# wind_turbines

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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.
•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
Courtesy of U.S. Department of Energy
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

 Pu 
i
Efficiency    i

 Pu 
i
0

   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
Velocity Downstream for a
single turbine:
Thrust Coefficient:
                 
                 
       2a                        CT  4a(1  a)
u  u 0 1             2 
        x  
 1    r   
The turbine thrust coefficient and the
    
        1          downstream rotor radius are linked to
the axial induction factor α, and the
rotor radius, Rr , by the Betz relations.
u = wind speed downstream
from the turbine
u0 = initial wind speed
α = entertainment constant
α =axial induction
x = distance downstream the
turbine
Modeling a Wind Farm
Resulting Velocity of n Turbines:
2
1 a                       u  n  ui 
r1  Rr                             1     1  
1  2a                    u           u 
    0  i 1   0 

Assuming that the K.E. deficit of a
mixed wake is equal to the sum of the
Entertainment Constant:              energy deficits.
0.5

  z 
 ln   
  z 
  0 
z0=surface roughness of the site
z = hub height of turbine
Cost and Fitness Functions
Cost Function:

 2 1 0.00174Nt2 
cost tot    Nt   e             
 3 3                              Fitness Function:

1        cost tot
Ptot=total Power
Nt =Number of Turbines
objective       w1           w2
Ptot       Ptot
Costtot=yearly cost
ω1,2=act as weights for the fitness function.
Results
Randomly Generated Result                      GA Generated Result
u0                                         u0

X           X            X   X   X        X    X   X   X   X    X   X   X   X   X
X       X   X
X   X   X   X   X        X
X               X    X
X       X   X        X       X
X   X   X       X        X   X            X    X   X   X   X    X   X   X   X   X
X       X   X   X    X   X
X   X   X   X    X   X       X
X   X        X   X   X   X
X   X                    X                X    X   X   X   X    X   X   X   X   X

•    Number of turbines is 50                 Number of turbines is 30
    Efficiency is 60.5%                      Efficiency is 92%
    Total power output is 15,669 kWyear      Total power output is 14,310 kWyear
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

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 views: 13 posted: 5/1/2011 language: English pages: 18