Optimization of wind farm including neighbouring turbines
In Topfarm you have the option to include neighbouring wind turbines in your optimization. This means that the wakes from these turbines will be considered when calulating the optimal AEP, but their positions are not considered design variables. Note that the accuaracy of this is dependent on the distance to the neighbouring wind turbines and your wind farm models ability to predict long distance wakes.
[1]:
# Install TopFarm if needed
import importlib
if not importlib.util.find_spec("topfarm"):
!pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/TopFarm2.git
[2]:
import numpy as np
import matplotlib.pyplot as plt
import topfarm
from topfarm import TopFarmProblem
from topfarm.constraint_components.boundary import XYBoundaryConstraint
from topfarm.constraint_components.spacing import SpacingConstraint
from topfarm.cost_models.py_wake_wrapper import PyWakeAEPCostModelComponentAdditionalTurbines
from topfarm.easy_drivers import EasyScipyOptimizeDriver
from topfarm.plotting import XYPlotComp
from topfarm.cost_models.cost_model_wrappers import AEPCostModelComponent
from py_wake.deficit_models.gaussian import BastankhahGaussian
from py_wake.utils.gradients import autograd
from py_wake.validation.lillgrund import wt_x, wt_y, LillgrundSite, ct_curve, power_curve
from py_wake.wind_turbines import WindTurbine
from py_wake.wind_turbines.power_ct_functions import PowerCtTabular
[3]:
x2 = np.array([363089.20620581, 362841.19815026, 363024.53745529, 363202.56273871,
362627.89297065, 363352.67353534, 362882.00280241, 362774.92495544,
363488.38307778, 362491.87485306, 363244.96531305, 363181.03168444,
362454.34857131, 363640.1295227 , 362609.32998744, 362909.74450436,
363554.08869674, 362254.36079251, 363543.89240439, 362963.61115875,
362482.47585633, 363819.8209275 , 362305.36330315, 363189.81567612,
363439.03577114, 362141.72363739, 363833.70922823, 362638.81518275,
362677.64959042, 363857.74204276, 362047.26220207, 363541.54387668,
363172.26863347, 362183.59639605, 364044.33022603, 362278.14662334,
363005.25808714, 363734.05077116, 361897.72732477, 363893.16789162,
362796.78418716, 362387.86536213, 364121.72384201, 361953.11392421,
363413.71283633, 363453.74796523, 361900.61873674, 364175.02685267,
362371.77324208])
y2 = np.array([6154000. , 6153854.5244973 , 6154279.59164709,
6153735.79277733, 6154065.82049407, 6154224.34203495,
6153561.05630649, 6154433.36830217, 6153821.6432833 ,
6153790.2533259 , 6154523.47664532, 6153422.84246344,
6154316.21615621, 6154140.73067986, 6153444.31210837,
6154696.49543065, 6153533.01345979, 6153969.1654778 ,
6154541.2455867 , 6153213.05775872, 6154620.16688662,
6153889.69425372, 6153516.6898791 , 6154843.74971121,
6153233.82403924, 6154273.81356891, 6154385.19480965,
6153136.96734381, 6154896.21625677, 6153549.19482153,
6153748.86137406, 6154842.22515422, 6152997.6181212 ,
6154632.26883894, 6154086.52062451, 6153219.69765135,
6155077.84457572, 6153190.81616147, 6154102.15838379,
6154677.88258593, 6152882.94617467, 6154972.74316899,
6153692.58200013, 6153462.7553504 , 6155115.91934059,
6152885.37941837, 6154521.01729715, 6154362.27333719,
6152928.04241305])
wind_turbines = WindTurbine('SWT2p3_93_65', 92.6, 65, PowerCtTabular(ct_curve[:,0],power_curve[:,1], 'kW', ct_curve[:,1]))
n_wt = len(wt_x)
site = LillgrundSite()
wf_model = BastankhahGaussian(site, wind_turbines)
constraint_comp = XYBoundaryConstraint(np.asarray([wt_x, wt_y]).T)
cost_comp = PyWakeAEPCostModelComponentAdditionalTurbines(windFarmModel=wf_model,
n_wt=n_wt,
add_wt_x=x2,
add_wt_y=y2,
grad_method=autograd)
plot_comp = XYPlotComp()
problem = TopFarmProblem(design_vars={'x': wt_x, 'y': wt_y},
constraints=[constraint_comp, SpacingConstraint(min_spacing=wind_turbines.diameter() * 2)],
cost_comp=cost_comp,
driver=EasyScipyOptimizeDriver(optimizer='SLSQP', maxiter=5),
plot_comp=plot_comp)
cost, state, recorder = problem.optimize(disp=True)
plt.figure()
plt.plot(np.concatenate((wt_x, x2)), np.concatenate((wt_y, y2)), '2k')
INFO: checking out_of_order...
INFO: out_of_order check complete (0.000542 sec).
INFO: checking system...
INFO: system check complete (0.000019 sec).
INFO: checking solvers...
INFO: solvers check complete (0.000139 sec).
INFO: checking dup_inputs...
INFO: dup_inputs check complete (0.000031 sec).
INFO: checking missing_recorders...
INFO: missing_recorders check complete (0.000005 sec).
INFO: checking unserializable_options...
INFO: unserializable_options check complete (0.000152 sec).
INFO: checking comp_has_no_outputs...
INFO: comp_has_no_outputs check complete (0.000046 sec).
INFO: checking auto_ivc_warnings...
INFO: auto_ivc_warnings check complete (0.000004 sec).
INFO: checking out_of_order...
INFO: out_of_order check complete (0.000143 sec).
INFO: checking system...
INFO: system check complete (0.000015 sec).
INFO: checking solvers...
INFO: solvers check complete (0.000123 sec).
INFO: checking dup_inputs...
INFO: dup_inputs check complete (0.000033 sec).
INFO: checking missing_recorders...
INFO: missing_recorders check complete (0.000004 sec).
INFO: checking unserializable_options...
INFO: unserializable_options check complete (0.000134 sec).
INFO: checking comp_has_no_outputs...
INFO: comp_has_no_outputs check complete (0.000032 sec).
INFO: checking auto_ivc_warnings...
INFO: auto_ivc_warnings check complete (0.000004 sec).
/builds/TOPFARM/TopFarm2/.pixi/envs/default/lib/python3.11/site-packages/py_wake/deficit_models/gaussian.py:124: UserWarning: The BastankhahGaussian model is not representative of the setup used in the literature. For this, use py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014 instead
DeprecatedModel.__init__(self, 'py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014')
Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.
Iteration limit reached (Exit mode 9)
Current function value: -36307.44846200584
Iterations: 5
Function evaluations: 5
Gradient evaluations: 5
Optimization FAILED.
Iteration limit reached
-----------------------------------
Optimized in 96.437s
[3]:
[<matplotlib.lines.Line2D at 0x7fc9e0bb2c90>]
Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.
