Power mask¶
This example demonstrates how to derate or boost turbines by using a turbine model called PowerMask. We need the following imports:
%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import foxes
import foxes.variables as FV
import foxes.constants as FC
/home/runner/work/foxes/foxes/foxes/core/engine.py:6: TqdmExperimentalWarning: Using `tqdm.autonotebook.tqdm` in notebook mode. Use `tqdm.tqdm` instead to force console mode (e.g. in jupyter console)
from tqdm.autonotebook import tqdm
We start by creating a simple states table, this time via a pandas.DataFrame object:
sdata = pd.DataFrame(index=range(8))
sdata.index.name = FC.STATE
sdata[FV.WS] = [5.0, 8.0, 11.0, 14.0, 18.0, 20.0, 22.0, 25.0]
print(sdata)
states = foxes.input.states.StatesTable(
data_source=sdata,
output_vars=[FV.WS, FV.WD, FV.TI, FV.RHO],
fixed_vars={FV.WD: 270.0, FV.TI: 0.05, FV.RHO: 1.225},
)
WS
state
0 5.0
1 8.0
2 11.0
3 14.0
4 18.0
5 20.0
6 22.0
7 25.0
Next, we create the power mask for these states. The idea is that for each state and turbine, we can set a maximal power value in a table.
If the calculated power value is above this value, the turbine is derated.
If the maximal power exceeds the nominal power of the turbine type and the calculated value is at nominal power, then the turbine is boosted to the maximal power value.
If the maximal power value in the power mask is
NaN, then the turbine is neither derated nor boosted (normal operation)
Again we create a DataFrame that contains the power mask data:
pmask = pd.DataFrame(index=sdata.index, columns=[f"PMax_{i}" for i in range(5)])
pmask.loc[np.s_[:4], "PMax_4"] = 1000
pmask.loc[np.s_[4:], "PMax_4"] = 6000
pmask.loc[np.s_[2:], "PMax_2"] = 3000
pmask.loc[0, "PMax_0"] = 300.0
pmask.loc[3, "PMax_0"] = 1000.0
print(pmask)
PMax_0 PMax_1 PMax_2 PMax_3 PMax_4
state
0 300.0 NaN NaN NaN 1000
1 NaN NaN NaN NaN 1000
2 NaN NaN 3000 NaN 1000
3 1000.0 NaN 3000 NaN 1000
4 NaN NaN 3000 NaN 6000
5 NaN NaN 3000 NaN 6000
6 NaN NaN 3000 NaN 6000
7 NaN NaN 3000 NaN 6000
Using this data we can now create the model book. Notice how the variable FV.MAX_P is set to the above values via the turbine model SetFarmVars:
mbook = foxes.models.ModelBook()
mbook.turbine_models["set_Pmax"] = foxes.models.turbine_models.SetFarmVars()
mbook.turbine_models["set_Pmax"].add_var(FV.MAX_P, pmask)
We can now create a wind farm that consists of 5 turbines in a row. Some thoughts about the turbine_models argument:
The actual
PowerMaskturbine model is pre-defined in the defaultModelBookunder the namePMask, so we can just add it to the turbine model list.It should appear after the turbine type model
NREL5, sincePMaskcorrects the results od the latter.Furthermore,
PMaskshould be placed somewhere after the above created turbine modelset_Pmaxin the list of turbine models, such that the values of the variableFV.MAX_Pare present at the time whenPMaskis called.The models
NREL5andset_Pmaxhave no influence on each other, so their order does not matter.
We choose the following pattern:
models = ["NREL5MW", "set_Pmax", "PMask"]
farm = foxes.WindFarm()
foxes.input.farm_layout.add_row(
farm,
xy_base=[0.0, 0.0],
xy_step=[600.0, 0.0],
n_turbines=5,
turbine_models=models,
)
Turbine 0, T0: xy=(0.00, 0.00), NREL5MW, set_Pmax, PMask
Turbine 1, T1: xy=(600.00, 0.00), NREL5MW, set_Pmax, PMask
Turbine 2, T2: xy=(1200.00, 0.00), NREL5MW, set_Pmax, PMask
Turbine 3, T3: xy=(1800.00, 0.00), NREL5MW, set_Pmax, PMask
Turbine 4, T4: xy=(2400.00, 0.00), NREL5MW, set_Pmax, PMask
We can now setup our algorithm and run the calculation:
algo = foxes.algorithms.Downwind(
farm,
states,
rotor_model="centre",
wake_models=["Bastankhah2014_linear_k002"],
mbook=mbook,
verbosity=0,
)
# run calculation with power mask:
farm_results = algo.calc_farm()
fr = farm_results.to_dataframe()
print(fr[[FV.WD, FV.AMB_REWS, FV.REWS, FV.MAX_P, FV.AMB_P, FV.P]])
o = foxes.output.FarmResultsEval(farm_results, algo=algo)
P0 = o.calc_mean_farm_power(ambient=True)
P = o.calc_mean_farm_power()
print(f"\nFarm power: {P / 1000:.1f} MW, Efficiency = {P / P0 * 100:.2f} %")
# this output is needed later:
o1 = foxes.output.StateTurbineMap(farm_results)
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 8 states for 5 turbines
SingleChunkEngine: Starting calculation using a single worker.
SingleChunkEngine: Completed all 1 chunks
WD AMB_REWS REWS MAXP AMB_P P
state turbine
0 0 270.0 5.0 5.000000 300.0 300.0 300.000000
1 270.0 5.0 3.814381 NaN 403.9 152.233017
2 270.0 5.0 3.004124 NaN 403.9 41.065774
3 270.0 5.0 2.701086 NaN 403.9 0.000000
4 270.0 5.0 3.393368 1000.0 403.9 94.470023
1 0 270.0 8.0 8.000000 NaN 1771.1 1771.100000
1 270.0 8.0 5.128471 NaN 1771.1 446.770655
2 270.0 8.0 4.359237 NaN 1771.1 258.959385
3 270.0 8.0 4.099815 NaN 1771.1 200.278202
4 270.0 8.0 3.951750 1000.0 1000.0 171.080144
2 0 270.0 11.0 11.000000 NaN 4562.5 4562.500000
1 270.0 11.0 7.077374 NaN 4562.5 1232.378551
2 270.0 11.0 6.019489 3000.0 3000.0 746.362135
3 270.0 11.0 5.535864 NaN 4562.5 582.717698
4 270.0 11.0 5.273676 1000.0 1000.0 495.225773
3 0 270.0 14.0 14.000000 1000.0 1000.0 1000.000000
1 270.0 14.0 13.700036 NaN 5000.0 5000.000000
2 270.0 14.0 11.839741 3000.0 3000.0 3000.000000
3 270.0 14.0 10.930815 NaN 5000.0 4485.421327
4 270.0 14.0 7.961950 1000.0 1000.0 1000.000000
4 0 270.0 18.0 18.000000 NaN 5000.0 5000.000000
1 270.0 18.0 17.187504 NaN 5000.0 5000.000000
2 270.0 18.0 16.463311 3000.0 3000.0 3000.000000
3 270.0 18.0 16.261366 NaN 5000.0 5000.000000
4 270.0 18.0 15.581278 6000.0 6000.0 6000.000000
5 0 270.0 20.0 20.000000 NaN 5000.0 5000.000000
1 270.0 20.0 19.377548 NaN 5000.0 5000.000000
2 270.0 20.0 18.860383 3000.0 3000.0 3000.000000
3 270.0 20.0 18.740478 NaN 5000.0 5000.000000
4 270.0 20.0 18.324505 6000.0 6000.0 6000.000000
6 0 270.0 22.0 22.000000 NaN 5000.0 5000.000000
1 270.0 22.0 21.479296 NaN 5000.0 5000.000000
2 270.0 22.0 21.069694 3000.0 3000.0 3000.000000
3 270.0 22.0 20.983152 NaN 5000.0 5000.000000
4 270.0 22.0 20.671550 6000.0 6000.0 6000.000000
7 0 270.0 25.0 25.000000 NaN 5000.0 5000.000000
1 270.0 25.0 24.716577 NaN 5000.0 5000.000000
2 270.0 25.0 24.480543 3000.0 3000.0 3000.000000
3 270.0 25.0 24.420013 NaN 5000.0 5000.000000
4 270.0 25.0 24.230301 6000.0 6000.0 6000.000000
Farm power: 15.2 MW, Efficiency = 87.64 %
For a visualization of the results, let’s re-run the case without the power mask:
# reset, for run calculation without power mask:
for t in farm.turbines:
t.models.remove("set_Pmax")
t.models.remove("PMask")
farm_results = algo.calc_farm()
o0 = foxes.output.StateTurbineMap(farm_results)
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 8 states for 5 turbines
SingleChunkEngine: Starting calculation using a single worker.
SingleChunkEngine: Completed all 1 chunks
We are now in the position to create plots that compare the turbine power results, using the two output objects o0 and o1:
# show power:
fig, axs = plt.subplots(1, 3, figsize=(15, 5))
o0.plot_map(
FV.P,
ax=axs[0],
edgecolor="white",
title="Power, no power mask",
cmap="YlOrRd",
vmin=0,
vmax=np.nanmax(pmask),
)
o1.plot_map(
FV.MAX_P,
ax=axs[1],
edgecolor="white",
cmap="YlOrRd",
title="Power mask",
vmin=0,
vmax=np.nanmax(pmask),
)
o1.plot_map(
FV.P,
ax=axs[2],
edgecolor="white",
cmap="YlOrRd",
title="Power, with power mask",
vmin=0,
vmax=np.nanmax(pmask),
)
plt.show()
Similarly, for the thrust coefficients:
# show ct:
fig, axs = plt.subplots(1, 3, figsize=(15, 5))
o0.plot_map(
FV.CT,
ax=axs[0],
edgecolor="white",
title="ct, no power mask",
cmap="YlGn",
vmin=0,
vmax=1.0,
)
o1.plot_map(
FV.MAX_P,
ax=axs[1],
edgecolor="white",
cmap="YlOrRd",
title="Power mask",
vmin=0,
vmax=np.nanmax(pmask),
)
o1.plot_map(
FV.CT,
ax=axs[2],
edgecolor="white",
cmap="YlGn",
title="ct, with power mask",
vmin=0,
vmax=1.0,
)
plt.show()
The above visualizations demonstrate that the power mask has effects on both the produced power and ct. Hence, also wakes are affected by derating and boosts.
We can also visualize the effect of the PowerMask model on power and thrust curve, here for the case of derating from 5 MW to 3 MW:
o = foxes.output.TurbineTypeCurves(mbook)
plot_data = o.calc_plot_data("NREL5MW", [FV.P, FV.CT], P_max=3000.0)
fig, axs = plt.subplots(1, 2, figsize=(10, 4))
o.plot_curves(plot_data, axs=axs)
plt.show()
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 301 states for 1 turbines
SingleChunkEngine: Starting calculation using a single worker.
SingleChunkEngine: Completed all 1 chunks
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 301 states for 1 turbines
SingleChunkEngine: Starting calculation using a single worker.
SingleChunkEngine: Completed all 1 chunks
