5-bus Market simulation with PowerSimulations.jl

Originally Contributed by: Clayton Barrows

Introduction

PowerSimulations.jl supports simulations that consist of sequential optimization problems where results from previous problems inform subsequent problems in a variety of ways. This example demonstrates some of these capabilities to represent electricity market clearing.

Dependencies and Data

First, let's create System to represent the Day-Ahead and Real-Time market clearing process with hourly, and 5-minute time series data, respectively.

Modeling Packages

using PowerSystems
using PowerSimulations
using PowerSystemCaseBuilder

Data management packages

using Dates
using DataFrames

Optimization packages

using HiGHS # mip solver
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])

5-bus Data

The five bus system data here includes hourly day-ahead data, 5-minute real-time market data, and 6-second actual data. We'll only use the hourly and 5-minute data for the example simulations below, but the 6-second data is included for future development.

sys_DA = build_system(SIIPExampleSystems, "5_bus_matpower_DA")
sys_RT = build_system(SIIPExampleSystems, "5_bus_matpower_RT")

System
Property	Value
System Units Base	SYSTEM_BASE
Base Power	100.0
Base Frequency	60.0
Num Components	30

Static Components
Type	Count	Has Static Time Series	Has Forecasts
Arc	6	false	false
Area	1	false	false
Bus	5	false	false
Line	5	false	false
LoadZone	1	false	false
PhaseShiftingTransformer	2	false	false
PowerLoad	3	true	true
RenewableDispatch	2	true	true
ThermalStandard	5	false	false

Time Series Summary
Property	Value
Components with time series data	5
Total StaticTimeSeries	5
Total Forecasts	5
Resolution	60 minutes
First initial time	2020-01-01T00:00:00
Last initial time	2020-03-24T12:00:00
Horizon	12
Interval	60 minutes
Forecast window count	2005

`ProblemTemplate`

template_uc = template_unit_commitment(use_slacks=true)
template_ed = template_economic_dispatch(
    network=NetworkModel(CopperPlatePowerModel, duals=[CopperPlateBalanceConstraint]),
)

Network Model
Network Model	PowerSimulations.CopperPlatePowerModel
Slacks	false
PTDF	false
Duals	PowerSimulations.CopperPlateBalanceConstraint

Device Models ┌───────────────────────────────────┬──────────────────────────────────────────┬────────┐ │ Device Type │ Formulation │ Slacks │ ├───────────────────────────────────┼──────────────────────────────────────────┼────────┤ │ PowerSystems.ThermalStandard │ PowerSimulations.ThermalBasicDispatch │ false │ │ PowerSystems.HydroEnergyReservoir │ PowerSimulations.HydroDispatchRunOfRiver │ false │ │ PowerSystems.RenewableDispatch │ PowerSimulations.RenewableFullDispatch │ false │ │ PowerSystems.PowerLoad │ PowerSimulations.StaticPowerLoad │ false │ │ PowerSystems.InterruptibleLoad │ PowerSimulations.InterruptiblePowerLoad │ false │ │ PowerSystems.RenewableFix │ PowerSimulations.FixedOutput │ false │ │ PowerSystems.HydroDispatch │ PowerSimulations.HydroDispatchRunOfRiver │ false │ └───────────────────────────────────┴──────────────────────────────────────────┴────────┘

Branch Models
Branch Type	Formulation	Slacks
PowerSystems.Transformer2W	PowerSimulations.StaticBranch	false
PowerSystems.Line	PowerSimulations.StaticBranch	false
PowerSystems.HVDCLine	PowerSimulations.HVDCDispatch	false
PowerSystems.TapTransformer	PowerSimulations.StaticBranch	false

Service Models
Service Type	Formulation	Slacks	Aggregated Model
PowerSystems.VariableReserve{PowerSystems.ReserveUp}	PowerSimulations.RangeReserve	false	true
PowerSystems.VariableReserve{PowerSystems.ReserveDown}	PowerSimulations.RangeReserve	false	true

Define the Simulation Sequence

models = SimulationModels(
    decision_models=[
        DecisionModel(template_uc, sys_DA, name="UC", optimizer=solver),
        DecisionModel(template_ed, sys_RT, name="ED", optimizer=solver),
    ],
)

feedforward = Dict(
    "ED" => [
        SemiContinuousFeedforward(
            component_type=ThermalStandard,
            source=OnVariable,
            affected_values=[ActivePowerVariable],
        ),
    ],
)

DA_RT_sequence = SimulationSequence(
    models=models,
    ini_cond_chronology=InterProblemChronology(),
    feedforwards=feedforward,
)

Simulation Sequence
Simulation Step Interval	24 hours
Number of Problems	2

Simulation Problems
Model Name	Horizon	Interval	Executions Per Step
UC	48	1440 minutes	1
ED	12	60 minutes	24

Feedforwards
Model Name	Feed Forward Type
ED	PowerSimulations.SemiContinuousFeedforward

`Simulation`

file_path = mktempdir(cleanup=true)
sim = Simulation(
    name="5bus-test",
    steps=1,
    models=models,
    sequence=DA_RT_sequence,
    simulation_folder=file_path,
)

Simulation
Simulation Name	5bus-test
Build Status	EMPTY
Run Status	NOT_READY
Initial Time	Unset Initial Time
Steps	1

Decision Models
Model Name	Model Type	Status	Output Directory
UC	PowerSimulations.GenericOpProblem	EMPTY	nothing
ED	PowerSimulations.GenericOpProblem	EMPTY	nothing

No Emulator Model Specified

Simulation Sequence
Simulation Step Interval	24 hours
Number of Problems	2

Simulation Problems
Model Name	Horizon	Interval	Executions Per Step
UC	48	1440 minutes	1
ED	12	60 minutes	24

Feedforwards
Model Name	Feed Forward Type
ED	PowerSimulations.SemiContinuousFeedforward

Build simulation

build!(sim)

PowerSimulations.BuildStatusModule.BuildStatus.BUILT = 0

Execute simulation

execute!(sim, enable_progress_bar=false)

# Results

PowerSimulations.RunStatusModule.RunStatus.SUCCESSFUL = 0

First we can load the result metadata

results = SimulationResults(sim);
uc_results = get_decision_problem_results(results, "UC")
ed_results = get_decision_problem_results(results, "ED");

Then we can read and examine the results of interest. For example, if we want to read marginal prices of the balance constraint, we can see what dual values are available:

list_dual_names(ed_results)

1-element Vector{String}:
 "CopperPlateBalanceConstraint__System"

Then, we can read the results of the dual

prices = read_dual(ed_results, "CopperPlateBalanceConstraint__System")

DataStructures.SortedDict{Dates.DateTime, DataFrames.DataFrame, Base.Order.ForwardOrdering} with 24 entries:
  DateTime("2020-01-01T00:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T00:00:00                                1000.0
   2 │ 2020-01-01T01:00:00                                1000.0
   3 │ 2020-01-01T02:00:00                                1000.0
   4 │ 2020-01-01T03:00:00                                1000.0
   5 │ 2020-01-01T04:00:00                                1000.0
   6 │ 2020-01-01T05:00:00                                1000.0
   7 │ 2020-01-01T06:00:00                                1000.0
   8 │ 2020-01-01T07:00:00                                1000.0
   9 │ 2020-01-01T08:00:00                                1000.0
  10 │ 2020-01-01T09:00:00                                1000.0
  11 │ 2020-01-01T10:00:00                                1000.0
  12 │ 2020-01-01T11:00:00                                1000.0
  DateTime("2020-01-01T01:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T01:00:00                                1000.0
   2 │ 2020-01-01T02:00:00                                1000.0
   3 │ 2020-01-01T03:00:00                                1000.0
   4 │ 2020-01-01T04:00:00                                1000.0
   5 │ 2020-01-01T05:00:00                                1000.0
   6 │ 2020-01-01T06:00:00                                1000.0
   7 │ 2020-01-01T07:00:00                                1000.0
   8 │ 2020-01-01T08:00:00                                1000.0
   9 │ 2020-01-01T09:00:00                                1000.0
  10 │ 2020-01-01T10:00:00                                1000.0
  11 │ 2020-01-01T11:00:00                                1000.0
  12 │ 2020-01-01T12:00:00                                1000.0
  DateTime("2020-01-01T02:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T02:00:00                                1000.0
   2 │ 2020-01-01T03:00:00                                1000.0
   3 │ 2020-01-01T04:00:00                                1000.0
   4 │ 2020-01-01T05:00:00                                1000.0
   5 │ 2020-01-01T06:00:00                                1000.0
   6 │ 2020-01-01T07:00:00                                1000.0
   7 │ 2020-01-01T08:00:00                                1000.0
   8 │ 2020-01-01T09:00:00                                1000.0
   9 │ 2020-01-01T10:00:00                                1000.0
  10 │ 2020-01-01T11:00:00                                1000.0
  11 │ 2020-01-01T12:00:00                                1000.0
  12 │ 2020-01-01T13:00:00                                1000.0
  DateTime("2020-01-01T03:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T03:00:00                                1000.0
   2 │ 2020-01-01T04:00:00                                1000.0
   3 │ 2020-01-01T05:00:00                                1000.0
   4 │ 2020-01-01T06:00:00                                1000.0
   5 │ 2020-01-01T07:00:00                                1000.0
   6 │ 2020-01-01T08:00:00                                1000.0
   7 │ 2020-01-01T09:00:00                                1000.0
   8 │ 2020-01-01T10:00:00                                1000.0
   9 │ 2020-01-01T11:00:00                                1000.0
  10 │ 2020-01-01T12:00:00                                1000.0
  11 │ 2020-01-01T13:00:00                                1000.0
  12 │ 2020-01-01T14:00:00                                1000.0
  DateTime("2020-01-01T04:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T04:00:00                                1000.0
   2 │ 2020-01-01T05:00:00                                1000.0
   3 │ 2020-01-01T06:00:00                                1000.0
   4 │ 2020-01-01T07:00:00                                1000.0
   5 │ 2020-01-01T08:00:00                                1000.0
   6 │ 2020-01-01T09:00:00                                1000.0
   7 │ 2020-01-01T10:00:00                                1000.0
   8 │ 2020-01-01T11:00:00                                1000.0
   9 │ 2020-01-01T12:00:00                                1000.0
  10 │ 2020-01-01T13:00:00                                1000.0
  11 │ 2020-01-01T14:00:00                                1000.0
  12 │ 2020-01-01T15:00:00                                1000.0
  DateTime("2020-01-01T05:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T05:00:00                                1000.0
   2 │ 2020-01-01T06:00:00                                1000.0
   3 │ 2020-01-01T07:00:00                                1000.0
   4 │ 2020-01-01T08:00:00                                1000.0
   5 │ 2020-01-01T09:00:00                                1000.0
   6 │ 2020-01-01T10:00:00                                1000.0
   7 │ 2020-01-01T11:00:00                                1000.0
   8 │ 2020-01-01T12:00:00                                1000.0
   9 │ 2020-01-01T13:00:00                                1000.0
  10 │ 2020-01-01T14:00:00                                1000.0
  11 │ 2020-01-01T15:00:00                                1000.0
  12 │ 2020-01-01T16:00:00                                1000.0
  DateTime("2020-01-01T06:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T06:00:00                                1000.0
   2 │ 2020-01-01T07:00:00                                1000.0
   3 │ 2020-01-01T08:00:00                                1000.0
   4 │ 2020-01-01T09:00:00                                1000.0
   5 │ 2020-01-01T10:00:00                                1000.0
   6 │ 2020-01-01T11:00:00                                1000.0
   7 │ 2020-01-01T12:00:00                                1000.0
   8 │ 2020-01-01T13:00:00                                1000.0
   9 │ 2020-01-01T14:00:00                                1000.0
  10 │ 2020-01-01T15:00:00                                1000.0
  11 │ 2020-01-01T16:00:00                                1000.0
  12 │ 2020-01-01T17:00:00                                1000.0
  DateTime("2020-01-01T07:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T07:00:00                                1000.0
   2 │ 2020-01-01T08:00:00                                1000.0
   3 │ 2020-01-01T09:00:00                                1000.0
   4 │ 2020-01-01T10:00:00                                1000.0
   5 │ 2020-01-01T11:00:00                                1000.0
   6 │ 2020-01-01T12:00:00                                1000.0
   7 │ 2020-01-01T13:00:00                                1000.0
   8 │ 2020-01-01T14:00:00                                1000.0
   9 │ 2020-01-01T15:00:00                                1000.0
  10 │ 2020-01-01T16:00:00                                1000.0
  11 │ 2020-01-01T17:00:00                                1000.0
  12 │ 2020-01-01T18:00:00                                1000.0
  DateTime("2020-01-01T08:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T08:00:00                                1000.0
   2 │ 2020-01-01T09:00:00                                1000.0
   3 │ 2020-01-01T10:00:00                                1000.0
   4 │ 2020-01-01T11:00:00                                1000.0
   5 │ 2020-01-01T12:00:00                                1000.0
   6 │ 2020-01-01T13:00:00                                1000.0
   7 │ 2020-01-01T14:00:00                                1000.0
   8 │ 2020-01-01T15:00:00                                1000.0
   9 │ 2020-01-01T16:00:00                                1000.0
  10 │ 2020-01-01T17:00:00                                1000.0
  11 │ 2020-01-01T18:00:00                                1000.0
  12 │ 2020-01-01T19:00:00                                1000.0
  DateTime("2020-01-01T09:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T09:00:00                                1000.0
   2 │ 2020-01-01T10:00:00                                1000.0
   3 │ 2020-01-01T11:00:00                                1000.0
   4 │ 2020-01-01T12:00:00                                1000.0
   5 │ 2020-01-01T13:00:00                                1000.0
   6 │ 2020-01-01T14:00:00                                1000.0
   7 │ 2020-01-01T15:00:00                                1000.0
   8 │ 2020-01-01T16:00:00                                1000.0
   9 │ 2020-01-01T17:00:00                                1000.0
  10 │ 2020-01-01T18:00:00                                1000.0
  11 │ 2020-01-01T19:00:00                                1000.0
  12 │ 2020-01-01T20:00:00                                1000.0
  DateTime("2020-01-01T10:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T10:00:00                                1000.0
   2 │ 2020-01-01T11:00:00                                1000.0
   3 │ 2020-01-01T12:00:00                                1000.0
   4 │ 2020-01-01T13:00:00                                1000.0
   5 │ 2020-01-01T14:00:00                                1000.0
   6 │ 2020-01-01T15:00:00                                1000.0
   7 │ 2020-01-01T16:00:00                                1000.0
   8 │ 2020-01-01T17:00:00                                1000.0
   9 │ 2020-01-01T18:00:00                                1000.0
  10 │ 2020-01-01T19:00:00                                1000.0
  11 │ 2020-01-01T20:00:00                                1000.0
  12 │ 2020-01-01T21:00:00                                1000.0
  DateTime("2020-01-01T11:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T11:00:00                                1000.0
   2 │ 2020-01-01T12:00:00                                1000.0
   3 │ 2020-01-01T13:00:00                                1000.0
   4 │ 2020-01-01T14:00:00                                1000.0
   5 │ 2020-01-01T15:00:00                                1000.0
   6 │ 2020-01-01T16:00:00                                1000.0
   7 │ 2020-01-01T17:00:00                                1000.0
   8 │ 2020-01-01T18:00:00                                1000.0
   9 │ 2020-01-01T19:00:00                                1000.0
  10 │ 2020-01-01T20:00:00                                1000.0
  11 │ 2020-01-01T21:00:00                                1000.0
  12 │ 2020-01-01T22:00:00                                1000.0
  DateTime("2020-01-01T12:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T12:00:00                                1000.0
   2 │ 2020-01-01T13:00:00                                1000.0
   3 │ 2020-01-01T14:00:00                                1000.0
   4 │ 2020-01-01T15:00:00                                1000.0
   5 │ 2020-01-01T16:00:00                                1000.0
   6 │ 2020-01-01T17:00:00                                1000.0
   7 │ 2020-01-01T18:00:00                                1000.0
   8 │ 2020-01-01T19:00:00                                1000.0
   9 │ 2020-01-01T20:00:00                                1000.0
  10 │ 2020-01-01T21:00:00                                1000.0
  11 │ 2020-01-01T22:00:00                                1000.0
  12 │ 2020-01-01T23:00:00                                1000.0
  DateTime("2020-01-01T13:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T13:00:00                                1000.0
   2 │ 2020-01-01T14:00:00                                1000.0
   3 │ 2020-01-01T15:00:00                                1000.0
   4 │ 2020-01-01T16:00:00                                1000.0
   5 │ 2020-01-01T17:00:00                                1000.0
   6 │ 2020-01-01T18:00:00                                1000.0
   7 │ 2020-01-01T19:00:00                                1000.0
   8 │ 2020-01-01T20:00:00                                1000.0
   9 │ 2020-01-01T21:00:00                                1000.0
  10 │ 2020-01-01T22:00:00                                1000.0
  11 │ 2020-01-01T23:00:00                                1000.0
  12 │ 2020-01-02T00:00:00                                1000.0
  DateTime("2020-01-01T14:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T14:00:00                                1000.0
   2 │ 2020-01-01T15:00:00                                1000.0
   3 │ 2020-01-01T16:00:00                                1000.0
   4 │ 2020-01-01T17:00:00                                1000.0
   5 │ 2020-01-01T18:00:00                                1000.0
   6 │ 2020-01-01T19:00:00                                1000.0
   7 │ 2020-01-01T20:00:00                                1000.0
   8 │ 2020-01-01T21:00:00                                1000.0
   9 │ 2020-01-01T22:00:00                                1000.0
  10 │ 2020-01-01T23:00:00                                1000.0
  11 │ 2020-01-02T00:00:00                                1000.0
  12 │ 2020-01-02T01:00:00                                1000.0
  DateTime("2020-01-01T15:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T15:00:00                                1000.0
   2 │ 2020-01-01T16:00:00                                1000.0
   3 │ 2020-01-01T17:00:00                                1000.0
   4 │ 2020-01-01T18:00:00                                1000.0
   5 │ 2020-01-01T19:00:00                                1000.0
   6 │ 2020-01-01T20:00:00                                1000.0
   7 │ 2020-01-01T21:00:00                                1000.0
   8 │ 2020-01-01T22:00:00                                1000.0
   9 │ 2020-01-01T23:00:00                                1000.0
  10 │ 2020-01-02T00:00:00                                1000.0
  11 │ 2020-01-02T01:00:00                                1000.0
  12 │ 2020-01-02T02:00:00                                1000.0
  DateTime("2020-01-01T16:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T16:00:00                                1000.0
   2 │ 2020-01-01T17:00:00                                1000.0
   3 │ 2020-01-01T18:00:00                                1000.0
   4 │ 2020-01-01T19:00:00                                1000.0
   5 │ 2020-01-01T20:00:00                                1000.0
   6 │ 2020-01-01T21:00:00                                1000.0
   7 │ 2020-01-01T22:00:00                                1000.0
   8 │ 2020-01-01T23:00:00                                1000.0
   9 │ 2020-01-02T00:00:00                                1000.0
  10 │ 2020-01-02T01:00:00                                1000.0
  11 │ 2020-01-02T02:00:00                                1000.0
  12 │ 2020-01-02T03:00:00                                1000.0
  DateTime("2020-01-01T17:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T17:00:00                                1000.0
   2 │ 2020-01-01T18:00:00                                1000.0
   3 │ 2020-01-01T19:00:00                                1000.0
   4 │ 2020-01-01T20:00:00                                1000.0
   5 │ 2020-01-01T21:00:00                                1000.0
   6 │ 2020-01-01T22:00:00                                1000.0
   7 │ 2020-01-01T23:00:00                                1000.0
   8 │ 2020-01-02T00:00:00                                1000.0
   9 │ 2020-01-02T01:00:00                                1000.0
  10 │ 2020-01-02T02:00:00                                1000.0
  11 │ 2020-01-02T03:00:00                                1000.0
  12 │ 2020-01-02T04:00:00                                1000.0
  DateTime("2020-01-01T18:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T18:00:00                                1000.0
   2 │ 2020-01-01T19:00:00                                1000.0
   3 │ 2020-01-01T20:00:00                                1000.0
   4 │ 2020-01-01T21:00:00                                1000.0
   5 │ 2020-01-01T22:00:00                                1000.0
   6 │ 2020-01-01T23:00:00                                1000.0
   7 │ 2020-01-02T00:00:00                                1000.0
   8 │ 2020-01-02T01:00:00                                1000.0
   9 │ 2020-01-02T02:00:00                                1000.0
  10 │ 2020-01-02T03:00:00                                1000.0
  11 │ 2020-01-02T04:00:00                                1000.0
  12 │ 2020-01-02T05:00:00                                1000.0
  DateTime("2020-01-01T19:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T19:00:00                                1000.0
   2 │ 2020-01-01T20:00:00                                1000.0
   3 │ 2020-01-01T21:00:00                                1000.0
   4 │ 2020-01-01T22:00:00                                1000.0
   5 │ 2020-01-01T23:00:00                                1000.0
   6 │ 2020-01-02T00:00:00                                1000.0
   7 │ 2020-01-02T01:00:00                                1000.0
   8 │ 2020-01-02T02:00:00                                1000.0
   9 │ 2020-01-02T03:00:00                                1000.0
  10 │ 2020-01-02T04:00:00                                1000.0
  11 │ 2020-01-02T05:00:00                                1000.0
  12 │ 2020-01-02T06:00:00                                1000.0
  DateTime("2020-01-01T20:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T20:00:00                                1000.0
   2 │ 2020-01-01T21:00:00                                1000.0
   3 │ 2020-01-01T22:00:00                                1000.0
   4 │ 2020-01-01T23:00:00                                1000.0
   5 │ 2020-01-02T00:00:00                                1000.0
   6 │ 2020-01-02T01:00:00                                1000.0
   7 │ 2020-01-02T02:00:00                                1000.0
   8 │ 2020-01-02T03:00:00                                1000.0
   9 │ 2020-01-02T04:00:00                                1000.0
  10 │ 2020-01-02T05:00:00                                1000.0
  11 │ 2020-01-02T06:00:00                                1000.0
  12 │ 2020-01-02T07:00:00                                1000.0
  DateTime("2020-01-01T21:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T21:00:00                                1000.0
   2 │ 2020-01-01T22:00:00                                1000.0
   3 │ 2020-01-01T23:00:00                                1000.0
   4 │ 2020-01-02T00:00:00                                1000.0
   5 │ 2020-01-02T01:00:00                                1000.0
   6 │ 2020-01-02T02:00:00                                1000.0
   7 │ 2020-01-02T03:00:00                                1000.0
   8 │ 2020-01-02T04:00:00                                1000.0
   9 │ 2020-01-02T05:00:00                                1000.0
  10 │ 2020-01-02T06:00:00                                1000.0
  11 │ 2020-01-02T07:00:00                                1000.0
  12 │ 2020-01-02T08:00:00                                1000.0
  DateTime("2020-01-01T22:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T22:00:00                                1000.0
   2 │ 2020-01-01T23:00:00                                1000.0
   3 │ 2020-01-02T00:00:00                                1000.0
   4 │ 2020-01-02T01:00:00                                1000.0
   5 │ 2020-01-02T02:00:00                                1000.0
   6 │ 2020-01-02T03:00:00                                1000.0
   7 │ 2020-01-02T04:00:00                                1000.0
   8 │ 2020-01-02T05:00:00                                1000.0
   9 │ 2020-01-02T06:00:00                                1000.0
  10 │ 2020-01-02T07:00:00                                1000.0
  11 │ 2020-01-02T08:00:00                                1000.0
  12 │ 2020-01-02T09:00:00                                1000.0
  DateTime("2020-01-01T23:00:00") => 12×2 DataFrame
 Row │ DateTime             CopperPlateBalanceConstraint__System
     │ DateTime             Float64
─────┼───────────────────────────────────────────────────────────
   1 │ 2020-01-01T23:00:00                                1000.0
   2 │ 2020-01-02T00:00:00                                1000.0
   3 │ 2020-01-02T01:00:00                                1000.0
   4 │ 2020-01-02T02:00:00                                1000.0
   5 │ 2020-01-02T03:00:00                                1000.0
   6 │ 2020-01-02T04:00:00                                1000.0
   7 │ 2020-01-02T05:00:00                                1000.0
   8 │ 2020-01-02T06:00:00                                1000.0
   9 │ 2020-01-02T07:00:00                                1000.0
  10 │ 2020-01-02T08:00:00                                1000.0
  11 │ 2020-01-02T09:00:00                                1000.0
  12 │ 2020-01-02T10:00:00                                1000.0

or if we want to look at the realized values

read_realized_dual(ed_results, "CopperPlateBalanceConstraint__System")

24 rows × 2 columns

	DateTime	CopperPlateBalanceConstraint__System
	DateTime	Float64
1	2020-01-01T00:00:00	1000.0
2	2020-01-01T01:00:00	1000.0
3	2020-01-01T02:00:00	1000.0
4	2020-01-01T03:00:00	1000.0
5	2020-01-01T04:00:00	1000.0
6	2020-01-01T05:00:00	1000.0
7	2020-01-01T06:00:00	1000.0
8	2020-01-01T07:00:00	1000.0
9	2020-01-01T08:00:00	1000.0
10	2020-01-01T09:00:00	1000.0
11	2020-01-01T10:00:00	1000.0
12	2020-01-01T11:00:00	1000.0
13	2020-01-01T12:00:00	1000.0
14	2020-01-01T13:00:00	1000.0
15	2020-01-01T14:00:00	1000.0
16	2020-01-01T15:00:00	1000.0
17	2020-01-01T16:00:00	1000.0
18	2020-01-01T17:00:00	1000.0
19	2020-01-01T18:00:00	1000.0
20	2020-01-01T19:00:00	1000.0
21	2020-01-01T20:00:00	1000.0
22	2020-01-01T21:00:00	1000.0
23	2020-01-01T22:00:00	1000.0
24	2020-01-01T23:00:00	1000.0

Note that in this simulation the prices are all equal to the balance slack penalty value of $100000/MWh because there is unserved energy in the result

CC BY-SA 4.0 "Dheepak Krishnamurthy". Last modified: August 26, 2022. Website built with Franklin.jl and the Julia programming language.