Power mask¶
This example demonstrates how to derate or boost turbines by using a turbine model called PowerMask. We need the following imports:
In [1]:
%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
We start by creating a simple states table, this time via a pandas.DataFrame object:
In [2]:
sdata = pd.DataFrame(index=range(8))
sdata.index.name = FC.STATE
sdata[FV.WS] = [5., 8., 11., 14., 18., 20., 22., 25.]
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:
In [3]:
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:
In [4]:
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:
In [5]:
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: NREL5MW, set_Pmax, PMask
Turbine 1, T1: NREL5MW, set_Pmax, PMask
Turbine 2, T2: NREL5MW, set_Pmax, PMask
Turbine 3, T3: NREL5MW, set_Pmax, PMask
Turbine 4, T4: NREL5MW, set_Pmax, PMask
We can now setup our algorithm and run the calculation:
In [6]:
algo = foxes.algorithms.Downwind(
mbook,
farm,
states=states,
rotor_model="centre",
wake_models=["Bastankhah2014_linear_k002"],
wake_frame="rotor_wd",
partial_wakes_model="auto",
chunks={FC.STATE: 1000},
verbosity=0,
)
In [7]:
# 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)
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)
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 3.806173 NaN 403.9 151.106903
2 270.0 5.0 2.997697 NaN 403.9 0.000000
3 270.0 5.0 3.651819 NaN 403.9 129.929624
4 270.0 5.0 2.840554 1000.0 403.9 0.000000
1 0 270.0 8.0 8.000000 NaN 1771.1 1771.100000
1 270.0 8.0 5.110762 NaN 1771.1 440.861136
2 270.0 8.0 4.348633 NaN 1771.1 256.560767
3 270.0 8.0 4.093786 NaN 1771.1 198.914426
4 270.0 8.0 3.946766 1000.0 1000.0 170.396261
2 0 270.0 11.0 11.000000 NaN 4562.5 4562.500000
1 270.0 11.0 7.053010 NaN 4562.5 1218.152294
2 270.0 11.0 6.001880 3000.0 3000.0 738.445084
3 270.0 11.0 5.522878 NaN 4562.5 578.384285
4 270.0 11.0 5.262615 1000.0 1000.0 491.534548
3 0 270.0 14.0 14.000000 1000.0 1000.0 1000.000000
1 270.0 14.0 13.697787 NaN 5000.0 5000.000000
2 270.0 14.0 11.823401 3000.0 3000.0 3000.000000
3 270.0 14.0 10.900005 NaN 5000.0 4451.096026
4 270.0 14.0 7.932216 1000.0 1000.0 1000.000000
4 0 270.0 18.0 18.000000 NaN 5000.0 5000.000000
1 270.0 18.0 17.181480 NaN 5000.0 5000.000000
2 270.0 18.0 16.452153 3000.0 3000.0 3000.000000
3 270.0 18.0 16.249557 NaN 5000.0 5000.000000
4 270.0 18.0 15.563693 6000.0 6000.0 6000.000000
5 0 270.0 20.0 20.000000 NaN 5000.0 5000.000000
1 270.0 20.0 19.372918 NaN 5000.0 5000.000000
2 270.0 20.0 18.852422 3000.0 3000.0 3000.000000
3 270.0 20.0 18.732653 NaN 5000.0 5000.000000
4 270.0 20.0 18.314050 6000.0 6000.0 6000.000000
6 0 270.0 22.0 22.000000 NaN 5000.0 5000.000000
1 270.0 22.0 21.475399 NaN 5000.0 5000.000000
2 270.0 22.0 21.063345 3000.0 3000.0 3000.000000
3 270.0 22.0 20.977087 NaN 5000.0 5000.000000
4 270.0 22.0 20.663709 6000.0 6000.0 6000.000000
7 0 270.0 25.0 25.000000 NaN 5000.0 5000.000000
1 270.0 25.0 24.714437 NaN 5000.0 5000.000000
2 270.0 25.0 24.476878 3000.0 3000.0 3000.000000
3 270.0 25.0 24.416355 NaN 5000.0 5000.000000
4 270.0 25.0 24.225378 6000.0 6000.0 6000.000000
Farm power: 15.2 MW, Efficiency = 87.58 %
For a visualization of the results, let’s re-run the case without the power mask:
In [8]:
# reset, for run calculation without power mask:
models.remove("set_Pmax")
models.remove("PMask")
In [9]:
farm_results = algo.calc_farm()
o0 = foxes.output.StateTurbineMap(farm_results)
We are now in the position to create plots that compare the turbine power results, using the two output objects o0 and o1:
In [10]:
# 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:
In [11]:
# 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:
In [12]:
fig, axs = plt.subplots(1, 2, figsize=(10, 4))
o = foxes.output.TurbineTypeCurves(mbook)
o.plot_curves("NREL5MW", [FV.P, FV.CT], axs=axs, P_max=3000.)
plt.show()
