Optimal Placement of Wind Turbines Using Genetic Algorithms

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Optimal Placement of Wind Turbines Using Genetic
Algorithms

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

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Outline

• Background
• Problem
• Genetic Algorithm
• Modeling of Wind Farm
• Results
• MATLAB Compiler
• Future Research

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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 technology.

Courtesy of U.S. Department of Energy
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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
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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.

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

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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.

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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

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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
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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
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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
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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 100efficiency or the number
  of generations you assign is reached

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Modeling a Wind Farm
Velocity Downstream for a single turbine
Thrust Coefficient
The turbine thrust coefficient and the downstream
rotor radius are linked to the axial induction
factor a, and the rotor radius, Rr , by the Betz
relations.
u wind speed downstream from the turbine u0
initial wind speed a entertainment constant
a axial induction r1 down stream rotor
radius x distance downstream the turbine
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Modeling a Wind Farm

• Resulting Velocity of n Turbines

• Downstream Rotor Radius

R r Rotor Radius
Assuming that the K.E. deficit of a mixed wake is
equal to the sum of the energy deficits.
Entertainment Constant
z0surface roughness of the site z hub
height of turbine
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Cost and Fitness Functions

• Cost Function

Fitness Function
Ptottotal Power Nt Number of Turbines Costtotye
arly cost ?1,2act as weights for the fitness
function.
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Results
Randomly Generated Result
GA Generated Result

• Number of turbines is 30
• Efficiency is 92
• Total power output is 14,310 kWyear

• Number of turbines is 50
• Efficiency is 60.5
• Total power output is 15,669 kWyear

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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
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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