AEP from rose after optimizing with serial refine

[Ana-GS]

Hello all, In the aep from rose example, I have seen that after calculating FLORIS for every WD and WS and returning the farm power:

farm_power_array = fi.get_farm_power()

Then FLORIS solutions are mapped to the wind rose dataframe:

wd_grid, ws_grid = np.meshgrid(wd_array, ws_array, indexing='ij')
interpolant = NearestNDInterpolator(
np.vstack([wd_grid.flatten(), ws_grid.flatten()]).T,
farm_power_array.flatten()
)

I am trying to calculate aep after yaw optimization with serial refine, to compare it with the baseline: df_opt_AEP = yaw_opt_AEP.optimize()

However, I am not able to map the FLORIS solutions after optimization to the wind rose dataframe:

wd_grid, ws_grid = np.meshgrid(wd_array, ws_array, indexing='ij')
interpolant_opt = NearestNDInterpolator(
np.vstack([wd_grid.flatten(), ws_grid.flatten()]).T,
df_opt_AEP.farm_power_opt.flatten()
)

It complains about df_opt_AEP.farm_power_opt.flatten() saying 'Series' object has no attribute 'flatten'.

Could you please advice how to calculate aep from rose after yaw optimization? Many thanks!

Kind regards

[Bartdoekemeijer]

Hi @Ana-GS,

You must note that farm_power_array is a two-dimensional matrix with shape (n_wind_directions, n_wind_speeds). That is what we call the "gridded" format and the conventional variable format inside FLORIS. You can turn this into a one-dimensional array using farm_power_array.flatten(), which has shape (n_wind_directions * n_wind_speeds, 1). This is what you can call the "flattened" format.

The end product of the yaw optimization will return df_opt, which is a dataframe which is already in flattened format. For example:

    wind_direction  wind_speed  turbulence_intensity                                                                   yaw_angles_opt  farm_power_opt  farm_power_baseline
0              0.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 15.0, 15.0, 15.0, 15.0, 15.0, 20.0, 20.0, 20.0, 20...    2.528925e+07         1.863937e+07
1              5.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 15.0, 15.0, 15.0, 15.0, 15.0, 17.5, 17.5, 17.5, 17...    3.353026e+07         2.739931e+07
2             10.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 6.25, 6.25, 6.25, 6.25, 7.5, 8.75, 8.75, 8.75, 8.7...    3.945621e+07         3.837638e+07
3             15.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.981120e+07         3.981120e+07
4             20.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.892033e+07         3.871670e+07
5             25.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.498197e+07         3.498197e+07
6             30.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 7.5, 7.5, 7.5, 12.5,...    3.869494e+07         3.775685e+07
7             35.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.967334e+07         3.959966e+07
8             40.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.459403e+07         3.459403e+07
9             45.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.5, 16.25, 20.0, 20.0, 0.0, 16.25, 19.375, ...    3.051654e+07         2.682011e+07
10            50.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 8.75, 11.25, 12.5, 15.0, 0.0, 8.75, 12.5, 13....    3.762637e+07         3.499734e+07
11            55.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.962557e+07         3.961671e+07
12            60.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.760042e+07         3.760042e+07
13            65.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 11.25, 15.0, 16.25, 0.0, 0.0, 11.25, 15....    3.712010e+07         3.510834e+07
14            70.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.868654e+07         3.868654e+07
15            75.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 10.0...    3.997398e+07         3.982914e+07
16            80.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.787021e+07         3.787021e+07
17            85.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    2.668607e+07         2.668607e+07
18            90.0         8.0                  0.06  [0.0, 15.0, 20.0, 20.0, 20.0, 0.0, 15.0, 20.0, 20.0, 20.0, 0.0, 15.0, 20.0, ...    2.528925e+07         1.863937e+07
19            95.0         8.0                  0.06  [0.0, 15.0, 18.125, 20.0, 20.0, 0.0, 15.0, 17.5, 20.0, 20.0, 0.0, 15.0, 17.5...    3.353026e+07         2.739931e+07
20           100.0         8.0                  0.06  [0.0, 7.5, 8.75, 8.75, 7.5, 0.0, 6.25, 8.75, 8.75, 7.5, 0.0, 6.25, 8.75, 8.7...    3.945621e+07         3.837638e+07
21           105.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.981120e+07         3.981120e+07
22           110.0         8.0                  0.06  [0.0, 0.0, 0.0, 8.75, 3.75, 0.0, 0.0, 0.0, 7.5, 3.75, 0.0, 0.0, 0.0, 7.5, 3....    3.892033e+07         3.871670e+07
23           115.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.498197e+07         3.498197e+07
24           120.0         8.0                  0.06  [0.0, 0.0, 12.5, 11.25, 12.5, 0.0, 0.0, 7.5, 7.5, 12.5, 0.0, 0.0, 7.5, 7.5, ...    3.869494e+07         3.775685e+07
25           125.0         8.0                  0.06  [0.0, 0.0, 0.0, 3.75, 6.25, 0.0, 0.0, 0.0, 0.0, 6.25, 0.0, 0.0, 0.0, 0.0, 2....    3.967334e+07         3.959966e+07
26           130.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.459403e+07         3.459403e+07
27           135.0         8.0                  0.06  [0.0, 20.0, 20.0, 20.0, 20.0, 0.0, 20.0, 20.0, 20.0, 20.0, 0.0, 16.25, 19.37...    3.051654e+07         2.682011e+07
28           140.0         8.0                  0.06  [0.0, 15.0, 17.5, 17.5, 18.125, 0.0, 12.5, 13.75, 13.75, 17.5, 0.0, 11.25, 1...    3.762637e+07         3.499734e+07
29           145.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.962557e+07         3.961671e+07
30           150.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.760042e+07         3.760042e+07
31           155.0         8.0                  0.06  [0.0, 16.25, 18.125, 18.125, 19.375, 0.0, 15.0, 15.0, 15.0, 16.25, 0.0, 11.2...    3.712010e+07         3.510834e+07
32           160.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.868654e+07         3.868654e+07
33           165.0         8.0                  0.06  [0.0, 10.0, 10.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0...    3.997398e+07         3.982914e+07
34           170.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.787021e+07         3.787021e+07
35           175.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    2.668607e+07         2.668607e+07
36           180.0         8.0                  0.06  [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20....    2.528925e+07         1.863937e+07
37           185.0         8.0                  0.06  [20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 19.375, 19.375, 19.375, 18.125, 1...    3.353026e+07         2.739931e+07
38           190.0         8.0                  0.06  [7.5, 7.5, 7.5, 7.5, 11.25, 8.75, 8.75, 8.75, 8.75, 8.75, 8.75, 8.75, 8.75, ...    3.945621e+07         3.837638e+07
39           195.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.981120e+07         3.981120e+07
40           200.0         8.0                  0.06  [3.75, 3.75, 3.75, 3.75, 0.0, 8.75, 7.5, 7.5, 7.5, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.892033e+07         3.871670e+07
41           205.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.498197e+07         3.498197e+07
42           210.0         8.0                  0.06  [12.5, 12.5, 12.5, 12.5, 0.0, 11.25, 7.5, 7.5, 8.75, 0.0, 12.5, 7.5, 7.5, 7....    3.869494e+07         3.775685e+07
43           215.0         8.0                  0.06  [6.25, 6.25, 2.5, 0.0, 0.0, 3.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0....    3.967334e+07         3.959966e+07
44           220.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.459403e+07         3.459403e+07
45           225.0         8.0                  0.06  [20.0, 20.0, 20.0, 20.0, 0.0, 20.0, 20.0, 20.0, 20.0, 0.0, 20.0, 20.0, 19.37...    3.051654e+07         2.682011e+07
46           230.0         8.0                  0.06  [18.125, 17.5, 17.5, 15.0, 0.0, 17.5, 13.75, 13.75, 11.25, 0.0, 17.5, 13.75,...    3.762637e+07         3.499734e+07
47           235.0         8.0                  0.06  [0.0, 0.0, 0.0, 2.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.962557e+07         3.961671e+07
48           240.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.760042e+07         3.760042e+07
49           245.0         8.0                  0.06  [19.375, 16.25, 16.25, 0.0, 0.0, 18.125, 15.0, 11.25, 0.0, 0.0, 18.125, 15.0...    3.712010e+07         3.510834e+07
50           250.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.868654e+07         3.868654e+07
51           255.0         8.0                  0.06  [10.0, 0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0....    3.997398e+07         3.982914e+07
52           260.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.787021e+07         3.787021e+07
53           265.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    2.668607e+07         2.668607e+07
54           270.0         8.0                  0.06  [20.0, 20.0, 20.0, 15.0, 0.0, 20.0, 20.0, 20.0, 15.0, 0.0, 20.0, 20.0, 20.0,...    2.528925e+07         1.863937e+07
55           275.0         8.0                  0.06  [20.0, 19.375, 17.5, 15.0, 0.0, 20.0, 19.375, 17.5, 15.0, 0.0, 20.0, 19.375,...    3.353026e+07         2.739931e+07
56           280.0         8.0                  0.06  [11.25, 8.75, 8.75, 6.25, 0.0, 7.5, 8.75, 8.75, 6.25, 0.0, 7.5, 8.75, 8.75, ...    3.945621e+07         3.837638e+07
57           285.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.981120e+07         3.981120e+07
58           290.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 3.75, 7.5, 0.0, 0.0, 0.0, 3.75, 7.5, 0.0, 0.0, 0.0...    3.892033e+07         3.871670e+07
59           295.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.498197e+07         3.498197e+07
60           300.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 12.5, 8.75, 7.5, 0.0, 0.0, 12.5, 7.5, 7.5, 0.0, 0....    3.869494e+07         3.775685e+07
61           305.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.5, 0.0, 0.0, 0.0, 0.0, ...    3.967334e+07         3.959966e+07
62           310.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.459403e+07         3.459403e+07
63           315.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 20.0, 20.0, 16.25, 12.5, 0.0, 20.0, 20.0, 19.375, ...    3.051654e+07         2.682011e+07
64           320.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 15.0, 11.25, 8.75, 8.75, 0.0, 17.5, 13.75, 12.5, 1...    3.762637e+07         3.499734e+07
65           325.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 2.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.962557e+07         3.961671e+07
66           330.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.760042e+07         3.760042e+07
67           335.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 16.25, 11.25, 11.25, 11.2...    3.712010e+07         3.510834e+07
68           340.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.868654e+07         3.868654e+07
69           345.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.997398e+07         3.982914e+07
70           350.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    3.787021e+07         3.787021e+07
71           355.0         8.0                  0.06  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...    2.668607e+07         2.668607e+07

[72 rows x 6 columns]

To put the optimal yaw angles from df_opt back into gridded format, you create a yaw angle interpolant from df_opt:

interpolant_opt = NearestNDInterpolator(
    df_opt[["wind_direction", "wind_speed"]],
    df_opt["yaw_angles_opt"]
)

This interpolant will return the optimal yaw angles for any wind direction and wind speed you insert. So, if wd_array and ws_array are the wind direction and wind speed arrays in FLORIS, then

wd_grid, ws_grid = np.meshgrid(wd_array, ws_array, indexing='ij')
yaw_angles_grid = interpolant_opt(wd_grid, ws_grid)
farm_AEP_opt = fi.get_farm_aep(
    freq=freq,
    yaw_angles=yaw_angles_grid
)

where freq is the frequency of each wind direction/speed bin, being a twodimensional matrix with shape (n_wind_directions, n_wind_speeds).

Does this answer your question?

[Bartdoekemeijer]

Also, adding a couple more things to consider:

1. To calculate the AEP, you need information about the wind rose. Thus, you need the frequency of occurrence for each wind direction and wind speed bin. This is what we define as freq in FLORIS and that two-dimensional matrix typically sums up to 1.0. An example is shown here:
   

   floris/examples/10_optimize_yaw.py

   Line 53 in fa9f63e

   def load_windrose():

2. The AEP is typically calculated for wind speeds from 0 to 25 m/s. With yaw optimizations, we typically only apply yaw offsets between, let's say, 4.0 and 10.0 m/s. You must take this into consideration when calculating the AEP uplift from wake steering. Namely, we often only optimize the yaw angles at one wind speed like 8.0 m/s, and then assume those yaw angles are also optimal for the entire wind speed range of 4.0 to 10.0 m/s. This is what is taken care of starting in line 147 in example 10_optimize_yaw.py:
   

   floris/examples/10_optimize_yaw.py

   Line 147 in fa9f63e

   # Now define how the optimal yaw angles for 8 m/s are applied over the other wind speeds

Generally, working through example 10_optimize_yaw.py should be very informative for your application.

[Ana-GS]

Thanks Bart. Very informative. I will look into floris/examples/10_optimize_yaw.py. I thought it would be similar to 08_opt_yaw_single_ws.py, 09_opt_yaw_multiple_ws.py and 12_compare_yaw_optimizers.py, so I did not look into that one and it seems that it had the answer to my question.

Thanks for the additional explanations that help understanding better what it is being done in 10_optimize_yaw.py.

Best regards

[Ana-GS]

Dear Floris team,

Using the example: floris/examples/10_optimize_yaw.py

I have calculated the AEP for my wind farm both baseline and after yaw optimization. However, I would like to calculate AEP after yaw optimization, optimizing not only for one wind speed which is then applied to a range of speeds, but optimizing for all wind speeds at steps of 1m/s. Then applying the yaw offsets for each wind speed to calculate the AEP gain. Do you have an example that does this you could share?

Many thanks!

Best regards,

Ana