1. Optimal Placement of Wind Turbines Using Genetic Algorithms
Michael Case, North Georgia College
Shannon Grady, Mentor

2. Outline Background Problem Genetic Algorithm Modeling of Wind Farm
Results
MATLAB Compiler
Future Research

3. 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

4. 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.

5. 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.

6. 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

7. 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.

8. 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

9. 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

10. 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 |
Chromosome 2
11011 |
Offspring 1
Offspring 2

11. 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
Original offspring 2
Mutated offspring 1
Mutated offspring 2

12. 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

13. 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 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 turbine

14. 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:
z0=surface roughness of the site
z = hub height of turbine

15. Cost and Fitness Functions
Cost Function:
Fitness Function:
Ptot=total Power
Nt =Number of Turbines
Costtot=yearly cost
ω1,2=act as weights for the fitness function.

16. Results Randomly Generated Result GA Generated ResultX X
Number of turbines is 50
Efficiency is 60.5%
Total power output is 15,669 kWyear
Number of turbines is 30
Efficiency is 92%
Total power output is 14,310 kWyear

17. 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.

18. 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