def N2_diagram(nRows, maxDirections):
from openmdao.api import view_tree
# Scaling grid case
nTurbines = nRows**2
probg = Problem(
root=OptAEP(nTurbines,
nDirections=maxDirections,
use_rotor_components=False,
wake_model=gauss_wrapper,
params_IdepVar_func=add_gauss_params_IndepVarComps,
wake_model_options={'nSamples': 0},
params_IndepVar_args=None))
probf = Problem(
root=OptAEP(nTurbines,
nDirections=maxDirections,
use_rotor_components=False,
wake_model=floris_wrapper,
differentiable=True,
params_IdepVar_func=add_floris_params_IndepVarComps,
wake_model_options=None,
params_IndepVar_args=None))
# initialize problem
probf.setup()
probg.setup()
view_tree(probf, show_browser=True, outfile='tree_floris.html')
view_tree(probg, show_browser=True, outfile='tree_gauss.html')
axialInduction = np.zeros(nTurbines) + axial_induction
rotorDiameter = np.zeros(nTurbines) + rotor_diameter
generatorEfficiency = np.zeros(nTurbines) + generator_efficiency
yaw = np.zeros(nTurbines) + yaw_init
Ct = np.zeros(nTurbines) + CT
Cp = np.zeros(nTurbines) + CP
# Define site measurements
nDirections = 1
wind_direction = 270.-0.523599*180./np.pi
wind_speed = 8. # m/s
air_density = 1.1716
# initialize problems
gauss_prob = Problem(root=OptAEP(nTurbines=nTurbines, nDirections=nDirections, use_rotor_components=False,
wake_model=gauss_wrapper, wake_model_options={'nSamples': 0}, datasize=0,
params_IdepVar_func=add_gauss_params_IndepVarComps, force_fd=True,
params_IndepVar_args={}))
floris_prob = Problem(root=OptAEP(nTurbines=nTurbines, nDirections=nDirections, use_rotor_components=False,
wake_model=floris_wrapper, wake_model_options=None, datasize=0,
params_IdepVar_func=add_floris_params_IndepVarComps,
params_IndepVar_args={}))
jensen_prob = Problem(root=OptAEP(nTurbines=nTurbines, nDirections=nDirections, use_rotor_components=False,
wake_model=jensen_wrapper, wake_model_options={'variant': 'CosineYaw_1R',
'radius multiplier': 1.0}, datasize=0,
params_IdepVar_func=add_jensen_params_IndepVarComps,
params_IndepVar_args={'use_angle': True}))
probs = [gauss_prob, floris_prob, jensen_prob]
names = ['gauss', 'floris', 'jensen']
def calc_data(nRows, maxDirections, savetxt=False):
# set up wind farm
rotor_diameter = 126.4
axialInduction = 1.0 / 3.0 # used only for initialization
generatorEfficiency = 0.944
hub_height = 90.0
Ct = 4.0 * axialInduction * (1.0 - axialInduction)
Cp = 0.7737 / 0.944 * 4.0 * 1.0 / 3.0 * np.power((1 - 1.0 / 3.0), 2)
# Scaling grid case
spacing = 4 # turbine grid spacing in diameters
nTurbines = nRows**2
# Set up position arrays
points = np.linspace(start=spacing * rotor_diameter,
stop=nRows * spacing * rotor_diameter,
num=nRows)
xpoints, ypoints = np.meshgrid(points, points)
turbineX = np.ndarray.flatten(xpoints)
turbineY = np.ndarray.flatten(ypoints)
print turbineX, turbineY
# initialize input variable arrays
rotorDiameter = np.ones(nTurbines) * rotor_diameter
axialInduction = np.ones(nTurbines) * axialInduction
Ct = np.ones(nTurbines) * Ct
Cp = np.ones(nTurbines) * Cp
generatorEfficiency = np.ones(nTurbines) * generatorEfficiency
yaw = np.zeros(nTurbines)
hubHeight = np.ones(nTurbines) * hub_height
# Define flow properties
wind_speed = 8.0 # m/s
air_density = 1.1716 # kg/m^3
# initialize results arrays
directions = np.arange(1, maxDirections + 2, 10)
time_ex_f = np.zeros_like(directions) * 0.0
time_ex_g = np.zeros_like(directions) * 0.0
time_fd_f = np.zeros_like(directions) * 0.0
time_fd_g = np.zeros_like(directions) * 0.0
AEPf = np.zeros_like(directions)
AEPg = np.zeros_like(directions)
index = 0
for d in directions:
# set up problem
probg = Problem(
root=OptAEP(nTurbines,
nDirections=d,
use_rotor_components=False,
wake_model=gauss_wrapper,
params_IdepVar_func=add_gauss_params_IndepVarComps,
wake_model_options={'nSamples': 0},
params_IndepVar_args=None))
probf = Problem(
root=OptAEP(nTurbines,
nDirections=d,
use_rotor_components=False,
wake_model=floris_wrapper,
differentiable=True,
params_IdepVar_func=add_floris_params_IndepVarComps,
wake_model_options=None,
params_IndepVar_args=None))
# initialize problem
# profile.setup(probf)
probf.setup()
probg.setup()
# assign values to constant inputs (not design variables)
probf['turbineX'] = probg['turbineX'] = turbineX
probf['turbineY'] = probg['turbineY'] = turbineY
probf['hubHeight'] = probg['hubHeight'] = hubHeight
probf['yaw0'] = probg['yaw0'] = yaw
probf['rotorDiameter'] = probg['rotorDiameter'] = rotorDiameter
probf['axialInduction'] = probg['axialInduction'] = axialInduction
probf['Ct_in'] = probg['Ct_in'] = Ct
probf['Cp_in'] = probg['Cp_in'] = Cp
probf['generatorEfficiency'] = probg[
'generatorEfficiency'] = generatorEfficiency
probf['windSpeeds'] = probg['windSpeeds'] = np.ones(d) * wind_speed
probf['air_density'] = probg['air_density'] = air_density
probf['windDirections'] = probg['windDirections'] = np.linspace(
0, 360, d)
probf['windFrequencies'] = probg['windFrequencies'] = np.ones(d) / d
# run problem
probf.run()
probg.run()
AEPf[index] = probf['AEP']
AEPg[index] = probg['AEP']
# pass results to self for use with unit test
tic = time()
# profile.start()
J = probf.calc_gradient(['turbineX', 'turbineY'], ['AEP'],
return_format='dict',
mode='auto')
# profile.stop()
toc = time()
time_ex_f[index] = toc - tic
tic = time()
# profile.start()
J = probf.calc_gradient(['turbineX', 'turbineY'], ['AEP'],
return_format='dict',
mode='fd')
# profile.stop()
toc = time()
time_fd_f[index] = toc - tic
tic = time()
# profile.start()
J = probg.calc_gradient(['turbineX', 'turbineY'], ['AEP'],
return_format='dict',
mode='auto')
# profile.stop()
toc = time()
time_ex_g[index] = toc - tic
tic = time()
# profile.start()
J = probg.calc_gradient(['turbineX', 'turbineY'], ['AEP'],
return_format='dict',
mode='fd')
# profile.stop()
toc = time()
time_fd_g[index] = toc - tic
index += 1
if savetxt:
np.savetxt(
'scaling_by_directions_combined_%i_turbines_%i_directions.txt' %
(nTurbines, maxDirections),
np.array([
time_ex_f, time_ex_g, time_fd_f, time_fd_g, AEPf, AEPg,
directions
]))
return np.array(
[time_ex_f, time_ex_g, time_fd_f, time_fd_g, AEPf, AEPg, directions])
rotorDiameter[turbI] = rotor_diameter # m
axialInduction[turbI] = 1.0 / 3.0
Ct[turbI] = 4.0 * axialInduction[turbI] * (1.0 - axialInduction[turbI])
Cp[turbI] = 0.7737 / 0.944 * 4.0 * 1.0 / 3.0 * np.power(
(1 - 1.0 / 3.0), 2)
generatorEfficiency[turbI] = 0.944
yaw[turbI] = 0. # deg.
# Define flow properties
air_density = 1.1716 # kg/m^3
# initialize problem
prob = Problem(impl=impl,
root=OptAEP(nTurbines=nTurbines,
nDirections=nDirections,
minSpacing=minSpacing,
differentiable=True,
use_rotor_components=False,
nVertices=nVertices))
# set up optimizer
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.add_objective('obj', scaler=1E-5)
# set optimizer options
# prob.driver.opt_settings['Verify level'] = 3
prob.driver.opt_settings[
'Print file'] = 'SNOPT_print_exampleOptAEP_amalia.out'
prob.driver.opt_settings[
'Summary file'] = 'SNOPT_summary_exampleOptAEP_amalia.out'
prob.driver.opt_settings['Major iterations limit'] = 1000
axialInduction = np.array([axialInduction, axialInduction])
rotorDiameter = np.array([rotorDiameter, rotorDiameter])
generatorEfficiency = np.array([generator_efficiency, generator_efficiency])
yaw = np.array([0., 0.])
# Define site measurements
wind_direction = 270.-0.523599*180./np.pi
wind_speed = 8. # m/s
air_density = 1.1716
Ct = np.array([CT, CT])
Cp = np.array([CP, CP])
global prob
prob = Problem(root=OptAEP(nTurbines=nTurbines, nDirections=nDirections, use_rotor_components=False,
wake_model=gauss_wrapper, wake_model_options={'nSamples': 0}, datasize=0,
params_IdepVar_func=add_gauss_params_IndepVarComps,
params_IndepVar_args={}))
prob.setup()
prob['model_params:integrate'] = False
prob['model_params:spread_mode'] = 'bastankhah'
prob['model_params:yaw_mode'] = 'bastankhah'
prob['model_params:n_std_dev'] = 4.
# prob['model_params:m'] = 0.33
# prob['model_params:Dw0'] = 1.3
tuning_obj_function(plot=True)
# initialize optimization problem
optProb = Optimization('Tuning Gaussian Model to SOWFA', tuning_obj_function)
optProb.addVarGroup('ke', 1, lower=0.0, upper=1.0, value=0.152, scalar=1)
yaw[turbI] = 0. # deg.
# Define flow properties
wind_speed = 8.0 # m/s
air_density = 1.1716 # kg/m^3
windDirections = np.linspace(0, 270, size)
windSpeeds = np.ones(size) * wind_speed
windFrequencies = np.ones(size) / size
# initialize problem
prob = Problem(impl=impl,
root=OptAEP(
nTurbines=nTurbs,
nDirections=windDirections.size,
nVertices=nVertices,
minSpacing=minSpacing,
differentiable=True,
use_rotor_components=False,
wake_model=gauss_wrapper,
params_IdepVar_func=add_gauss_params_IndepVarComps,
params_IndepVar_args={}))
# prob.root.deriv_options['type'] = 'fd'
# prob.root.deriv_options['form'] = 'central'
# prob.root.deriv_options['step_size'] = 1.0e-8
# set up optimizer
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.add_objective('obj', scaler=1E0)
# prob.driver.options['gradient method'] = 'snopt_fd'
samplesX = np.linspace(0, 3000, res)
samplesY = np.linspace(0, 3000, res)
samplesX, samplesY = np.meshgrid(samplesX, samplesY)
samplesX = samplesX.flatten()
samplesY = samplesY.flatten()
samplesZ = np.ones(samplesX.shape) * hub_height
# initialize problems
gauss_prob = Problem(
root=OptAEP(nTurbines=nTurbines,
nDirections=nDirections,
use_rotor_components=False,
wake_model=gauss_wrapper,
wake_model_options={'nSamples': res**2},
datasize=0,
params_IdepVar_func=add_gauss_params_IndepVarComps,
force_fd=True,
params_IndepVar_args={}))
wake_model_options = {
'differentiable': True,
'use_rotor_components': False,
'nSamples': res**2,
'verbose': False
}
floris_prob = Problem(
root=OptAEP(nTurbines=nTurbines,
nDirections=nDirections,
use_rotor_components=False,
(1 - 1.0 / 3.0), 2)
generatorEfficiency[turbI] = 0.944
yaw[turbI] = 0. # deg.
# Define flow properties
wind_speed = 8.0 # m/s
air_density = 1.1716 # kg/m^3
windDirections = np.linspace(0, 270, size)
windSpeeds = np.ones(size) * wind_speed
windFrequencies = np.ones(size) / size
# initialize problem
prob = Problem(impl=impl,
root=OptAEP(nTurbines=nTurbs,
nDirections=windDirections.size,
minSpacing=minSpacing,
differentiable=True,
use_rotor_components=False))
# set up optimizer
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.add_objective('obj', scaler=1E-5)
# set optimizer options
prob.driver.opt_settings['Verify level'] = 3
prob.driver.opt_settings['Print file'] = 'SNOPT_print_exampleOptAEP.out'
prob.driver.opt_settings[
'Summary file'] = 'SNOPT_summary_exampleOptAEP.out'
prob.driver.opt_settings['Major iterations limit'] = 1000
Cp[turbI] = 0.7737 / 0.944 * 4.0 * 1.0 / 3.0 * np.power(
(1 - 1.0 / 3.0), 2)
generatorEfficiency[turbI] = 0.944
yaw[turbI] = 0. # deg.
# Define flow properties
wind_speed = 8.0 # m/s
air_density = 1.1716 # kg/m^3
windDirections = np.linspace(0, 270, nDirections)
windFrequencies = np.ones_like(windDirections) * 1.0 / nDirections
# initialize problem
prob = Problem(impl=impl,
root=OptAEP(nTurbines=nTurbs,
nDirections=windDirections.size,
minSpacing=minSpacing,
use_rotor_components=use_rotor_components,
datasize=datasize))
# set up optimizer
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.add_objective('obj', scaler=1E-8)
# set optimizer options
prob.driver.opt_settings['Verify level'] = 0
prob.driver.opt_settings[
'Print file'] = 'SNOPT_print_exampleOptAEP-Rotor.out'
prob.driver.opt_settings[
'Summary file'] = 'SNOPT_summary_exampleOptAEP-Rotor.out'
prob.driver.opt_settings['Major iterations limit'] = 1000
# 1:TI by Niayifar and Porte Agel altered by Annoni and Thomas,
# 2:TI by Niayifar and Porte Agel 2016,
# 3:no yet implemented]
calc_k_star = False
z_ref = 90.0
z_0 = 0.0
TI = 0.06
# k_calc = 0.022
k_calc = 0.3837 * TI + 0.003678
nRotorPoints = 16
prob = Problem(
root=OptAEP(nTurbines=nTurbines,
nDirections=nDirections,
use_rotor_components=False,
wake_model=gauss_wrapper,
wake_model_options={'nSamples': 0},
datasize=0,
params_IdepVar_func=add_gauss_params_IndepVarComps,
params_IndepVar_args={}))
prob.setup()
prob['model_params:wake_combination_method'] = wake_combination_method
prob['model_params:ti_calculation_method'] = ti_calculation_method
prob['model_params:calc_k_star'] = calc_k_star
prob['model_params:sort'] = sort_turbs
prob['model_params:z_ref'] = z_ref
prob['model_params:z_0'] = z_0
prob['model_params:ky'] = k_calc
prob['model_params:kz'] = k_calc
prob['model_params:I'] = TI