Cables

Try this yourself (requires google account)

TOPFARM can use the Electrical Network Design package EDWIN to optimize the carray cabels as well as the substation position at each iteration of the layout optimization

Install TOPFARM if needed

# Install TopFarm if needed
import importlib
if not importlib.util.find_spec("topfarm"):
    !pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/TopFarm2.git

# Install EDWIN if needed
import importlib
if not importlib.util.find_spec("ed_win"):
    !pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/edwin.git#egg=ed_win[interarray]

DEPRECATION: git+https://gitlab.windenergy.dtu.dk/TOPFARM/edwin.git#egg=ed_win[interarray] contains an egg fragment with a non-PEP 508 name pip 25.0 will enforce this behaviour change. A possible replacement is to use the req @ url syntax, and remove the egg fragment. Discussion can be found at https://github.com/pypa/pip/issues/11617
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WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager, possibly rendering your system unusable.It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv. Use the --root-user-action option if you know what you are doing and want to suppress this warning.

Import

import numpy as np
from scipy.interpolate import RegularGridInterpolator
import matplotlib.pyplot as plt

from topfarm.constraint_components.spacing import SpacingConstraint
from topfarm.constraint_components.boundary import XYBoundaryConstraint
from topfarm.easy_drivers import EasyScipyOptimizeDriver
from topfarm.cost_models.cost_model_wrappers import CostModelComponent
from topfarm._topfarm import TopFarmProblem, TopFarmGroup
from topfarm.cost_models.py_wake_wrapper import PyWakeAEPCostModelComponent
from topfarm.plotting import XYPlotComp
from topfarm.utils import plot_list_recorder
from topfarm.cost_models.economic_models.dtu_wind_cm_main import economic_evaluation

from py_wake.examples.data.iea37._iea37 import IEA37_WindTurbines
from py_wake import BastankhahGaussian
from py_wake.examples.data.hornsrev1 import Hornsrev1Site

from ed_win.wind_farm_network import WindFarmNetwork

Site

n_wt = 30
initial = np.asarray([np.random.random(30)*6000, np.random.random(30)*-10000]).T
x_init = initial[:,0]
y_init = initial[:,1]
boundary = np.array([(0, 0), (6000, 0), (6000, -10000), (0, -10000)])  # turbine boundaries
drivers = [EasyScipyOptimizeDriver(maxiter=10)]
windTurbines = IEA37_WindTurbines()
site = Hornsrev1Site()
wfm = BastankhahGaussian(site, windTurbines)

/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')

Bathymetry

sigma = 3000.0
mu = 0.0

x_peak_1 = 1000
y_peak_1 = -1000
x_peak_2 = 4000
y_peak_2 = -8000
x1, y1 = np.meshgrid(np.linspace(0 - x_peak_1, 6000- x_peak_1, 100), np.linspace(-10000 - y_peak_1, 0 - y_peak_1, 100))
d1 = np.sqrt(x1*x1 + y1*y1)
g1 = np.exp(-((d1 - mu)**2 / (2.0 * sigma**2)))
x2, y2 = np.meshgrid(np.linspace(0 - x_peak_2, 6000- x_peak_2, 100), np.linspace(-10000 - y_peak_2, 0 - y_peak_2, 100))
d2 = np.sqrt(x2*x2 + y2*y2)
g2 = np.exp(-((d2 - mu)**2 / (2.0 * sigma**2)))
g = 5 * g1 - 8 * g2 - 30

plt.imshow(g, extent=(-1000, 7000, -11000, 1000), origin='lower', cmap='viridis')
plt.colorbar()
plt.title('2D Gaussian Function')
plt.show()

x = np.linspace(-1000, 7000, 100)
y = np.linspace(-11000, 1000, 100)

f = RegularGridInterpolator((x, y), g)

Cables

x_ss_init = x_init.mean()
y_ss_init = y_init.mean()
turbines_pos=np.asarray([x_init, y_init]).T
substations_pos = np.asarray([[x_ss_init], [y_ss_init]]).T

cables = np.array([[500, 3, 100], [800, 5, 150], [1000, 10, 250]])  # Here you set up cables [<cable cross section>, <number of turbines can be connected>, <price in € per meter>]

wfn = WindFarmNetwork(turbines_pos=turbines_pos, substations_pos=substations_pos, cables=cables)
G = wfn.optimize(turbines_pos)
cable_cost_ref = G.size(weight="cost")  # euro
cable_length_ref = G.size(weight="length")  # m
cost_per_length_ref = cable_cost_ref / cable_length_ref # euro / m

G.plot()

Solving with heuristic(cpew)

<Axes: >

Economy

Drotor_vector = [windTurbines.diameter()] * n_wt
power_rated_vector = [float(windTurbines.power(20))*1e-6] * n_wt
hub_height_vector = [windTurbines.hub_height()] * n_wt

# add additional cost model inputs for shore distance, energy price, project lifetime, rated rotor speed and water depth
distance_from_shore = 30         # [km]
energy_price = 0.1               # [Euro/kWh] What we get per kWh
project_duration = 25            # [years]
rated_rpm_array = [12] * n_wt    # [rpm]
simres = wfm(x_init, y_init)
aep = simres.aep().values.sum()
CF = aep / (windTurbines.power(20)*1e-9 * 24*365*n_wt)

eco_eval = economic_evaluation(distance_from_shore, energy_price, project_duration)
npv_ref = eco_eval.calculate_npv(rated_rpm_array, Drotor_vector, power_rated_vector, hub_height_vector, 30, aep/n_wt * np.ones(n_wt)*10**6, cabling_cost=cable_cost_ref)

Python Functions

# Water Depth
def water_depth_func(x, y, **kwargs):
    xnew, ynew = np.meshgrid(x, y)
    points = np.array([xnew.flatten(), ynew.flatten()]).T
    return - np.diag(f(points).reshape(n_wt, n_wt).T)

# Cables
def cable_func(x, y, x_substation, y_substation, **kwargs):
    G = wfn.optimize(turbines_pos= np.asarray([x, y]).T, substations_pos=np.asarray([[float(x_substation[0])], [float(y_substation[0])]]).T)
    return G.size(weight="cost"), {'cabling_length': G.size(weight="length")}

# Economy
def npv_func(AEP, water_depth, cabling_cost, **kwargs):
    eco_eval.calculate_npv(rated_rpm_array, Drotor_vector, power_rated_vector, hub_height_vector, water_depth, AEP/n_wt * np.ones(n_wt)*10**6, cabling_cost=cabling_cost)
    eco_eval.calculate_irr(rated_rpm_array, Drotor_vector, power_rated_vector, hub_height_vector, water_depth, AEP/n_wt * np.ones(n_wt)*10**6, cabling_cost=cabling_cost)
    CAPEX = eco_eval.project_costs_sums["CAPEX"]
    OPEX = eco_eval.project_costs_sums["OPEX"]
    return eco_eval.NPV, {'irr': eco_eval.IRR,
                          'OPEX': OPEX,
                          'CAPEX': CAPEX,}

Components

# Water Depth
water_depth_component = CostModelComponent(input_keys=[('x', x_init),('y', y_init)],
                                          n_wt=n_wt,
                                          cost_function=water_depth_func,
                                          objective=False,
                                          output_keys=[('water_depth', np.zeros(n_wt))])

# Cables
cable_component = CostModelComponent(input_keys=[('x', x_init),('y', y_init), ('x_substation', x_ss_init), ('y_substation', y_ss_init)],
                                     n_wt=n_wt,
                                     cost_function=cable_func,
                                     objective=False,
                                     output_keys=[('cabling_cost', 0)],
                                     additional_output=[('cabling_length', 0)])

# Economy
npv_comp = CostModelComponent(input_keys=[('AEP', 0), ('water_depth', 30*np.ones(n_wt)), ('cabling_cost', 100000)],
                              n_wt=n_wt,
                              cost_function=npv_func,
                              objective=True,
                              maximize=True,
                              output_keys=[('npv', 0)],
                              additional_output=[('irr', 0),
                                                 ('CAPEX', 0),
                                                 ('OPEX', 0)])

# AEP
aep_comp = PyWakeAEPCostModelComponent(wfm, n_wt, objective=False)

Problem Assembly

cost_comp = TopFarmGroup([PyWakeAEPCostModelComponent(wfm, n_wt, objective=False), water_depth_component, cable_component, npv_comp])


tf = TopFarmProblem(
    design_vars=dict(zip('xy', initial.T), x_substation=x_ss_init, y_substation=y_ss_init),
    cost_comp=cost_comp,
    constraints=[XYBoundaryConstraint(boundary),
                 SpacingConstraint(500)
                 ],
    driver=drivers[0],
    plot_comp=XYPlotComp()
)

INFO: checking out_of_order...
INFO:     out_of_order check complete (0.000586 sec).
INFO: checking system...
INFO:     system check complete (0.000024 sec).
INFO: checking solvers...
INFO:     solvers check complete (0.000179 sec).
INFO: checking dup_inputs...
INFO:     dup_inputs check complete (0.000046 sec).
INFO: checking missing_recorders...
INFO:     missing_recorders check complete (0.000004 sec).
INFO: checking unserializable_options...
INFO:     unserializable_options check complete (0.000173 sec).
INFO: checking comp_has_no_outputs...
INFO:     comp_has_no_outputs check complete (0.000047 sec).
INFO: checking auto_ivc_warnings...
INFO:     auto_ivc_warnings check complete (0.000004 sec).

Optimize

cost, _, recorder = tf.optimize()

INFO: checking out_of_order...
INFO:     out_of_order check complete (0.000235 sec).
INFO: checking system...
INFO:     system check complete (0.000019 sec).
INFO: checking solvers...
INFO:     solvers check complete (0.000152 sec).
INFO: checking dup_inputs...
INFO:     dup_inputs check complete (0.000041 sec).
INFO: checking missing_recorders...
INFO:     missing_recorders check complete (0.000005 sec).
INFO: checking unserializable_options...
INFO:     unserializable_options check complete (0.000153 sec).
INFO: checking comp_has_no_outputs...
INFO:     comp_has_no_outputs check complete (0.000044 sec).
INFO: checking auto_ivc_warnings...
INFO:     auto_ivc_warnings check complete (0.000003 sec).
Solving with heuristic(cpew)

Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.
Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

Solving with heuristic(cpew)

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Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.
Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.

Iteration limit reached    (Exit mode 9)
            Current function value: -146791506.4463278
            Iterations: 10
            Function evaluations: 17
            Gradient evaluations: 10
Optimization FAILED.
Iteration limit reached
-----------------------------------

Plot

plot_list_recorder(recorder)

/builds/TOPFARM/TopFarm2/topfarm/utils.py:602: UserWarning: The figure layout has changed to tight
  plt.tight_layout()

x_opt = recorder['x'][-1]
y_opt = recorder['y'][-1]
x_sub_opt = recorder['x_substation'][-1]
y_sub_opt = recorder['y_substation'][-1]
G = wfn.optimize(np.asarray([x_opt, y_opt]).T,
                 substations_pos=np.asarray([[float(x_sub_opt)], [float(y_sub_opt)]]).T,
                 )
G.plot()

Solving with heuristic(cpew)

<Axes: >