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Research Papers

An Extended Pattern Search Approach to Wind Farm Layout Optimization

[+] Author and Article Information
Bryony L. Du Pont

Integrated Design Innovation Group, Department of Mechanical Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213bryony@cmu.edu

Jonathan Cagan

Integrated Design Innovation Group, Department of Mechanical Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213cagan@cmu.edu

J. Mech. Des 134(8), 081002 (Jul 23, 2012) (18 pages) doi:10.1115/1.4006997 History: Received March 14, 2011; Revised May 02, 2012; Published July 23, 2012; Online July 23, 2012

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.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Immediate speed reduction and eventual asymptotic approach to initial windspeed (12 m/s) within a wake

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Figure 2

Schematic of wake model

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Figure 3

Flowchart for current EPS

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Figure 4

Comparison of solution spaces—(a) discretized and (b) continuous

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Figure 5

Illustration of wind directions and speed—(a) case a, (b) case b, and (c) case c

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Figure 6

(a) Mosetti —26 turbine layout—case (a) and (b) discretized EPS - 26-turbine layout—case (a)

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Figure 7

Grady , Huang, Bilbao and Alba, and discretized EPS - 30 turbines—case (a)

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Figure 8

EPS 26-turbine layout—case (a)

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Figure 9

EPS 30-turbine layout—case (a)

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Figure 10

Objective function evaluation versus number of turbines—case (a)

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Figure 14

(a) Grady 39-turbine layout—case (b) and (b) EPS 39-turbine layout—case (b)

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Figure 17

Optimal 44-turbine EPS layout—case (b)

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Figure 20

(a) Grady 39-turbine layout—case (c) and (b) EPS 39-turbine layout—case (c)

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Figure 21

(a) Huang 47-turbine layout—case (c), (b) Bilbao and Alba 47-turbine layout—case (c), and (c) EPS 47-turbine layout—case (c)

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Figure 22

Optimal EPS 44-turbine layout—case (c)

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Figure 11

Optimal 54-turbine EPS layout—case (a)

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Figure 12

100% efficient 56-turbine layout—case (a)

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Figure 13

(a) Mosetti 19-turbine layout—case (b) and (b) and EPS 19-turbine layout—case (b)

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Figure 15

(a) Huang 37-turbine layout—case (b), (b) Bilbao and Alba 37-turbine layout—case (b), and (c) EPS 37-turbine layout—case (b)

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Figure 16

Objective function evaluation versus number of turbines—case (b)

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Figure 18

Bar graph of weighting fractions—case (c)

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Figure 19

(a) Mosetti 15-turbine layout—case (c) and (b) EPS 15-turbine layout—case (c)

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