03: Simplified Floating

In this example, we run Ard on a simplified floating platform problem.

We follow Example 02 closely, so descriptions are more sparse.

from pathlib import Path  # optional, for nice path specifications

import pprint as pp  # optional, for nice printing
import numpy as np  # numerics library
import matplotlib.pyplot as plt  # plotting capabilities

import windIO

import ard  # technically we only really need this
from ard.utils.io import load_yaml  # we grab a yaml loader here
from ard.api import set_up_ard_model  # the secret sauce
from ard.viz.layout import plot_layout  # a plotting tool!

import openmdao.api as om  # for N2 diagrams from the OpenMDAO backend

# import optiwindnet.plotting

%matplotlib inline

# load input
path_inputs = Path.cwd().absolute() / "inputs"
input_dict = load_yaml(path_inputs / "ard_system.yaml")

# set up system
prob = set_up_ard_model(input_dict=input_dict, root_data_path=path_inputs)

Adding top_level
Adding layout2aep
Adding layout to layout2aep
Adding aepFLORIS to layout2aep
	Activating approximate totals on layout2aep
Adding landuse
Adding collection
Adding mooring_design
Adding mooring_constraint
Adding spacing_constraint
Adding tcc
Adding orbit
Adding opex
Adding financese

Some new components are added to the Ard model here, comparing to Example 02:

• mooring_design: designs the mooring system, here simply by doing straight-line mooring lines to the constant-valued seafloor

• mooring_constraint: a module to compute a constraint function to make sure the moorings don't violate regulatory requirements on proximity

# visualize model
if False:
    om.n2(prob)

# run the model
prob.run_model()

# collapse the test result data
test_data = {
    "AEP_val": float(prob.get_val("AEP_farm", units="GW*h")[0]),
    "CapEx_val": float(prob.get_val("tcc.tcc", units="MUSD")[0]),
    "BOS_val": float(prob.get_val("orbit.total_capex", units="MUSD")[0]),
    "OpEx_val": float(prob.get_val("opex.opex", units="MUSD/yr")[0]),
    "LCOE_val": float(prob.get_val("financese.lcoe", units="USD/MW/h")[0]),
    "area_tight": float(prob.get_val("landuse.area_tight", units="km**2")[0]),
    "coll_length": float(prob.get_val("collection.total_length_cables", units="km")[0]),
    "mooring_spacing": float(
        np.min(prob.get_val("mooring_constraint.mooring_spacing", units="km"))
    ),
    "turbine_spacing": float(
        np.min(prob.get_val("spacing_constraint.turbine_spacing", units="km"))
    ),
}

print("\n\nRESULTS:\n")
pp.pprint(test_data)
print("\n\n")

RuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:328
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:163
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_velocity/gauss.py:80
invalid value encountered in divide

ORBIT library intialized at '/opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/library'


RESULTS:

{'AEP_val': 409.5573528371712,
 'BOS_val': 992.9941014540512,
 'CapEx_val': 118.75948972475001,
 'LCOE_val': 226.41888540401234,
 'OpEx_val': 9.350000000000001,
 'area_tight': 13.2496,
 'coll_length': 21.89865877023397,
 'mooring_spacing': 0.042875983926893214,
 'turbine_spacing': 0.91}

optimize = True  # set to False to skip optimization
if optimize:
    # run the optimization
    prob.run_driver()
    prob.cleanup()

    prob.check_totals(compact_print=True, show_only_incorrect=True)

    # collapse the test result data
    test_data = {
        "spacing_primary": float(prob.get_val("spacing_primary")[0]),
        "spacing_secondary": float(prob.get_val("spacing_secondary")[0]),
        "angle_orientation": float(prob.get_val("angle_orientation")[0]),
        "angle_skew": float(prob.get_val("angle_skew")[0]),
        "AEP_val": float(prob.get_val("AEP_farm", units="GW*h")[0]),
        "CapEx_val": float(prob.get_val("tcc.tcc", units="MUSD")[0]),
        "BOS_val": float(prob.get_val("orbit.total_capex", units="MUSD")[0]),
        "OpEx_val": float(prob.get_val("opex.opex", units="MUSD/yr")[0]),
        "LCOE_val": float(prob.get_val("financese.lcoe", units="USD/MW/h")[0]),
        "area_tight": float(prob.get_val("landuse.area_tight", units="km**2")[0]),
        "coll_length": float(
            prob.get_val("collection.total_length_cables", units="km")[0]
        ),
        "mooring_spacing": float(
            np.min(prob.get_val("mooring_constraint.mooring_spacing", units="km"))
        ),
        "turbine_spacing": float(
            np.min(prob.get_val("spacing_constraint.turbine_spacing", units="km"))
        ),
    }

    # clean up the recorder
    prob.cleanup()

    # print the results
    print("\n\nRESULTS (opt):\n")
    pp.pprint(test_data)
    print("\n\n")

    # plot convergence
    ## read cases
    cr = om.CaseReader(
        prob.get_outputs_dir() / input_dict["analysis_options"]["recorder"]["filepath"]
    )

    # Extract the driver cases
    cases = cr.get_cases("driver")

    # Initialize lists to store iteration data
    iterations = []
    objective_values = []

    # Loop through the cases and extract iteration number and objective value
    for i, case in enumerate(cases):
        iterations.append(i)
        objective_values.append(
            case.get_objectives()[input_dict["analysis_options"]["objective"]["name"]]
        )

    # Plot the convergence
    plt.figure(figsize=(8, 6))
    plt.plot(iterations, objective_values, marker="o", label="Objective (LCOE)")
    plt.xlabel("Iteration")
    plt.ylabel("Objective Value (Total Cable Length (m))")
    plt.title("Convergence Plot")
    plt.legend()
    plt.grid()
    plt.show()

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|0
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([0.]),
 'angle_skew': array([0.]),
 'spacing_primary': array([7.]),
 'spacing_secondary': array([7.])}

RuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:328
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:163
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_velocity/gauss.py:80
invalid value encountered in divide

Objectives
{'collection.total_length_cables': array([21898.65877023])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|1
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([0.]),
 'angle_skew': array([0.]),
 'spacing_primary': array([7.]),
 'spacing_secondary': array([7.])}

RuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:328
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_deflection/gauss.py:163
invalid value encountered in divideRuntimeWarning: /opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/floris/core/wake_velocity/gauss.py:80
invalid value encountered in divide

Objectives
{'collection.total_length_cables': array([21898.65877023])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|2
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.00152482]),
 'angle_skew': array([-0.00212941]),
 'spacing_primary': array([6.98214515]),
 'spacing_secondary': array([6.97888724])}

Objectives
{'collection.total_length_cables': array([21837.48886431])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|3
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.0134454]),
 'angle_skew': array([-0.01591441]),
 'spacing_primary': array([6.89286615]),
 'spacing_secondary': array([6.87331762])}

Objectives
{'collection.total_length_cables': array([21531.61465702])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|4
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.04631602]),
 'angle_skew': array([-0.05811006]),
 'spacing_primary': array([6.6109433]),
 'spacing_secondary': array([6.55384981])}

Objectives
{'collection.total_length_cables': array([20589.26912816])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|5
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.04987987]),
 'angle_skew': array([-0.06064898]),
 'spacing_primary': array([6.5793372]),
 'spacing_secondary': array([6.55384493])}

Objectives
{'collection.total_length_cables': array([20544.11186061])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|6
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05358642]),
 'angle_skew': array([-0.05709423]),
 'spacing_primary': array([6.55384935]),
 'spacing_secondary': array([6.55384477])}

Objectives
{'collection.total_length_cables': array([20507.71138641])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|7
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05368697]),
 'angle_skew': array([-0.05724457]),
 'spacing_primary': array([6.55384638]),
 'spacing_secondary': array([6.55384294])}

Objectives
{'collection.total_length_cables': array([20507.70364551])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|8
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|9
--------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05357226]),
 'angle_skew': array([-0.05721647]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384302])}

Objectives
{'collection.total_length_cables': array([20507.70374865])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|10
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05371663]),
 'angle_skew': array([-0.05724821]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.5538429])}

Objectives
{'collection.total_length_cables': array([20507.70326917])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|11
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373107]),
 'angle_skew': array([-0.05725139]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70322122])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|12
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373251]),
 'angle_skew': array([-0.05725171]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321642])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|13
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373266]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321594])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|14
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.7032159])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|15
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|16
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|17
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|18
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|19
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|20
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05349895]),
 'angle_skew': array([-0.05722202]),
 'spacing_primary': array([6.55384629]),
 'spacing_secondary': array([6.55384294])}

Objectives
{'collection.total_length_cables': array([20507.70384224])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|21
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.0537093]),
 'angle_skew': array([-0.05724877]),
 'spacing_primary': array([6.55384621]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70327853])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|22
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373034]),
 'angle_skew': array([-0.05725144]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70322215])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|23
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373244]),
 'angle_skew': array([-0.05725171]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321652])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|24
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373265]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321595])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|25
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.7032159])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|26
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|27
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|28
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|29
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|30
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373267]),
 'angle_skew': array([-0.05725174]),
 'spacing_primary': array([6.5538462]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20507.70321589])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|31
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05406678]),
 'angle_skew': array([-0.05730734]),
 'spacing_primary': array([10.]),
 'spacing_secondary': array([6.55384341])}

Objectives
{'collection.total_length_cables': array([23191.5650973])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|32
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05390075]),
 'angle_skew': array([-0.05727971]),
 'spacing_primary': array([8.28745408]),
 'spacing_secondary': array([6.55384315])}

Objectives
{'collection.total_length_cables': array([21857.39719147])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|33
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05381768]),
 'angle_skew': array([-0.05726589]),
 'spacing_primary': array([7.43071191]),
 'spacing_secondary': array([6.55384302])}

Objectives
{'collection.total_length_cables': array([21190.23334482])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|34
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05377544]),
 'angle_skew': array([-0.05725886]),
 'spacing_primary': array([6.99496225]),
 'spacing_secondary': array([6.55384296])}

Objectives
{'collection.total_length_cables': array([20851.01098058])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|35
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05375427]),
 'angle_skew': array([-0.05725533]),
 'spacing_primary': array([6.77660775]),
 'spacing_secondary': array([6.55384292])}

Objectives
{'collection.total_length_cables': array([20681.05926522])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|36
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05374362]),
 'angle_skew': array([-0.05725356]),
 'spacing_primary': array([6.66676683]),
 'spacing_secondary': array([6.55384291])}

Objectives
{'collection.total_length_cables': array([20595.57614555])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|37
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373824]),
 'angle_skew': array([-0.05725267]),
 'spacing_primary': array([6.61126178]),
 'spacing_secondary': array([6.5538429])}

Objectives
{'collection.total_length_cables': array([20552.38213878])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|38
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373551]),
 'angle_skew': array([-0.05725221]),
 'spacing_primary': array([6.58309845]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20530.46610812])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|39
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373412]),
 'angle_skew': array([-0.05725198]),
 'spacing_primary': array([6.56876448]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20519.31192873])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|40
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373341]),
 'angle_skew': array([-0.05725186]),
 'spacing_primary': array([6.56146586]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20513.63245308])}

Driver debug print for iter coord: rank0:ScipyOptimize_SLSQP|41
---------------------------------------------------------------
Design Vars
{'angle_orientation': array([-0.05373305]),
 'angle_skew': array([-0.0572518]),
 'spacing_primary': array([6.55774182]),
 'spacing_secondary': array([6.55384289])}

Objectives
{'collection.total_length_cables': array([20510.73457342])}

Iteration limit reached    (Exit mode 9)
            Current function value: 1.025536728670826
            Iterations: 10
            Function evaluations: 41
            Gradient evaluations: 11
Optimization FAILED.
Iteration limit reached
-----------------------------------

-----------------
Total Derivatives
-----------------

+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| 'of' variable                      | 'wrt' variable    | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc        |
+====================================+===================+=====================+===================+========================+===================+
| AEP_farm                           | angle_orientation |        7.104786e+15 |     -1.366993e+10 |           7.104799e+15 |  7.104799e+15>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| AEP_farm                           | angle_skew        |        2.191600e+15 |      7.156147e+07 |           2.191600e+15 |  2.191600e+15>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| AEP_farm                           | spacing_primary   |        1.156144e+10 |     -1.763543e+10 |           2.919685e+10 |  2.919685e+10>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| AEP_farm                           | spacing_secondary |       -1.176875e+09 |     -3.018025e+10 |           2.900334e+10 |  2.900334e+10>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| collection.total_length_cables     | angle_orientation |        1.335683e+00 |      1.550476e+00 |           2.147911e-01 |  2.147911e-01>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| collection.total_length_cables     | angle_skew        |        1.958553e+00 |      1.689594e+00 |           2.689571e-01 |  2.689571e-01>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| spacing_constraint.turbine_spacing | angle_orientation |       -4.494811e-04 |      9.313226e-10 |           4.494820e-04 |  4.494820e-04>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| spacing_constraint.turbine_spacing | angle_skew        |        1.347451e-04 |     -5.943468e-05 |           1.941797e-04 |  1.941797e-04>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| spacing_constraint.turbine_spacing | spacing_primary   |        7.304162e-15 |     -4.656613e-10 |           4.656681e-10 |  4.656681e-10>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+
| spacing_constraint.turbine_spacing | spacing_secondary |       -3.409816e-16 |      2.328306e-10 |           2.328308e-10 |  2.328308e-10>TOL |
+------------------------------------+-------------------+---------------------+-------------------+------------------------+-------------------+


RESULTS (opt):

{'AEP_val': 405.466307721131,
 'BOS_val': 992.4519249216308,
 'CapEx_val': 118.75948972475001,
 'LCOE_val': 228.60310297897527,
 'OpEx_val': 9.350000000000001,
 'angle_orientation': -0.053733050029812865,
 'angle_skew': -0.057251803446950855,
 'area_tight': 11.621361959921153,
 'coll_length': 20.510734573416517,
 'mooring_spacing': -0.0010986122876681097,
 'spacing_primary': 6.5577418219826615,
 'spacing_secondary': 6.553842890097031,
 'turbine_spacing': 0.8520000010588968}

plot_layout(prob, input_dict=input_dict, show_image=True, include_cable_routing=True)

<Axes: >