Optimizing Wind Farm Layouts With Genetic Algorithms
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A Computer Science Paper
Presented to
Junior Science, Engineering and Humanities Symposium
University of Missouri-St. Louis
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by
Logan Gilbert
Sophomore
Camdenton High School
P.O. Box 1409
Camdenton, MO 65020
August 18, 2010-February 10, 2011
Mr. Chris Reeves and Mrs. Kim Griggs
Science Research Instructors
Camdenton, MO 65020
1
NAME:
HOME ADDRESS:
SCHOOL:
SPONSOR/TEACHER:
TITLE:
Logan Gilbert
285 Fox Ridge Road
Montreal, MO 65591
Camdenton High School
Mr. Christopher Reeves
Optimizing Wind Farm Layouts With Genetic
Algorithms
As traditional sources of energy are becoming more expensive and less accessible,
alternative energies are becoming an integral part of the energy infrastructure. One of
these alternative sources is wind power, but its price advantage remains too
insignificant to encourage large-scale development of wind farms in favor of coal mines
and oil wells. The purpose of this study was to optimize the placement of a given
number of wind turbines for maximum energy capture within a wind farm of a given
area. Layouts were optimized through the use of genetic algorithms and were tested
with a wind simulation program, similar to the work performed by Kusiak and Song
(2009). It was found that traditional optimization techniques produce results which are
very consistent even given varying initial conditions.
2
Contents
Purposes
4
Hypotheses
5
Variables
6
Introduction
7
Method
8
Discussion of Results
11
Tables and Figures
12
Statistical Analyses
13
Future Studies and Applications
16
Acknowledgements
17
Bibliography
18
3
Purposes
The purpose of this study was to:
1. Determine the consistency of traditional algorithms in wind turbine placement.
2. Apply a genetic algorithm to the problem of wind turbine placement.
3. Compare the efficiency and effectiveness of the traditional algorithm and the
genetic algorithm.
4
Hypotheses
It was hypothesized that:
1. The traditional algorithm would generate inconsistent results.
2. The genetic algorithm would generate consistent results.
3. The genetic algorithm would reach a solution similar to the best solution
reached by the traditional algorithm but in fewer iterations.
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Variables
1. The independent variable in this study was the type of algorithm used to place
the wind turbines.
2. The dependent variables were the energy produced by the most productive
wind farm layout achieved and the number of iterations it took to reach this
layout.
3. The controlled variables were the virtual landscape on which the turbines
were being placed and the software used to measure the resulting energy
produced.
6
Introduction
The United States accounts for about 19% of all carbon dioxide emissions produced
around the world (EPA, 2008). However, the United States contains only about 4% of
the world’s people. This disproportionate burning of fossil fuels cannot be sustained
forever. Alternative sources of energy must become an integral part of our energy
infrastructure. Wind power is readily accessible everywhere but requires large amounts
of space to be useful on a commercial scale. One way to make wind power more
practical is to make wind farms more efficient, thus reducing the size of a commercially
viable farm.
Inefficiencies exist in each step of the power production process. Still, the overall power
production can be increased without tediously examining turbine designs, analyzing
losses in transport, or finding only the windiest sites. Instead, one can improve the
process by which wind turbines are originally placed in the field. The current process
involves monitoring wind conditions for about a year and then feeding the information
gathered into wind farm software. The software uses an optimization technique to find
the optimal placements for the wind turbines. However, the optimization technique used
is taken for granted. Many other optimization techniques exist, including an evolutionbased “genetic” algorithm. It is the purpose of this study to examine the effectiveness of
the genetic algorithm on wind turbine placement because it has been successful in
many other contexts (Koza, 2003).
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Method
Traditional Algorithm:
After contacting Chris Ziesler and Peter Young, engineers at Wind Capital Group, it was
decided to use openWind as the software which would provide the traditional algorithm
and would generate energy capture reports for all wind farm layouts.
openWind’s optimizer follows the following process: The optimizer attempts to find a
new legal position for each turbine. If the turbine made a good move last iteration, it will
attempt the same direction this time. Otherwise, it adds a gaussianly distributed random
value to the turbine’s x and y coordinates. If the new position is not a legal position or it
obstructs another turbine’s new position, then a new random change is made until all
turbines have new legal positions (turbines cannot be placed too close to one another or
to various land features). The optimizer then calculates the captured energy (including
wake effects) and accepts the new layout as a whole if the captured energy is greater
than the energy captured by the turbines in their previous positions. The optimizer then
repeats this process. If, however, the new layout was not accepted as a whole, then the
optimizer looks at each turbine individually. If a particular turbine captured less than its
benchmark energy, then the change is discarded and the turbine is returned to its
previous position. The optimizer then sums the total captured energies from the turbines
and accepts the new positions and energies as the new benchmark energies and
returns to the beginning if it is equal to or greater than the benchmark energy. If not,
then the changes are discarded and the optimizer returns to the beginning. (adapted
from the openWind website)
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To test openWind’s algorithm, 7 tests of its optimizer were run. For each test, openWind
generated an initial random layout of windmills in a simulated plot of land. Based on
industry norms as described by Wind Capital, the turbines were constrained to a
minimum separation of 3 rotor diameters apart along the y axis and 10 rotor diameters
apart along the x axis. They were also prevented from being placed too closely to roads,
power lines, and other land features. Its optimizer was then run until 100 iterations of
the algorithm no longer yielded at least a 1% increase in energy captured by the
windmills. This typically took about 4500 iterations.
After completion of the optimization process, openWind generated an energy capture
report detailing the energy captured by each turbine and by the layout as a whole, which
allowed analysis of supposedly optimal turbine placements.
Genetic Algorithm:
After reviewing the appropriate literature and researching various optimization
techniques, it was determined that a genetic algorithm would generate results
competitive with the traditional algorithm. This is because turbines that are placed in
locally optimal locations have no way to move to better local maxima or to the global
maximum; they remain stuck in the local maxima. However, a genetic algorithm
approach avoids this problem by combining aspects of many different layouts. As long
as one of the turbines in one of the many layouts is originally placed close to the global
maximum, it is very likely that the wind farm layout produced in the end will also have a
turbine stationed in that position.
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Genetic algorithms follow an evolutionary process: A large number of random
“individuals” (in this case, wind farm layouts) are generated. These individuals are then
combined using a method known as crossover: the coordinates of one turbine in Layout
1 might be swapped with the coordinates of another turbine in Layout 17. This allows
good turbine positions to be spread to other layout. After crossover, the layouts are
mutated: the coordinates of some of the turbines are randomly changed by a small
amount. Mutation prevents premature conversion on a solution and adds diversity to the
population of layouts. Finally, the layouts are tested and the best are selected to go
through the cycle again.
It was decided that the Evolving Objects codebase would provide this functionality.
However, the Evolving Objects program needed to be interfaced with openWind so that
the layouts produced by the genetic algorithm could be tested.
Evolving Objects Specifics:
Based on prior research, it was determined that the initial set of wind farms would
contain 500 random layouts. The least productive 10% of the wind farms would be
discarded from the evolutionary process after each testing in openWind. The crossover
operator would randomly select pairs of layouts for crossover with probability .8.
Mutation of a turbine’s x or y coordinate would also be done randomly with probability
.2.
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Discussion of Results
Traditional Algorithm:
It was found that the traditional algorithm produced layouts with very consistent power
production capacities (p=6.64E-23). Additionally, variances among individual turbine
power outputs and among end turbine locations were negligible.
Among turbines that were in the same relative locations in their respective trials, a small
variance in position was not correlated with large amounts of power produced by the
turbine. That is, the most productive turbines were not also the turbines that were the
most precisely placed. This suggests that openWind cannot place turbines in the
windiest locations more accurately or consistently than it can place turbines in
somewhat windy locations. This reinforces the idea that a genetic algorithm- based
optimizer may have the ability to access wind energy better than the traditional method.
See figure 1.
Genetic Algorithm:
Work on interfacing EO and openWind is underway to further determine the differences
between the efficiency and effectiveness of the two optimizers.
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Tables and Figures
Figure 1: Turbine productivity and variance in position
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Statistical Analyses
Table 1: Wind Farm Layout Output
Anova: Single Factor
SUMMARY
Groups
Net Yield (GWH)
Array Efficiency
ANOVA
Source of Variation
Between Groups
Within Groups
Total
Count
7
7
SS
1643.99265
0.424152357
Sum
Average Variance
540.442234 77.20603 0.066567
692.152145 98.87888 0.004125
df
MS
F
P-value
F crit
1 1643.993 46511.38 6.64E-23 4.747225
12 0.035346
1644.416802
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Table 2: Individual Turbine Output
Anova: Single Factor
SUMMARY
Groups
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10
Row 11
Row 12
Row 13
Row 14
Row 15
Row 16
Row 17
Row 18
Row 19
Count
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
ANOVA
Source of Variation
Between Groups
Within Groups
SS
6578896
2644582
Total
9223479
Sum
27190.09
27300.36
27291.39
27218.43
28466.87
27679.79
28053.78
27963.38
27703.2
27681.98
27791.27
27715.52
28404.57
30541.04
33811.46
28470.86
28047.69
28795.13
30392.86
df
Average
3884.299
3900.052
3898.77
3888.347
4066.696
3954.256
4007.682
3994.769
3957.6
3954.569
3970.181
3959.361
4057.796
4363.006
4830.209
4067.266
4006.813
4113.589
4341.837
Variance
39.75615
270.9309
287.5741
115.9192
37421.33
9283.747
24227.33
15411.52
975.3354
286.9464
1012.845
1617.06
62777.42
171758.2
7868.696
64868.22
1548.141
16294.42
24698.36
MS
F
P-value
F crit
18 365494.2 15.75536 4.26E-23 1.695025
114 23198.09
132
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Table 3: Individual Turbine Placement
Anova: Single Factor
Output
SUMMARY
Groups
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10
Row 11
Row 12
Row 13
Row 14
Row 15
Row 16
Row 17
Row 18
Row 19
Count
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
ANOVA
Source of Variation
Between Groups
Within Groups
SS
1348.636
50.83742
Total
1399.473
Sum
39221.71
39214.96
39209.17
39204.09
39201.59
39199.75
39198.25
39196.21
39194.84
39193.9
39192.63
39190.77
39186.42
39181.29
39178.75
39173.01
39158.85
39141.67
39134.05
df
Average
5603.102
5602.137
5601.31
5600.584
5600.227
5599.965
5599.749
5599.459
5599.263
5599.129
5598.947
5598.682
5598.06
5597.328
5596.964
5596.145
5594.122
5591.667
5590.579
Variance
0.343049
0.006647
0.494643
0.101038
0.125483
0.055211
0.031658
0.062909
0.026902
0.012279
0.080453
0.103669
0.262022
0.246007
0.000969
0.184917
2.294894
0.737267
3.302886
MS
F
P-value
F crit
18 74.92421 168.0133 3.23E-73 1.695025
114 0.445942
132
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Future Studies and Applications
This research could provide a basis for future studies that would:
1. Use different selection, crossover, and/or mutation operators.
2. Test the effectiveness of other optimization techniques at placing windmills.
3. Compare optimization techniques with respect to computing power used.
4. Compare a generalized version of openWind’s algorithm to the genetic
algorithm in other problem areas.
This research could also be used in industry to improve wind farm layouts and
awareness of the impact of a single turbine on an entire wind farm, allowing more
energy to be produced per acre of land used.
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Acknowledgments
Dr. Lee Spector, Professor of Computer Science at Hampshire College
- Inspired the project and guided its beginnings
Mr. Chris Ziesler and Mr. Peter Young, Engineers at Wind Capital Group
- Provided insightful information about the industry
Mr. Chris Reeves and Mrs. Kim Griggs, Science Research Instructors
- Provided support and guidance throughout the year
Mrs. Sarah Rolf
- Made science research seem like a great alternative to grammar
Mom and Dad
- Motivated me to get things done
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Bibliography
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Within Wind Farm by Genetic Algorithms.” Renewable Energy 35: 1559-1564. Retrieved
September 28, 2010 from www.elsevier..com/locate/renene.
J.Castro Mora et al. (2007). “An Evolutive Algorithm for Wind Farm Optimal Design.”
Neurocomputing 70: 2651-2658. Retrieved September 28, 2010 from
www.sciencedirect.com.
Koza, John (2003). “Human-Competitive Applications of Genetic Programming.” Advances in
Evolutionary Computing.
Kusiak, Andrew, and Zhe Song (2010). “Design of Wind Farm Layout for Maximum Wind
Energy Capture.” Renewable Energy 35: 685-694. Retrieved September 28, 2010 from
www.elsevier.com/locate/renene.
K. Matous et al. (2000). “Applying Genetic Algorithms to Selected Topics Commonly
Encountered in Engineering Practice.” Computer Methods in Applied Mechanics and
Engineering 190: 1629-1650. Retrieved September 28, 2010 from
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Poli, Riccardo, and W.B. Langdon (2010). “On the Search Properties of Different Crossover
Operators in Genetic Programming.” Proceedings of Genetic Programming. Retrieved
September 16, 2010 from cswww.essex.ac.uk/staff/poli/papers/Poli-GP1998.pdf.
S.A. Grady et al. (2005). “Placement of Wind Turbines Using Genetic Algorithms.” Renewable
Energy 30: 259-270. Retrieved September 28, 2010 from www.sciencedirect.com.
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