42e-14 2.95e-13 1.02392903e+04 1.02392845e+04 3.08e-08 61s
65 1.42e-14 1.46e-12 1.02392900e+04 1.02392874e+04 1.37e-08 61s
66 1.07e-14 5.17e-12 1.02392895e+04 1.02392888e+04 3.76e-09 62s
67* 1.42e-14 3.08e-12 1.02392891e+04 1.02392890e+04 3.57e-10 62s
68* 1.42e-14 4.08e-12 1.02392891e+04 1.02392891e+04 4.85e-11 62s
69* 1.42e-14 3.69e-12 1.02392891e+04 1.02392891e+04 9.52e-12 62s
70* 1.42e-14 1.83e-12 1.02392891e+04 1.02392891e+04 1.83e-12 62s
71* 1.78e-14 7.22e-12 1.02392891e+04 1.02392891e+04 4.13e-14 63s
72* 1.42e-14 6.20e-12 1.02392891e+04 1.02392891e+04 4.51e-18 63s
Running crossover as requested
Primal residual before push phase: 4.73e-09
Dual residual before push phase: 6.20e-12
Number of dual pushes required: 31290
Number of primal pushes required: 2494
Summary
Runtime: 62.84s
Status interior point solve: optimal
Status crossover: optimal
objective value: 1.02392891e+04
interior solution primal residual (abs/rel): 2.10e-13 / 1.28e-14
interior solution dual residual (abs/rel): 6.20e-12 / 1.54e-14
interior solution objective gap (abs/rel): -2.04e-10 / -1.99e-14
basic solution primal infeasibility: 7.64e-14
basic solution dual infeasibility: 2.10e-15
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 72
Crossover iterations: 1881
Objective value : 1.0239289084e+04
HiGHS run time : 63.07
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120139
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116442 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCCO2Cap_slack, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCTotalCO2CapSlack, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 63.40430498123169)value.(EP4[:eCTotalCO2CapSlack])2816.8936379034667totCap4 = value.(EP4[:eTotalCap])
totCapB4 = [totCap4[1] + totCap4[2] + totCap4[3], totCap4[4] + totCap4[6],
totCap4[5] + totCap4[7], totCap4[8] + totCap4[9] + totCap4[10]]
println(DataFrame([RT totCap4],["Resource Type","Total Capacity"]))
println(" ")
println("Objective Value: ", objective_value(EP4))
G4 = groupedbar(transpose(totCapB4), bar_position = :stack, bar_width=0.1,size=(400,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors,
title="CO2 Mass Cap, Zero + Slack Tolerance \n Obj Val: $(round(objective_value(EP4),digits=6))")
plot(G4,G3,G2,size=(900,450),layout=(1,3),titlefontsize=8)DataFrame
Row │Resource Type Total Capacity
│Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 6.20579
2 │ CT_natural_gas_combined_cycle 7.42028
3 │ ME_natural_gas_combined_cycle 0.0
4 │ MA_solar_pv 14.2444
5 │ CT_onshore_wind 12.0451
6 │ CT_solar_pv 5.26796
7 │ ME_onshore_wind 8.48774
8 │ MA_battery 2.29813
9 │ CT_battery 2.86763
10 │ ME_battery 0.390909
Objective Value: 10239.289084181632
Adding in the slack variables allowed for some natural gas to be used once again and decreased the overall cost (objective function).
Demand-based Cap
Another way to set the CO$_2$ emissions cap is to limit emissions as a function of the total demand in that region. This can be done by setting CO2Cap to "2" in the setup:
setup["CO2Cap"] = 2;Let's set the CO2_cap.csv back to it's original data, and remove the slack cap:
rm(joinpath(case,"policies/CO2_cap_slack.csv"))
CSV.write(joinpath(case,"policies/CO2_cap.csv"),CO2Cap)"example_systems/1_three_zones/policies/CO2_cap.csv"inputs = GenX.load_inputs(setup, case)
EP5 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP5,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Non-served Energy Module
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118158 rows, 81204 cols, 467187 nonzeros
110739 rows, 73785 cols, 468729 nonzeros
Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 468729(-46757)
Solving the presolved LP
IPX model has 110739 rows, 73785 columns and 468729 nonzeros
Input
Number of variables: 73785
Number of free variables: 3696
Number of constraints: 110739
Number of equality constraints: 16605
Number of matrix entries: 468729
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 4e+03]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 4.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 1.71e+03 3.41e+02 2.96378701e+06 -4.23587199e+06 5.75e+05 0s
1 1.13e+03 1.31e+02 -4.89641638e+08 -8.84226731e+06 3.61e+05 0s
2 1.09e+03 1.07e+02 -4.90812561e+08 -3.51675964e+07 4.11e+05 1s
3 3.74e+02 5.23e+01 -3.72143959e+08 -3.93800995e+07 1.67e+05 1s
Constructing starting basis...
4 1.74e+02 2.59e+01 -1.89656388e+08 -4.38688644e+07 8.52e+04 3s
5 1.55e+02 2.32e+01 -1.66927356e+08 -4.54471496e+07 8.00e+04 5s
6 2.66e+01 8.62e+00 9.40431644e+06 -4.92415912e+07 2.67e+04 6s
7 2.77e+00 7.85e-01 1.11318915e+07 -4.76427177e+07 3.01e+03 8s
8 6.28e-01 3.10e-01 1.16295577e+07 -3.03610025e+07 1.13e+03 10s
9 2.91e-01 1.04e-01 1.07968497e+07 -1.69468432e+07 4.87e+02 11s
10 1.59e-01 8.85e-02 1.01816820e+07 -1.56044371e+07 4.27e+02 12s
11 8.12e-02 5.53e-02 8.96818818e+06 -1.14192748e+07 2.85e+02 13s
12 3.88e-02 3.75e-02 7.95015583e+06 -9.07252228e+06 2.05e+02 14s
13 1.86e-02 2.40e-02 6.21487140e+06 -6.41755461e+06 1.30e+02 15s
14 6.01e-03 1.42e-02 4.80373854e+06 -4.66630024e+06 8.23e+01 18s
15 2.80e-03 8.10e-03 3.07276238e+06 -2.78932663e+06 4.44e+01 19s
16 1.05e-08 1.61e-03 1.54522332e+06 -1.15219019e+06 1.60e+01 20s
17 3.81e-09 1.40e-04 4.33083581e+05 -9.75643163e+04 2.89e+00 21s
18 2.40e-09 3.64e-05 1.17725979e+05 -2.92212886e+04 7.91e-01 22s
19 9.04e-10 1.11e-05 6.41480326e+04 -1.64155777e+04 4.33e-01 23s
20 7.36e-10 6.49e-06 4.91641901e+04 -1.03802768e+04 3.20e-01 24s
21 6.56e-10 4.00e-06 4.47995622e+04 -6.50448658e+03 2.75e-01 25s
22 3.74e-10 2.11e-06 3.33171246e+04 -2.19844201e+03 1.91e-01 25s
23 4.11e-10 1.17e-06 3.13473710e+04 -2.25128297e+02 1.69e-01 27s
24 5.32e-10 9.05e-07 3.07180077e+04 6.59187318e+02 1.61e-01 30s
25 2.07e-10 5.74e-07 2.40909020e+04 2.36880496e+03 1.17e-01 31s
26 1.46e-10 3.48e-07 1.95591688e+04 3.82235596e+03 8.44e-02 33s
27 9.56e-11 2.77e-07 1.91099002e+04 4.16735208e+03 8.02e-02 35s
28 1.16e-10 1.72e-07 1.68130157e+04 5.05922686e+03 6.31e-02 37s
29 1.10e-10 1.14e-07 1.58420855e+04 5.68901990e+03 5.45e-02 39s
30 1.00e-10 9.13e-08 1.50304186e+04 6.09927663e+03 4.79e-02 41s
31 4.79e-11 4.62e-08 1.44849049e+04 6.49417572e+03 4.29e-02 43s
32 5.38e-11 3.14e-08 1.33010538e+04 7.09832458e+03 3.33e-02 44s
33 1.97e-11 2.65e-08 1.31349015e+04 7.15881992e+03 3.21e-02 48s
34 4.25e-11 2.05e-08 1.26742180e+04 7.39203286e+03 2.83e-02 49s
35 3.24e-11 1.56e-08 1.23110122e+04 7.63239675e+03 2.51e-02 51s
36 4.28e-11 1.03e-08 1.20230845e+04 7.85317825e+03 2.24e-02 53s
37 1.56e-11 7.64e-09 1.12986653e+04 8.11596241e+03 1.71e-02 54s
38 2.81e-11 5.87e-09 1.11528506e+04 8.19787914e+03 1.59e-02 56s
39 2.28e-11 3.67e-09 1.06041200e+04 8.51424102e+03 1.12e-02 59s
40 1.25e-11 3.02e-09 1.05115674e+04 8.58142162e+03 1.04e-02 62s
41 7.03e-12 2.68e-09 1.03942162e+04 8.63482986e+03 9.44e-03 63s
42 1.77e-11 2.01e-09 1.03904932e+04 8.70538318e+03 9.04e-03 65s
43 4.66e-11 1.63e-09 1.03579306e+04 8.76566015e+03 8.54e-03 66s
44 1.96e-11 1.36e-09 1.01427363e+04 8.86378332e+03 6.86e-03 67s
45 3.52e-11 9.40e-10 1.00522553e+04 9.00927911e+03 5.60e-03 69s
46 4.02e-11 6.12e-10 9.95594984e+03 9.12097703e+03 4.48e-03 70s
47 4.90e-12 4.94e-10 9.90731026e+03 9.18680967e+03 3.87e-03 72s
48 1.55e-11 4.61e-10 9.90647522e+03 9.19643998e+03 3.81e-03 73s
49 1.17e-11 4.18e-10 9.90023591e+03 9.20935084e+03 3.71e-03 74s
50 3.61e-11 3.73e-10 9.89683026e+03 9.21663764e+03 3.65e-03 75s
51 1.84e-11 3.46e-10 9.85096096e+03 9.23460950e+03 3.31e-03 76s
52 7.42e-12 2.95e-10 9.78480033e+03 9.27774527e+03 2.72e-03 77s
53 3.37e-11 2.51e-10 9.78057662e+03 9.30246448e+03 2.56e-03 78s
54 1.43e-11 1.70e-10 9.77649230e+03 9.34200543e+03 2.33e-03 79s
55 9.01e-12 1.18e-10 9.73939839e+03 9.39121374e+03 1.87e-03 80s
56 4.50e-11 9.00e-11 9.72960001e+03 9.41702931e+03 1.68e-03 81s
57 3.25e-11 6.25e-11 9.70849173e+03 9.44892074e+03 1.39e-03 82s
58 9.01e-11 5.72e-11 9.69018439e+03 9.45729846e+03 1.25e-03 83s
59 6.80e-11 4.15e-11 9.68317655e+03 9.47569218e+03 1.11e-03 84s
60 1.68e-11 2.38e-11 9.67429417e+03 9.51041472e+03 8.79e-04 85s
61 4.47e-11 1.79e-11 9.65746593e+03 9.53257688e+03 6.70e-04 86s
62 3.95e-11 1.43e-11 9.65470621e+03 9.54043028e+03 6.13e-04 87s
63 7.96e-11 8.76e-12 9.64849756e+03 9.56065424e+03 4.71e-04 87s
64 6.17e-12 5.12e-12 9.64469171e+03 9.57460001e+03 3.76e-04 88s
65 7.14e-11 4.06e-12 9.63840771e+03 9.58058736e+03 3.10e-04 89s
66 1.43e-11 2.70e-12 9.63355725e+03 9.58844693e+03 2.42e-04 90s
67 8.82e-12 2.42e-12 9.62962513e+03 9.59238503e+03 2.00e-04 90s
68 5.56e-11 1.68e-12 9.62718274e+03 9.59579105e+03 1.68e-04 91s
69 6.50e-12 1.05e-12 9.62258889e+03 9.60351437e+03 1.02e-04 92s
70 2.18e-11 9.95e-13 9.62203860e+03 9.60540964e+03 8.92e-05 92s
71 1.79e-10 3.84e-13 9.62055756e+03 9.61022195e+03 5.54e-05 93s
72 5.57e-11 6.82e-13 9.61970045e+03 9.61377588e+03 3.18e-05 94s
73 6.29e-11 5.40e-13 9.61958853e+03 9.61443607e+03 2.76e-05 94s
74 1.14e-10 3.13e-13 9.61921628e+03 9.61498366e+03 2.27e-05 95s
75 6.88e-11 1.85e-13 9.61887340e+03 9.61542318e+03 1.85e-05 96s
76 5.60e-10 3.69e-13 9.61870185e+03 9.61564680e+03 1.64e-05 96s
77 5.59e-10 4.83e-13 9.61842859e+03 9.61678126e+03 8.84e-06 97s
78 6.89e-10 5.12e-13 9.61807911e+03 9.61688976e+03 6.38e-06 97s
79 3.62e-10 3.98e-13 9.61785021e+03 9.61733220e+03 2.78e-06 98s
80 1.09e-10 3.98e-13 9.61769612e+03 9.61747059e+03 1.21e-06 99s
81 2.20e-10 3.02e-13 9.61761335e+03 9.61750430e+03 5.85e-07 99s
82 1.17e-09 8.24e-13 9.61757268e+03 9.61751083e+03 3.32e-07 100s
83 4.79e-10 8.53e-13 9.61755931e+03 9.61753499e+03 1.30e-07 101s
84 5.65e-10 1.72e-12 9.61755460e+03 9.61753993e+03 7.87e-08 101s
85 6.45e-10 3.25e-12 9.61754798e+03 9.61754458e+03 1.83e-08 102s
86 5.31e-10 5.47e-12 9.61754612e+03 9.61754560e+03 2.83e-09 103s
87 2.06e-10 2.54e-12 9.61754586e+03 9.61754575e+03 5.86e-10 103s
88* 1.53e-09 8.29e-12 9.61754581e+03 9.61754579e+03 7.40e-11 105s
89* 8.48e-10 4.73e-12 9.61754580e+03 9.61754580e+03 1.14e-11 107s
Running crossover as requested
Primal residual before push phase: 1.05e-05
Dual residual before push phase: 3.29e-06
Number of dual pushes required: 25720
Number of primal pushes required: 3952
Summary
Runtime: 110.60s
Status interior point solve: optimal
Status crossover: optimal
objective value: 9.61754580e+03
interior solution primal residual (abs/rel): 2.90e-08 / 7.03e-12
interior solution dual residual (abs/rel): 9.59e-09 / 2.38e-11
interior solution objective gap (abs/rel): 2.01e-06 / 2.09e-10
basic solution primal infeasibility: 7.86e-13
basic solution dual infeasibility: 1.59e-15
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 89
Crossover iterations: 2840
Objective value : 9.6175458026e+03
HiGHS run time : 110.86
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120139
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 111.20706605911255)totCap5 = value.(EP5[:eTotalCap])
totCapB5 = [totCap5[1] + totCap5[2] + totCap5[3], totCap5[4] + totCap5[6],
totCap5[5] + totCap5[7], totCap5[8] + totCap5[9] + totCap5[10]]
toPlot = [transpose(totCapB2);transpose(totCapB5)]
println(DataFrame([RT totCap5],["Resource Type","Total Capacity"]))
println(" ")
G5 = groupedbar(transpose(totCapB5), bar_position = :stack, bar_width=.8,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors,
title="CO2 Demand Rate Cap \n Obj Val: $(round(objective_value(EP5),digits=6))")
plot(G5,G2,size=(800,450), titlefontsize=9) 10x2 DataFrame
Row | Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 8.3383
2 │ CT_natural_gas_combined_cycle 2.0596
3 │ ME_natural_gas_combined_cycle 0.527558
4 │ MA_solar_pv 18.4836
5 │ CT_onshore_wind 13.1932
6 │ CT_solar_pv 13.4186
7 │ ME_onshore_wind 11.3012
8 │ MA_battery 4.24838
9 │ CT_battery 4.50189
10 │ ME_battery 1.02331
Generator-based Cap
Finally, the third type of emissions cap in GenX is where the constraint is based on the ratio between the CO$_2$ cap and the generation of each node.
setup["CO2Cap"] = 3;inputs = GenX.load_inputs(setup, case)
EP6 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP6,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge ModuleThermal.csv Successfully Read. Vre.csv Successfully Read. Storage.csv Successfully Read. Resourceenergysharerequirement.csv Successfully Read. Resourcecapacityreservemargin.csv Successfully Read. Resourceminimumcapacity_requirement.csv Successfully Read.
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118158 rows, 81204 cols, 439344 nonzeros
110739 rows, 73785 cols, 440886 nonzeros
Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 440886(-54272)
Solving the presolved LP
IPX model has 110739 rows, 73785 columns and 440886 nonzeros
Input
Number of variables: 73785
Number of free variables: 3696
Number of constraints: 110739
Number of equality constraints: 16605
Number of matrix entries: 440886
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 4.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 8.76e+00 3.68e+02 3.33955953e+06 -4.97437905e+06 3.24e+03 0s
1 4.28e+00 1.43e+02 -2.33497546e+05 -5.06214948e+06 1.60e+03 0s
2 3.87e+00 8.66e+01 -3.47321172e+05 -1.15250215e+07 1.45e+03 1s
3 2.40e+00 4.93e+01 -6.12062937e+05 -1.60606245e+07 1.08e+03 1s
Constructing starting basis...
4 1.00e+00 2.05e+01 1.18453276e+05 -1.28403154e+07 4.55e+02 3s
5 7.57e-01 1.68e+01 1.98998600e+05 -1.20496551e+07 3.90e+02 7s
6 4.01e-01 1.11e+01 3.68752096e+05 -9.85292291e+06 2.70e+02 9s
7 1.69e-01 2.89e+00 4.01592303e+05 -3.46185082e+06 8.23e+01 10s
8 1.94e-02 8.41e-01 2.49236130e+05 -1.42423792e+06 2.40e+01 12s
9 3.13e-03 3.34e-01 1.41607109e+05 -6.32482360e+05 9.69e+00 13s
10 1.53e-03 2.07e-01 1.23187989e+05 -4.48100415e+05 6.79e+00 14s
11 4.26e-04 1.34e-01 1.20904571e+05 -3.54933673e+05 5.58e+00 15s
12 1.92e-04 8.44e-02 1.04908501e+05 -2.54959177e+05 3.93e+00 16s
13 8.09e-05 4.83e-02 8.49988300e+04 -1.63933485e+05 2.44e+00 18s
14 4.62e-05 2.72e-02 7.06545133e+04 -1.02323699e+05 1.51e+00 19s
15 1.94e-05 1.68e-02 5.24639561e+04 -6.95227074e+04 9.61e-01 20s
16 1.02e-05 9.84e-03 3.77185714e+04 -4.17894192e+04 5.70e-01 22s
17 6.81e-06 6.93e-03 3.08242939e+04 -2.91084107e+04 4.08e-01 23s
18 3.58e-06 3.36e-03 2.57406414e+04 -1.44027309e+04 2.52e-01 24s
19 1.77e-06 2.13e-03 2.24464783e+04 -8.64942680e+03 1.87e-01 26s
20 8.10e-07 1.60e-03 2.00886717e+04 -5.98699450e+03 1.53e-01 27s
21 4.67e-07 9.13e-04 1.76885055e+04 -1.32644122e+03 1.08e-01 29s
22 2.19e-07 5.64e-04 1.53684619e+04 1.46187383e+03 7.78e-02 31s
23 1.74e-07 4.77e-04 1.49485301e+04 2.12578093e+03 7.14e-02 34s
24 1.03e-07 2.97e-04 1.37756560e+04 3.92211046e+03 5.43e-02 35s
25 8.23e-08 2.03e-04 1.33224182e+04 4.96097392e+03 4.58e-02 37s
26 6.69e-08 1.35e-04 1.28827892e+04 5.89161111e+03 3.81e-02 39s
27 5.54e-08 5.85e-05 1.24932478e+04 7.23288405e+03 2.85e-02 41s
28 3.67e-08 4.30e-05 1.17469879e+04 7.63959217e+03 2.22e-02 43s
29 3.44e-08 3.56e-05 1.16936961e+04 7.73126184e+03 2.14e-02 46s
30 1.64e-08 2.46e-05 1.09468658e+04 8.09132155e+03 1.54e-02 48s
31 1.28e-08 1.98e-05 1.08111979e+04 8.22677378e+03 1.39e-02 50s
32 8.98e-09 1.32e-05 1.06618652e+04 8.43574381e+03 1.20e-02 54s
33 6.40e-09 1.23e-05 1.05084042e+04 8.48572171e+03 1.09e-02 55s
34 6.03e-09 8.69e-06 1.04928796e+04 8.61992062e+03 1.01e-02 56s
35 3.31e-09 6.98e-06 1.02642253e+04 8.74639498e+03 8.17e-03 58s
36 3.12e-09 6.41e-06 1.02570400e+04 8.76891800e+03 8.00e-03 59s
37 2.68e-09 4.60e-06 1.02120829e+04 8.91995727e+03 6.95e-03 60s
38 1.41e-09 3.18e-06 1.01085720e+04 9.01554382e+03 5.87e-03 62s
39 1.37e-09 2.31e-06 1.01047794e+04 9.08685475e+03 5.47e-03 63s
40 1.06e-09 1.98e-06 1.00606064e+04 9.12387842e+03 5.03e-03 64s
41 5.24e-10 1.13e-06 9.91648667e+03 9.28792782e+03 3.38e-03 65s
42 4.98e-10 1.10e-06 9.91527075e+03 9.29016011e+03 3.36e-03 67s
43 3.69e-10 1.02e-06 9.88770629e+03 9.30443644e+03 3.13e-03 69s
44 3.55e-10 7.63e-07 9.88504084e+03 9.33991073e+03 2.93e-03 70s
45 2.06e-10 4.05e-07 9.82906056e+03 9.43570351e+03 2.11e-03 71s
46 2.02e-10 3.62e-07 9.82827522e+03 9.44146127e+03 2.08e-03 74s
47 1.90e-10 3.22e-07 9.82379653e+03 9.45113014e+03 2.00e-03 75s
48 9.94e-11 2.15e-07 9.78341274e+03 9.48706810e+03 1.59e-03 76s
49 8.38e-11 2.01e-07 9.77551388e+03 9.49181672e+03 1.52e-03 77s
50 4.59e-11 1.75e-07 9.74064260e+03 9.50762968e+03 1.25e-03 78s
51 3.34e-11 1.19e-07 9.72951560e+03 9.54230950e+03 1.00e-03 79s
52 2.62e-11 9.58e-08 9.72573311e+03 9.55294569e+03 9.27e-04 79s
53 2.08e-11 4.63e-08 9.70432411e+03 9.59417118e+03 5.91e-04 80s
54 9.60e-12 4.06e-08 9.69614280e+03 9.59920478e+03 5.20e-04 82s
55 6.07e-12 2.67e-08 9.69178503e+03 9.61073037e+03 4.35e-04 82s
56 1.02e-11 1.94e-08 9.68738193e+03 9.62154935e+03 3.53e-04 83s
57 2.69e-11 8.60e-09 9.67895715e+03 9.63526917e+03 2.34e-04 84s
58 1.57e-11 4.55e-09 9.67420309e+03 9.64278621e+03 1.69e-04 85s
59 2.28e-11 2.55e-09 9.67122848e+03 9.64774778e+03 1.26e-04 85s
60 3.88e-11 1.82e-09 9.66945757e+03 9.65096502e+03 9.92e-05 86s
61 2.83e-11 1.00e-09 9.66699692e+03 9.65455335e+03 6.68e-05 86s
62 2.73e-11 8.69e-10 9.66606426e+03 9.65556481e+03 5.63e-05 87s
63 1.83e-11 7.05e-10 9.66498918e+03 9.65678888e+03 4.40e-05 88s
64 1.56e-11 6.47e-10 9.66447640e+03 9.65724431e+03 3.88e-05 88s
65 2.19e-11 2.62e-10 9.66409009e+03 9.66025109e+03 2.06e-05 89s
66 7.78e-12 9.83e-11 9.66368883e+03 9.66207263e+03 8.67e-06 89s
67 1.84e-11 7.20e-11 9.66349991e+03 9.66236162e+03 6.11e-06 90s
68 2.47e-11 1.74e-11 9.66350655e+03 9.66290499e+03 3.23e-06 90s
69 1.18e-11 5.33e-12 9.66339437e+03 9.66318656e+03 1.11e-06 91s
70 1.13e-11 1.59e-12 9.66335658e+03 9.66328211e+03 3.99e-07 91s
71 4.69e-11 4.26e-13 9.66334140e+03 9.66331249e+03 1.55e-07 92s
72 1.37e-11 1.99e-13 9.66333277e+03 9.66332230e+03 5.62e-08 93s
73 9.00e-12 4.83e-13 9.66332930e+03 9.66332548e+03 2.05e-08 93s
74 1.55e-11 1.62e-12 9.66332820e+03 9.66332729e+03 4.84e-09 94s
75 5.26e-11 1.23e-12 9.66332779e+03 9.66332745e+03 1.79e-09 94s
76* 5.68e-11 2.59e-12 9.66332773e+03 9.66332767e+03 3.36e-10 95s
77* 2.07e-11 5.92e-12 9.66332772e+03 9.66332771e+03 4.70e-11 96s
78* 1.07e-10 7.45e-12 9.66332771e+03 9.66332771e+03 5.07e-12 98s
79* 2.20e-10 9.85e-12 9.66332771e+03 9.66332771e+03 3.44e-13 98s
80* 1.15e-10 6.51e-12 9.66332771e+03 9.66332771e+03 6.25e-14 99s
Running crossover as requested
Primal residual before push phase: 3.25e-07
Dual residual before push phase: 2.20e-08
Number of dual pushes required: 26184
Number of primal pushes required: 3501
Summary
Runtime: 101.61s
Status interior point solve: optimal
Status crossover: optimal
objective value: 9.66332771e+03
interior solution primal residual (abs/rel): 1.27e-09 / 7.78e-11
interior solution dual residual (abs/rel): 1.40e-10 / 3.48e-13
interior solution objective gap (abs/rel): 6.66e-09 / 6.89e-13
basic solution primal infeasibility: 5.33e-14
basic solution dual infeasibility: 4.34e-14
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 80
Crossover iterations: 2929
Objective value : 9.6633277143e+03
HiGHS run time : 101.86
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120139
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 102.19283390045166)totCap6 = value.(EP6[:eTotalCap])
totCapB6 = [totCap6[1] + totCap6[2] + totCap6[3], totCap6[4] + totCap6[6],
totCap6[5] + totCap6[7], totCap6[8] + totCap6[9] + totCap6[10]]
println(DataFrame([RT totCap6],["Resource Type","Total Capacity"]))
println(" ")
G6 = groupedbar(transpose(totCapB6), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors,
title="CO2 Generation Rate Cap \n Obj Val: $(round(objective_value(EP6),digits=6))",ylabelfontsize=8)
plot(G2,G5,G6,size=(900,450), titlefontsize=8,layout=(1,3),)10×2 DataFrame
Row │ Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 4.08764
2 │ CT_natural_gas_combined_cycle 5.84863
3 │ ME_natural_gas_combined_cycle 0.887681
4 │ MA_solar_pv 20.0639
5 │ CT_onshore_wind 13.6798
6 │ CT_solar_pv 13.3512
7 │ ME_onshore_wind 9.61782
8 │ MA_battery 3.73538
9 │ CT_battery 4.85316
10 │ ME_battery 1.21815
Energy Share Requirement
Many countries have policies that demand a certain percentage of energy provided to consumers comes from renewable energy (in the US, these are called renewable portfolio standards. In GenX, this policy can be implemented by setting Energy_share_requirement to 1 in the setup, and adding a file called Energy_share_requirement.csv to the policies folder.
ESR = CSV.read(joinpath(case,"policies/Energy_share_requirement.csv"),DataFrame,missingstring="NA")3×4 DataFrame
| Row | Column1 | Network_zones | ESR_1 | ESR_2 |
|---|---|---|---|---|
| String3 | String3 | Float64 | Float64 | |
| 1 | MA | z1 | 0.259 | 0.348 |
| 2 | CT | z2 | 0.44 | 0.44 |
| 3 | ME | z3 | 0.776 | 0.776 |
setup["CO2Cap"] = 0 # set back to 0 to compare
setup["EnergyShareRequirement"] = 1;inputs = GenX.load_inputs(setup, case)
EP7 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP7,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
Energy_share_requirement.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
Energy Share Requirement Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118157 rows, 81204 cols, 433677 nonzeros
110999 rows, 74047 cols, 428770 nonzeros
Presolve : Reductions: rows 110999(-42395); columns 74047(-46089); elements 428770(-57145)
Solving the presolved LP
IPX model has 110999 rows, 74047 columns and 428770 nonzeros
Input
Number of variables: 74047
Number of free variables: 3696
Number of constraints: 110999
Number of equality constraints: 16867
Number of matrix entries: 428770
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 5e+04]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 1.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 3.25e+03 3.28e+02 2.96057527e+06 -4.42499145e+06 1.05e+06 0s
1 2.15e+03 1.54e+02 -3.67625092e+08 -9.92129159e+06 7.04e+05 0s
2 2.00e+03 1.45e+02 -4.48234657e+08 -1.62120314e+07 6.90e+05 0s
Constructing starting basis...
3 1.80e+03 1.38e+02 -1.57967721e+09 -1.32554204e+07 6.35e+05 3s
4 4.26e+02 4.25e+01 -8.07136821e+08 -1.80687324e+07 1.79e+05 4s
5 2.74e+02 1.46e+01 -4.80957944e+08 -2.11824340e+07 8.47e+04 5s
6 2.31e+02 1.06e+01 -3.88916132e+08 -2.25389566e+07 7.06e+04 7s
7 3.97e+01 2.56e+00 -8.90467652e+06 -2.42140640e+07 1.74e+04 8s
8 1.49e+00 1.05e+00 1.55238132e+07 -2.27145059e+07 4.78e+03 9s
9 4.23e-01 9.61e-02 1.52981739e+07 -2.07731077e+07 7.27e+02 9s
10 2.43e-02 1.03e-02 8.29803125e+06 -3.74951138e+06 1.06e+02 10s
11 2.19e-03 2.07e-03 2.70601909e+06 -1.07157895e+06 2.38e+01 14s
12 3.20e-04 3.41e-05 7.22109443e+05 -1.33114881e+05 4.62e+00 15s
13 2.18e-05 5.81e-06 4.97580885e+04 -2.36873031e+04 3.94e-01 16s
14 8.07e-06 1.45e-06 3.01069381e+04 -8.59032120e+03 2.08e-01 18s
15 4.16e-06 6.72e-07 1.93254730e+04 -3.46407201e+03 1.22e-01 19s
16 2.30e-06 3.55e-07 1.43100849e+04 -8.01714933e+02 8.10e-02 22s
17 1.34e-06 1.67e-07 1.16397836e+04 8.01991381e+02 5.81e-02 25s
18 7.61e-07 9.17e-08 9.47348310e+03 1.85600560e+03 4.08e-02 27s
19 4.47e-07 5.75e-08 8.09797935e+03 2.54641687e+03 2.98e-02 30s
20 3.33e-07 3.47e-08 7.62653275e+03 3.04869441e+03 2.45e-02 35s
21 1.98e-07 1.57e-08 6.79376066e+03 3.83391059e+03 1.59e-02 40s
22 1.00e-07 1.07e-08 6.23436569e+03 4.07366075e+03 1.16e-02 43s
23 5.72e-08 8.56e-09 5.90537240e+03 4.22893896e+03 8.98e-03 52s
24 3.15e-08 7.40e-09 5.69783264e+03 4.32217640e+03 7.37e-03 56s
25 1.96e-08 6.71e-09 5.60290779e+03 4.37626021e+03 6.57e-03 60s
26 1.62e-08 6.58e-09 5.58260471e+03 4.38624817e+03 6.41e-03 61s
27 9.83e-09 4.68e-09 5.47138439e+03 4.58570163e+03 4.75e-03 63s
28 7.08e-09 4.32e-09 5.43675159e+03 4.61957103e+03 4.38e-03 66s
29 5.90e-09 3.78e-09 5.44745537e+03 4.64477569e+03 4.30e-03 68s
30 2.60e-09 3.39e-09 5.38567861e+03 4.68523417e+03 3.75e-03 69s
31 1.86e-09 3.13e-09 5.40360769e+03 4.70093259e+03 3.76e-03 71s
32 5.79e-10 1.84e-09 5.32616721e+03 4.86253824e+03 2.48e-03 72s
33 5.26e-10 1.66e-09 5.32704123e+03 4.87901733e+03 2.40e-03 74s
34 3.48e-10 1.52e-09 5.32856456e+03 4.89218629e+03 2.34e-03 75s
35 1.82e-10 1.07e-09 5.29562500e+03 4.96409486e+03 1.78e-03 76s
36 1.42e-10 8.01e-10 5.28983765e+03 5.00359981e+03 1.53e-03 78s
37 8.66e-11 7.18e-10 5.28033482e+03 5.01649890e+03 1.41e-03 79s
38 4.00e-11 5.38e-10 5.27675684e+03 5.03862584e+03 1.28e-03 81s
39 2.74e-11 4.02e-10 5.26154650e+03 5.07181296e+03 1.02e-03 82s
40 1.33e-11 3.51e-10 5.26154482e+03 5.07895810e+03 9.78e-04 83s
41 9.37e-12 1.52e-10 5.25770976e+03 5.11634640e+03 7.57e-04 84s
42 6.61e-11 6.56e-11 5.24263265e+03 5.14509162e+03 5.23e-04 85s
43 2.70e-11 5.14e-11 5.23939943e+03 5.15308245e+03 4.62e-04 86s
44 1.07e-11 4.52e-11 5.23760193e+03 5.15544594e+03 4.40e-04 87s
45 2.14e-11 3.78e-11 5.23695511e+03 5.15880466e+03 4.19e-04 88s
46 4.52e-11 2.37e-11 5.22793680e+03 5.16829652e+03 3.20e-04 89s
47 3.88e-11 1.68e-11 5.22613710e+03 5.17238445e+03 2.88e-04 90s
48 3.04e-11 9.86e-12 5.22130177e+03 5.18278901e+03 2.06e-04 91s
49 1.60e-11 8.28e-12 5.21769964e+03 5.18522708e+03 1.74e-04 91s
50 2.50e-11 5.20e-12 5.21732077e+03 5.18949974e+03 1.49e-04 92s
51 1.46e-11 2.94e-12 5.21565661e+03 5.19332457e+03 1.20e-04 93s
52 6.28e-12 1.96e-12 5.21252321e+03 5.19649375e+03 8.59e-05 93s
53 1.10e-11 1.34e-12 5.21137346e+03 5.19788591e+03 7.23e-05 94s
54 4.52e-11 1.05e-12 5.20952040e+03 5.19902667e+03 5.62e-05 95s
55 1.97e-13 9.66e-13 5.20946552e+03 5.19915263e+03 5.52e-05 95s
56 1.03e-10 6.57e-13 5.20878855e+03 5.20069905e+03 4.33e-05 96s
57 1.00e-10 7.67e-13 5.20790740e+03 5.20157745e+03 3.39e-05 97s
58 1.08e-11 3.41e-13 5.20718489e+03 5.20231634e+03 2.61e-05 97s
59 5.84e-11 5.04e-13 5.20697661e+03 5.20275991e+03 2.26e-05 98s
60 6.10e-11 4.83e-13 5.20642800e+03 5.20316879e+03 1.75e-05 98s
61 1.21e-11 2.34e-13 5.20626891e+03 5.20342248e+03 1.52e-05 99s
62 4.88e-11 5.97e-13 5.20609848e+03 5.20403285e+03 1.11e-05 99s
63 4.11e-11 2.27e-13 5.20583889e+03 5.20443275e+03 7.53e-06 100s
64 4.08e-11 2.84e-13 5.20572643e+03 5.20464048e+03 5.82e-06 100s
65 1.77e-12 2.84e-13 5.20565183e+03 5.20500872e+03 3.45e-06 101s
66 3.26e-12 5.12e-13 5.20546080e+03 5.20514462e+03 1.69e-06 101s
67 8.10e-11 2.27e-13 5.20539707e+03 5.20527700e+03 6.43e-07 102s
68 1.14e-10 2.84e-13 5.20537158e+03 5.20530783e+03 3.42e-07 102s
69 7.20e-11 5.19e-13 5.20535889e+03 5.20534226e+03 8.91e-08 102s
70 8.66e-11 2.51e-12 5.20535373e+03 5.20534725e+03 3.47e-08 103s
71 1.74e-11 3.55e-12 5.20534982e+03 5.20534876e+03 5.66e-09 103s
72 7.05e-12 3.38e-12 5.20534916e+03 5.20534900e+03 8.61e-10 104s
73* 3.63e-13 3.95e-12 5.20534910e+03 5.20534906e+03 1.93e-10 104s
74* 2.57e-11 7.55e-12 5.20534908e+03 5.20534907e+03 3.92e-11 105s
75* 9.13e-11 2.43e-12 5.20534908e+03 5.20534908e+03 5.53e-12 105s
Running crossover as requested
Primal residual before push phase: 4.25e-06
Dual residual before push phase: 1.04e-06
Number of dual pushes required: 31721
Number of primal pushes required: 2358
Summary
Runtime: 105.88s
Status interior point solve: optimal
Status crossover: optimal
objective value: 5.20534908e+03
interior solution primal residual (abs/rel): 1.25e-10 / 2.61e-15
interior solution dual residual (abs/rel): 4.75e-09 / 1.18e-11
interior solution objective gap (abs/rel): 1.03e-06 / 1.98e-10
basic solution primal infeasibility: 2.45e-14
basic solution dual infeasibility: 2.50e-16
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 75
Crossover iterations: 2950
Objective value : 5.2053490785e+03
HiGHS run time : 106.12
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120136
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20333 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 106.45424795150757)totCap7 = value.(EP7[:eTotalCap])
totCapB7 = [totCap7[1] + totCap7[2] + totCap7[3], totCap7[4] + totCap7[6],
totCap7[5] + totCap7[7], totCap7[8] + totCap7[9] + totCap7[10]]
println(DataFrame([RT totCap7],["Resource Type","Total Capacity"]))
println(" ")
G7 = groupedbar(transpose(totCapB7), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors,
title="Energy Share Requirement \n Obj Val: $(round(objective_value(EP7),digits=6))",ylabelfontsize=8)
plot(G7,G2,G5,G6,size=(900,900), titlefontsize=8,layout=(2,2))10×2 DataFrame
Row │ Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 8.58778
2 │ CT_natural_gas_combined_cycle 9.43521
3 │ ME_natural_gas_combined_cycle 0.0
4 │ MA_solar_pv 2.99333
5 │ CT_onshore_wind 5.61694
6 │ CT_solar_pv 0.242229
7 │ ME_onshore_wind 6.28897
8 │ MA_battery 0.253804
9 │ CT_battery 0.0
10 │ ME_battery 0.723348
The Energy Share Requriement policy also has the possibiliy to be run with slack variables
Capacity Reserve Margin
The Capacity Reserve Margin constraint demands that a certain amount of energy always be available in each zone, expressed as a fraction of the demand. Once again, we can enforce a Capacity Reserve Margin by setting its option to "1" in the setup and adding the relevant file, Capacity_reserve_margin.csv.
CapacityReserve = CSV.read(joinpath(case,"policies/Capacity_reserve_margin.csv"),DataFrame,missingstring="NA")3×3 DataFrame
| Row | Column1 | Network_zones | CapRes_1 |
|---|---|---|---|
| String3 | String3 | Float64 | |
| 1 | MA | z1 | 0.156 |
| 2 | CT | z2 | 0.156 |
| 3 | ME | z3 | 0.156 |
setup["CapacityReserveMargin"] = 1;inputs = GenX.load_inputs(setup, case)
EP8 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP8,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
Capacity_reserve_margin.csv Successfully Read!
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Energy_share_requirement.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
Energy Share Requirement Policies Module
Capacity Reserve Margin Policies Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
131093 rows, 97836 cols, 538890 nonzeros
123634 rows, 90378 cols, 543137 nonzeros
Presolve : Reductions: rows 123634(-42696); columns 90378(-46390); elements 543137(-47991)
Solving the presolved LP
IPX model has 123634 rows, 90378 columns and 543137 nonzeros
Input
Number of variables: 90378
Number of free variables: 3696
Number of constraints: 123634
Number of equality constraints: 22110
Number of matrix entries: 543137
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 5e+04]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 1.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 4.21e+03 3.50e+02 3.04628199e+06 -5.21772232e+06 1.46e+06 0s
1 2.81e+03 1.90e+02 -5.15281627e+08 -1.06058690e+07 1.02e+06 0s
2 2.45e+03 1.56e+02 -6.44386109e+08 -2.55847744e+07 9.81e+05 1s
3 1.18e+03 1.41e+02 -8.43467846e+08 -2.60789874e+07 6.78e+05 1s
Constructing starting basis...
4 7.54e+02 4.73e+01 -7.60379207e+08 -3.49951229e+07 3.40e+05 3s
5 6.33e+01 1.39e+01 -5.44467100e+05 -3.65314462e+07 6.81e+04 4s
6 2.27e+01 2.74e+00 -1.77683713e+06 -4.81835016e+07 1.90e+04 10s
7 9.77e-01 6.10e-01 1.48697352e+07 -4.12620606e+07 3.32e+03 13s
8 1.52e-01 4.78e-02 1.42095518e+07 -1.48990864e+07 4.03e+02 14s
9 1.65e-02 1.88e-02 7.71351293e+06 -6.37275792e+06 1.39e+02 15s
10 3.46e-03 2.65e-03 4.64755286e+06 -1.55341587e+06 3.68e+01 18s
11 4.76e-04 1.28e-03 9.51929576e+05 -7.48785467e+05 8.94e+00 20s
12 8.26e-05 6.15e-05 2.94145739e+05 -7.77919316e+04 1.78e+00 21s
13 3.54e-05 6.20e-06 1.35212127e+05 -1.45337724e+04 7.13e-01 22s
14 2.53e-05 7.28e-12 1.14387567e+05 -2.21312822e+04 6.50e-01 23s
15 2.33e-05 7.28e-12 1.13339554e+05 -2.13641483e+04 6.41e-01 24s
16 7.71e-06 4.55e-12 4.42306187e+04 -1.29028659e+04 2.72e-01 25s
17 7.64e-07 1.82e-12 1.81970294e+04 -4.92740686e+03 1.10e-01 26s
18 3.72e-07 3.64e-12 1.39021979e+04 -1.32749886e+03 7.24e-02 30s
19 2.03e-07 9.09e-13 1.13821414e+04 7.45236578e+02 5.06e-02 32s
20 1.05e-07 9.09e-13 9.13639056e+03 2.30432056e+03 3.25e-02 35s
21 7.73e-08 4.55e-13 8.59719038e+03 3.17398498e+03 2.58e-02 38s
22 3.33e-08 3.69e-13 7.37618406e+03 3.92635014e+03 1.64e-02 43s
23 1.53e-08 9.09e-13 6.71318380e+03 4.46082497e+03 1.07e-02 52s
24 7.16e-09 2.98e-13 6.28228488e+03 4.71698031e+03 7.44e-03 56s
25 5.19e-09 9.09e-13 6.18110316e+03 4.82937601e+03 6.43e-03 62s
26 2.24e-09 4.55e-13 5.92131571e+03 5.04272325e+03 4.18e-03 66s
27 1.26e-09 4.55e-13 5.85499040e+03 5.13102116e+03 3.44e-03 73s
28 5.94e-10 4.55e-13 5.79725408e+03 5.18715779e+03 2.90e-03 76s
29 3.86e-10 4.83e-13 5.76431193e+03 5.26258597e+03 2.38e-03 79s
30 2.36e-10 3.69e-13 5.74367493e+03 5.28432035e+03 2.18e-03 81s
31 1.68e-10 2.56e-13 5.72937706e+03 5.32860855e+03 1.90e-03 83s
32 6.05e-11 2.27e-13 5.70998585e+03 5.35418213e+03 1.69e-03 85s
33 5.53e-11 2.42e-13 5.70850651e+03 5.40373271e+03 1.45e-03 86s
34 2.90e-11 2.42e-13 5.68596077e+03 5.43998304e+03 1.17e-03 88s
35 2.67e-11 4.26e-13 5.67637386e+03 5.45111176e+03 1.07e-03 91s
36 2.99e-11 2.27e-13 5.67168974e+03 5.46214213e+03 9.96e-04 92s
37 1.99e-11 1.42e-13 5.65940618e+03 5.48204771e+03 8.43e-04 93s
38 6.70e-11 4.55e-13 5.65532213e+03 5.49686649e+03 7.53e-04 94s
39 6.23e-11 3.13e-13 5.64168791e+03 5.51202371e+03 6.16e-04 95s
40 3.89e-11 3.27e-13 5.63853210e+03 5.52780109e+03 5.26e-04 97s
41 1.20e-11 1.99e-13 5.63441684e+03 5.54194604e+03 4.40e-04 98s
42 1.79e-11 4.55e-13 5.63069684e+03 5.54896357e+03 3.88e-04 100s
43 2.83e-11 2.42e-13 5.62970471e+03 5.55078636e+03 3.75e-04 101s
44 7.99e-11 5.40e-13 5.61992128e+03 5.55549414e+03 3.06e-04 103s
45 3.20e-11 2.56e-13 5.61211218e+03 5.56079764e+03 2.44e-04 104s
46 1.21e-11 3.41e-13 5.61177375e+03 5.56505674e+03 2.22e-04 106s
47 4.72e-11 2.56e-13 5.60993414e+03 5.56837792e+03 1.98e-04 107s
48 4.70e-12 3.41e-13 5.60465748e+03 5.57191765e+03 1.56e-04 108s
49 2.44e-11 3.69e-13 5.60465096e+03 5.57377173e+03 1.47e-04 109s
50 2.47e-11 3.41e-13 5.60235807e+03 5.58002161e+03 1.06e-04 109s
51 3.24e-11 2.56e-13 5.60149552e+03 5.58255142e+03 9.00e-05 110s
52 3.31e-11 1.71e-13 5.60101493e+03 5.58433865e+03 7.93e-05 111s
53 2.00e-11 3.13e-13 5.59892601e+03 5.58668138e+03 5.82e-05 112s
54 7.84e-11 1.60e-13 5.59885342e+03 5.58685974e+03 5.70e-05 112s
55 4.61e-11 2.27e-13 5.59865140e+03 5.58847015e+03 4.84e-05 113s
56 7.16e-11 2.56e-13 5.59762653e+03 5.58975937e+03 3.74e-05 114s
57 1.03e-11 2.56e-13 5.59747335e+03 5.59024473e+03 3.44e-05 115s
58 7.64e-12 3.13e-13 5.59715338e+03 5.59061047e+03 3.11e-05 115s
59 2.17e-11 3.13e-13 5.59711186e+03 5.59070395e+03 3.05e-05 116s
60 1.40e-11 2.27e-13 5.59696797e+03 5.59107740e+03 2.80e-05 117s
61 7.00e-11 4.26e-13 5.59606722e+03 5.59162281e+03 2.11e-05 117s
62 4.94e-11 6.25e-13 5.59525601e+03 5.59289962e+03 1.12e-05 118s
63 1.92e-11 2.27e-13 5.59505259e+03 5.59297104e+03 9.89e-06 119s
64 1.11e-11 3.69e-13 5.59462252e+03 5.59327739e+03 6.39e-06 120s
65 8.66e-13 3.13e-13 5.59453155e+03 5.59338209e+03 5.46e-06 120s
66 2.17e-11 3.13e-13 5.59446120e+03 5.59350884e+03 4.53e-06 121s
67 1.12e-11 3.13e-13 5.59440854e+03 5.59367478e+03 3.49e-06 122s
68 4.11e-11 3.98e-13 5.59427052e+03 5.59378913e+03 2.29e-06 122s
69 1.04e-11 2.27e-13 5.59416188e+03 5.59391997e+03 1.15e-06 123s
70 4.31e-12 2.56e-13 5.59412273e+03 5.59393435e+03 8.95e-07 124s
71 8.96e-11 3.98e-13 5.59408396e+03 5.59399407e+03 4.27e-07 124s
72 1.26e-10 4.26e-13 5.59405507e+03 5.59402936e+03 1.22e-07 125s
73 3.69e-11 3.98e-13 5.59405082e+03 5.59403909e+03 5.58e-08 126s
74 1.24e-12 2.36e-12 5.59404612e+03 5.59404129e+03 2.30e-08 126s
75 1.33e-11 5.07e-12 5.59404352e+03 5.59404265e+03 4.10e-09 127s
76 1.91e-11 4.70e-12 5.59404309e+03 5.59404298e+03 5.09e-10 127s
77* 6.85e-11 7.82e-12 5.59404305e+03 5.59404303e+03 1.27e-10 128s
78* 6.30e-11 2.17e-12 5.59404305e+03 5.59404304e+03 2.84e-11 128s
79* 1.53e-11 1.32e-12 5.59404305e+03 5.59404304e+03 6.24e-12 129s
Running crossover as requested
Primal residual before push phase: 1.85e-05
Dual residual before push phase: 1.60e-06
Number of dual pushes required: 40477
Number of primal pushes required: 2267
Summary
Runtime: 129.76s
Status interior point solve: optimal
Status crossover: optimal
objective value: 5.59404305e+03
interior solution primal residual (abs/rel): 4.70e-09 / 9.83e-14
interior solution dual residual (abs/rel): 6.10e-09 / 1.52e-11
interior solution objective gap (abs/rel): 1.29e-06 / 2.30e-10
basic solution primal infeasibility: 3.88e-14
basic solution dual infeasibility: 1.21e-15
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 79
Crossover iterations: 5019
Objective value : 5.5940430448e+03
HiGHS run time : 130.05
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 136768
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 40656 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 27725 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 133071 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCapacityResMargin, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSOCMinCapRes, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cVSoCBalInterior, cVSoCBalStart, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_in_virtual, eCVar_out, eCVar_out_virtual, eCapResMarBalance, eCapResMarBalanceNSE, eCapResMarBalanceStor, eCapResMarBalanceStorVirtual, eCapResMarBalanceThermal, eCapResMarBalanceTrans, eCapResMarBalanceVRE, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarInT_virtual, eTotalCVarIn_virtual, eTotalCVarOut, eTotalCVarOutT, eTotalCVarOutT_virtual, eTotalCVarOut_virtual, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCAPRES_charge, vCAPRES_discharge, vCAPRES_socinreserve, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 130.46769380569458)totCap8 = value.(EP8[:eTotalCap])
totCapB8 = [totCap8[1] + totCap8[2] + totCap8[3], totCap8[4] + totCap8[6],
totCap8[5] + totCap8[7], totCap8[8] + totCap8[9] + totCap8[10]]
println(DataFrame([RT totCap8],["Resource Type","Total Capacity"]))
println(" ")
G8 = groupedbar(transpose(totCapB8), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors,
title="Capacity Reserve Margin + ESR \n Obj Val: $(round(objective_value(EP8),digits=6))",ylabelfontsize=8)
plot(G8,G7,G2,size=(900,450), titlefontsize=8,layout=(1,3))10×2 DataFrame
Row │ Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 8.59939
2 │ CT_natural_gas_combined_cycle 14.7124
3 │ ME_natural_gas_combined_cycle 0.0
4 │ MA_solar_pv 2.89028
5 │ CT_onshore_wind 5.82195
6 │ CT_solar_pv 0.0
7 │ ME_onshore_wind 6.28764
8 │ MA_battery 0.346698
9 │ CT_battery 0.0
10 │ ME_battery 0.586507
Capacity Reserve Margin also has the possibiliy to be run with slack variables.
Minimum Capacity Requirement
The last policy we'll talk about is [Minimum Capacity Requirement], which requires the grid to produce at least a certain amount of energy from renewables, as specified in the input file:
MinCapacity = CSV.read(joinpath(case,"policies/Minimum_capacity_requirement.csv"),DataFrame,missingstring="NA")3×3 DataFrame
| Row | MinCapReqConstraint | ConstraintDescription | Min_MW |
|---|---|---|---|
| Int64 | String15 | Int64 | |
| 1 | 1 | MA_PV | 5000 |
| 2 | 2 | CT_Wind | 10000 |
| 3 | 3 | All_Batteries | 6000 |
This policy ensures some renewable energy is used in the grid regardless of emissions constraints. If a fourth column containing price cap requirements exists (not shown above), that column is treated as a slack variable.
setup["CapacityReserveMargin"] = 0
setup["EnergyShareRequirement"] = 0
setup["MinCapReq"] = 1;inputs = GenX.load_inputs(setup, case)
EP9 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP9,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
Minimum_capacity_requirement.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Non-served Energy ModuleThermal.csv Successfully Read. Vre.csv Successfully Read. Storage.csv Successfully Read. Resourceenergysharerequirement.csv Successfully Read. Resourcecapacityreservemargin.csv Successfully Read. Resourceminimumcapacity_requirement.csv Successfully Read.
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
Minimum Capacity Requirement Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
118156 rows, 81204 cols, 422838 nonzeros
110999 rows, 74047 cols, 423352 nonzeros
Presolve : Reductions: rows 110999(-42396); columns 74047(-46089); elements 423352(-47784)
Solving the presolved LP
IPX model has 110999 rows, 74047 columns and 423352 nonzeros
Input
Number of variables: 74047
Number of free variables: 3696
Number of constraints: 110999
Number of equality constraints: 16867
Number of matrix entries: 423352
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 2e+01]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 1.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 2.34e+01 3.82e+02 3.30488922e+06 -5.33223155e+06 8.91e+03 0s
1 1.39e+01 1.13e+02 -3.26111454e+06 -8.08059083e+06 4.78e+03 0s
2 1.34e+01 8.13e+01 -3.30809039e+06 -2.14818717e+07 5.04e+03 0s
3 5.10e+00 4.43e+01 -3.63727490e+06 -2.49670027e+07 2.64e+03 1s
Constructing starting basis...
4 2.75e+00 1.66e+01 -1.55659888e+06 -2.27832740e+07 1.26e+03 3s
5 2.41e+00 1.37e+01 -1.18396821e+06 -2.13578247e+07 1.11e+03 4s
6 1.39e+00 4.43e+00 -4.94217397e+04 -1.44985483e+07 5.28e+02 6s
7 6.13e-02 7.91e-01 8.34862433e+05 -6.93418288e+06 9.35e+01 7s
8 3.76e-03 7.97e-02 4.24408301e+05 -1.09263439e+06 1.31e+01 8s
9 2.88e-04 1.00e-02 1.65630895e+05 -1.75207574e+05 2.37e+00 9s
10 6.57e-05 2.60e-03 6.19697724e+04 -5.01450660e+04 6.76e-01 10s
11 3.78e-05 3.11e-04 4.59001513e+04 -1.47138829e+04 3.33e-01 10s
12 2.79e-05 3.01e-04 5.07134714e+04 -1.34380343e+04 3.51e-01 11s
13 1.85e-05 3.28e-05 3.85580458e+04 -4.46651304e+03 2.31e-01 12s
14 1.19e-05 1.47e-05 3.43652640e+04 -5.85635923e+03 2.16e-01 13s
15 5.83e-06 5.94e-06 2.04363590e+04 -8.78181923e+02 1.14e-01 13s
16 3.62e-06 3.07e-06 1.57058304e+04 7.47097166e+02 8.02e-02 15s
17 1.73e-06 1.98e-06 1.14474070e+04 1.51572830e+03 5.33e-02 18s
18 7.85e-07 1.23e-06 8.92169592e+03 2.32540240e+03 3.54e-02 19s
19 4.32e-07 8.80e-07 7.80843740e+03 2.81479174e+03 2.68e-02 20s
20 2.62e-07 4.48e-07 7.20548085e+03 3.52684341e+03 1.97e-02 22s
21 1.47e-07 2.24e-07 6.67664231e+03 4.07755176e+03 1.39e-02 25s
22 6.82e-08 1.82e-07 6.25539980e+03 4.21836942e+03 1.09e-02 28s
23 5.27e-08 1.49e-07 6.14225406e+03 4.35222081e+03 9.59e-03 30s
24 5.23e-08 1.48e-07 6.19401540e+03 4.41443087e+03 9.54e-03 32s
25 4.08e-08 1.37e-07 6.11156615e+03 4.46928744e+03 8.80e-03 34s
26 2.62e-08 1.04e-07 5.99485482e+03 4.65688588e+03 7.17e-03 35s
27 1.01e-08 5.40e-08 5.91238184e+03 4.88375941e+03 5.51e-03 36s
28 9.25e-09 4.67e-08 5.88906267e+03 4.95194014e+03 5.02e-03 39s
29 8.47e-09 4.18e-08 5.87830260e+03 4.97446884e+03 4.84e-03 42s
30 2.90e-09 3.49e-08 5.71712195e+03 5.04256956e+03 3.61e-03 45s
31 1.58e-09 1.80e-08 5.66248175e+03 5.22792362e+03 2.33e-03 50s
32 9.36e-10 1.16e-08 5.62108661e+03 5.31620530e+03 1.63e-03 53s
33 7.54e-10 9.50e-09 5.61131446e+03 5.34069905e+03 1.45e-03 56s
34 3.64e-10 6.78e-09 5.58350503e+03 5.37914296e+03 1.09e-03 57s
35 1.61e-10 4.60e-09 5.57381755e+03 5.40507612e+03 9.04e-04 58s
36 9.58e-11 3.34e-09 5.55921197e+03 5.43192782e+03 6.82e-04 60s
37 5.96e-11 1.90e-09 5.55589825e+03 5.45455261e+03 5.43e-04 62s
38 3.27e-11 6.28e-10 5.54709869e+03 5.48816147e+03 3.16e-04 63s
39 2.12e-11 4.02e-10 5.54216424e+03 5.49586924e+03 2.48e-04 64s
40 1.40e-11 2.87e-10 5.53737841e+03 5.50195705e+03 1.90e-04 64s
41 8.74e-12 7.64e-11 5.53451883e+03 5.51121430e+03 1.25e-04 65s
42 4.45e-12 5.82e-11 5.53082515e+03 5.51293739e+03 9.58e-05 65s
43 2.69e-12 4.91e-11 5.52895320e+03 5.51381040e+03 8.11e-05 66s
44 1.49e-12 3.09e-11 5.52752865e+03 5.51632502e+03 6.00e-05 66s
45 1.12e-12 2.18e-11 5.52678261e+03 5.51817779e+03 4.61e-05 66s
46 9.73e-13 1.64e-11 5.52653183e+03 5.51873543e+03 4.18e-05 67s
47 6.75e-13 1.09e-11 5.52588469e+03 5.51976155e+03 3.28e-05 67s
48 5.12e-13 7.28e-12 5.52538622e+03 5.52088538e+03 2.41e-05 68s
49 3.62e-13 7.28e-12 5.52505789e+03 5.52116706e+03 2.08e-05 68s
50 1.21e-13 1.46e-11 5.52401306e+03 5.52162795e+03 1.28e-05 68s
51 7.82e-14 7.28e-12 5.52389039e+03 5.52195984e+03 1.03e-05 69s
52 4.97e-14 7.28e-12 5.52369651e+03 5.52214739e+03 8.30e-06 69s
53 2.13e-14 7.28e-12 5.52355424e+03 5.52243013e+03 6.02e-06 69s
54 2.13e-14 7.28e-12 5.52339956e+03 5.52263709e+03 4.08e-06 70s
55 2.13e-14 7.28e-12 5.52340007e+03 5.52266984e+03 3.91e-06 70s
56 2.84e-14 7.28e-12 5.52339771e+03 5.52268533e+03 3.82e-06 70s
57 2.13e-14 7.28e-12 5.52333480e+03 5.52273001e+03 3.24e-06 71s
58 2.13e-14 7.28e-12 5.52333465e+03 5.52276044e+03 3.08e-06 71s
59 2.13e-14 7.28e-12 5.52331312e+03 5.52282782e+03 2.60e-06 71s
60 2.13e-14 7.28e-12 5.52329636e+03 5.52284551e+03 2.42e-06 72s
61 2.13e-14 7.28e-12 5.52328626e+03 5.52292698e+03 1.92e-06 72s
62 2.13e-14 7.28e-12 5.52328402e+03 5.52294138e+03 1.84e-06 72s
63 2.13e-14 1.92e-13 5.52322974e+03 5.52307280e+03 8.41e-07 73s
64 2.84e-14 7.28e-12 5.52320719e+03 5.52313866e+03 3.67e-07 73s
65 2.84e-14 1.17e-13 5.52319028e+03 5.52316431e+03 1.39e-07 73s
66 2.13e-14 1.82e-12 5.52318739e+03 5.52317535e+03 6.45e-08 73s
67 2.13e-14 4.55e-13 5.52318545e+03 5.52317686e+03 4.60e-08 74s
68 2.13e-14 7.28e-12 5.52318141e+03 5.52317952e+03 1.01e-08 74s
69 2.84e-14 7.28e-12 5.52318051e+03 5.52318024e+03 1.41e-09 74s
70* 2.13e-14 6.90e-12 5.52318041e+03 5.52318036e+03 2.41e-10 74s
71* 2.84e-14 4.07e-12 5.52318040e+03 5.52318040e+03 3.09e-11 75s
72* 3.55e-14 5.53e-12 5.52318040e+03 5.52318040e+03 5.06e-12 75s
73* 4.26e-14 7.88e-12 5.52318040e+03 5.52318040e+03 6.38e-13 75s
74* 3.55e-14 2.81e-12 5.52318040e+03 5.52318040e+03 1.07e-13 75s
Running crossover as requested
Primal residual before push phase: 2.03e-08
Dual residual before push phase: 5.16e-09
Number of dual pushes required: 26618
Number of primal pushes required: 2605
Summary
Runtime: 75.26s
Status interior point solve: optimal
Status crossover: optimal
objective value: 5.52318040e+03
interior solution primal residual (abs/rel): 7.73e-11 / 4.73e-12
interior solution dual residual (abs/rel): 4.28e-10 / 1.07e-12
interior solution objective gap (abs/rel): 9.06e-09 / 1.64e-12
basic solution primal infeasibility: 6.22e-15
basic solution dual infeasibility: 3.25e-15
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 74
Crossover iterations: 2077
Objective value : 5.5231804025e+03
HiGHS run time : 75.47
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 120136
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20334 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cZoneMinCapReq, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eMinCapRes, eMinCapResInvest, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 75.7959840297699)totCap9 = value.(EP9[:eTotalCap])
totCapB9 = [totCap9[1] + totCap9[2] + totCap9[3], totCap9[4] + totCap9[6],
totCap9[5] + totCap9[7], totCap9[8] + totCap9[9] + totCap9[10]]
println(DataFrame([RT totCap9],["Resource Type","Total Capacity"]))
println(" ")
G9 = groupedbar(transpose(totCapB9), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors,
title="Minimum Capacity Requirement \n Obj Val: $(round(objective_value(EP9),digits=6))",ylabelfontsize=8)
plot(G9,G8,G7,G2,size=(900,900), titlefontsize=8,layout=(2,2))10×2 DataFrame
Row │ Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 9.47511
2 │ CT_natural_gas_combined_cycle 8.40465
3 │ ME_natural_gas_combined_cycle 0.0
4 │ MA_solar_pv 5.0
5 │ CT_onshore_wind 10.0
6 │ CT_solar_pv 0.0
7 │ ME_onshore_wind 0.0
8 │ MA_battery 0.128507
9 │ CT_battery 4.28065
10 │ ME_battery 1.59085
All Together
1_three_zones has defaults of CO2Cap = 2 and MinCapReq = 1. To see how everything comes together, let's add ESR and CRM in as well:
setup["MinCapReq"] = 1
setup["CO2Cap"] = 2
setup["EnergyShareRequirement"] = 1
setup["CapacityReserveMargin"] = 1;inputs = GenX.load_inputs(setup, case)
EP10 = GenX.generate_model(setup,inputs,OPTIMIZER)
GenX.solve_model(EP10,setup)Reading Input CSV Files
Network.csv Successfully Read!
Demand (load) data Successfully Read!
Fuels_data.csv Successfully Read!
Summary of resources loaded into the model:
-------------------------------------------------------
Resource type Number of resources
=======================================================
Thermal 3
VRE 4
Storage 3
=======================================================
Total number of resources: 10
-------------------------------------------------------
Generators_variability.csv Successfully Read!
Validating time basis
Capacity_reserve_margin.csv Successfully Read!
Minimum_capacity_requirement.csv Successfully Read!
Energy_share_requirement.csv Successfully Read!
CO2_cap.csv Successfully Read!
CSV Files Successfully Read In From example_systems/1_three_zones
Discharge Module
Thermal.csv Successfully Read.
Vre.csv Successfully Read.
Storage.csv Successfully Read.
Resource_energy_share_requirement.csv Successfully Read.
Resource_capacity_reserve_margin.csv Successfully Read.
Resource_minimum_capacity_requirement.csv Successfully Read.
Non-served Energy Module
Investment Discharge Module
Unit Commitment Module
Fuel Module
CO2 Module
Investment Transmission Module
Transmission Module
Dispatchable Resources Module
Storage Resources Module
Storage Investment Module
Storage Core Resources Module
Storage Resources with Symmetric Charge/Discharge Capacity Module
Thermal (Unit Commitment) Resources Module
CO2 Policies Module
Energy Share Requirement Policies Module
Capacity Reserve Margin Policies Module
Minimum Capacity Requirement Module
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Presolving model
131097 rows, 97836 cols, 583245 nonzeros
123901 rows, 90641 cols, 586406 nonzeros
Presolve : Reductions: rows 123901(-42435); columns 90641(-46130); elements 586406(-49082)
Solving the presolved LP
IPX model has 123901 rows, 90641 columns and 586406 nonzeros
Input
Number of variables: 90641
Number of free variables: 3696
Number of constraints: 123901
Number of equality constraints: 22373
Number of matrix entries: 586406
Matrix range: [4e-07, 1e+01]
RHS range: [7e-01, 5e+04]
Objective range: [1e-04, 4e+02]
Bounds range: [2e-03, 2e+01]
Preprocessing
Dualized model: no
Number of dense columns: 15
Range of scaling factors: [5.00e-01, 4.00e+00]
IPX version 1.0
Interior Point Solve
Iter P.res D.res P.obj D.obj mu Time
0 5.30e+03 3.22e+02 3.13997460e+06 -4.50780216e+06 1.69e+06 0s
1 3.53e+03 1.84e+02 -3.86867578e+08 -1.04799903e+07 1.20e+06 0s
2 2.99e+03 1.79e+02 -4.64684777e+08 -1.23686026e+07 1.12e+06 1s
Constructing starting basis...
3 2.03e+03 1.48e+02 -2.85325444e+09 -1.06915573e+07 9.68e+05 3s
4 1.45e+03 5.36e+01 -2.20472171e+09 -2.15853094e+07 5.20e+05 6s
5 5.72e+02 2.55e+01 -7.34160531e+08 -2.85605099e+07 2.70e+05 8s
6 1.52e+02 9.55e+00 -6.47264055e+07 -2.78488489e+07 9.45e+04 10s
7 2.02e+01 1.79e+00 2.31123203e+07 -2.71227296e+07 1.70e+04 14s
8 1.25e+00 1.73e-01 2.78294575e+07 -2.15984056e+07 1.70e+03 17s
9 6.87e-01 1.01e-01 2.46933049e+07 -1.61205280e+07 1.04e+03 20s
10 3.29e-01 6.17e-02 2.40546197e+07 -1.56062552e+07 7.59e+02 22s
11 1.55e-01 3.97e-02 2.03010629e+07 -1.19472220e+07 4.90e+02 24s
12 6.17e-02 2.00e-02 1.58293799e+07 -7.68786756e+06 2.58e+02 26s
13 3.21e-02 7.58e-03 1.16341185e+07 -3.68819752e+06 1.19e+02 28s
14 5.73e-03 2.53e-03 4.99822439e+06 -1.84838835e+06 4.06e+01 31s
15 2.04e-04 2.53e-09 9.67831330e+05 -2.16110538e+05 5.64e+00 33s
16 6.41e-05 6.62e-10 3.11314108e+05 -5.67635644e+04 1.75e+00 37s
17 1.87e-05 1.78e-10 1.02250933e+05 -1.96360216e+04 5.79e-01 39s
18 9.31e-06 9.91e-11 7.06100466e+04 -1.48397467e+04 4.06e-01 40s
19 3.70e-06 5.73e-11 3.96082759e+04 -8.05455770e+03 2.26e-01 41s
20 3.28e-06 4.27e-11 3.82171130e+04 -6.25733365e+03 2.11e-01 43s
21 1.59e-06 2.73e-11 2.68362068e+04 -2.39421912e+03 1.39e-01 44s
22 1.15e-06 2.36e-11 2.56652324e+04 -1.92773607e+03 1.31e-01 48s
23 6.03e-07 1.36e-11 2.08387443e+04 9.30026259e+02 9.45e-02 50s
24 3.68e-07 8.19e-12 1.81640559e+04 2.92313732e+03 7.24e-02 52s
25 3.10e-07 5.91e-12 1.72489969e+04 3.83317942e+03 6.37e-02 56s
26 2.39e-07 4.09e-12 1.61203457e+04 4.88465026e+03 5.33e-02 59s
27 1.73e-07 3.64e-12 1.48295799e+04 5.55407232e+03 4.40e-02 61s
28 1.44e-07 2.73e-12 1.42754988e+04 6.29135803e+03 3.79e-02 64s
29 8.49e-08 1.14e-12 1.28069756e+04 7.07462835e+03 2.72e-02 67s
30 7.31e-08 9.09e-13 1.26298795e+04 7.31806811e+03 2.52e-02 71s
31 5.30e-08 9.09e-13 1.20848925e+04 7.73537437e+03 2.06e-02 73s
32 4.21e-08 1.82e-12 1.18122159e+04 8.13586949e+03 1.75e-02 75s
33 2.39e-08 9.09e-13 1.14149641e+04 8.30558496e+03 1.48e-02 77s
34 1.60e-08 4.55e-13 1.10801208e+04 8.63533586e+03 1.16e-02 79s
35 1.30e-08 3.69e-13 1.09411593e+04 8.83346002e+03 1.00e-02 83s
36 8.91e-09 4.83e-13 1.07431756e+04 8.89580519e+03 8.77e-03 85s
37 5.99e-09 2.27e-13 1.05961030e+04 9.02764246e+03 7.45e-03 88s
38 4.85e-09 3.13e-13 1.05383085e+04 9.05248333e+03 7.05e-03 89s
39 4.45e-09 3.41e-13 1.05136942e+04 9.13561353e+03 6.54e-03 91s
40 4.23e-09 1.99e-13 1.04966448e+04 9.18695690e+03 6.22e-03 93s
41 2.40e-09 6.25e-13 1.03049603e+04 9.27134867e+03 4.91e-03 94s
42 1.47e-09 4.55e-13 1.02280746e+04 9.41441297e+03 3.86e-03 96s
43 1.03e-09 2.27e-13 1.01746657e+04 9.47565695e+03 3.32e-03 99s
44 8.01e-10 3.41e-13 1.01513061e+04 9.48693587e+03 3.15e-03 101s
45 5.03e-10 2.84e-13 1.00966206e+04 9.52771181e+03 2.70e-03 102s
46 3.06e-10 2.84e-13 1.00688557e+04 9.57071855e+03 2.36e-03 103s
47 2.44e-10 5.40e-13 1.00557587e+04 9.57656156e+03 2.27e-03 105s
48 1.89e-10 1.81e-13 1.00328512e+04 9.61968546e+03 1.96e-03 106s
49 1.64e-10 5.97e-13 1.00260933e+04 9.63360286e+03 1.86e-03 107s
50 1.86e-10 2.27e-13 9.99901149e+03 9.65578822e+03 1.63e-03 108s
51 8.00e-11 8.81e-13 9.99387541e+03 9.67539200e+03 1.51e-03 109s
52 8.00e-11 2.56e-13 9.99333474e+03 9.68646833e+03 1.46e-03 110s
53 6.18e-11 3.98e-13 9.98008312e+03 9.70915205e+03 1.29e-03 110s
54 8.00e-11 2.27e-13 9.96536538e+03 9.73027009e+03 1.12e-03 111s
55 5.46e-11 5.68e-13 9.94153050e+03 9.78635740e+03 7.37e-04 112s
56 2.95e-11 3.13e-13 9.93239666e+03 9.79987086e+03 6.29e-04 113s
57 4.37e-11 6.25e-13 9.92881475e+03 9.81037466e+03 5.62e-04 114s
58 9.09e-11 2.56e-13 9.92687487e+03 9.81524886e+03 5.30e-04 115s
59 8.37e-11 3.13e-13 9.91943642e+03 9.82987624e+03 4.25e-04 116s
60 2.94e-11 7.39e-13 9.90937510e+03 9.84468538e+03 3.07e-04 117s
61 1.09e-11 1.99e-13 9.90384575e+03 9.84900802e+03 2.60e-04 118s
62 4.73e-11 1.99e-13 9.89878174e+03 9.86141678e+03 1.77e-04 119s
63 1.43e-11 2.84e-13 9.89460308e+03 9.86618770e+03 1.35e-04 120s
64 5.21e-11 1.99e-13 9.89193935e+03 9.86936430e+03 1.07e-04 120s
65 4.37e-11 7.11e-13 9.89058874e+03 9.87123409e+03 9.19e-05 121s
66 1.06e-10 1.42e-13 9.88773562e+03 9.87325788e+03 6.87e-05 122s
67 2.18e-11 4.55e-13 9.88672573e+03 9.87498544e+03 5.57e-05 123s
68 6.55e-11 5.68e-13 9.88612597e+03 9.87857947e+03 3.58e-05 124s
69 1.75e-10 4.26e-13 9.88493177e+03 9.87912210e+03 2.76e-05 124s
70 3.96e-10 2.27e-13 9.88436495e+03 9.88063726e+03 1.77e-05 125s
71 2.09e-10 3.13e-13 9.88433519e+03 9.88080074e+03 1.68e-05 126s
72 1.12e-10 6.82e-13 9.88391819e+03 9.88129195e+03 1.25e-05 126s
73 4.78e-10 8.24e-13 9.88340973e+03 9.88203826e+03 6.51e-06 127s
74 2.83e-10 3.13e-13 9.88340067e+03 9.88230236e+03 5.21e-06 128s
75 3.21e-10 1.21e-13 9.88336541e+03 9.88238526e+03 4.65e-06 129s
76 1.84e-10 2.56e-13 9.88330624e+03 9.88266293e+03 3.05e-06 129s
77 3.08e-10 3.41e-13 9.88330730e+03 9.88300302e+03 1.44e-06 130s
78 3.40e-10 1.34e-12 9.88324655e+03 9.88310691e+03 6.63e-07 131s
79 5.61e-10 6.22e-13 9.88321826e+03 9.88313132e+03 4.13e-07 132s
80 1.33e-10 1.04e-12 9.88320942e+03 9.88313520e+03 3.52e-07 132s
81 6.55e-10 1.40e-12 9.88319429e+03 9.88314640e+03 2.27e-07 133s
82 3.26e-10 7.11e-13 9.88318935e+03 9.88315310e+03 1.72e-07 134s
83 3.31e-10 1.55e-12 9.88318186e+03 9.88315734e+03 1.16e-07 134s
84 1.07e-09 3.55e-12 9.88317725e+03 9.88316598e+03 5.35e-08 135s
85 4.30e-10 3.68e-12 9.88317303e+03 9.88316877e+03 2.03e-08 135s
86 6.50e-10 4.82e-12 9.88317188e+03 9.88317115e+03 3.46e-09 136s
87* 4.99e-10 5.93e-12 9.88317181e+03 9.88317173e+03 3.40e-10 137s
88* 1.01e-09 8.27e-12 9.88317178e+03 9.88317177e+03 5.01e-11 138s
89* 4.77e-10 1.42e-11 9.88317178e+03 9.88317178e+03 8.36e-12 140s
Running crossover as requested
Primal residual before push phase: 3.57e-05
Dual residual before push phase: 2.51e-06
Number of dual pushes required: 30806
Number of primal pushes required: 4202
Summary
Runtime: 144.53s
Status interior point solve: optimal
Status crossover: optimal
objective value: 9.88317178e+03
interior solution primal residual (abs/rel): 3.06e-08 / 6.40e-13
interior solution dual residual (abs/rel): 7.13e-09 / 1.77e-11
interior solution objective gap (abs/rel): 1.66e-06 / 1.68e-10
basic solution primal infeasibility: 3.19e-12
basic solution dual infeasibility: 6.25e-08
Ipx: IPM optimal
Ipx: Crossover optimal
Solving the original LP from the solution after postsolve
Model status : Optimal
IPM iterations: 89
Crossover iterations: 3032
Objective value : 9.8831717769e+03
HiGHS run time : 144.82
LP solved for primal
(A JuMP Model
Minimization problem with:
Variables: 136771
Objective function type: AffExpr
`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 40656 constraints
`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 27728 constraints
`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints
`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints
`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 133071 constraints
Model mode: AUTOMATIC
CachingOptimizer state: ATTACHED_OPTIMIZER
Solver name: HiGHS
Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cCapacityResMargin, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSOCMinCapRes, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cVSoCBalInterior, cVSoCBalStart, cZoneMinCapReq, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_in_virtual, eCVar_out, eCVar_out_virtual, eCapResMarBalance, eCapResMarBalanceNSE, eCapResMarBalanceStor, eCapResMarBalanceStorVirtual, eCapResMarBalanceThermal, eCapResMarBalanceTrans, eCapResMarBalanceVRE, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eMinCapRes, eMinCapResInvest, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarInT_virtual, eTotalCVarIn_virtual, eTotalCVarOut, eTotalCVarOutT, eTotalCVarOutT_virtual, eTotalCVarOut_virtual, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCAPRES_charge, vCAPRES_discharge, vCAPRES_socinreserve, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 145.17469787597656)totCap10 = value.(EP10[:eTotalCap])
totCapB10 = [totCap10[1] + totCap10[2] + totCap10[3], totCap10[4] + totCap10[6],
totCap10[5] + totCap10[7], totCap10[8] + totCap10[9] + totCap10[10]]
println(DataFrame([RT totCap10],["Resource Type","Total Capacity"]))
println(" ")
G10 = groupedbar(transpose(totCapB10), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW",
labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors,
title="MCR + ESR + CSM + CO2 Demand Cap \n Obj Val: $(round(objective_value(EP10),digits=6))",ylabelfontsize=8)
plot(G10, titlefontsize=8)10×2 DataFrame
Row │ Resource Type Total Capacity
│ Any Any
─────┼───────────────────────────────────────────────
1 │ MA_natural_gas_combined_cycle 8.51325
2 │ CT_natural_gas_combined_cycle 5.43676
3 │ ME_natural_gas_combined_cycle 0.552834
4 │ MA_solar_pv 17.9707
5 │ CT_onshore_wind 12.5249
6 │ CT_solar_pv 14.9714
7 │ ME_onshore_wind 11.4099
8 │ MA_battery 4.55918
9 │ CT_battery 4.08421
10 │ ME_battery 0.764153