Turbine-based ambient flow data

In some cases the inflow data is directly known at the turbine locations, in terms of (state, turbine)-type data. Such data can be simulated with foxes by using the TurbinePointCloud states class, as demonstrated here.

We start by importing the necessary packages and setting up the engine:

%matplotlib inline
import numpy as np
from xarray import Dataset, date_range
import matplotlib.pyplot as plt

import foxes
import foxes.variables as FV

/home/runner/work/foxes/foxes/foxes/core/engine.py:4: TqdmExperimentalWarning: Using `tqdm.autonotebook.tqdm` in notebook mode. Use `tqdm.tqdm` instead to force console mode (e.g. in jupyter console)
  from tqdm.autonotebook import tqdm

engine = foxes.Engine.new("default", verbosity=0)

The first step is the creation of a regular grid of wind turbines:

n_turbines_x = 2
n_turbines_y = 3
n_turbines = n_turbines_x * n_turbines_y

farm = foxes.WindFarm()
foxes.input.farm_layout.add_grid(
    farm,
    xy_base=[1000, 1000],
    step_vectors=[[500, 0], [0, 500]],
    steps=[n_turbines_x, n_turbines_y],
    turbine_models=["DTU10MW"],
    verbosity=0,
)

o = foxes.output.FarmLayoutOutput(farm)
o.get_figure()
plt.show()
../_images/d3c6630c30f463a58896281ed7d2b013642139cf039188e3db001ba1a1df5470.png

Next, let’s create an artificial Dataset object that represents data with (time, turbine) dimensions, representing a timeseries in January 2026 measured at he turbines of the above wind farm:

n_times = 10
times = date_range("2026-01-01", periods=n_times, freq="10min", unit="s")
times

DatetimeIndex(['2026-01-01 00:00:00', '2026-01-01 00:10:00',
               '2026-01-01 00:20:00', '2026-01-01 00:30:00',
               '2026-01-01 00:40:00', '2026-01-01 00:50:00',
               '2026-01-01 01:00:00', '2026-01-01 01:10:00',
               '2026-01-01 01:20:00', '2026-01-01 01:30:00'],
              dtype='datetime64[s]', freq='10min')

np.random.seed(42)

# Turbine i has wind speed (10 + i.x) m/s, where x grows linear with time
ws = np.zeros((n_times, n_turbines))
ws[:] = 10 + np.arange(n_turbines)[None, :]
ws += np.linspace(0, 1, n_times, endpoint=False)[:, None]

# the wind directions are randomly selected from a southern sector:
wd = np.random.uniform(0, 190, (n_times, n_turbines))

sdata = Dataset(
    coords={"time": times},
    data_vars={
        "ws": (("time", "turbine"), ws),
        "wd": (("time", "turbine"), wd),
        "ti": ("time", 0.1 + np.arange(n_times) / 100),
        "rho": ("turbine", 1.2 + np.arange(n_turbines) / 100),
    },
)
sdata

<xarray.Dataset> Size: 1kB
Dimensions:  (time: 10, turbine: 6)
Coordinates:
  * time     (time) datetime64[s] 80B 2026-01-01 ... 2026-01-01T01:30:00
Dimensions without coordinates: turbine
Data variables:
    ws       (time, turbine) float64 480B 10.0 11.0 12.0 13.0 ... 13.9 14.9 15.9
    wd       (time, turbine) float64 480B 71.16 180.6 139.1 ... 8.593 61.81
    ti       (time) float64 80B 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19
    rho      (turbine) float64 48B 1.2 1.21 1.22 1.23 1.24 1.25

This is what the wind speed per turbine looks like, increasing linearly with time as described above:

for t in range(0, n_times):
    plt.scatter(sdata["turbine"], sdata["ws"][t])
plt.xticks(sdata["turbine"])
plt.xlabel("turbine")
plt.ylabel("ws [m/s]")
plt.show()
../_images/cdcde931bcb49c4a5b8be8aa36658abbd5dc7549bf26cf9480cefa0ecb826a90.png

The data frame sdata is the base for our ambient states object:

states = foxes.input.states.TurbinePointCloud(
    data_source=sdata,
    states_coord="time",
    turbine_coord="turbine",
    output_vars=[FV.WS, FV.WD, FV.TI, FV.RHO],
    var2ncvar={
        FV.WS: "ws",
        FV.WD: "wd",
        FV.TI: "ti",
        FV.RHO: "rho",
    },
)

Next, let’s create the algorithm object:

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

We now run the farm calculation:

with engine:
    farm_results = algo.calc_farm()

Initializing model 'TurbinePointCloud'

Initializing algorithm 'Downwind'

------------------------------------------------------------
  Algorithm: Downwind
  Running Downwind: calc_farm
------------------------------------------------------------
  n_states : 10
  n_turbines: 6
------------------------------------------------------------
  states    : TurbinePointCloud()
  rotor     : CentreRotor()
  controller: BasicFarmController()
  deflection: NoDeflection()
  wake frame: RotorWD()
  wake lngth: None
------------------------------------------------------------
  wakes:
    0) TurbOPark: TurbOParkWake(ws_quadratic, induction=Madsen, k=0.04*AMB_TI)
------------------------------------------------------------
  partial wakes:
    0) TurbOPark: axiwake6, PartialAxiwake(n=6)
------------------------------------------------------------
  turbine models:
    0) DTU10MW: PCtFile(D=178.3, H=119.0, P_nominal=10000.0, P_unit=kW, rho=1.225, var_ws_ct=REWS2, var_ws_P=REWS3)
------------------------------------------------------------


--------------------------------------------------
  Model oder
--------------------------------------------------
00) basic_ctrl
01) InitFarmData
02) centre
03) basic_ctrl
  03.0) Post-rotor: DTU10MW
04) SetAmbFarmResults
05) FarmWakesCalculation
06) ReorderFarmOutput
--------------------------------------------------


Input data:

 <xarray.Dataset> Size: 1kB
Dimensions:                  (state: 10, turbine: 6,
                              TurbinePointCloud_vars0: 2,
                              TurbinePointCloud_vars1: 1, tmodels: 1)
Coordinates:
  * state                    (state) datetime64[s] 80B 2026-01-01 ... 2026-01...
  * TurbinePointCloud_vars0  (TurbinePointCloud_vars0) <U2 16B 'WS' 'WD'
  * TurbinePointCloud_vars1  (TurbinePointCloud_vars1) <U2 8B 'TI'
  * tmodels                  (tmodels) <U7 28B 'DTU10MW'
Dimensions without coordinates: turbine
Data variables:
    TurbinePointCloud_data0  (state, turbine, TurbinePointCloud_vars0) float64 960B ...
    TurbinePointCloud_data1  (state, TurbinePointCloud_vars1) float64 80B 0.1...
    tmodel_sels              (state, turbine, tmodels) bool 60B True ... True 


Farm variables: AMB_CT, AMB_P, AMB_REWS, AMB_REWS2, AMB_REWS3, AMB_RHO, AMB_TI, AMB_WD, AMB_YAW, CT, D, H, P, REWS, REWS2, REWS3, RHO, TI, WD, X, Y, YAW, order, order_inv, order_ssel, weight

Output variables: AMB_CT, AMB_P, AMB_REWS, AMB_REWS2, AMB_REWS3, AMB_RHO, AMB_TI, AMB_WD, AMB_YAW, CT, D, H, P, REWS, REWS2, REWS3, RHO, TI, WD, X, Y, YAW, order, order_inv, order_ssel, weight
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 10 states for 6 turbines
SingleChunkEngine: Starting calculation using a single worker.
SingleChunkEngine: Completed all 1 chunks

The results demonstrate that all data was correctly passed from the flow states to ambient variables:

farm_results.to_dataframe()[
    [FV.AMB_WD, FV.AMB_RHO, FV.AMB_TI, FV.AMB_REWS, FV.REWS, FV.P]
]
AMB_WD AMB_RHO AMB_TI AMB_REWS REWS P
state turbine
2026-01-01 00:00:00 0 71.162623 1.20 0.10 10.0 8.870120 5010.384802
1 180.635718 1.21 0.10 11.0 10.952161 9474.664608
2 139.078849 1.22 0.10 12.0 8.375921 4307.026775
3 113.745112 1.23 0.10 13.0 13.000000 10648.337500
4 29.643542 1.24 0.10 14.0 14.000000 10641.826857
5 29.638959 1.25 0.10 15.0 15.000000 10679.473520
2026-01-01 00:10:00 0 11.035886 1.20 0.11 10.1 10.099999 7360.829038
1 164.573468 1.21 0.11 11.1 8.843683 5007.340784
2 114.211852 1.22 0.11 12.1 11.307228 9972.847398
3 134.533790 1.23 0.11 13.1 13.100000 10647.416250
4 3.911054 1.24 0.11 14.1 14.100000 10646.284885
5 184.282872 1.25 0.11 15.1 15.100000 10675.275344
2026-01-01 00:20:00 0 158.164102 1.20 0.12 10.2 10.016835 7184.258808
1 40.344431 1.21 0.12 11.2 11.197560 9840.989324
2 34.546744 1.22 0.12 12.2 11.338420 10002.152370
3 34.846857 1.23 0.12 13.2 13.200000 10646.495000
4 57.806026 1.24 0.12 14.2 14.200000 10650.742955
5 99.703722 1.25 0.12 15.2 15.200000 10671.077167
2026-01-01 00:30:00 0 82.069554 1.20 0.13 10.3 9.897905 6951.016997
1 55.333537 1.21 0.13 11.3 11.299817 9936.798585
2 116.252050 1.22 0.13 12.3 12.228169 10641.088185
3 26.503834 1.23 0.13 13.3 13.300000 10645.573750
4 55.507483 1.24 0.13 14.3 14.300000 10655.201004
5 69.608750 1.25 0.13 15.3 15.300000 10666.878991
2026-01-01 00:40:00 0 86.653297 1.20 0.14 10.4 8.815365 4924.405208
1 149.183433 1.21 0.14 11.4 11.344388 9978.559102
2 37.938019 1.22 0.14 12.4 12.398959 10642.691429
3 97.704543 1.23 0.14 13.4 13.230629 10646.212826
4 112.558768 1.24 0.14 14.4 13.468027 10643.690460
5 8.825578 1.25 0.14 15.4 15.400000 10662.680814
2026-01-01 00:50:00 0 115.433522 1.20 0.15 10.5 10.500000 8318.943186
1 32.399584 1.21 0.15 11.5 11.500000 10124.358512
2 12.359803 1.22 0.15 12.5 12.500000 10643.639918
3 180.288252 1.23 0.15 13.5 13.500000 10643.731250
4 183.470086 1.24 0.15 14.5 12.322961 10642.606719
5 153.595496 1.25 0.15 15.5 12.173622 10641.505264
2026-01-01 01:00:00 0 57.876616 1.20 0.16 10.6 8.886403 5035.953749
1 18.557702 1.21 0.16 11.6 11.600000 10218.052941
2 130.004275 1.22 0.16 12.6 11.252646 9921.565977
3 83.628974 1.23 0.16 13.6 13.568073 10643.104132
4 23.187265 1.24 0.16 14.6 14.600000 10668.575151
5 94.083613 1.25 0.16 15.6 15.600000 10654.284461
2026-01-01 01:10:00 0 6.533819 1.20 0.17 10.7 10.607070 8575.405397
1 172.770876 1.21 0.17 11.7 11.026436 9653.068240
2 49.168197 1.22 0.17 12.7 11.814770 10449.692396
3 125.879234 1.23 0.17 13.7 13.700000 10641.888750
4 59.225104 1.24 0.17 14.7 14.700000 10673.033200
5 98.812924 1.25 0.17 15.7 15.700000 10650.086285
2026-01-01 01:20:00 0 103.874953 1.20 0.18 10.8 10.800000 9037.527277
1 35.122347 1.21 0.18 11.8 11.548786 10170.068407
2 184.221079 1.22 0.18 12.8 12.251232 10641.304685
3 147.275236 1.23 0.18 13.8 13.800000 10640.967500
4 178.504799 1.24 0.18 14.8 14.799416 10677.465227
5 170.017197 1.25 0.18 15.8 14.137962 10649.667015
2026-01-01 01:30:00 0 113.600996 1.20 0.19 10.9 10.899155 9275.030750
1 175.156105 1.21 0.19 11.9 11.529127 10151.648575
2 16.813575 1.22 0.19 12.9 12.897184 10647.368358
3 37.236744 1.23 0.19 13.9 12.873414 10647.474504
4 8.593185 1.24 0.19 14.9 14.900000 10681.949298
5 61.812763 1.25 0.19 15.9 15.900000 10641.985129

For completeness, the states results at off-turbine evaluation points will be interpolated by point cloud methods.