An extended pattern search approach is presented for the optimization of the placement of wind turbines on a wind farm. Problem-specific extensions infuse stochastic characteristics into the deterministic pattern search, inhibiting convergence on local optima and yielding better results than pattern search alone. The optimal layout for a wind farm is considered here to be one that maximizes the power generation of the farm while minimizing the farm cost. To estimate the power output, an established wake model is used to account for the aerodynamic effects of turbine blades on downstream wind speed, as the oncoming wind speed for any turbine is proportional to the amount of power the turbine can produce. As turbines on a wind farm are in close proximity, the interaction of turbulent wakes developed by the turbines can have a significant effect on the power development capability of the farm. The farm cost is estimated using an accepted simplified model that is a function of the number of turbines. The algorithm develops a two-dimensional layout for a given number of turbines, performing local turbine movement while applying global evaluation. Three test cases are presented: (a) constant, unidirectional wind, (b) constant, multidirectional wind, and (c) varying, multidirectional wind. The purpose of this work is to explore the ability of an extended pattern search (EPS) algorithm to solve the wind farm layout problem, as EPS has been shown to be particularly effective in solving multimodal layout problems. It is also intended to show that the inclusion of extensions into the algorithm can better inform the search than algorithms that have been previously presented in the literature. Resulting layouts created by this extended pattern search algorithm develop more power than previously explored algorithms using the same evaluation models and objective functions. In addition, the algorithm’s resulting layouts motivate a heuristic that aids in the manual development of the best layout found to date. The results of this work validate the application of an extended pattern search algorithm to the wind farm layout problem, and that its performance is enhanced by the use of problem-specific extensions that aid in developing results that are superior to those developed by previous algorithms.

References

References
1.
US Department of Energy, 2008, “
Wind Energy by 2030: Increasing Wind Energy’s Contribution to U.S. Electricity Supply
,” http://www.nrel.gov/docs/fy08osti/41869.pdf
2.
Mosetti
,
G.
,
Poloni
,
C.
, and
Diviacco
,
B.
, 1994, “
Optimization of Wind Turbine Positioning on Large Wind Farms by Means of a Genetic Algorithm
,”
J. Wind. Eng. Ind. Aerodyn.
,
51
(
1
), pp.
105
116
.
3.
Jensen
,
N. O.
, 1983,
A Note on Wind Generator Interaction
,
Risø National Laboratory
,
Roskilde, Denmark
.
4.
Grady
,
S. A.
,
Hussaini
,
M. Y.
, and
Abdullah
,
M. M.
, 2005, “
Placement of Wind Turbines Using Genetic Algorithms
,”
Renewable Energy
,
30
, pp.
259
270
.
5.
Wan
,
C.
,
Wang
,
J.
,
Yang
,
G.
, and
Zhang
,
X.
, 2009, “
Optimal Siting of Wind Turbines Using Real-Coded Genetic Algorithms
,”
European Wind Energy Conference and Exhibition (EWEC)
, Marseille, France.
6.
Mittal
,
A.
, 2010, “
Optimization of the Layout of Large Wind Farms Using a Genetic Algorithm
,” Master’s Thesis, Case Western Reserve University, Department of Mechanical Engineering, Cleveland, OH.
7.
Marmidis
,
G.
,
Lazarou
,
S.
, and
Pyrgioti
,
E.
, 2008, “
Optimal Placement of Wind Turbines in a Wind Park Using Monte Carlo Simulation
,”
Renewable Energy
,
33
, pp.
1455
1460
.
8.
Bilbao
,
M.
, and
Alba
,
E.
, 2009, “
Simulated Annealing for Optimization of Wind Farm Annual Profit
,”
2nd International Symposium on Logistics and Industrial Informatics (LINDI)
, Linz, Austria.
9.
Huang
,
H. S.
, 2007, “
Distributed Genetic Algorithm for Optimization of Wind Farm Annual Profits
,”
The 14th International Conference on Intelligent Systems Applications to Power Systems (ISAP)
, Kaohsiung, Taiwan.
10.
Elkinton
,
C. N.
,
Manwell
,
J. F.
, and
McGowan
,
J. G.
, 2006, “
Offshore Wind Farm Layout Optimization (OWFLO) Project: Preliminary Results
,”
Proceedings of 44th AIAA Aerospace Science Meeting and Exhibit
,
AIAA
,
Reno, NV
.
11.
Sisbot
,
S.
,
Turgut
,
O.
, and
Tunc
,
M.
, 2009, “
Optimal Positioning of Wind Turbines on Gokceada Using Multi-Objective Genetic Algorithm
,”
Wind Energy
,
11
(4)
, pp.
297
306
.
12.
Emami
,
A.
, and
Noghreh
,
P.
, 2010, “
New Approach on Optimization in Placement of Wind Turbines Within Wind Farm by Genetic Algorithms
,”
Renewable Energy
,
35
(
7
), pp.
1559
1564
.
13.
Kusiak
,
A.
, and
Zheng
,
H.
, 2010, “
Optimization of Wind Turbine Energy and Power Factor With an Evolutionary Computation Algorithm
,”
Energy
,
35
, pp.
1324
1332
.
14.
Gonzalez
,
J. S.
,
Rodriguez
,
A. G. G.
,
Mora
,
C.
,
Santos
,
J. S.
, and
Payan
,
M. B.
, 2010, “
Optimization of Wind Farm Turbines Layout Using an Evolutive Algorithm
,”
Renewable Energy
,
35
, pp.
1671
1681
.
15.
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
.
16.
Chowdhury
,
S.
,
Zhang
,
J.
,
Messac
,
A.
, and
Castillo
,
L.
, 2012, “
Unrestricted Wind Farm Layout Optimization (UWFLO): Investigating Key Factors Influencing the Maximum Power Generation
,”
Renewable Energy
,
38
(
1
), pp.
16
30
.
17.
Mustakerov
,
I.
, and
Borissova
,
D.
, 2010, “
Wind Turbines Type and Number Choice Using Combinatorial Optimization
,”
Renewable Energy
,
35
(
9
), pp.
1887
1894
.
18.
Ituarte-Villarreal
,
C. M.
, and
Espiritu
,
J. F.
, 2011, “
Optimization of Wind Turbine Placement Using a Viral Based Optimization Algorithm
,”
Procedia Comput. Sci.
,
6
, pp.
469
474
.
19.
Yin
,
S.
, and
Cagan
,
J.
, 2000, “
An Extended Pattern Search Algorithm for Three-Dimensional Component Layout
,”
J. Mech. Des.
,
122
(
1
), pp.
102
109
.
20.
Aladahalli
,
C.
,
Cagan
,
J.
, and
Shimada
,
K.
, 2007, “
Objective Function Effect Based Pattern Search—An Implementation for 3D Component Layout
,”
J. Mech. Des.
,
129
(
3
), pp.
255
265
.
21.
Manwell
,
J. F.
,
McGowan
,
J. G.
, and
Rogers
,
A. L.
, 2009,
Wind Energy Explained: Theory, Design, and Application
,
2nd ed.
,
John Wiley and Sons
,
Chichester, UK
.
22.
Katic
,
I.
,
Hojstrup
,
J.
, and
Jensen
,
N. O.
, 1986, “
A Simple Model for Cluster Efficiency
,”
European Wind Energy Association Conference and Exhibition
. Rome, Italy.
23.
Torczon
,
V.
, and
Trosset
,
M. W.
, 1998, “
From Evolutionary Operation to Parallel Direct Search: Pattern Search Algorithms for Numerical Optimization
,” Comput. Sci. Stat., pp.
396
401
.
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