# Optimal Placement of Wind Turbines Using Genetic Algorithms

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23 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Optimal Placement of Wind
Turbines Using Genetic Algorithms

Michael Case, North Georgia College

Outline

Background

Problem

Genetic Algorithm

Modeling of Wind Farm

Results

MATLAB Compiler

Future Research

Future of Wind Turbines in U.S.

Courtesy of U.S. Department of Energy

6% of U.S. land area are
good wind areas

These areas have the
potential to supply more than
one and a half times the
current electricity
consumption of the United
States

This is why the development
of placement and
performance algorithms will
be essential in escalating the
development of turbine
technology.

Wind Energy Research and Development

A very conventional wind
farm located in Denmark.

The method used to the
position the turbines seen
here produces results similar
to the genetic algorithm
method employed here.

http://www.afm.dtu.dk/wind/turbines/gallery.htm

Offshore Turbine Development

Denmark is one of the
Turbine technology, and is
wind farm development.

D.O.E. plans to convert
abandoned offshore oil rigs
into wind farms off the
in action.

http://www.afm.dtu.dk/wind/turbines/gallery.htm

Why Use Genetic Algorithms?

Efficiency is affected by positioning in wind
farms for multi
-
megawatt energy production

Genetic Algorithms optimize the power output
without dependence on gradients or local
maxima

The Problem

To use genetic search algorithms to support the
findings of scientists in the wind industry who have
sought to find the optimal positioning for wind
turbines based on cost and power output. Genetic
Algorithms converge rapidly for the

NP
-
Complete

class of problems, as more parameters are introduced
into a system genetic algorithms usually become more
and more efficient then other search algorithms that
have been used to solve nonlinear problems of this
class, which makes it ideal for our research involving
turbine placement.

Genetic Algorithm

Initially
-

Generate random population of
n

chromosomes
(sqrt(200)*n, preferably)

Fitness
-

Evaluate the fitness
f(x)
of each chromosome
x

in
the population

New population
-
Create a new population by repeating
following steps until the new population is complete

Genetic Algorithms

Selection
-

Chromosomes from a population are selected
according to their fitness (more fit individuals have greater
chance)

See roulette wheel for example

No.

String

Fitness

% of Total

1

01101

169

14.4

2

11000

576

49.2

3

01000

64

5.5

4

10011

361

30.9

Total

1170

100.0

Genetic Algorithms

Crossover
-

With a crossover probability cross over the
parents to form new offspring (children). If no crossover
was performed, offspring is the exact copy of parents. We
used a crossover rate of .75.

Chromosome 1

11011 | 00100110110

Chromosome 2

11011 | 11000011110

Offspring 1

11011 | 11000011110

Offspring 2

11011 | 00100110110

Genetic Algorithms

Mutation
-

With a mutation probability mutate new
offspring at each locus (position in chromosome). It is
important to keep the mutation rate low (.001) to keep
the search from becoming random.

Original offspring 1

1101111000011110

Original offspring 2

1101100100110110

Mutated offspring 1

1100111000011110

Mutated offspring 2

1101101100110110

Genetic Algorithm

Replacement
-

Use new generated population for a further
run of the algorithm

Evaluate
-
If the end condition is satisfied, stop, and return
the best solution in current population

Loop
-

Continue evaluating Fitness until the search
terminates at 100%efficiency or the number of generations
you assign is reached

Modeling a Wind Farm

u = wind speed downstream
from the turbine

u
0

= initial wind speed

α = entertainment constant

α =axial induction

r
1

x = distance downstream the
turbine

The turbine thrust coefficient and the
the axial induction factor
α, and the
r

, by the Betz relations.

Velocity Downstream for a
single turbine:

Thrust Coefficient:

Modeling a Wind Farm

R
r

Entertainment Constant:

z
0
=surface roughness of the site

z = hub height of turbine

Resulting Velocity of n Turbines:

Assuming that the K.E. deficit of a
mixed wake is equal to the sum of the
energy deficits.

Cost and Fitness Functions

Cost Function:

P
tot
=total Power

N
t

=Number of Turbines

Cost
tot
=yearly cost

ω
1,2
=act as weights for the fitness function.

Fitness Function:

Results

Number of turbines is 50

Efficiency is 60.5%

Total power output is 15,669 kWyear

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Randomly Generated Result

Number of turbines is 30

Efficiency is 92%

Total power output is 14,310 kWyear

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GA Generated Result

The MATLAB Compiler

The MATLAB Compiler
is a very powerful tool
that can be used to create
code from M
-
Files to C,
C++, or Fortran 90/95 for
a various number of
platforms, and will allow
for thousands of
generations to be run on
SP3 here at CSIT.

http://www.csit.fsu.edu/supercomputer/fsu
-
sp.html

Future Research

Parametric study of objective function and cost functions
for various turbine models on land and sea

Stochastic wind modeling and evaluation of equilibrium
techniques

Incorporation of helical wake model

Introduction of simulated annealing into the optimization
process

Evaluation and development of cost/maintenance models