Operations problems with PowerSimulations.jl

Originally Contributed by: Clayton Barrows

Introduction

PowerSimulations.jl supports the construction and solution of optimal power system scheduling problems (Operations Problems). Operations problems form the fundamental building blocks for sequential simulations. This example shows how to specify and customize a the mathematics that will be applied to the data with an ProblemTemplate, build and execute an DecisionModel, and access the results.

Load Packages

using PowerSystems
using PowerSimulations
using HydroPowerSimulations
using PowerSystemCaseBuilder
using HiGHS # solver
using Dates

Data

Note

PowerSystemCaseBuilder.jl is a helper library that makes it easier to reproduce examples in the documentation and tutorials. Normally you would pass your local files to create the system data instead of calling the function build_system. For more details visit PowerSystemCaseBuilder Documentation

sys = build_system(PSISystems, "modified_RTS_GMLC_DA_sys")
System
Property Value
Name
Description
System Units Base SYSTEM_BASE
Base Power 100.0
Base Frequency 60.0
Num Components 501
Static Components
Type Count
ACBus 73
Arc 109
Area 3
FixedAdmittance 3
HydroDispatch 1
Line 105
LoadZone 21
PowerLoad 51
RenewableDispatch 29
RenewableNonDispatch 31
TapTransformer 15
ThermalStandard 54
TwoTerminalHVDCLine 1
VariableReserve{ReserveDown} 1
VariableReserve{ReserveUp} 4
Time Series Summary
owner_type owner_category time_series_type time_series_category initial_timestamp resolution_ms count
String String String String String Int64 Int64
Area Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 3
Area Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 3
FixedAdmittance Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 3
FixedAdmittance Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 3
HydroDispatch Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 2
HydroDispatch Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 2
PowerLoad Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 51
PowerLoad Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 51
RenewableDispatch Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 29
RenewableDispatch Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 29
RenewableNonDispatch Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 31
RenewableNonDispatch Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 31
VariableReserve Component DeterministicSingleTimeSeries Forecast 2020-01-01T00:00:00 3600000 5
VariableReserve Component SingleTimeSeries StaticTimeSeries 2020-01-01T00:00:00 3600000 5

Define a problem specification with an ProblemTemplate

You can create an empty template with:

template_uc = ProblemTemplate()
Network Model
Network Model CopperPlatePowerModel
Slacks false
PTDF false
Duals None
Device Models
Device Type Formulation Slacks

Now, you can add a DeviceModel for each device type to create an assignment between PowerSystems device types and the subtypes of AbstractDeviceFormulation. PowerSimulations has a variety of different AbstractDeviceFormulation subtypes that can be applied to different PowerSystems device types, each dispatching to different methods for populating optimization problem objectives, variables, and constraints. Documentation on the formulation options for various devices can be found in the formulation library docs

Branch Formulations

Here is an example of relatively standard branch formulations. Other formulations allow for selective enforcement of transmission limits and greater control on transformer settings.

set_device_model!(template_uc, Line, StaticBranch)
set_device_model!(template_uc, Transformer2W, StaticBranch)
set_device_model!(template_uc, TapTransformer, StaticBranch)

Injection Device Formulations

Here we define template entries for all devices that inject or withdraw power on the network. For each device type, we can define a distinct AbstractDeviceFormulation. In this case, we're defining a basic unit commitment model for thermal generators, curtailable renewable generators, and fixed dispatch (net-load reduction) formulations for HydroDispatch and RenewableNonDispatch devices.

set_device_model!(template_uc, ThermalStandard, ThermalStandardUnitCommitment)
set_device_model!(template_uc, RenewableDispatch, RenewableFullDispatch)
set_device_model!(template_uc, PowerLoad, StaticPowerLoad)
set_device_model!(template_uc, HydroDispatch, HydroDispatchRunOfRiver)
set_device_model!(template_uc, RenewableNonDispatch, FixedOutput)

Service Formulations

We have two VariableReserve types, parameterized by their direction. So, similar to creating DeviceModels, we can create ServiceModels. The primary difference being that DeviceModel objects define how constraints get created, while ServiceModel objects define how constraints get modified.

set_service_model!(template_uc, VariableReserve{ReserveUp}, RangeReserve)
set_service_model!(template_uc, VariableReserve{ReserveDown}, RangeReserve)

Network Formulations

Finally, we can define the transmission network specification that we'd like to model. For simplicity, we'll choose a copper plate formulation. But there are dozens of specifications available through an integration with PowerModels.jl. Note that many formulations will require appropriate data and may be computationally intractable

set_network_model!(template_uc, NetworkModel(CopperPlatePowerModel))

DecisionModel

Now that we have a System and an ProblemTemplate, we can put the two together to create an DecisionModel that we solve.

Optimizer

It's most convenient to define an optimizer instance upfront and pass it into the DecisionModel constructor. For this example, we can use the free HiGHS solver with a relatively relaxed MIP gap (ratioGap) setting to improve speed.

solver = optimizer_with_attributes(HiGHS.Optimizer, "mip_rel_gap" => 0.5)
MathOptInterface.OptimizerWithAttributes(HiGHS.Optimizer, Pair{MathOptInterface.AbstractOptimizerAttribute, Any}[MathOptInterface.RawOptimizerAttribute("mip_rel_gap") => 0.5])

Build an DecisionModel

The construction of an DecisionModel essentially applies an ProblemTemplate to System data to create a JuMP model.

problem = DecisionModel(template_uc, sys; optimizer = solver, horizon = Hour(24))
build!(problem, output_dir = mktempdir())
InfrastructureSystems.Optimization.ModelBuildStatusModule.ModelBuildStatus.BUILT = 0
Tip

The principal component of the DecisionModel is the JuMP model. But you can serialize to a file using the following command:

    serialize_optimization_model(problem, save_path)

Keep in mind that if the setting "storevariablenames" is set to False then the file won't show the model's names.

Solve an DecisionModel

solve!(problem)
InfrastructureSystems.Simulation.RunStatusModule.RunStatus.SUCCESSFULLY_FINALIZED = 0

Results Inspection

PowerSimulations collects the DecisionModel results into a OptimizationProblemResults struct:

res = OptimizationProblemResults(problem)

Start: 2020-01-01T00:00:00

End: 2020-01-01T23:00:00

Resolution: 60 minutes

PowerSimulations Problem Auxiliary variables Results
TimeDurationOff__ThermalStandard
TimeDurationOn__ThermalStandard
HydroEnergyOutput__HydroDispatch
PowerSimulations Problem Expressions Results
ProductionCostExpression__RenewableDispatch
ActivePowerBalance__System
ProductionCostExpression__HydroDispatch
ProductionCostExpression__ThermalStandard
PowerSimulations Problem Parameters Results
ActivePowerTimeSeriesParameter__PowerLoad
RequirementTimeSeriesParameter__VariableReserve__ReserveUp__Reg_Up
RequirementTimeSeriesParameter__VariableReserve__ReserveDown__Reg_Down
ActivePowerTimeSeriesParameter__RenewableDispatch
RequirementTimeSeriesParameter__VariableReserve__ReserveUp__Spin_Up_R2
RequirementTimeSeriesParameter__VariableReserve__ReserveUp__Spin_Up_R3
RequirementTimeSeriesParameter__VariableReserve__ReserveUp__Spin_Up_R1
ActivePowerTimeSeriesParameter__HydroDispatch
ActivePowerTimeSeriesParameter__RenewableNonDispatch
PowerSimulations Problem Variables Results
ActivePowerReserveVariable__VariableReserve__ReserveUp__Spin_Up_R1
ActivePowerReserveVariable__VariableReserve__ReserveUp__Spin_Up_R3
StopVariable__ThermalStandard
StartVariable__ThermalStandard
ActivePowerReserveVariable__VariableReserve__ReserveUp__Reg_Up
ActivePowerVariable__HydroDispatch
ActivePowerReserveVariable__VariableReserve__ReserveDown__Reg_Down
ActivePowerReserveVariable__VariableReserve__ReserveUp__Spin_Up_R2
ActivePowerVariable__ThermalStandard
ActivePowerVariable__RenewableDispatch
OnVariable__ThermalStandard

Optimizer Stats

The optimizer summary is included

get_optimizer_stats(res)
1×21 DataFrame
Rowdetailed_statsobjective_valuetermination_statusprimal_statusdual_statussolver_solve_timeresult_counthas_valueshas_dualsobjective_boundrelative_gapdual_objective_valuesolve_timebarrier_iterationssimplex_iterationsnode_counttimed_solve_timetimed_calculate_aux_variablestimed_calculate_dual_variablessolve_bytes_allocsec_in_gc
BoolFloat64Int64Int64Int64Float64Int64BoolBoolMissingMissingMissingFloat64MissingMissingMissingFloat64Float64Float64Float64Float64
1false2.3571e6110NaN1falsefalsemissingmissingmissing0.630498missingmissingmissing0.7110420.3464970.0004271822.94527e70.0

Objective Function Value

get_objective_value(res)
2.357099085649291e6

Variable, Parameter, Auxillary Variable, Dual, and Expression Values

The solution value data frames for variables, parameters, auxillary variables, duals and expressions can be accessed using the read_ methods:

read_variables(res)
Dict{String, DataFrames.DataFrame} with 11 entries:
  "ActivePowerReserveVaria… => 24×52 DataFrame…
  "StopVariable__ThermalSt… => 24×55 DataFrame…
  "ActivePowerReserveVaria… => 24×52 DataFrame…
  "OnVariable__ThermalStan… => 24×55 DataFrame…
  "ActivePowerVariable__Hy… => 24×2 DataFrame…
  "ActivePowerReserveVaria… => 24×19 DataFrame…
  "StartVariable__ThermalS… => 24×55 DataFrame…
  "ActivePowerVariable__Th… => 24×55 DataFrame…
  "ActivePowerVariable__Re… => 24×30 DataFrame…
  "ActivePowerReserveVaria… => 24×18 DataFrame…
  "ActivePowerReserveVaria… => 24×17 DataFrame…

Or, you can read a single parameter values for parameters that exist in the results.

list_parameter_names(res)
read_parameter(res, "ActivePowerTimeSeriesParameter__RenewableDispatch")
24×30 DataFrame
RowDateTime122_WIND_1324_PV_3312_PV_1102_PV_1101_PV_1324_PV_2313_PV_2104_PV_1101_PV_2309_WIND_1310_PV_2113_PV_1317_WIND_1314_PV_1324_PV_1103_PV_1303_WIND_1314_PV_2102_PV_2314_PV_3320_PV_1101_PV_3319_PV_1314_PV_4310_PV_1215_PV_1313_PV_1101_PV_4119_PV_1
DateTimeFloat64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64
12020-01-01T00:00:00713.20.00.00.00.00.00.00.00.0142.80.00.0795.10.00.00.0480.80.00.00.00.00.00.00.00.00.00.00.00.0
22020-01-01T01:00:00712.80.00.00.00.00.00.00.00.0139.10.00.0794.40.00.00.0634.90.00.00.00.00.00.00.00.00.00.00.00.0
32020-01-01T02:00:00708.40.00.00.00.00.00.00.00.0145.30.00.0773.60.00.00.0487.30.00.00.00.00.00.00.00.00.00.00.00.0
42020-01-01T03:00:00710.70.00.00.00.00.00.00.00.0144.80.00.0767.30.00.00.0432.70.00.00.00.00.00.00.00.00.00.00.00.0
52020-01-01T04:00:00701.40.00.00.00.00.00.00.00.0137.10.00.0752.20.00.00.0407.90.00.00.00.00.00.00.00.00.00.00.00.0
62020-01-01T05:00:00682.50.00.00.00.00.00.00.00.098.60.00.0719.40.00.00.0440.20.00.00.00.00.00.00.00.00.00.00.00.0
72020-01-01T06:00:00614.70.00.00.00.00.00.00.00.062.20.00.0655.30.00.00.0377.30.00.00.00.00.00.00.00.00.00.00.00.0
82020-01-01T07:00:00517.736.452.230.629.636.462.229.830.447.338.299.4594.647.444.829.8199.346.630.063.847.830.6179.246.438.2127.662.228.827.2
92020-01-01T08:00:00426.663.497.436.834.863.496.035.037.048.961.4126.2579.161.265.258.4110.667.036.4100.061.437.4248.067.061.4164.695.635.456.6
102020-01-01T09:00:00274.271.2118.038.036.471.4117.636.638.230.766.8133.2466.869.068.076.63.669.837.6121.869.838.8273.469.866.8172.2116.835.874.8
112020-01-01T10:00:0093.072.2132.037.836.472.2130.836.638.027.470.2134.2301.470.270.289.82.472.237.4129.070.438.6277.872.270.4173.2128.437.488.2
122020-01-01T11:00:006.370.6135.237.035.070.6134.235.437.260.969.8135.2110.767.070.298.056.272.436.6128.667.237.6263.272.469.6170.0133.238.691.6
132020-01-01T12:00:003.867.4131.036.235.467.4129.635.636.420.467.8133.078.967.268.294.091.570.235.8128.267.437.0267.470.267.6169.0128.837.890.6
142020-01-01T13:00:001.165.2125.435.235.065.2123.635.435.41.667.2126.6107.967.065.881.4103.067.634.8119.667.035.8258.867.667.0161.8122.835.879.2
152020-01-01T14:00:000.060.2109.631.031.060.4108.031.431.20.063.2110.222.359.462.659.439.764.230.8107.059.431.6227.864.262.8143.2106.831.459.0
162020-01-01T15:00:000.042.069.020.219.242.065.620.620.22.645.062.824.642.444.825.487.746.220.065.843.420.6151.646.243.882.262.820.427.8
172020-01-01T16:00:000.90.00.00.00.00.00.00.00.037.90.00.010.80.00.00.092.30.00.00.00.00.00.00.00.00.00.00.00.0
182020-01-01T17:00:00276.30.00.00.00.00.00.00.00.046.90.00.0243.20.00.00.089.40.00.00.00.00.00.00.00.00.00.00.00.0
192020-01-01T18:00:00272.90.00.00.00.00.00.00.00.024.00.00.0375.20.00.00.090.40.00.00.00.00.00.00.00.00.00.00.00.0
202020-01-01T19:00:00345.60.00.00.00.00.00.00.00.024.00.00.0568.40.00.00.081.10.00.00.00.00.00.00.00.00.00.00.00.0
212020-01-01T20:00:00411.70.00.00.00.00.00.00.00.027.40.00.0636.10.00.00.0172.90.00.00.00.00.00.00.00.00.00.00.00.0
222020-01-01T21:00:00376.60.00.00.00.00.00.00.00.06.50.00.0719.20.00.00.0326.90.00.00.00.00.00.00.00.00.00.00.00.0
232020-01-01T22:00:00561.30.00.00.00.00.00.00.00.01.30.00.0734.90.00.00.0256.70.00.00.00.00.00.00.00.00.00.00.00.0
242020-01-01T23:00:00568.40.00.00.00.00.00.00.00.00.10.00.0729.10.00.00.0141.10.00.00.00.00.00.00.00.00.00.00.00.0

Plotting

Take a look at the plotting capabilities in PowerGraphics.jl