Originally Contributed by: Sourabh Dalvi
PowerSimulations.jl supports linear PTDF optimal power flow formulation. This example shows a single multi-period optimization of economic dispatch with a linearized DC-OPF representation of using PTDF power flow and how to extract duals values or locational marginal prices for energy.
using PowerSystems
using PowerSimulations
const PSI = PowerSimulations
using PowerSystemCaseBuilder
using DataFramesSince we'll be retrieving duals, we need a solver that returns duals values here we use HiGHS.
using HiGHS # mip solver
solver = optimizer_with_attributes(HiGHS.Optimizer, "mip_rel_gap" => 0.05)MathOptInterface.OptimizerWithAttributes(HiGHS.Optimizer, Pair{MathOptInterface.AbstractOptimizerAttribute, Any}[MathOptInterface.RawOptimizerAttribute("mip_rel_gap") => 0.05])We can use the same RTS data and some of the initialization as in OperationsProblem example
sys = build_system(PSITestSystems, "modified_RTS_GMLC_DA_sys")| Property | Value |
|---|---|
| System Units Base | SYSTEM_BASE |
| Base Power | 100.0 |
| Base Frequency | 60.0 |
| Num Components | 500 |
| Type | Count | Has Static Time Series | Has Forecasts |
|---|---|---|---|
| Arc | 109 | false | false |
| Area | 3 | true | true |
| Bus | 73 | false | false |
| FixedAdmittance | 3 | true | true |
| HydroDispatch | 1 | true | true |
| Line | 105 | false | false |
| LoadZone | 21 | false | false |
| PowerLoad | 51 | true | true |
| RenewableDispatch | 29 | true | true |
| RenewableFix | 31 | true | true |
| TapTransformer | 15 | false | false |
| ThermalStandard | 54 | false | false |
| VariableReserve{PowerSystems.ReserveDown} | 1 | true | true |
| VariableReserve{PowerSystems.ReserveUp} | 4 | true | true |
| Property | Value |
|---|---|
| Components with time series data | 123 |
| Total StaticTimeSeries | 124 |
| Total Forecasts | 124 |
| Resolution | 60 minutes |
| First initial time | 2020-01-01T00:00:00 |
| Last initial time | 2020-12-30T00:00:00 |
| Horizon | 48 |
| Interval | 1440 minutes |
| Forecast window count | 365 |
Here, we want do define an economic dispatch (linear generation decisions) with linear DC-OPF using PTDF network representation. So, starting with the network, we can select from almost any of the endpoints on this tree:
print_tree(PowerSimulations.PM.AbstractPowerModel)LoadError: UndefVarError: print_tree not defined
Stacktrace:
Calculate the PTDF matrix.
PTDF_matrix = PTDF(sys)PowerNetworkMatrix
Dimension 1, ["A1", "A2", "A3", "A4", "A5", "A6", "A7", "A8", "A9", "A10" … "CB-1", "C31-2", "C31-1", "C32-2", "C32-1", "C33-2", "C33-1", "C34", "C35", "CA-1"]
Dimension 2, [101, 102, 103, 104, 105, 106, 107, 108, 109, 110 … 316, 317, 318, 319, 320, 321, 322, 323, 324, 325]
And data, a (120, 73):
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template = template_unit_commitment(
network = NetworkModel(
StandardPTDFModel,
PTDF = PTDF_matrix,
duals = [CopperPlateBalanceConstraint],
use_slacks = false,
),
use_slacks = true,
)
for (k, v) in template.branches
v.duals = [NetworkFlowConstraint]
endNow we can build a 4-hour economic dispatch / OPF problem with the RTS data.
Here, we have to pass the keyword argument constraint_duals to OperationsProblem
with the name of the constraint for which duals are required for them to be returned in the results.
problem = DecisionModel(template, sys, horizon = 24, optimizer = solver)
build!(problem, output_dir = mktempdir())PowerSimulations.BuildStatusModule.BuildStatus.BUILT = 0And solve the problem and collect the results
solve!(problem)PowerSimulations.RunStatusModule.RunStatus.SUCCESSFUL = 0Here we collect the dual values from the results for the :CopperPlateBalance and :network_flow
constraints. In the case of PTDF network formulation we need to compute the final LMP for each bus in the system by
subtracting the duals (μ) of :network_flow constraints multiplied by the PTDF matrix
from the dual (λ) of :CopperPlateBalance constraint.
res = ProblemResults(problem)
duals = Dict([
k => read_dual(res, k) for
k in list_dual_keys(res) if PSI.get_entry_type(k) == NetworkFlowConstraint
])
λ = read_dual(res, "CopperPlateBalanceConstraint__System")[:, 2]
flow_duals = outerjoin(values(duals)..., on = :DateTime)
μ = Matrix(flow_duals[:, PTDF_matrix.axes[1]])24×120 Matrix{Union{Missing, Float64}}:
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-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0Here we calculate LMP as λ + congestion component of the LMP which is a product of μ and the PTDF matrix.
LMP = flow_duals[:, [:DateTime]]
for bus in get_components(Bus, sys)
LMP[:, get_name(bus)] = λ .+ μ * PTDF_matrix[:, get_number(bus)]
endFinally here we have the LMPs
LMP24 rows × 74 columns
| DateTime | Bacon | Cobb | Cole | Adams | Aston | Curie | Attlee | Bajer | Bates | Adler | Cabell | Bailey | Alder | Cary | Allen | Chuhsi | Barton | Comte | Bach | Caesar | Carew | Bain | Chase | Bell | Carrel | Ali | Caruso | Avery | Asser | Aubrey | Bardeen | Chifa | Alger | Bloch | Agricola | Astor | Aiken | Clay | Barlow | Caine | Bordet | Banks | Curtiss | Basov | Balzac | Camus | Chain | Caxton | Alber | Clark | Attar | Anna | Arthur | Cecil | Beethoven | Austen | Attila | Abel | Balch | Carter | Clive | Behring | Calvin | Cabot | Bayle | Bede | Arnold | Baker | Barry | Barkla | Arne | Baffin | Archer | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| DateTime | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | 2020-01-01T00:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 2 | 2020-01-01T01:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 3 | 2020-01-01T02:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 4 | 2020-01-01T03:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 5 | 2020-01-01T04:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 6 | 2020-01-01T05:00:00 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 | 2273.25 |
| 7 | 2020-01-01T06:00:00 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 |
| 8 | 2020-01-01T07:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 9 | 2020-01-01T08:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 10 | 2020-01-01T09:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 11 | 2020-01-01T10:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 12 | 2020-01-01T11:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 13 | 2020-01-01T12:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 14 | 2020-01-01T13:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 15 | 2020-01-01T14:00:00 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 | 2312.9 |
| 16 | 2020-01-01T15:00:00 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 |
| 17 | 2020-01-01T16:00:00 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 |
| 18 | 2020-01-01T17:00:00 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 | 3152.92 |
| 19 | 2020-01-01T18:00:00 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 | 3027.76 |
| 20 | 2020-01-01T19:00:00 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 | 2679.07 |
| 21 | 2020-01-01T20:00:00 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 | 2462.17 |
| 22 | 2020-01-01T21:00:00 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 | 2257.7 |
| 23 | 2020-01-01T22:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 24 | 2020-01-01T23:00:00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |