Newer
Older
from numpy import newaxis as na
import numpy as np
class AreaOverlappingFactor():
def overlapping_area_factor(self, wake_radius_ijlk, dw_ijlk, cw_ijlk, D_src_il, D_dst_ijl):
"""Calculate overlapping factor
Parameters
----------
dw_jl : array_like
down wind distance [m]
cw_jl : array_like
cross wind distance [m]
D_src_l : array_like
Diameter of source turbines [m]
D_dst_jl : array_like or None
Diameter of destination turbines [m]. If None destination is assumed to be a point
Returns
-------
A_ol_factor_jl : array_like
area overlaping factor
"""
if np.all(D_dst_ijl == 0) or D_dst_ijl is None:
if wake_radius_ijlk.ndim == 5:
return self._cal_overlapping_area_factor(wake_radius_ijlk[..., 0],
(D_dst_ijl[..., na] / 2),
np.abs(cw_ijlk[..., 0]))[..., na]
else:
return self._cal_overlapping_area_factor(wake_radius_ijlk,
(D_dst_ijl[..., na] / 2),
np.abs(cw_ijlk))
def _cal_overlapping_area_factor(self, R1, R2, d):
""" Calculate the overlapping area of two circles with radius R1 and
R2, centers distanced d.
The calculation formula can be found in Eq. (A1) of :
[Ref] Feng J, Shen WZ, Solving the wind farm layout optimization
problem using Random search algorithm, Renewable Energy 78 (2015)
182-192
Note that however there are typos in Equation (A1), '2' before alpha
and beta should be 1.
Parameters
----------
R1: array:float
Radius of the first circle [m]
R2: array:float
Radius of the second circle [m]
d: array:float
Distance between two centers [m]
Returns
-------
A_ol: array:float
Overlapping area [m^2]
"""
# treat all input as array
R1, R2, d = [np.asarray(a) for a in [R1, R2, d]]
if R2.shape != R1.shape:
R2 = np.zeros_like(R1) + R2
if d.shape != R1.shape:
d = np.zeros_like(R1) + d
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
A_ol_f = np.zeros(np.maximum(R1.shape, R2.shape))
p = (R1 + R2 + d) / 2.0
# make sure R_big >= R_small
Rmax = np.where(R1 < R2, R2, R1)
Rmin = np.where(R1 < R2, R1, R2)
# full wake cases
index_fullwake = (d <= (Rmax - Rmin))
A_ol_f[index_fullwake] = 1
# partial wake cases
mask = (d > (Rmax - Rmin)) & (d < (Rmin + Rmax))
# in somecases cos_alpha or cos_beta can be larger than 1 or less than
# -1.0, cause problem to arccos(), resulting nan values, here fix this
# issue.
def arccos_lim(x):
return np.arccos(np.maximum(np.minimum(x, 1), -1))
alpha = arccos_lim((Rmax[mask]**2.0 + d[mask]**2 - Rmin[mask]**2) /
(2.0 * Rmax[mask] * d[mask]))
beta = arccos_lim((Rmin[mask]**2.0 + d[mask]**2 - Rmax[mask]**2) /
(2.0 * Rmin[mask] * d[mask]))
A_triangle = np.sqrt(p[mask] * (p[mask] - Rmin[mask]) *
(p[mask] - Rmax[mask]) * (p[mask] - d[mask]))
A_ol_f[mask] = (alpha * Rmax[mask]**2 + beta * Rmin[mask]**2 -
2.0 * A_triangle) / (R2[mask]**2 * np.pi)
return A_ol_f