Example: Optimize yaw for multiple wind directions and multiple wind speeds.

This example demonstrates how to perform a yaw optimization for multiple wind directionsand multiple wind speeds using the WindRose objectFirst, we initialize our Floris Interface, and then generate a 3 turbine wind farm.Next, we create the yaw optimization object yaw_opt and perform the optimization usingthe SerialRefine method. Finally, we plot the results.

import matplotlib.pyplot as plt
import numpy as np

from floris import FlorisModel, WindRose
from floris.optimization.yaw_optimization.yaw_optimizer_sr import YawOptimizationSR


# Load the default example floris object
fmodel = FlorisModel("../inputs/gch.yaml") # GCH model matched to the default "legacy_gauss" of V2
# fmodel = FlorisModel("inputs/cc.yaml") # New CumulativeCurl model

# Define a WindRose object with uniform TI and frequency table
wind_rose = WindRose(
    wind_directions=np.arange(0.0, 360.0, 3.0),
    wind_speeds=np.arange(2.0, 18.0, 1.0),
    ti_table=0.06,
)



# Reinitialize as a 3-turbine farm with range of WDs and WSs
D = 126.0 # Rotor diameter for the NREL 5 MW
fmodel.set(
    layout_x=[0.0, 5 * D, 10 * D],
    layout_y=[0.0, 0.0, 0.0],
    wind_data=wind_rose,
)

# Initialize optimizer object and run optimization using the Serial-Refine method
# Now, we enable the verify_convergence option. This function is useful to prevent
# yaw misalignment that increases the wind farm power production by a negligible
# amount. For example, at high wind speeds (e.g., 16 m/s), a turbine might yaw
# by a substantial amount to increase the power production by less than 1 W. This
# is typically the result of numerical imprecision of the power coefficient curve,
# which slightly differs for different above-rated wind speeds. The option
# verify_convergence therefore refines and validates the yaw angle choices
# but has no effect on the predicted power uplift from wake steering.
# Hence, it should mostly be used when actually synthesizing a practicable
# wind farm controller.
yaw_opt = YawOptimizationSR(fmodel)
df_opt = yaw_opt.optimize()

print("Optimization results:")
print(df_opt)

# Split out the turbine results
for t in range(3):
    df_opt['t%d' % t] = df_opt.yaw_angles_opt.apply(lambda x: x[t])

# Show the results: optimal yaw angles
fig, axarr = plt.subplots(
    nrows=4,
    ncols=4,
    sharex=True,
    sharey=True,
    figsize=(10, 8)
)
jj = 0
for ii, ws in enumerate(np.unique(fmodel.wind_speeds)):
    xi = np.remainder(ii, 4)
    if ((ii > 0) & (xi == 0)):
        jj += 1
    ax = axarr[np.remainder(ii, 4)][jj]
    ids = (df_opt.wind_speed == ws)
    wd = df_opt.loc[ids, "wind_direction"]
    for t in range(3):
        yaw_opt = df_opt.loc[ids, "t{:d}".format(t)]
        ax.plot(wd, yaw_opt, label='Turbine {:d}'.format(t))
    ax.set_title("Wind speed = {:.1f} m/s".format(ws), size=10)
    if ((ii == 0) & (jj == 0)):
        ax.legend()
    ax.grid(True)
    if jj == 0:
        ax.set_ylabel('Yaw angle (deg)', size=10)
    if xi == 3:
        axarr[xi][jj].set_xlabel('Wind Direction (deg)', size=10)

    plt.tight_layout()

# Show the results: baseline and optimized farm power
fig, axarr = plt.subplots(
    nrows=4,
    ncols=4,
    sharex=True,
    sharey=True,
    figsize=(10, 8)
)
jj = 0
for ii, ws in enumerate(np.unique(fmodel.wind_speeds)):
    xi = np.remainder(ii, 4)
    if ((ii > 0) & (xi == 0)):
        jj += 1
    ax = axarr[np.remainder(ii, 4)][jj]
    ids = (df_opt.wind_speed == ws)
    wd = df_opt.loc[ids, "wind_direction"]
    power_baseline = df_opt.loc[ids, "farm_power_baseline"]
    power_opt = df_opt.loc[ids, "farm_power_opt"]
    ax.plot(wd, power_baseline / 1e6, color='k', label='Baseline')
    ax.plot(wd, power_opt / 1e6, color='r', label='Optimized')
    ax.set_title("Wind speed = {:.1f} m/s".format(ws), size=10)
    ax.set_ylim([0.0, 16.0])
    if ((ii == 0) & (jj == 0)):
        ax.legend()
    ax.grid(True)
    if jj == 0:
        ax.set_ylabel('Farm Power (MW)', size=10)
    if xi == 3:
        axarr[xi][jj].set_xlabel('Wind Direction (deg)', size=10)

    plt.tight_layout()

plt.show()
import warnings
warnings.filterwarnings('ignore')

[Serial Refine] Processing pass=0, turbine_depth=0 (0.0%)

[Serial Refine] Processing pass=0, turbine_depth=1 (16.7%)

[Serial Refine] Processing pass=0, turbine_depth=2 (33.3%)

[Serial Refine] Processing pass=1, turbine_depth=0 (50.0%)

[Serial Refine] Processing pass=1, turbine_depth=1 (66.7%)

[Serial Refine] Processing pass=1, turbine_depth=2 (83.3%)

Optimization results:
      wind_direction  wind_speed  turbulence_intensity   yaw_angles_opt  \
0                0.0         2.0                  0.06  [0.0, 0.0, 0.0]   
1                0.0         3.0                  0.06  [0.0, 0.0, 0.0]   
2                0.0         4.0                  0.06  [0.0, 0.0, 0.0]   
3                0.0         5.0                  0.06  [0.0, 0.0, 0.0]   
4                0.0         6.0                  0.06  [0.0, 0.0, 0.0]   
...              ...         ...                   ...              ...   
1915           357.0        13.0                  0.06  [0.0, 0.0, 0.0]   
1916           357.0        14.0                  0.06  [0.0, 0.0, 0.0]   
1917           357.0        15.0                  0.06  [0.0, 0.0, 0.0]   
1918           357.0        16.0                  0.06  [0.0, 0.0, 0.0]   
1919           357.0        17.0                  0.06  [0.0, 0.0, 0.0]   

      farm_power_opt  farm_power_baseline  
0       0.000000e+00         0.000000e+00  
1       1.095593e+05         1.095593e+05  
2       5.276012e+05         5.276012e+05  
3       1.200541e+06         1.200541e+06  
4       2.193010e+06         2.193010e+06  
...              ...                  ...  
1915    1.500000e+07         1.500000e+07  
1916    1.500000e+07         1.500000e+07  
1917    1.500000e+07         1.500000e+07  
1918    1.500000e+07         1.500000e+07  
1919    1.500000e+07         1.500000e+07  

[1920 rows x 6 columns]