Abstract

The wind farm layout optimization (WFLO) problem is a complex and nonconvex optimization problem. Even though many different heuristic algorithms and mathematical programming methods have been tested and discussed, there is no consensus about which algorithm is the most suitable approach for solving WFLO problems. Every algorithm presents its own advantages and disadvantages in solving different optimization problems; thus, multi-stage approaches may combine the advantages of multiple algorithms and offer superior performance. One multi-stage approach used for solving WFLO problems is to apply an algorithm in the first stage to produce an optimized layout which serves as the initial condition for a second-stage algorithm to perform further refinement. This paper presents a comparison between two types of multi-stage methods: the Heuristic-Gradient-based (H-G) model which consists of a heuristic algorithm in stage 1 and a gradient-based algorithm in stage 2 and the Discrete-Continuous (D-C) model which consists of a heuristic algorithm in the discrete scheme in stage 1 and an algorithm in the continuous scheme in stage 2. Annual energy production (AEP) is used as the objective function while the computational time associated with each approach is documented. Three scenarios are investigated in this paper with different complexity in the wind conditions. It was observed that the D-C models provide the optimal solutions with an average of 0.67% higher AEP and an average of 6.2% lower computational time in comparison with the H-G models. The results from this study provide a basis for selecting a proper optimization algorithm for solving WFLO problems which can lead to a significant increase in the overall annual energy production and a large reduction in computational time.

References

1.
Najafi
,
H.
,
2012
,
Evaluation of Alternative Cooling Techniques for Photovoltaic Panels
,
University of Alabama
,
Tuscaloosa, AL
.
2.
Global Wind Energy Council
,
2021
, Global Wind Report 2021, https://gwec.net/global-wind-report-2021/, Accessed February 2022.
3.
Chen
,
L.
, and
MacDonald
,
E.
,
2017
, “
Wind Farm Layout Sensitivity Analysis and Probabilistic Model of Landowner Decisions
,”
ASME J. Energy Resour. Technol.
,
139
(
3
), p.
031202
.
4.
Fawzy
,
D.
,
Moussa
,
S.
, and
Badr
,
N.
,
2018
, “
Trio-V Wind Analyzer: A Generic Integral System for Wind Farm Suitability Design and Power Prediction Using Big Data Analytics
,”
ASME J. Energy Resour. Technol.
,
140
(
5
), p.
051202
.
5.
Hasan
,
A. S.
,
Jackson
,
R. S.
, and
Amano
,
R. S.
,
2019
, “
Experimental Study of the Wake Regions in Wind Farms
,”
ASME J. Energy Resour. Technol.
,
141
(
5
), p.
051209
.
6.
Hasan
,
A. S.
,
Elgammal
,
T.
,
Jackson
,
R. S.
, and
Amano
,
R. S.
,
2020
, “
Comparative Study of the Inline Configuration Wind Farm
,”
ASME J. Energy Resour. Technol.
,
142
(
6
), p.
061302
.
7.
Okulov
,
V. L.
,
Mikkelsen
,
R.
,
Sørensen
,
J. N.
,
Naumov
,
I. V.
, and
Tsoy
,
M. A.
,
2017
, “
Power Properties of Two Interacting Wind Turbine Rotors
,”
ASME J. Energy Resour. Technol.
,
139
(
5
), p.
051210
.
8.
Al Sam
,
A.
,
Szasz
,
R.
, and
Revstedt
,
J.
,
2017
, “
An Investigation of Wind Farm Power Production for Various Atmospheric Boundary Layer Heights
,”
ASME J. Energy Resour. Technol.
,
139
(
5
), p.
051216
.
9.
Mosetti
,
G.
,
Poloni
,
C.
, and
Diviacco
,
B.
,
1994
, “
Optimization of Wind Turbine Positioning in Large Windfarms by Means of a Genetic Algorithm
,”
J. Wind Eng. Ind. Aerodyn.
,
51
(
1
), pp.
105
116
.
10.
Azlan
,
F.
,
Kurnia
,
J. C.
,
Tan
,
B. T.
, and
Ismadi
,
M. Z.
,
2021
, “
Review on Optimisation Methods of Wind Farm Array Under Three Classical Wind Condition Problems
,”
Renewable Sustainable Energy Rev.
,
135
, p.
110047
.
11.
DuPont
,
B.
,
Cagan
,
J.
, and
Moriarty
,
P.
,
2016
, “
An Advanced Modeling System for Optimization of Wind Farm Layout and Wind Turbine Sizing Using a Multi-Level Extended Pattern Search Algorithm
,”
Energy
,
106
, pp.
802
814
.
12.
Feng
,
J.
, and
Shen
,
W. Z.
,
2015
, “
Solving the Wind Farm Layout Optimization Problem Using Random Search Algorithm
,”
Renewable Energy
,
78
, pp.
182
192
.
13.
Robinson
,
T. D.
,
Eldred
,
M. S.
,
Willcox
,
K. E.
, and
Haimes
,
R.
,
2008
, “
Surrogate-Based Optimization Using Multifidelity Models With Variable Parameterization and Corrected Space Mapping
,”
AIAA J.
,
46
(
11
), pp.
2814
2822
.
14.
Saavedra-Moreno
,
B.
,
Salcedo-Sanz
,
S.
,
Paniagua-Tineo
,
A.
,
Prieto
,
L.
, and
Portilla-Figueras
,
A.
,
2011
, “
Seeding Evolutionary Algorithms With Heuristics for Optimal Wind Turbines Positioning in Wind Farms
,”
Renewable Energy
,
36
(
11
), pp.
2838
2844
.
15.
Réthoré
,
P. E.
,
Fuglsang
,
P.
,
Larsen
,
G. C.
,
Buhl
,
T.
,
Larsen
,
T. J.
, and
Madsen
,
H. A.
,
2014
, “
TOPFARM: Multi-Fidelity Optimization of Wind Farms
,”
Wind Energy
,
17
(
12
), pp.
1797
1816
.
16.
Gelotte
,
L.
, and
Nilsson
,
A. L.
,
2017
,
Optimal Placement of Floating Two-Turbine Foundations in Offshore Wind Farms, MS Thesis, KTH Industrial Engineering and Management, Energy Technology EGI-2017-0045-MSC EKV1191
.
17.
Mahulja
,
S.
,
Larsen
,
G. C.
, and
Elham
,
A.
,
2018
, “
Engineering an Optimal Wind Farm Using Surrogate Models
,”
Wind Energy
,
21
(
12
), pp.
1296
1308
.
18.
Nagpal
,
S. V.
,
Liu
,
M. V.
, and
Anderson
,
C. L.
,
2021
, “
A Comparison of Deterministic Refinement Techniques for Wind Farm Layout Optimization
,”
Renewable Energy
,
168
, pp.
581
592
.
19.
NREL
,
2020
, “FLORIS. Version 2.4,” GitHub Repository, GitHub, https://github. com/NREL/floris, Accessed August 2021.
20.
Yang
,
P.
, and
Najafi
,
H.
,
2022
, “
The Effect of Using Different Wake Models on Wind Farm Layout Optimization: A Comparative Study
,”
ASME J. Energy Resour. Technol.
,
144
(
7
), p.
070904
.
21.
Blank
,
J.
, and
Deb
,
K.
,
2020
, “
Pymoo: Multi-Objective Optimization in Python
,”
IEEE Access
,
8
, pp.
89497
89509
.
22.
Virtanen
,
P.
,
Gommers
,
R.
,
Oliphant
,
T. E.
,
Haberland
,
M.
,
Reddy
,
T.
,
Cournapeau
,
D.
,
Burovski
,
E.
, et al
,
2020
, “
SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
,”
Nat. Methods
,
17
(
3
), pp.
261
272
.
23.
Grady
,
S. A.
,
Hussaini
,
M. Y.
, and
Abdullah
,
M. M.
,
2005
, “
Placement of Wind Turbines Using Genetic Algorithms
,”
Renewable Energy
,
30
(
2
), pp.
259
270
.
24.
Bastankhah
,
M.
, and
Porté-Agel
,
F.
,
2014
, “
A New Analytical Model for Wind-Turbine Wakes
,”
Renewable Energy
,
70
, pp.
116
123
.
25.
Bastankhah
,
M.
, and
Porté-Agel
,
F.
,
2016
, “
Experimental and Theoretical Study of Wind Turbine Wakes in Yawed Conditions
,”
J. Fluid Mech.
,
806
, pp.
506
541
.
26.
Abkar
,
M.
, and
Porté-Agel
,
F.
,
2015
, “
Influence of Atmospheric Stability on Wind-Turbine Wakes: A Large-Eddy Simulation Study
,”
Phys. Fluids
,
27
(
3
), p.
35104
.
27.
Niayifar
,
A.
, and
Porté-Agel
,
F.
,
2016
, “
Analytical Modeling of Wind Farms: A New Approach for Power Prediction
,”
Energies
,
9
(
9
), pp.
1
13
.
28.
Dilip
,
D.
, and
Porté-Agel
,
F.
,
2017
, “
Wind Turbine Wake Mitigation Through Blade Pitch Offset
,”
Energies
,
10
(
6
), p.
757
.
29.
Thomas
,
J. J.
, and
Ning
,
A.
,
2018
, “
A Method for Reducing Multi-Modality in the Wind Farm Layout Optimization Problem
,”
J. Phys. Conf. Ser.
,
1037
(
4
), p.
42012
.
30.
Katic
,
I.
,
Hojstrup
,
J.
, and
Jensen
,
N. O.
,
1987
, “
A Simple Model for Cluster Efficiency
,”
European Wind Energy Association Conference and Exhibition
,
Rome, Italy
,
Oct 7–9, 1986
, Vol. 1, pp.
407
410
.
31.
Annoni
,
J.
,
Fleming
,
P.
,
Scholbrock
,
A.
,
Roadman
,
J.
,
Dana
,
S.
,
Adcock
,
C.
,
Porte-Agel
,
F.
,
Raach
,
S.
,
Haizmann
,
F.
, and
Schlipf
,
D.
,
2018
, “
Analysis of Control-Oriented Wake Modeling Tools Using Lidar Field Results
,”
Wind Energy Sci.
,
3
(
2
), pp.
819
831
.
32.
Bianchi
,
F. D.
,
De Battista
,
H.
, and
Mantz
,
R. J.
,
2006
,
Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design
,
Springer Science & Business Media
,
Germany
.
33.
Gao
,
X.
,
Li
,
B.
,
Wang
,
T.
,
Sun
,
H.
,
Yang
,
H.
,
Li
,
Y.
,
Wang
,
Y.
, and
Zhao
,
F.
,
2020
, “
Investigation and Validation of 3D Wake Model for Horizontal-Axis Wind Turbines Based on Field Measurements
,”
Appl. Energy
,
260
, p.
114272
.
34.
Draxl
,
C.
,
Hodge
,
B.-M.
,
Clifton
,
A.
, and
Mccaa
,
J.
,
2015
,
Overview and Meteorological Validation of the Wind Integration National Dataset Toolkit
,
National Renewable Energy Lab. (NREL)
,
Golden, CO
. www.nrel.gov/publications
35.
Draxl
,
C.
,
Clifton
,
A.
,
Hodge
,
B. M.
, and
McCaa
,
J.
,
2015
, “
The Wind Integration National Dataset (WIND) Toolkit
,”
Appl. Energy
,
151
, pp.
355
366
.
36.
Lieberman-Cribbin
,
W.
,
Draxl
,
C.
, and
Clifton
,
A.
,
2014
,
Guide to Using the Wind Toolkit Validation Code
,
National Renewable Energy Lab. (NREL)
,
Golden, CO
.
37.
King
,
J.
,
Clifton
,
A.
, and
Hodge
,
B.-M.
,
2014
,
Validation of Power Output for the WIND Toolkit
,
National Renewable Energy Lab. (NREL)
,
Golden, CO
.
38.
Manwell
,
J. F.
,
McGowan
,
J. G.
, and
Rogers
,
A. L.
,
2010
,
Wind Energy Explained: Theory, Design and Application
,
John Wiley & Sons,
New York
.
39.
Deb
,
K.
,
Sindhya
,
K.
, and
Okabe
,
T.
,
2007
, “
Self-Adaptive Simulated Binary Crossover for Real-Parameter Optimization
,”
Proceedings of GECCO 2007: Genetic and Evolutionary Computation Conference
,
London, UK
,
July 7–11
, pp.
1187
1194
.
40.
Kraft
,
D.
,
1988
,
A Software Package for Sequential Quadratic Programming
,
DFVLR Obersfaffeuhofen
,
Germany
.
41.
Long
,
H.
,
Zhang
,
Z.
,
Song
,
Z.
, and
Kusiak
,
A.
,
2017
, “
Formulation and Analysis of Grid and Coordinate Models for Planning Wind Farm Layouts
,”
IEEE Access
,
5
, pp.
1810
1819
.
42.
Chen
,
K.
,
Song
,
M. X.
,
He
,
Z. Y.
, and
Zhang
,
X.
,
2013
, “
Wind Turbine Positioning Optimization of Wind Farm Using Greedy Algorithm
,”
J. Renewable Sustain. Energy
,
5
(
2
), p.
23128
.
You do not currently have access to this content.