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					   Optimal Placement of Wind
Turbines Using Genetic Algorithms

    Michael Case, North Georgia College
          Shannon Grady, Mentor
   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
•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
     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.

   Offshore Turbine Development
•Denmark   is one of the
leading nations in Wind
Turbine technology, and is
leading the way in offshore
wind farm development.

•D.O.E.  plans to convert
abandoned offshore oil rigs
into wind farms off the
Louisiana Coast are already
in action.
Why Use Genetic Algorithms?

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

                                 Pu 
                 Efficiency    i

                                 Pu 

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

 •    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
    r1 =down stream rotor radius
    x = distance downstream the
Modeling a Wind Farm
                                     Resulting Velocity of n Turbines:
Downstream Rotor Radius:
                  1 a                       u  n  ui 
      r1  Rr                             1     1  
                 1  2a                    u           u 
                                              0  i 1   0 

      R r =Rotor Radius
                                      Assuming that the K.E. deficit of a
                                      mixed wake is equal to the sum of the
 Entertainment Constant:              energy deficits.
              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.
    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.  
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
   Incorporation of helical wake model
   Introduction of simulated annealing into the optimization
   Evaluation and development of cost/maintenance models

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