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Mads M. Pedersen authored- All2AllIterative: Use PropagateDownwind WS_eff as initial guess, determine unstable flow cases and limit WS_eff of idling WT in unstable flow cases to max previuos WS_eff - Apply rotor average model on blockage deficit - Speed up Rathmann and SelfSemilarity by implementing calc_layout_terms etc.
Mads M. Pedersen authored- All2AllIterative: Use PropagateDownwind WS_eff as initial guess, determine unstable flow cases and limit WS_eff of idling WT in unstable flow cases to max previuos WS_eff - Apply rotor average model on blockage deficit - Speed up Rathmann and SelfSemilarity by implementing calc_layout_terms etc.
engineering_models.py 39.84 KiB
from abc import abstractmethod
from numpy import newaxis as na
import numpy as np
from py_wake.superposition_models import SuperpositionModel, LinearSum, WeightedSum
from py_wake.wind_farm_models.wind_farm_model import WindFarmModel
from py_wake.deflection_models.deflection_model import DeflectionModel
from py_wake.utils.gradients import use_autograd_in, autograd
from py_wake.rotor_avg_models.rotor_avg_model import RotorCenter, RotorAvgModel
from py_wake.turbulence_models.turbulence_model import TurbulenceModel
from py_wake.deficit_models.deficit_model import ConvectionDeficitModel, BlockageDeficitModel, WakeDeficitModel
from tqdm import tqdm
from py_wake.wind_turbines._wind_turbines import WindTurbines
from py_wake.utils.model_utils import check_model
from py_wake.utils.functions import mean_deg
class EngineeringWindFarmModel(WindFarmModel):
"""
Base class for engineering wake models
General suffixes:
- i: turbines ordered by id
- j: downstream points/turbines
- k: wind speeds
- l: wind directions
Arguments available for calc_deficit (specifiy in args4deficit):
- WS_ilk: Local wind speed without wake effects
- TI_ilk: Local turbulence intensity without wake effects
- TI_std_ilk: Standard deviation of local turbulence intensity
- WS_eff_ilk: Local wind speed with wake effects
- TI_eff_ilk: Local turbulence intensity with wake effects
- D_src_il: Diameter of source turbine
- D_dst_ijl: Diameter of destination turbine
- dw_ijlk: Downwind distance from turbine i to point/turbine j
- hcw_ijlk: Horizontal cross wind distance from turbine i to point/turbine j
- dh_ijl: vertical distance from turbine i to point/turbine j
- cw_ijlk: Cross wind(horizontal and vertical) distance from turbine i to point/turbine j
- ct_ilk: Thrust coefficient
"""
default_grid_resolution = 500
def __init__(self, site, windTurbines: WindTurbines, wake_deficitModel, rotorAvgModel, superpositionModel,
blockage_deficitModel=None, deflectionModel=None, turbulenceModel=None):
WindFarmModel.__init__(self, site, windTurbines)
for model, cls, name in [(wake_deficitModel, WakeDeficitModel, 'wake_deficitModel'),
(rotorAvgModel, RotorAvgModel, 'rotorAvgModel'),
(superpositionModel, SuperpositionModel, 'superpositionModel'),
(blockage_deficitModel, BlockageDeficitModel, 'blockage_deficitModel'),
(deflectionModel, DeflectionModel, 'deflectionModel'),
(turbulenceModel, TurbulenceModel, 'turbulenceModel')]:
check_model(model, cls, name)
if model is not None:
setattr(model, 'windFarmModel', self)
setattr(self, name, model)
if isinstance(superpositionModel, WeightedSum):
assert isinstance(wake_deficitModel, ConvectionDeficitModel)
assert rotorAvgModel.__class__ is RotorCenter, "Multiple rotor average points not implemented for WeightedSum"
# TI_eff requires a turbulence model
assert 'TI_eff_ilk' not in wake_deficitModel.args4deficit or turbulenceModel
self.wake_deficitModel = wake_deficitModel
self.rotorAvgModel = rotorAvgModel
self.superpositionModel = superpositionModel
self.blockage_deficitModel = blockage_deficitModel
self.deflectionModel = deflectionModel
self.turbulenceModel = turbulenceModel
# wake expansion continuation (wake-width scale factor) see
self.wec = 1
# Thomas, J. J. and Ning, A., “A Method for Reducing Multi-Modality in the Wind Farm Layout Optimization Problem,”
# Journal of Physics: Conference Series, Vol. 1037, The Science of Making
# Torque from Wind, Milano, Italy, jun 2018, p. 10.
self.deficit_initalized = False
self.args4deficit = self.wake_deficitModel.args4deficit
self.args4deficit = set(self.args4deficit) | {'yaw_ilk'} | set(self.rotorAvgModel.args4rotor_avg_deficit)
if self.blockage_deficitModel:
self.args4deficit = set(self.args4deficit) | set(self.blockage_deficitModel.args4deficit)
if self.blockage_deficitModel.groundModel:
self.args4deficit = set(self.args4deficit) | set(self.blockage_deficitModel.groundModel.args4deficit)
elif self.wake_deficitModel.groundModel:
self.args4deficit = set(self.args4deficit) | set(self.wake_deficitModel.groundModel.args4deficit)
self.args4all = set(self.args4deficit)
if self.turbulenceModel:
if self.turbulenceModel.rotorAvgModel is None:
self.turbulenceModel.rotorAvgModel = rotorAvgModel
self.args4addturb = set(self.turbulenceModel.args4addturb) | set(
self.turbulenceModel.rotorAvgModel.args4rotor_avg_deficit)
self.args4all = self.args4all | set(self.turbulenceModel.args4addturb)
if self.deflectionModel:
self.args4all = self.args4all | set(self.deflectionModel.args4deflection)
def __str__(self):
def name(o):
return o.__class__.__name__
models = [self.__class__.__bases__[0].__name__, "%s-wake" % name(self.wake_deficitModel)]
if self.blockage_deficitModel:
models.append("%s-blockage" % name(self.blockage_deficitModel))
models.append("%s-rotor-average" % (name(self.rotorAvgModel)))
models.append("%s-superposition" % (name(self.superpositionModel)))
if self.deflectionModel:
models.append("%s-deflection" % name(self.deflectionModel))
if self.turbulenceModel:
models.append("%s-turbulence" % name(self.turbulenceModel))
return "%s(%s)" % (name(self), ", ".join(models))
def _init_deficit(self, **kwargs):
"""Calculate layout dependent wake (and blockage) deficit terms"""
self.rotorAvgModel._calc_layout_terms(self.wake_deficitModel, **kwargs)
self.wake_deficitModel.deficit_initalized = True
if self.blockage_deficitModel:
if self.blockage_deficitModel != self.wake_deficitModel:
self.rotorAvgModel._calc_layout_terms(self.blockage_deficitModel, **kwargs)
self.blockage_deficitModel.deficit_initalized = True
def _reset_deficit(self):
self.wake_deficitModel.deficit_initalized = False
if self.blockage_deficitModel:
self.blockage_deficitModel.deficit_initalized = False
def _add_blockage(self, deficit, dw_ijlk, **kwargs):
# the split line between wake and blockage is set slightly upstream to handle
# numerical inaccuracy in the trigonometric functions that calculates dw_ijlk
rotor_pos = -1e-10
blockage = np.zeros_like(deficit)
if self.blockage_deficitModel is None:
deficit *= (dw_ijlk > rotor_pos)
elif (self.blockage_deficitModel != self.wake_deficitModel):
blockage = self.blockage_deficitModel.groundModel(lambda **kwargs: self.rotorAvgModel(self.blockage_deficitModel.calc_blockage_deficit, **kwargs),
dw_ijlk=dw_ijlk, **kwargs)
deficit *= (dw_ijlk > rotor_pos)
return deficit, blockage
def _calc_deficit(self, dw_ijlk, **kwargs):
"""Calculate wake (and blockage) deficit"""
deficit = self.wake_deficitModel.groundModel(lambda **kwargs: self.rotorAvgModel(self.wake_deficitModel.calc_deficit_downwind, **kwargs),
dw_ijlk=dw_ijlk, **kwargs)
deficit, blockage = self._add_blockage(deficit, dw_ijlk, **kwargs)
return deficit, blockage
def _calc_deficit_convection(self, dw_ijlk, **kwargs):
"""Calculate wake convection deficit (and blockage)"""
deficit, uc, sigma_sqr = self.rotorAvgModel.calc_deficit_convection(
self.wake_deficitModel, dw_ijlk=dw_ijlk, **kwargs)
deficit, blockage = self._add_blockage(deficit, dw_ijlk, **kwargs)
return deficit, uc, sigma_sqr, blockage
def calc_wt_interaction(self, x_i, y_i, h_i=None, type_i=0, wd=None, ws=None, time=False,
yaw_ilk=None, tilt_ilk=None, **kwargs):
"""See WindFarmModel.calc_wt_interaction"""
h_i, D_i = self.windTurbines.get_defaults(len(x_i), type_i, h_i)
x_i, y_i, type_i = [np.asarray(v) for v in [x_i, y_i, type_i]]
wd, ws = self.site.get_defaults(wd, ws)
# Find local wind speed, wind direction, turbulence intensity and probability
lw = self.site.local_wind(x_i=x_i, y_i=y_i, h_i=h_i, wd=wd, ws=ws, time=time)
# Calculate down-wind and cross-wind distances
self._validate_input(x_i, y_i)
I, L, K, = len(x_i), len(wd), (1, len(ws))[time is False]
for v in ['WS', 'WD', 'TI']:
if v in kwargs:
lw.add_ilk(v, kwargs[v])
WS_eff_ilk = lw.WS.ilk((I, L, K)).copy()
TI_eff_ilk = lw.TI.ilk((I, L, K)).copy()
# add eps to avoid non-differentiable 0
# eps = 2 * np.finfo(float).eps ** 2 if 'autograd' in np.__name__ else 0
self.site.distance.setup(x_i, y_i, h_i)
# cw_iil = np.sqrt(hcw_iil**2 + dh_iil**2 + eps)
wt_kwargs = kwargs
ri, oi = self.windTurbines.function_inputs
unused_inputs = set(wt_kwargs) - set(ri) - set(oi) - {'WS', 'WD', 'TI'}
if unused_inputs:
raise TypeError("""got unexpected keyword argument(s): '%s'
required arguments: %s
optional arguments: %s""" % ("', '".join(unused_inputs), ['ws'] + ri, oi))
def arg2ilk(k, v):
# if v is None:
# return v
v = np.asarray(v)
if v.shape not in {(), (I,), (I, L), (I, L, K), (L,), (L, K)}:
valid_shapes = f"(), ({I}), ({I},{L}), ({I},{L},{K})"
raise ValueError(
f"Argument, {k}(shape={v.shape}), has unsupported shape. Valid shapes are {valid_shapes}")
if v.shape == (L,) or v.shape == (L, K):
return np.broadcast_to(v[na], (I,) + v.shape)
else:
return v
wt_kwargs = {k: arg2ilk(k, v)for k, v in wt_kwargs.items()}
def add_arg(name, optional):
if name in wt_kwargs: # custom WindFarmModel.__call__ arguments
return
elif name in {'yaw', 'tilt', 'type'}: # fixed WindFarmModel.__call__ arguments
wt_kwargs[name] = {'yaw': yaw_ilk, 'tilt': tilt_ilk, 'type': type_i}[name]
elif name in lw:
wt_kwargs[name] = lw[name].values
elif name in self.site.ds:
wt_kwargs[name] = self.site.interp(self.site.ds[name], lw.coords).values
elif name in ['TI_eff']:
if self.turbulenceModel:
wt_kwargs['TI_eff'] = None
elif optional is False:
raise KeyError("Argument, TI_eff, needed to calculate power and ct requires a TurbulenceModel")
elif name in ['dw_ijl', 'cw_ijl', 'hcw_ijl']:
pass
elif optional:
pass
else:
raise KeyError("Argument, %s, required to calculate power and ct not found" % name)
for opt, lst in zip([False, True], self.windTurbines.function_inputs):
for k in lst:
add_arg(k, opt)
if yaw_ilk is None:
yaw_ilk = np.zeros((I, L, K))
if tilt_ilk is None:
tilt_ilk = np.zeros((I, L, K))
kwargs = {'localWind': lw,
'WS_eff_ilk': WS_eff_ilk, 'TI_eff_ilk': TI_eff_ilk,
'x_i': x_i, 'y_i': y_i, 'h_i': h_i, 'D_i': D_i,
'yaw_ilk': yaw_ilk, 'tilt_ilk': tilt_ilk,
'I': I, 'L': L, 'K': K, **wt_kwargs}
WS_eff_ilk, TI_eff_ilk, ct_ilk = self._calc_wt_interaction(**kwargs)
if 'TI_eff' in wt_kwargs:
wt_kwargs['TI_eff'] = TI_eff_ilk
d_ijl_keys = ({k for l in self.windTurbines.function_inputs for k in l} &
{'dw_ijl', 'hcw_ijl', 'dh_ijl', 'cw_ijl'})
if d_ijl_keys:
d_ijl_dict = {k: lambda v=v: v for k, v in zip(['dw_ijl', 'hcw_ijl', 'dh_ijl'], self.site.distance(wd[na]))}
d_ijl_dict['cw_ijl'] = lambda d_ijl_dict=d_ijl_dict: np.sqrt(
d_ijl_dict['dw_ijl']**2 + d_ijl_dict['hcw_ijl']**2)
wt_kwargs.update({k: d_ijl_dict[k]() for k in d_ijl_keys})
wt_kwargs_keys = set(self.windTurbines.powerCtFunction.required_inputs +
self.windTurbines.powerCtFunction.optional_inputs)
power_ilk = self.windTurbines.power(WS_eff_ilk, **{k: v for k, v in wt_kwargs.items() if k in wt_kwargs_keys})
return WS_eff_ilk, TI_eff_ilk, power_ilk, ct_ilk, lw, wt_kwargs
@abstractmethod
def _calc_wt_interaction(self, **kwargs):
"""calculate WT interaction"""
def _flow_map(self, x_j, y_j, h_j, sim_res_data):
"""call this function via SimulationResult.flow_map"""
# calculate distances
wt_d_i = self.windTurbines.diameter(sim_res_data.type)
wt_x_i, wt_y_i, wt_h_i, wd, ws = [sim_res_data[k] for k in ['x', 'y', 'h', 'wd', 'ws']]
lw_j = self.site.local_wind(x_i=x_j, y_i=y_j, h_i=h_j, wd=wd, ws=ws)
I, J, L, K = [len(x) for x in [wt_x_i, x_j, wd, ws]]
WS_eff_jlk = np.zeros((len(x_j), L, K))
TI_eff_jlk = np.zeros((len(x_j), L, K))
self.site.distance.setup(wt_x_i, wt_y_i, wt_h_i, (x_j, y_j, h_j))
for l in tqdm(range(L), disable=L <= 1 or not self.verbose, desc='Calculate flow map', unit='wd'):
dw_ijl, hcw_ijl, dh_ijl = self.site.distance(
wd_l=sim_res_data.wd[l:l + 1].values, WD_il=sim_res_data.WD.ilk((I, L, K))[:, l:l + 1, :].mean(2))
if self.wec != 1:
hcw_ijl = hcw_ijl / self.wec
def get_ilk(k):
def wrap():
v = sim_res_data[k].ilk((I, L, K))
l_ = [l, 0][v.shape[1] == 1]
return v[:, l_][:, na]
return wrap
arg_funcs = {'WS_ilk': get_ilk('WS'),
'WS_eff_ilk': get_ilk('WS_eff'),
'TI_ilk': get_ilk('TI'),
'TI_eff_ilk': get_ilk('TI_eff'),
'yaw_ilk': get_ilk('yaw'),
'tilt_ilk': get_ilk('tilt'),
'D_src_il': lambda: wt_d_i[:, na],
'D_dst_ijl': lambda: np.zeros_like(dh_ijl),
'h_il': lambda: wt_h_i.data[:, na],
'ct_ilk': get_ilk('CT')}
if self.deflectionModel:
dw_ijlk, hcw_ijlk, dh_ijlk = self.deflectionModel.calc_deflection(
dw_ijl=dw_ijl, hcw_ijl=hcw_ijl, dh_ijl=dh_ijl,
** {k: arg_funcs[k]() for k in self.deflectionModel.args4deflection})
else:
dw_ijlk, hcw_ijlk, dh_ijlk = dw_ijl[..., na], hcw_ijl[..., na], dh_ijl[..., na]
arg_funcs.update({'cw_ijlk': lambda: np.hypot(dh_ijlk, hcw_ijlk),
'dw_ijlk': lambda: dw_ijlk, 'hcw_ijlk': lambda: hcw_ijlk, 'dh_ijlk': lambda: dh_ijlk})
args = {k: arg_funcs[k]() for k in self.args4deficit if k != 'dw_ijlk'}
arg_funcs['wake_radius_ijlk'] = lambda: self.wake_deficitModel.wake_radius(dw_ijlk=dw_ijlk, **args)
if self.turbulenceModel:
args.update({k: arg_funcs[k]() for k in self.turbulenceModel.args4addturb
if k not in self.args4deficit and k != 'dw_ijlk'})
if I * J * K * 8 / 1024**2 > 10:
# one wt at the time to avoid memory problems
deficit_ijk = np.zeros((I, J, K))
blockage_ijk = np.zeros((I, J, K))
add_turb_ijk = np.zeros((I, J, K))
uc_ijk = np.zeros((I, J, K))
sigma_sqr_ijk = np.zeros((I, J, K))
for i in tqdm(range(I), disable=I <= 1 or not self.verbose,
desc="Calculate flow map for wd=%d" % l, unit='wt'):
args_i = {k: v[i][na] for k, v in args.items()}
if isinstance(self.superpositionModel, WeightedSum):
deficit, uc, sigma_sqr, blockage = self._calc_deficit_convection(
dw_ijlk=dw_ijlk[i][na], **args_i)
deficit_ijk[i] = deficit[0, :, 0]
uc_ijk[i] = uc[0, :, 0]
sigma_sqr_ijk[i] = sigma_sqr[0, :, 0]
else:
deficit_ijk[i], blockage_ijk[i] = [v[0, :, 0]
for v in self._calc_deficit(dw_ijlk=dw_ijlk[i][na], **args_i)]
if self.turbulenceModel:
add_turb_ijk[i] = self.turbulenceModel.calc_added_turbulence(
dw_ijlk=dw_ijlk[i][na], **args_i)[0, :, 0]
else:
if isinstance(self.superpositionModel, WeightedSum):
deficit, uc, sigma_sqr, blockage = self._calc_deficit_convection(dw_ijlk=dw_ijlk, **args)
deficit_ijk = deficit[:, :, 0]
blockage_ijk = blockage[:, :, 0]
uc_ijk = uc[:, :, 0]
sigma_sqr_ijk = sigma_sqr[:, :, 0]
else:
deficit_ijk, blockage_ijk = self._calc_deficit(dw_ijlk=dw_ijlk, **args)
deficit_ijk, blockage_ijk = deficit_ijk[:, :, 0], blockage_ijk[:, :, 0]
if self.turbulenceModel:
add_turb_ijk = self.turbulenceModel.calc_added_turbulence(dw_ijlk=dw_ijlk, **args)[:, :, 0]
l_ = [l, 0][lw_j.WS_ilk.shape[1] == 1]
if isinstance(self.superpositionModel, WeightedSum):
cw_ijk = np.hypot(dh_ijl[..., na], hcw_ijlk)[:, :, 0]
hcw_ijk, dh_ijk = hcw_ijlk[:, :, 0], dh_ijl[:, :, 0, na]
WS_eff_jlk[:, l] = lw_j.WS_ilk[:, l_] - self.superpositionModel(lw_j.WS_ilk[:, l_], deficit_ijk, uc_ijk,
sigma_sqr_ijk, cw_ijk, hcw_ijk, dh_ijk)
if self.blockage_deficitModel:
blockage_superpositionModel = self.blockage_deficitModel.superpositionModel or LinearSum()
WS_eff_jlk[:, l] -= blockage_superpositionModel(blockage_ijk)
else:
WS_eff_jlk[:, l] = lw_j.WS_ilk[:, l_] - self.superpositionModel(deficit_ijk)
if self.blockage_deficitModel:
blockage_superpositionModel = self.blockage_deficitModel.superpositionModel or self.superpositionModel
WS_eff_jlk[:, l] -= blockage_superpositionModel(blockage_ijk)
if self.turbulenceModel:
l_ = [l, 0][lw_j.TI_ilk.shape[1] == 1]
TI_eff_jlk[:, l] = self.turbulenceModel.calc_effective_TI(lw_j.TI_ilk[:, l_], add_turb_ijk)
return lw_j, WS_eff_jlk, TI_eff_jlk
def _validate_input(self, x_i, y_i):
i1, i2 = np.where((np.abs(
x_i[:, na] - x_i[na]) + np.abs(y_i[:, na] - y_i[na]) + np.eye(len(x_i))) == 0)
if len(i1):
msg = "\n".join(["Turbines %d and %d are at the same position" % (i1[i], i2[i]) for i in range(len(i1))])
raise ValueError(msg)
def dAEPdn(self, argnum, gradient_method):
def aep(x, y, h=None, type=0, wd=None, ws=None, yaw_ilk=None): # @ReservedAssignment
if gradient_method == autograd:
with use_autograd_in():
return self.aep(x, y, h, type, wd, ws, yaw_ilk)
else:
return self.aep(x, y, h, type, wd, ws, yaw_ilk)
return gradient_method(aep, True, argnum)
def dAEPdxy(self, gradient_method, normalize_probabilities=False, with_wake_loss=True, gradient_method_kwargs={}):
def wrap(x, y, h=None, type=0, wd=None, ws=None, yaw_ilk=None): # @ReservedAssignment
def aep(x, y, h, type, wd, ws, yaw_ilk): # @ReservedAssignment
if gradient_method == autograd:
with use_autograd_in():
return self.aep(x, y, h, type, wd, ws, yaw_ilk,
normalize_probabilities=normalize_probabilities, with_wake_loss=with_wake_loss)
else:
return self.aep(x, y, h, type, wd, ws, yaw_ilk,
normalize_probabilities=normalize_probabilities, with_wake_loss=with_wake_loss)
return (gradient_method(aep, True, 0, **gradient_method_kwargs)(x, y, h, type, wd, ws, yaw_ilk),
gradient_method(aep, True, 1, **gradient_method_kwargs)(x, y, h, type, wd, ws, yaw_ilk))
return wrap
class PropagateDownwind(EngineeringWindFarmModel):
"""Downstream wake deficits calculated and propagated in downstream direction.
Very fast, but ignoring blockage effects
"""
def __init__(self, site, windTurbines, wake_deficitModel,
rotorAvgModel=RotorCenter(), superpositionModel=LinearSum(),
deflectionModel=None, turbulenceModel=None):
"""Initialize flow model
Parameters
----------
site : Site
Site object
windTurbines : WindTurbines
WindTurbines object representing the wake generating wind turbines
wake_deficitModel : DeficitModel
Model describing the wake(downstream) deficit
rotorAvgModel : RotorAvgModel, optional
Model defining one or more points at the down stream rotors to
calculate the rotor average wind speeds from.
Default is RotorCenter, i.e. one point at rotor center
superpositionModel : SuperpositionModel
Model defining how deficits sum up
deflectionModel : DeflectionModel
Model describing the deflection of the wake due to yaw misalignment, sheared inflow, etc.
turbulenceModel : TurbulenceModel
Model describing the amount of added turbulence in the wake
"""
EngineeringWindFarmModel.__init__(self, site, windTurbines, wake_deficitModel, rotorAvgModel, superpositionModel,
blockage_deficitModel=None, deflectionModel=deflectionModel, turbulenceModel=turbulenceModel)
def _calc_wt_interaction(self, localWind,
WS_eff_ilk, TI_eff_ilk,
x_i, y_i, h_i, D_i, yaw_ilk, tilt_ilk,
I, L, K, **kwargs):
"""
Additional suffixes:
- m: turbines and wind directions (il.flatten())
- n: from_turbines, to_turbines and wind directions (iil.flatten())
"""
lw = localWind
deficit_nk = []
uc_nk = []
sigma_sqr_nk = []
cw_nk = []
hcw_nk = []
dh_nk = []
def ilk2mk(x_ilk):
return np.broadcast_to(x_ilk.astype(float), (I, L, K)).reshape((I * L, K))
indices = np.arange(I * I * L).reshape((I, I, L))
TI_mk = ilk2mk(lw.TI_ilk)
WS_mk = ilk2mk(lw.WS_ilk)
WS_eff_mk = []
TI_eff_mk = []
yaw_mk = ilk2mk(yaw_ilk)
tilt_mk = ilk2mk(tilt_ilk)
ct_jlk = []
if self.turbulenceModel:
add_turb_nk = np.zeros((I * I * L, K))
i_wd_l = np.arange(L)
wd = mean_deg(lw.WD_ilk, (0, 2))
dw_order_indices_dl = self.site.distance.dw_order_indices(wd)
# Iterate over turbines in down wind order
for j in tqdm(range(I), disable=I <= 1 or not self.verbose, desc="Calculate flow interaction", unit="wt"):
i_wt_l = dw_order_indices_dl[:, j]
# current wt (j'th most upstream wts for all wdirs)
m = i_wt_l * L + i_wd_l
# generate indexes of up wind(n_uw) and down wind(n_dw) turbines
n_uw = indices[:, i_wt_l, i_wd_l][dw_order_indices_dl[:, :j].T, np.arange(L)]
n_dw = indices[i_wt_l, :, i_wd_l][np.arange(L), dw_order_indices_dl[:, j + 1:].T]
# Calculate effectiv wind speed at current turbines(all wind directions and wind speeds) and
# look up power and thrust coefficient
if j == 0: # Most upstream turbines (no wake)
WS_eff_lk = WS_mk[m]
WS_eff_mk.append(WS_eff_lk)
if self.turbulenceModel:
TI_eff_mk.append(TI_mk[m])
else: # 2..n most upstream turbines (wake)
if isinstance(self.superpositionModel, WeightedSum):
deficit2WT = np.array([d_nk2[i] for d_nk2, i in zip(deficit_nk, range(j)[::-1])])
uc2WT = np.array([d_nk2[i] for d_nk2, i in zip(uc_nk, range(j)[::-1])])
sigmasqr2WT = np.array([d_nk2[i] for d_nk2, i in zip(sigma_sqr_nk, range(j)[::-1])])
cw2WT = np.array([d_nk2[i] for d_nk2, i in zip(cw_nk, range(j)[::-1])])
hcw2WT = np.array([d_nk2[i] for d_nk2, i in zip(hcw_nk, range(j)[::-1])])
dh2WT = np.array([d_nk2[i] for d_nk2, i in zip(dh_nk, range(j)[::-1])])
WS_eff_lk = WS_mk[m] - self.superpositionModel(WS_mk[m],
deficit2WT, uc2WT, sigmasqr2WT, cw2WT, hcw2WT, dh2WT)
else:
deficit2WT = np.array([d_nk2[i] for d_nk2, i in zip(deficit_nk, range(j)[::-1])])
WS_eff_lk = WS_mk[m] - self.superpositionModel(deficit2WT)
WS_eff_mk.append(WS_eff_lk)
if self.turbulenceModel:
TI_eff_mk.append(self.turbulenceModel.calc_effective_TI(TI_mk[m], add_turb_nk[n_uw]))
# Calculate Power/CT
def mask(k, v):
if v is None or isinstance(v, (int, float)) or len(np.asarray(v).shape) == 0:
return v
v = np.asarray(v)
if len(v.shape) == 1 and len(v) == I:
return v[i_wt_l]
elif v.shape[:2] == (I, L):
return v[i_wt_l, i_wd_l]
# elif v.shape == (L,):
# return v[i_wd_l]
# else:
# valid_shapes = f"(), ({I}), ({I},{L}), ({I},{L},{K}), ({L}), ({L},{K})"
# raise ValueError(
# f"Argument, {k}(shape={v.shape}), has unsupported shape. Valid shapes are {valid_shapes}")
keys = self.windTurbines.powerCtFunction.required_inputs + self.windTurbines.powerCtFunction.optional_inputs
_kwargs = {k: mask(k, v) for k, v in kwargs.items() if k in keys}
if 'TI_eff' in _kwargs:
_kwargs['TI_eff'] = TI_eff_mk[-1]
ct_lk = self.windTurbines.ct(WS_eff_lk, **_kwargs)
ct_jlk.append(ct_lk)
if j < I - 1:
# Calculate required args4deficit parameters
arg_funcs = {'WS_ilk': lambda: WS_mk[m][na],
'WS_eff_ilk': lambda: WS_eff_mk[-1][na],
'TI_ilk': lambda: TI_mk[m][na],
'TI_eff_ilk': lambda: TI_eff_mk[-1][na],
'D_src_il': lambda: D_i[i_wt_l][na],
'yaw_ilk': lambda: yaw_mk[m][na],
'tilt_ilk': lambda: tilt_mk[m][na],
'D_dst_ijl': lambda: D_i[dw_order_indices_dl[:, j + 1:]].T[na],
'h_il': lambda: h_i[i_wt_l][na],
'ct_ilk': lambda: ct_lk[na],
'wake_radius_ijlk': lambda: wake_radius_ijlk
}
i_dw = dw_order_indices_dl[:, j + 1:]
dw_jl, hcw_jl, dh_jl = self.site.distance(
wd_l=lw.wd.values, WD_il=wd, src_idx=i_wt_l, dst_idx=i_dw.T)
if self.wec != 1:
hcw_jl = hcw_jl / self.wec
if self.deflectionModel:
dw_ijlk, hcw_ijlk, dh_ijlk = self.deflectionModel.calc_deflection(
dw_ijl=dw_jl[na], hcw_ijl=hcw_jl[na], dh_ijl=dh_jl[na],
** {k: arg_funcs[k]() for k in self.deflectionModel.args4deflection})
else:
dw_ijlk, hcw_ijlk, dh_ijlk = [v[na, :, :, na] for v in [dw_jl, hcw_jl, dh_jl]]
# sqrt(a**2+b**2) as hypot does not support complex numbers
cw_ijlk = np.sqrt(dh_ijlk**2 + hcw_ijlk**2)
arg_funcs.update(
{'hcw_ijlk': lambda: hcw_ijlk, 'cw_ijlk': lambda: cw_ijlk, 'dh_ijlk': lambda: dh_ijlk})
args = {k: arg_funcs[k]() for k in self.args4deficit if k != "dw_ijlk"}
hcw_nk.append(hcw_ijlk[0])
dh_nk.append(dh_ijlk[0])
cw_nk.append(cw_ijlk[0])
# Calculate deficit
if isinstance(self.superpositionModel, WeightedSum):
deficit, uc, sigma_sqr, blockage = self._calc_deficit_convection(dw_ijlk=dw_ijlk, **args)
deficit += blockage
uc_nk.append(uc[0])
sigma_sqr_nk.append(sigma_sqr[0])
else:
deficit, _ = self._calc_deficit(dw_ijlk=dw_ijlk, **args)
deficit_nk.append(deficit[0])
if self.turbulenceModel:
if 'wake_radius_ijlk' in self.args4addturb:
wake_radius_ijlk = self.wake_deficitModel.wake_radius(dw_ijlk=dw_ijlk, **args)
arg_funcs['wake_radius_ijlk'] = lambda: wake_radius_ijlk
turb_args = {k: arg_funcs[k]() for k in self.args4addturb if k != "dw_ijlk"}
# Calculate added turbulence
add_turb_nk[n_dw] = self.turbulenceModel.rotorAvgModel(
self.turbulenceModel.calc_added_turbulence, dw_ijlk=dw_ijlk, **turb_args)
WS_eff_jlk, ct_jlk = np.array(WS_eff_mk), np.array(ct_jlk)
dw_inv_indices = (np.argsort(dw_order_indices_dl, 1).T * L + np.arange(L)[na]).flatten()
WS_eff_ilk = WS_eff_jlk.reshape((I * L, K))[dw_inv_indices].reshape((I, L, K))
ct_ilk = ct_jlk.reshape((I * L, K))[dw_inv_indices].reshape((I, L, K))
if self.turbulenceModel:
TI_eff_ilk = np.reshape(TI_eff_mk, (I * L, K))[dw_inv_indices].reshape((I, L, K))
return WS_eff_ilk, TI_eff_ilk, ct_ilk
class All2AllIterative(EngineeringWindFarmModel):
"""Wake and blockage deficits calculated from all wt to all points of interest (wt/map points).
The calculations are iteratively repeated until convergence (change of effective wind speed < convergence_tolerance)"""
def __init__(self, site, windTurbines, wake_deficitModel,
rotorAvgModel=RotorCenter(), superpositionModel=LinearSum(),
blockage_deficitModel=None, deflectionModel=None, turbulenceModel=None,
convergence_tolerance=1e-6):
"""Initialize flow model
Parameters
----------
site : Site
Site object
windTurbines : WindTurbines
WindTurbines object representing the wake generating wind turbines
wake_deficitModel : DeficitModel
Model describing the wake(downstream) deficit
rotorAvgModel : RotorAvgModel
Model defining one or more points at the down stream rotors to
calculate the rotor average wind speeds from.\n
Defaults to RotorCenter that uses the rotor center wind speed (i.e. one point) only
superpositionModel : SuperpositionModel
Model defining how deficits sum up
blockage_deficitModel : DeficitModel
Model describing the blockage(upstream) deficit
deflectionModel : DeflectionModel
Model describing the deflection of the wake due to yaw misalignment, sheared inflow, etc.
turbulenceModel : TurbulenceModel
Model describing the amount of added turbulence in the wake
convergence_tolerance : float
maximum accepted change in WS_eff_ilk [m/s]
"""
EngineeringWindFarmModel.__init__(self, site, windTurbines, wake_deficitModel, rotorAvgModel, superpositionModel,
blockage_deficitModel=blockage_deficitModel, deflectionModel=deflectionModel,
turbulenceModel=turbulenceModel)
self.convergence_tolerance = convergence_tolerance
def _calc_wt_interaction(self, localWind,
WS_eff_ilk, TI_eff_ilk,
x_i, y_i, h_i, D_i, yaw_ilk, tilt_ilk,
I, L, K, **kwargs):
# calculate WS_eff without blockage as a first guess
WS_eff_ilk = PropagateDownwind._calc_wt_interaction(self, localWind, WS_eff_ilk, TI_eff_ilk, x_i, y_i, h_i, D_i,
yaw_ilk, tilt_ilk, I, L, K, **kwargs)[0]
lw = localWind
WS_eff_ilk_last = WS_eff_ilk.copy()
diff_lk = np.zeros((L, K))
diff_lk_last, diff_lk_lastlast = None, None
dw_iil, hcw_iil, dh_iil = self.site.distance(wd_l=lw.wd.values, WD_il=mean_deg(lw.WD_ilk, 2))
ct_ilk = self.windTurbines.ct(lw.WS.ilk((I, L, K)), **kwargs)
ct_ilk_idle = self.windTurbines.ct(0.1 * np.ones_like(lw.WS.ilk((I, L, K))), **kwargs)
unstable_lk = np.zeros((L, K), dtype=bool)
ioff = ct_ilk < -1 # index of off/idling turbines
D_src_il = D_i[:, na]
args = {'WS_ilk': lw.WS.ilk((I, L, K)),
'WS_eff_ilk': WS_eff_ilk,
'TI_ilk': lw.TI.ilk(),
'TI_eff_ilk': lw.TI.ilk(),
'yaw_ilk': yaw_ilk,
'tilt_ilk': tilt_ilk,
'D_src_il': D_src_il,
'D_dst_ijl': D_src_il[na],
'dw_ijlk': dw_iil[..., na],
'hcw_ijlk': hcw_iil[..., na],
'cw_ijlk': np.sqrt(hcw_iil**2 + dh_iil**2)[..., na],
'dh_ijlk': dh_iil[..., na],
'h_il': h_i[:, na]
}
if not self.deflectionModel:
self._init_deficit(**args)
# Iterate until convergence
for j in tqdm(range(I), disable=I <= 1 or not self.verbose,
desc="Calculate flow interaction", unit="Iteration"):
ct_ilk = self.windTurbines.ct(np.maximum(WS_eff_ilk, 0), **kwargs)
ioff |= (unstable_lk)[na] & (ct_ilk <= ct_ilk_idle)
args['ct_ilk'] = ct_ilk
args['WS_eff_ilk'] = WS_eff_ilk
if self.deflectionModel:
dw_ijlk, hcw_ijlk, dh_ijlk = self.deflectionModel.calc_deflection(
dw_ijl=dw_iil, hcw_ijl=hcw_iil, dh_ijl=dh_iil, **args)
args.update({'dw_ijlk': dw_ijlk, 'hcw_ijlk': hcw_ijlk, 'dh_ijlk': dh_ijlk,
'cw_ijlk': np.hypot(dh_iil[..., na], hcw_ijlk)})
self._reset_deficit()
if self.turbulenceModel:
args['TI_eff_ilk'] = TI_eff_ilk
if 'wake_radius_ijlk' in self.turbulenceModel.args4addturb:
args['wake_radius_ijlk'] = self.wake_deficitModel.wake_radius(**args)
# Calculate deficit
if isinstance(self.superpositionModel, WeightedSum):
deficit_iilk, uc_iilk, sigmasqr_iilk, blockage_iilk = self._calc_deficit_convection(**args)
else:
deficit_iilk, blockage_iilk = self._calc_deficit(**args)
# Calculate effective wind speed
if isinstance(self.superpositionModel, WeightedSum):
WS_eff_ilk = lw.WS_ilk - self.superpositionModel(lw.WS_ilk, deficit_iilk,
uc_iilk, sigmasqr_iilk,
args['cw_ijlk'],
args['hcw_ijlk'],
dh_iil[..., na])
# Add blockage as linear effect
if self.blockage_deficitModel:
WS_eff_ilk -= (self.blockage_deficitModel.superpositionModel or LinearSum())(blockage_iilk)
else:
WS_eff_ilk = lw.WS_ilk.astype(float) - self.superpositionModel(deficit_iilk)
if self.blockage_deficitModel:
WS_eff_ilk -= (self.blockage_deficitModel.superpositionModel or self.superpositionModel)(blockage_iilk)
# ensure idling wt in unstable flow cases do not cutin even if ws increases due to speedup
# this helps to converge
WS_eff_ilk[ioff] = np.minimum(WS_eff_ilk[ioff], WS_eff_ilk_last[ioff])
if self.turbulenceModel:
add_turb_ijlk = self.turbulenceModel.rotorAvgModel(
self.turbulenceModel.calc_added_turbulence, **args)
TI_eff_ilk = self.turbulenceModel.calc_effective_TI(
lw.TI_ilk, add_turb_ijlk)
# Check if converged
diff_ilk = np.abs(WS_eff_ilk_last - WS_eff_ilk)
diff_lk = diff_ilk.max(0)
max_diff = np.max(diff_lk)
if (self.convergence_tolerance and max_diff < self.convergence_tolerance):
break
# i_, l_, k_ = list(zip(*np.where(diff_ilk == max_diff)))[0]
# print("Iteration: %d, max diff_ilk: %.8f, WT: %d, WD: %d, WS: %f, WS_eff: %f" %
# (j, max_diff, i_, lw.wd[l_], lw.ws[k_], WS_eff_ilk[i_, l_, k_]))
# assume flow case to be unstable if slope of improvement of two iterations is lower than
# needed to converge within next 20 iteration
if j > 1:
unstable_lk |= (diff_lk_lastlast - diff_lk) / 2 <= (diff_lk -
self.convergence_tolerance) / min(20, (I - j))
WS_eff_ilk_last = WS_eff_ilk.copy()
diff_lk_lastlast = diff_lk_last
diff_lk_last = diff_lk
# print("All2AllIterative converge after %d iterations" % j)
self._reset_deficit()
return WS_eff_ilk, TI_eff_ilk, ct_ilk
def main():
if __name__ == '__main__':
from py_wake.examples.data.iea37 import IEA37Site, IEA37_WindTurbines
from py_wake.deficit_models.selfsimilarity import SelfSimilarityDeficit
from py_wake.deficit_models.gaussian import ZongGaussianDeficit
from py_wake.turbulence_models.stf import STF2017TurbulenceModel
from py_wake.flow_map import XYGrid
import matplotlib.pyplot as plt
site = IEA37Site(16)
x, y = site.initial_position.T
windTurbines = IEA37_WindTurbines()
from py_wake.deficit_models.noj import NOJDeficit
from py_wake.superposition_models import SquaredSum
# NOJ wake model
noj = PropagateDownwind(site, windTurbines, wake_deficitModel=NOJDeficit(), superpositionModel=SquaredSum())
# NOJ wake and selfsimilarity blockage
noj_ss = All2AllIterative(site, windTurbines, wake_deficitModel=NOJDeficit(), superpositionModel=SquaredSum(),
blockage_deficitModel=SelfSimilarityDeficit())
# Zong convection superposition
zongp_ss = PropagateDownwind(site, windTurbines, wake_deficitModel=ZongGaussianDeficit(), superpositionModel=WeightedSum(),
turbulenceModel=STF2017TurbulenceModel())
# Zong convection superposition
zong_ss = All2AllIterative(site, windTurbines, wake_deficitModel=ZongGaussianDeficit(), superpositionModel=WeightedSum(),
blockage_deficitModel=SelfSimilarityDeficit(), turbulenceModel=STF2017TurbulenceModel())
for wm in [noj, noj_ss, zongp_ss, zong_ss]:
sim = wm(x=x, y=y, wd=[30], ws=[9])
plt.figure()
sim.flow_map(XYGrid(resolution=200)).plot_wake_map()
plt.title(' AEP: %.3f GWh' % sim.aep().sum())
plt.show()
main()