import numpy as np
from floris.core.turbine.operation_models import POWER_SETPOINT_DISABLED
from floris.utilities import rotate_coordinates_rel_west
from .yaw_optimization_base import YawOptimization
[docs]
class YawOptimizationGeometric(YawOptimization):
"""
YawOptimizationGeometric is a subclass of
:py:class:`floris.optimization.general_library.YawOptimization` that is
used to provide a rough estimate of optimal yaw angles based purely on the
wind farm geometry. Main use case is for coupled layout and yaw optimization.
See Stanley et al. (2023) for details: https://wes.copernicus.org/articles/8/1341/2023/
"""
def __init__(
self,
fmodel,
minimum_yaw_angle=0.0,
maximum_yaw_angle=25.0,
):
"""
Instantiate YawOptimizationGeometric object with a FlorisModel
object assign parameter values.
"""
super().__init__(
fmodel=fmodel,
minimum_yaw_angle=minimum_yaw_angle,
maximum_yaw_angle=maximum_yaw_angle,
calc_baseline_power=False
)
[docs]
def optimize(self):
"""
Find rough yaw angles based on wind farm geometry.
Assumes all wind turbines have the same rotor diameter.
Returns:
opt_yaw_angles (np.array): Optimal yaw angles in degrees. This
array is equal in length to the number of turbines in the farm.
"""
# Loop through every WD individually. WS ignored!
wd_array = self.fmodel_subset.core.flow_field.wind_directions
active_turbines = self.fmodel_subset.core.farm.power_setpoints > POWER_SETPOINT_DISABLED
for nwdi, wd in enumerate(wd_array):
self._yaw_angles_opt_subset[nwdi, active_turbines[nwdi]] = geometric_yaw(
self.fmodel_subset.layout_x[active_turbines[nwdi]],
self.fmodel_subset.layout_y[active_turbines[nwdi]],
wd,
self.fmodel.core.farm.turbine_definitions[0]["rotor_diameter"],
top_left_yaw_upper=self.maximum_yaw_angle[0, 0],
bottom_left_yaw_upper=self.maximum_yaw_angle[0, 0],
top_left_yaw_lower=self.minimum_yaw_angle[0, 0],
bottom_left_yaw_lower=self.minimum_yaw_angle[0, 0],
)
# Finalize optimization, i.e., retrieve full solutions
df_opt = self._finalize()
# Otherwise, df_opt will just copy the farm_power_baseline in
return df_opt
[docs]
def geometric_yaw(
turbine_x,
turbine_y,
wind_direction,
rotor_diameter,
left_x=0.0,
top_left_y=1.0,
right_x=25.0,
top_right_y=1.0,
top_left_yaw_upper=30.0,
top_right_yaw_upper=0.0,
bottom_left_yaw_upper=30.0,
bottom_right_yaw_upper=0.0,
top_left_yaw_lower=-30.0,
top_right_yaw_lower=0.0,
bottom_left_yaw_lower=-30.0,
bottom_right_yaw_lower=0.0,
):
"""
Main function to compute geometric yaw angles based on wind farm layout for a single wind
direction.
Arguments:
turbine_x: unrotated x turbine coords
turbine_y: unrotated y turbine coords
wind_direction: float, degrees
rotor_diameter: float
left_x: where we start the trapezoid. Should be left as 0.
top_left_y: trapezoid top left coord
right_x: where to stop the trapezoid downstream.
Max coord after which the upstream turbine won't yaw.
top_right_y: trapezoid top right coord
top_left_yaw_upper: yaw angle associated with top left point (upper trapezoid)
top_right_yaw_upper: yaw angle associated with top right point
bottom_left_yaw_upper: yaw angle associated with bottom left point
bottom_right_yaw_upper: yaw angle associated with bottom right point
top_left_yaw_lower: yaw angle associated with top left point (lower trapezoid)
top_right_yaw_lower: yaw angle associated with top right point
bottom_left_yaw_lower: yaw angle associated with bottom left point
bottom_right_yaw_lower: yaw angle associated with bottom right point
Returns:
yaw_array: yaw angles for all turbines for the present wind direction.
"""
nturbs = len(turbine_x)
turbine_coordinates_array = np.zeros((nturbs,3))
turbine_coordinates_array[:,0] = turbine_x[:]
turbine_coordinates_array[:,1] = turbine_y[:]
rotated_x, rotated_y, _, _, _ = rotate_coordinates_rel_west(
np.array([wind_direction]),
turbine_coordinates_array
)
processed_x, processed_y = _process_layout(rotated_x[0], rotated_y[0], rotor_diameter)
yaw_array = np.zeros(nturbs)
for i in range(nturbs):
# TODO: fix shape of top left yaw etc?
yaw_array[i] = _get_yaw_angles(
processed_x[i],
processed_y[i],
left_x,
top_left_y,
right_x,
top_right_y,
top_left_yaw_upper,
top_right_yaw_upper,
bottom_left_yaw_upper,
bottom_right_yaw_upper,
top_left_yaw_lower,
top_right_yaw_lower,
bottom_left_yaw_lower,
bottom_right_yaw_lower,
)
return yaw_array
def _process_layout(
turbine_x,
turbine_y,
rotor_diameter,
spread=0.1
):
"""
Returns the distance from each turbine to the nearest downstream waked turbine
normalized by the rotor diameter. Right now "waked" is determined by a Jensen-like
wake spread, but this could/should be modified to be the same as the trapezoid rule
used to determine the yaw angles.
Arguments:
turbine_x: turbine x coords (rotated)
turbine_y: turbine y coords (rotated)
rotor_diameter: turbine rotor diameter (float)
spread=0.1: Jensen alpha wake spread value
Returns:
dx: distance to nearest downstream turbine in rotor diameters for all turbines
dy: lateral distance to nearest downstream turbine in rotor diameters for all turbines
"""
# Compute distances
x_dists = turbine_x.reshape(-1,1).T - turbine_x.reshape(-1,1)
y_dists = turbine_y.reshape(-1,1).T - turbine_y.reshape(-1,1)
# Any turbines upstream or at the turbine location are ineligible
x_dists[x_dists <= 0.] = np.inf
# Check within Jensen model spread
in_Jensen_wake = (abs(y_dists) < spread * x_dists + rotor_diameter/2.0)
x_dists[~in_Jensen_wake] = np.inf
# Get minimums (and arguments to select the correct y values also)
dx = x_dists.min(axis=1)
dy = y_dists[range(len(turbine_x)), x_dists.argmin(axis=1)]
return dx/rotor_diameter, dy/rotor_diameter
def _get_yaw_angles(
x,
y,
left_x,
top_left_y,
right_x,
top_right_y,
top_left_yaw_upper,
top_right_yaw_upper,
bottom_left_yaw_upper,
bottom_right_yaw_upper,
top_left_yaw_lower,
top_right_yaw_lower,
bottom_left_yaw_lower,
bottom_right_yaw_lower
):
"""
For a given turbine, return the geometric yaw angle based on its position relative to the
nearest downstream turbine.
Arguments:
x: downstream distance to the nearest downstream turbine in rotor diameters with
turbines rotated so wind is coming left to right
y: lateral distance to the nearest downstream turbine in rotor diameters with
turbines rotated so wind is coming left to right
left_x: where we start the trapezoid. Should be left as 0.
top_left_y: trapezoid top left coord
right_x: where to stop the trapezoid downstream.
Max coord after which the upstream turbine won't yaw.
top_right_y: trapezoid top right coord
top_left_yaw_upper: yaw angle associated with top left point (upper trapezoid)
top_right_yaw_upper: yaw angle associated with top right point
bottom_left_yaw_upper: yaw angle associated with bottom left point
bottom_right_yaw_upper: yaw angle associated with bottom right point
top_left_yaw_lower: yaw angle associated with top left point (lower trapezoid)
top_right_yaw_lower: yaw angle associated with top right point
bottom_left_yaw_lower: yaw angle associated with bottom left point
bottom_right_yaw_lower: yaw angle associated with bottom right point
Returns:
(yaw angle): float, geometric yaw angle for the given turbine
"""
dx = (x-left_x)/(right_x-left_x)
if dx >= 1.0:
return 0.0
edge_y = top_left_y + (top_right_y-top_left_y)*dx
if abs(y) > edge_y:
return 0.0
elif y >= -0.01: # Tolerance to handle numerical issues
top_yaw = top_left_yaw_upper + (top_right_yaw_upper-top_left_yaw_upper)*dx
bottom_yaw = bottom_left_yaw_upper + (bottom_right_yaw_upper-bottom_left_yaw_upper)*dx
return bottom_yaw + (top_yaw-bottom_yaw)*abs(y)/edge_y
elif y < -0.01:
top_yaw = top_left_yaw_lower + (top_right_yaw_lower-top_left_yaw_lower)*dx
bottom_yaw = bottom_left_yaw_lower + (bottom_right_yaw_lower-bottom_left_yaw_lower)*dx
return bottom_yaw + (top_yaw-bottom_yaw)*abs(y)/edge_y
