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)])

       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()


We can now create a wind farm that consists of 5 turbines in a row. Some thoughts about the turbine_models argument:

• The actual PowerMask turbine model is pre-defined in the default ModelBook under the name PMask, so we can just add it to the turbine model list.

• It should appear after the turbine type model NREL5, since PMask corrects the results od the latter.

• Furthermore, PMask should be placed somewhere after the above created turbine model set_Pmax in the list of turbine models, such that the values of the variable FV.MAX_P are present at the time when PMask is called.

• The models NREL5 and set_Pmax have 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()
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:

In [6]:

algo = foxes.algorithms.Downwind(
farm,
states,
rotor_model="centre",
wake_models=["Bastankhah2014_linear_k002"],
mbook=mbook,
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")

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",
cmap="YlOrRd",
vmin=0,
)
o1.plot_map(
FV.MAX_P,
ax=axs[1],
edgecolor="white",
cmap="YlOrRd",
vmin=0,
)
o1.plot_map(
FV.P,
ax=axs[2],
edgecolor="white",
cmap="YlOrRd",
vmin=0,
)
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",
cmap="YlGn",
vmin=0,
vmax=1.0,
)
o1.plot_map(
FV.MAX_P,
ax=axs[1],
edgecolor="white",
cmap="YlOrRd",
vmin=0,
)
o1.plot_map(
FV.CT,
ax=axs[2],
edgecolor="white",
cmap="YlGn",
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()