def determine_if_in_wake(xt, yt, xw, yw, k, r0,
alpha): # According to Jensen Model only
# Eq. of centreline is Y = tan (d) (X - Xt) + Yt
# Distance from point to line
alpha = deg2rad(alpha + 180)
distance_to_centre = abs(-tan(alpha) * xw + yw + tan(alpha) * xt -
yt) / sqrt(1.0 + tan(alpha)**2.0)
# print distance_to_centre
# Coordinates of the intersection between closest path from turbine in wake to centreline.
X_int = (xw + tan(alpha) * yw + tan(alpha) *
(tan(alpha) * xt - yt)) / (tan(alpha)**2.0 + 1.0)
Y_int = (-tan(alpha) * (-xw - tan(alpha) * yw) - tan(alpha) * xt +
yt) / (tan(alpha)**2.0 + 1.0)
# Distance from intersection point to turbine
distance_to_turbine = sqrt((X_int - xt)**2.0 + (Y_int - yt)**2.0)
# Radius of wake at that distance
radius = wake_radius(r0, k, distance_to_turbine)
# print radius
if (xw - xt) * cos(alpha) + (yw - yt) * sin(alpha) <= 0.0:
if abs(radius) >= abs(distance_to_centre):
if abs(radius) >= abs(distance_to_centre) + r0:
fraction = 1.0
return fraction, distance_to_turbine
elif abs(radius) < abs(distance_to_centre) + r0:
fraction = area.AreaReal(r0, radius, distance_to_centre).area()
return fraction, distance_to_turbine
elif abs(radius) < abs(distance_to_centre):
if abs(radius) <= abs(distance_to_centre) - r0:
fraction = 0.0, distance_to_turbine
return fraction
elif abs(radius) > abs(distance_to_centre) - r0:
fraction = area.AreaReal(r0, radius, distance_to_centre).area()
return fraction, distance_to_turbine
else:
return 0.0, distance_to_turbine
def determine_if_in_wake(x_upstream,
y_upstream,
x_downstream,
y_downstream,
wind_direction,
k=jensen_k,
r0=rotor_radius): # According to Jensen Model only
# Eq. of centreline is Y = tan (d) (X - Xt) + Yt
# Distance from point to line
wind_direction = deg2rad(wind_direction + 180.0)
distance_to_centre = abs(-tan(wind_direction) * x_downstream +
y_downstream + tan(wind_direction) * x_upstream -
y_upstream) / sqrt(1.0 + tan(wind_direction)**2.0)
# print distance_to_centre
# Coordinates of the intersection between closest path from turbine in wake to centreline.
X_int = (x_downstream + tan(wind_direction) * y_downstream +
tan(wind_direction) *
(tan(wind_direction) * x_upstream - y_upstream)) / (
tan(wind_direction)**2.0 + 1.0)
Y_int = (-tan(wind_direction) *
(-x_downstream - tan(wind_direction) * y_downstream) -
tan(wind_direction) * x_upstream +
y_upstream) / (tan(wind_direction)**2.0 + 1.0)
# Distance from intersection point to turbine
distance_to_turbine = sqrt((X_int - x_upstream)**2.0 +
(Y_int - y_upstream)**2.0)
# # Radius of wake at that distance
radius = wake_radius(distance_to_turbine, r0, k)
if (x_downstream - x_upstream) * cos(wind_direction) + (
y_downstream - y_upstream) * sin(wind_direction) <= 0.0:
if abs(radius) >= abs(distance_to_centre):
if abs(radius) >= abs(distance_to_centre) + r0:
fraction = 1.0
return fraction, distance_to_turbine
elif abs(radius) < abs(distance_to_centre) + r0:
fraction = area.AreaReal(r0, radius, distance_to_centre).area()
return fraction, distance_to_turbine
elif abs(radius) < abs(distance_to_centre):
if abs(radius) <= abs(distance_to_centre) - r0:
fraction = 0.0
return fraction, distance_to_turbine
elif abs(radius) > abs(distance_to_centre) - r0:
fraction = area.AreaReal(r0, radius, distance_to_centre).area()
return fraction, distance_to_turbine
else:
return 0.0, distance_to_turbine
def partial_wake_deficit(Ct, k, x, r0, d):
shadow_area = area.AreaReal(r0, wake_radius(r0, k, x), d)
return shadow_area.area() * (1.0 - (1.0 - sqrt(1.0 - Ct)) / (1.0 +
(k * x) / r0))