Energy yield with PyWake

This page computes energy yield and wake loss for an OOWL farm with PyWake. Layout optimization with TOPFARM optimizes the same farm.

PyWake is not an OOWL dependency.

%%capture
%pip install --quiet py-wake

Import OOWL and the PyWake components.

import matplotlib.pyplot as plt
import numpy as np
import xarray as xr
from py_wake.literature.gaussian_models import Bastankhah_PorteAgel_2014
from py_wake.site import XRSite
from py_wake.wind_turbines import WindTurbine
from py_wake.wind_turbines.power_ct_functions import PowerCtTabular

import oowl
from oowl import boundaries as B
from oowl import layouts as L
from oowl import resources as R
from oowl import turbines as T

The OOWL farm

A notched seven-sided 36 km² boundary holds 16 turbines on a Sunflower spiral under a resource with one dominant direction, defined at hub height.

boundary = B.RandomRadialPolygon(
    n_vertices=7, area=36e6, radius_jitter=0.4, angular_jitter=0.4, seed=16
)
turbine = T.Idealized(
    rated_power=15e6, rotor_diameter=240.0, hub_height=150.0, cp_max=0.48
)
resource = R.WindResource(
    direction=R.VonMises(n_modes=1, seed=3),
    n_sectors=12,
    mean_wind_speed=9.5,
    weibull_k=2.2,
    turbulence=R.SurfaceLayer(intensity=0.07),
    reference_height=turbine.hub_height,
)
farm = oowl.Sampler(
    boundary,
    L.Sunflower(n_turbines=16, seed=5),
    resource,
    turbines=turbine,
    seed=4,
).sample()[0]
farm.plot();

OOWL → PyWake

OOWL object	Becomes	Used for
turbines.Idealized	PyWake WindTurbine with a PowerCtTabular curve	power and thrust
resources.WindResource sector arrays	PyWake XRSite dataset	wind climate

Turbine mapping, OOWL Idealized → PyWake WindTurbine

The turbine is sampled on a speed grid. Power is in watts, hence "W".

speeds = np.arange(0.0, 30.5, 0.5)
wind_turbine = WindTurbine(
    name="OOWL idealized 15 MW",
    diameter=turbine.rotor_diameter,
    hub_height=turbine.hub_height,
    powerCtFunction=PowerCtTabular(
        speeds, turbine.power(speeds), "W", turbine.ct(speeds)
    ),
)

fig, axes = plt.subplots(1, 2, figsize=(9, 3), constrained_layout=True)
axes[0].plot(speeds, wind_turbine.power(speeds) / 1e6)
axes[0].set(xlabel="wind speed [m/s]", ylabel="power [MW]")
axes[1].plot(speeds, wind_turbine.ct(speeds))
axes[1].set(xlabel="wind speed [m/s]", ylabel="$C_T$ [-]");

Wind resource mapping, OOWL sectors → PyWake XRSite

Sector probabilities, Weibull \(A\) and \(k\) and turbulence intensity per sector center (\(\theta_i = 360 i / n\)) transfer directly.

site = XRSite(
    xr.Dataset(
        data_vars={
            "Sector_frequency": ("wd", resource.probability),
            "Weibull_A": ("wd", resource.weibull_a),
            "Weibull_k": ("wd", resource.weibull_k),
            "TI": ("wd", resource.sector_turbulence_intensity),
        },
        coords={"wd": resource.theta},
    )
)
_ = site.plot_wd_distribution(n_wd=12)

AEP and wake loss

Wake loss is the share of gross AEP lost to wakes, \(1 - \text{net}/\text{gross}\).

wfm = Bastankhah_PorteAgel_2014(site, wind_turbine, k=0.0324555)
simulation = wfm(farm.x, farm.y)

net = float(simulation.aep().sum())
gross = float(simulation.aep(with_wake_loss=False).sum())
print(f"Gross AEP: {gross:8.1f} GWh")
print(f"Net AEP:   {net:8.1f} GWh")
print(f"Wake loss: {100 * (1 - net / gross):8.2f} %")

Gross AEP:   1258.5 GWh
Net AEP:     1186.9 GWh
Wake loss:     5.69 %

The wake map shows one wind direction.

fig, ax = plt.subplots(figsize=(7, 5), constrained_layout=True)
wfm(farm.x, farm.y, wd=225, ws=10).flow_map().plot_wake_map(ax=ax)
boundary.plot(ax=ax)
ax.set_title("Wake map, 225°, 10 m/s");