def ainsliefull_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius, TI):
layout_xD = []
layout_yD = []
D = 2.0 * rotor_radius # Diameter
for x in range(len(layout_x)):
layout_xD.append(layout_x[x] / D)
for x in range(len(layout_y)):
layout_yD.append(layout_y[x] / D)
nt = len(layout_y)
U0 = wind_speed # Free stream wind speed
angle3 = angle + 180.0
wake_deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
U = [U0 for _ in range(nt)]
U = U
TI *= 100.0
for tur in range(nt):
distance[tur] = [distance_to_front(layout_xD[tur], layout_yD[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += wake_deficit_matrix[distance[turbine][1]][
distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
parallel_distance = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
parallel_distance[distance[i][1]] = determine_front(angle3, layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]],
layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
perpendicular_distance[distance[i][1]] = wake.crosswind_distance(radians(angle3),
layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]],
layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
if perpendicular_distance[distance[i][1]] <= 2.0 and parallel_distance[
distance[i][1]] > 0.0: ## 1.7 gives same results as a bigger distance, many times faster.
wake_deficit_matrix[distance[i][1]][distance[turbine][1]] = ainslie_full(
Ct(U[distance[turbine][1]]), U[distance[turbine][1]],
parallel_distance[distance[i][1]], perpendicular_distance[distance[i][1]], TI)
else:
wake_deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
# print angle, sum([power(U[i]) for i in range(len(U))])
return U
def jensen_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius, k):
U0 = wind_speed # Free stream wind speed
nt = len(layout_y) # Number of turbines ## Length of layout list
r0 = rotor_radius # Turbine rotor radius
# angle2 = - 270.0 - angle # To read windroses where N is 0 and E is 90.
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
proportion = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
def loop1(i):
Parallel(n_jobs=-1)(delayed(loop2)(i) for i in range(turbine + 1, nt))
def loop2(i):
determ = wake.determine_if_in_wake(layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]],
layout_y[distance[i][1]], k, r0,
angle3)
proportion[distance[turbine][1]][distance[i][1]] = determ[0]
if proportion[distance[turbine][1]][distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][1]] = proportion[
distance[turbine][1]][distance[i][1]] * wake.wake_deficit(
Ct(U[distance[turbine][1]]), k, determ[1], r0)
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
return deficit_matrix[distance[i][1]][distance[turbine][1]]
for tur in range(nt):
distance[tur] = [
distance_to_front(layout_x[tur], layout_y[tur], angle), tur
]
distance.sort()
deficit_matrix[distance[i][1]][distance[turbine][1]] = Parallel(n_jobs=-1)(
delayed(loop1)(i) for i in range(turbine + 1, nt))
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[
distance[turbine][1]][distance[num][1]]**2.0
total_deficit[distance[turbine][1]] = sqrt(
total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 -
total_deficit[distance[turbine][1]])
return U
def solve_nonlinear(self, params, unknowns, resids):
U0 = params['mean_ambient_wind_speed'] # Free stream wind speed
layout_x = params['layout_x']
layout_y = params['layout_y']
k = params['k'] = 0.04 # Decay constant
r0 = params['rotor_radius'] # Turbine rotor radius
angle = params['wind_direction']
nt = num_turb
# angle2 = - 270.0 - angle # To read windroses where N is 0 and E is 90.
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
proportion = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [
distance_to_front(layout_x[tur], layout_y[tur], angle), tur
]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[
distance[turbine][1]][distance[num][1]]**2.0
total_deficit[distance[turbine][1]] = sqrt(
total_deficit[distance[turbine][1]])
U[distance[turbine]
[1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
for i in range(turbine + 1, nt):
determ = wake.determine_if_in_wake(
layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]], layout_x[distance[i][1]],
layout_y[distance[i][1]], k, r0, angle3)
proportion[distance[turbine][1]][distance[i][1]] = determ[0]
if proportion[distance[turbine][1]][distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][
1]] = proportion[distance[turbine][1]][
distance[i][1]] * wake.wake_deficit(
Ct(U[distance[turbine][1]]), k, determ[1], r0)
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
# return [list(_) for _ in zip(
# zip([x for (y, x) in sorted(zip([item[0] for item in distance], layout_x))], [x for (y, x) in sorted(
# zip([item[0] for item in distance], layout_y))]), U)]
unknowns['U'] = array(U)
def solve_nonlinear(self, params, unknowns, resids):
D = 2.0 * params['rotor_radius'] # Diameter
layout_x = params['layout_x']
layout_y = params['layout_y']
layout_xD = array(layout_x) / D
layout_yD = array(layout_y) / D
U0 = params['mean_ambient_wind_speed'] # Free stream wind speed
angle = params['wind_direction']
nt = num_turb
angle3 = angle + 180.0
wake_deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
U = [U0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_xD[tur], layout_yD[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += wake_deficit_matrix[distance[turbine][1]][
distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
parallel_distance = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
parallel_distance[distance[i][1]] = determine_front(angle3, layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]],
layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
perpendicular_distance[distance[i][1]] = wake.crosswind_distance(radians(angle3),
layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]],
layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
if perpendicular_distance[distance[i][1]] <= 1.7 and parallel_distance[
distance[i][1]] > 0.0: ## 1.7 gives same results as a bigger distance, many times faster.
wake_deficit_matrix[distance[i][1]][distance[turbine][1]] = ainslie(
Ct(U[distance[turbine][1]]), U[distance[turbine][1]],
parallel_distance[distance[i][1]], perpendicular_distance[distance[i][1]], params['TI'])
else:
wake_deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
unknowns['U'] = array(U)
def solve_nonlinear(self, params, unknowns, resids):
layout_x = params['layout_x']
layout_y = params['layout_y']
angle = params['angle']
distance = [[] for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur, layout_x[tur], layout_y[tur]]
distance.sort()
unknowns['turbine_index'] = array([x[1] for x in distance])
unknowns['ordered_layout_x'] = array([x[2] for x in distance])
unknowns['ordered_layout_y'] = array([x[3] for x in distance])
def solve_nonlinear(self, params, unknowns, resids):
layout_x = params["layout_x"]
layout_y = params["layout_y"]
angle = params["angle"]
distance = [[] for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur, layout_x[tur], layout_y[tur]]
distance.sort()
unknowns["turbine_index"] = array([x[1] for x in distance])
unknowns["ordered_layout_x"] = array([x[2] for x in distance])
unknowns["ordered_layout_y"] = array([x[3] for x in distance])
def solve_nonlinear(self, params, unknowns, resids):
U0 = params['mean_ambient_wind_speed'] # Free stream wind speed
layout_x = params['layout_x']
layout_y = params['layout_y']
k = params['k'] = 0.04 # Decay constant
r0 = params['rotor_radius'] # Turbine rotor radius
angle = params['wind_direction']
nt = num_turb
# angle2 = - 270.0 - angle # To read windroses where N is 0 and E is 90.
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
proportion = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[distance[turbine][1]][distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
for i in range(turbine + 1, nt):
determ = wake.determine_if_in_wake(layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]], layout_y[distance[i][1]], k,
r0, angle3)
proportion[distance[turbine][1]][distance[i][1]] = determ[0]
if proportion[distance[turbine][1]][distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][1]] = proportion[distance[turbine][1]][
distance[i][1]] * wake.wake_deficit(
Ct(U[distance[turbine][1]]), k, determ[1], r0)
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
# return [list(_) for _ in zip(
# zip([x for (y, x) in sorted(zip([item[0] for item in distance], layout_x))], [x for (y, x) in sorted(
# zip([item[0] for item in distance], layout_y))]), U)]
unknowns['U'] = array(U)
def jensen_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius, k):
U0 = wind_speed # Free stream wind speed
nt = len(layout_y) # Number of turbines ## Length of layout list
r0 = rotor_radius # Turbine rotor radius
# angle2 = - 270.0 - angle # To read windroses where N is 0 and E is 90.
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
proportion = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[distance[turbine][1]][distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
for i in range(turbine + 1, nt):
determ = wake.determine_if_in_wake(layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]], layout_y[distance[i][1]], k,
r0, angle3)
proportion[distance[turbine][1]][distance[i][1]] = determ[0]
if proportion[distance[turbine][1]][distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][1]] = proportion[distance[turbine][1]][
distance[i][1]] * wake.wake_deficit(
Ct(U[distance[turbine][1]]), k, determ[1], r0)
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
return U
def ainslie_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius, TI):
layout_xD = []
layout_yD = []
D = 2.0 * rotor_radius # Diameter
for x in range(len(layout_x)):
layout_xD.append(layout_x[x] / D)
for x in range(len(layout_y)):
layout_yD.append(layout_y[x] / D)
nt = len(layout_y)
U0 = wind_speed # Free stream wind speed
angle3 = angle + 180.0
wake_deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
U = [U0 for _ in range(nt)]
U = U
TI *= 100.0
for tur in range(nt):
distance[tur] = [
distance_to_front(layout_xD[tur], layout_yD[tur], angle), tur
]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += wake_deficit_matrix[
distance[turbine][1]][distance[num][1]]**2.0
total_deficit[distance[turbine][1]] = sqrt(
total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 -
total_deficit[distance[turbine][1]])
parallel_distance = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
parallel_distance[distance[i][1]] = determine_front(
angle3, layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]], layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
perpendicular_distance[distance[i][1]] = wake.crosswind_distance(
radians(angle3), layout_xD[distance[turbine][1]],
layout_yD[distance[turbine][1]], layout_xD[distance[i][1]],
layout_yD[distance[i][1]])
if perpendicular_distance[
distance[i]
[1]] <= 1.7 and parallel_distance[distance[i][
1]] > 0.0: ## 1.7 gives same results as a bigger distance, many times faster.
wake_deficit_matrix[distance[i][1]][
distance[turbine][1]] = ainslie(
Ct(U[distance[turbine][1]]), U[distance[turbine][1]],
parallel_distance[distance[i][1]],
perpendicular_distance[distance[i][1]], TI)
else:
wake_deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
return U
def larsen_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius,
hub_height, TI):
U0 = wind_speed
r0 = rotor_radius
nt = len(layout_y) # Number of turbines
D = 2.0 * r0
A = pi * r0**2.0
H = hub_height # Hub height
ia = TI # Ambient turbulence intensity according to vanluvanee. 8% on average
def deff(u1):
return D * sqrt(
(1.0 + sqrt(1.0 - Ct(u1))) / (2.0 * sqrt(1.0 - Ct(u1))))
rnb = max(1.08 * D, 1.08 * D + 21.7 * D * (ia - 0.05))
r95 = 0.5 * (rnb + min(H, rnb))
def x0(u2):
return 9.5 * D / ((2.0 * r95 / deff(u2))**3.0 - 1.0)
def c1(u3):
return (deff(u3) / 2.0)**(5.0 / 2.0) * (105.0 / 2.0 / pi)**(
-1.0 / 2.0) * (Ct(u3) * A * x0(u3))**(-5.0 / 6.0
) # Prandtl mixing length
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [
distance_to_front(layout_x[tur], layout_y[tur], angle), tur
]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[
distance[turbine][1]][distance[num][1]]**2.0
total_deficit[distance[turbine][1]] = sqrt(
total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 -
total_deficit[distance[turbine][1]])
flag = [False for _ in range(nt)]
proportion = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
parallel_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
proportion[distance[i][1]], flag[distance[i][1]], perpendicular_distance[distance[i][1]], \
parallel_distance[distance[i][1]] = wake_larsen.determine_if_in_wake_larsen(
layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]],
layout_y[distance[i][1]], A,
c1(U[distance[turbine][1]]),
Ct(U[distance[turbine][1]]), angle3,
r0, x0(U[distance[turbine][1]]))
if parallel_distance[distance[i][1]] > 0.0:
if proportion[distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][
distance[turbine][1]] = proportion[
distance[i][1]] * wake_larsen.wake_deficit(
U[distance[turbine][1]],
Ct(U[distance[turbine][1]]), A,
parallel_distance[distance[i][1]] +
x0(U[distance[turbine][1]]),
perpendicular_distance[distance[i][1]],
c1(U[distance[turbine][1]]))
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
return U
def solve_nonlinear(self, params, unknowns, resids):
U0 = params['mean_ambient_wind_speed']
layout_y = params['layout_y']
layout_x = params['layout_x']
angle = params['wind_direction']
nt = num_turb
r0 = params['rotor_radius'] # Turbine rotor radius
D = 2.0 * r0
A = pi * r0**2.0
ia = params[
'TI'] # Ambient turbulence intensity according to vanluvanee. 8% on average
H = params['hub_height']
def deff(U0):
return D * sqrt(
(1.0 + sqrt(1.0 - Ct(U0))) / (2.0 * sqrt(1.0 - Ct(U0))))
rnb = max(1.08 * D, 1.08 * D + 21.7 * D * (ia - 0.05))
r95 = 0.5 * (rnb + min(H, rnb))
def x0(U0):
return 9.5 * D / ((2.0 * r95 / deff(U0))**3.0 - 1.0)
def c1(U0):
return (deff(U0) / 2.0)**(5.0 / 2.0) * (105.0 / 2.0 / pi)**(
-1.0 / 2.0) * (Ct(U0) * A * x0(U0))**(
-5.0 / 6.0) # Prandtl mixing length
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [
distance_to_front(layout_x[tur], layout_y[tur], angle), tur
]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[
distance[turbine][1]][distance[num][1]]**2.0
total_deficit[distance[turbine][1]] = sqrt(
total_deficit[distance[turbine][1]])
U[distance[turbine]
[1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
flag = [False for _ in range(nt)]
proportion = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
parallel_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
proportion[distance[i][1]], flag[distance[i][1]], perpendicular_distance[distance[i][1]], \
parallel_distance[distance[i][1]] = wake_larsen.determine_if_in_wake_larsen(
layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]],
layout_y[distance[i][1]], A,
c1(U[distance[turbine][1]]),
Ct(U[distance[turbine][1]]), angle3,
r0, x0(U[distance[turbine][1]]))
if parallel_distance[distance[i][1]] > 0.0:
if proportion[distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][
distance[turbine][1]] = proportion[
distance[i][1]] * wake_larsen.wake_deficit(
U[distance[turbine][1]],
Ct(U[distance[turbine][1]]), A,
parallel_distance[distance[i][1]] +
x0(U[distance[turbine][1]]),
perpendicular_distance[distance[i][1]],
c1(U[distance[turbine][1]]))
else:
deficit_matrix[distance[i][1]][distance[turbine]
[1]] = 0.0
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
unknowns['U'] = array(U)
def larsen_1angle(layout_x, layout_y, wind_speed, angle, rotor_radius, hub_height, TI):
U0 = wind_speed
r0 = rotor_radius
nt = len(layout_y) # Number of turbines
D = 2.0 * r0
A = pi * r0 ** 2.0
H = hub_height # Hub height
ia = TI # Ambient turbulence intensity according to vanluvanee. 8% on average
def deff(u1):
return D * sqrt((1.0 + sqrt(1.0 - Ct(u1))) / (2.0 * sqrt(1.0 - Ct(u1))))
rnb = max(1.08 * D, 1.08 * D + 21.7 * D * (ia - 0.05))
r95 = 0.5 * (rnb + min(H, rnb))
def x0(u2):
return 9.5 * D / ((2.0 * r95 / deff(u2)) ** 3.0 - 1.0)
def c1(u3):
return (deff(u3) / 2.0) ** (5.0 / 2.0) * (105.0 / 2.0 / pi) ** (- 1.0 / 2.0) * (Ct(u3) * A * x0(u3)) ** (
- 5.0 / 6.0) # Prandtl mixing length
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[distance[turbine][1]][distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
flag = [False for _ in range(nt)]
proportion = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
parallel_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
proportion[distance[i][1]], flag[distance[i][1]], perpendicular_distance[distance[i][1]], \
parallel_distance[distance[i][1]] = wake_larsen.determine_if_in_wake_larsen(
layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]],
layout_y[distance[i][1]], A,
c1(U[distance[turbine][1]]),
Ct(U[distance[turbine][1]]), angle3,
r0, x0(U[distance[turbine][1]]))
if parallel_distance[
distance[i][1]] > 0.0:
if proportion[distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][1]] = proportion[
distance[i][
1]] * wake_larsen.wake_deficit(
U[distance[turbine][1]], Ct(U[distance[turbine][1]]), A,
parallel_distance[distance[i][1]] + x0(U[distance[turbine][1]]),
perpendicular_distance[distance[i][1]], c1(U[distance[turbine][1]]))
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
return U
def solve_nonlinear(self, params, unknowns, resids):
U0 = params['mean_ambient_wind_speed']
layout_y = params['layout_y']
layout_x = params['layout_x']
angle = params['wind_direction']
nt = num_turb
r0 = params['rotor_radius'] # Turbine rotor radius
D = 2.0 * r0
A = pi * r0 ** 2.0
ia = params['TI'] # Ambient turbulence intensity according to vanluvanee. 8% on average
H = params['hub_height']
def deff(U0):
return D * sqrt((1.0 + sqrt(1.0 - Ct(U0))) / (2.0 * sqrt(1.0 - Ct(U0))))
rnb = max(1.08 * D, 1.08 * D + 21.7 * D * (ia - 0.05))
r95 = 0.5 * (rnb + min(H, rnb))
def x0(U0):
return 9.5 * D / ((2.0 * r95 / deff(U0)) ** 3.0 - 1.0)
def c1(U0):
return (deff(U0) / 2.0) ** (5.0 / 2.0) * (105.0 / 2.0 / pi) ** (- 1.0 / 2.0) * (Ct(U0) * A * x0(U0)) ** (
- 5.0 / 6.0) # Prandtl mixing length
angle3 = angle + 180.0
deficit_matrix = [[0.0 for _ in range(nt)] for _ in range(nt)]
distance = [[0.0 for _ in range(2)] for _ in range(nt)]
U = [U0 for _ in range(nt)]
total_deficit = [0.0 for _ in range(nt)]
for tur in range(nt):
distance[tur] = [distance_to_front(layout_x[tur], layout_y[tur], angle), tur]
distance.sort()
for turbine in range(nt):
for num in range(turbine):
total_deficit[distance[turbine][1]] += deficit_matrix[distance[turbine][1]][distance[num][1]] ** 2.0
total_deficit[distance[turbine][1]] = sqrt(total_deficit[distance[turbine][1]])
U[distance[turbine][1]] = U0 * (1.0 - total_deficit[distance[turbine][1]])
flag = [False for _ in range(nt)]
proportion = [0.0 for _ in range(nt)]
perpendicular_distance = [0.0 for _ in range(nt)]
parallel_distance = [0.0 for _ in range(nt)]
for i in range(turbine + 1, nt):
proportion[distance[i][1]], flag[distance[i][1]], perpendicular_distance[distance[i][1]], \
parallel_distance[distance[i][1]] = wake_larsen.determine_if_in_wake_larsen(
layout_x[distance[turbine][1]],
layout_y[distance[turbine][1]],
layout_x[distance[i][1]],
layout_y[distance[i][1]], A,
c1(U[distance[turbine][1]]),
Ct(U[distance[turbine][1]]), angle3,
r0, x0(U[distance[turbine][1]]))
if parallel_distance[
distance[i][1]] > 0.0:
if proportion[distance[i][1]] != 0.0:
deficit_matrix[distance[i][1]][distance[turbine][1]] = proportion[
distance[i][
1]] * wake_larsen.wake_deficit(
U[distance[turbine][1]], Ct(U[distance[turbine][1]]), A,
parallel_distance[distance[i][1]] + x0(U[distance[turbine][1]]),
perpendicular_distance[distance[i][1]], c1(U[distance[turbine][1]]))
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
else:
deficit_matrix[distance[i][1]][distance[turbine][1]] = 0.0
unknowns['U'] = array(U)