This example demonstrates how to derate or boost turbines by using a turbine model called PowerMask. We need the following imports:

In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

import foxes
import foxes.variables as FV


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 = FV.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: 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=["Bastankhah_linear_k002"],
wake_frame="rotor_wd",
partial_wakes_model="auto",
chunks={FV.STATE: 1000},
verbosity=0,
)

In [7]:

# run calculation with power mask:
farm_results = algo.calc_farm(vars_to_amb=[FV.REWS, FV.P])

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   4.100622     NaN   403.9   200.460668
2        270.0       5.0   3.230759     NaN   403.9    72.160101
3        270.0       5.0   2.836726     NaN   403.9     0.000000
4        270.0       5.0   3.448432  1000.0   403.9   102.024826
1     0        270.0       8.0   8.000000     NaN  1771.1  1771.100000
1        270.0       8.0   5.969501     NaN  1771.1   727.422438
2        270.0       8.0   5.109672     NaN  1771.1   440.497551
3        270.0       8.0   4.664896     NaN  1771.1   328.099527
4        270.0       8.0   4.346418  1000.0  1000.0   256.059846
2     0        270.0      11.0  11.000000     NaN  4562.5  4562.500000
1        270.0      11.0   8.218395     NaN  4562.5  1934.349917
2        270.0      11.0   7.026105  3000.0  3000.0  1202.442515
3        270.0      11.0   6.419438     NaN  4562.5   926.179190
4        270.0      11.0   6.069268  1000.0  1000.0   768.743105
3     0        270.0      14.0  14.000000  1000.0  1000.0  1000.000000
1        270.0      14.0  13.740422     NaN  5000.0  5000.000000
2        270.0      14.0  12.265493  3000.0  3000.0  3000.000000
3        270.0      14.0  11.610241     NaN  5000.0  4829.480538
4        270.0      14.0   9.737726  1000.0  1000.0  1000.000000
4     0        270.0      18.0  18.000000     NaN  5000.0  5000.000000
1        270.0      18.0  17.305147     NaN  5000.0  5000.000000
2        270.0      18.0  16.704317  3000.0  3000.0  3000.000000
3        270.0      18.0  16.538785     NaN  5000.0  5000.000000
4        270.0      18.0  16.001123  6000.0  6000.0  6000.000000
5     0        270.0      20.0  20.000000     NaN  5000.0  5000.000000
1        270.0      20.0  19.463783     NaN  5000.0  5000.000000
2        270.0      20.0  19.027022  3000.0  3000.0  3000.000000
3        270.0      20.0  18.922952     NaN  5000.0  5000.000000
4        270.0      20.0  18.572237  6000.0  6000.0  6000.000000
6     0        270.0      22.0  22.000000     NaN  5000.0  5000.000000
1        270.0      22.0  21.549852     NaN  5000.0  5000.000000
2        270.0      22.0  21.200276  3000.0  3000.0  3000.000000
3        270.0      22.0  21.124457     NaN  5000.0  5000.000000
4        270.0      22.0  20.856675  6000.0  6000.0  6000.000000
7     0        270.0      25.0  25.000000     NaN  5000.0  5000.000000
1        270.0      25.0  24.753726     NaN  5000.0  5000.000000
2        270.0      25.0  24.552823  3000.0  3000.0  3000.000000
3        270.0      25.0  24.501976     NaN  5000.0  5000.000000
4        270.0      25.0  24.340518  6000.0  6000.0  6000.000000

Farm power: 15.6 MW, Efficiency = 89.71 %


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(vars_to_amb=[FV.REWS, FV.P])
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()