Keywords: optimal design, evolutionary algorithms, energy systems, wind power, computational fluid dynamics.

This paper shows a method to obtain optimal chord and twist distributions in wind turbine blades using genetic algorithms. The distributions are computed to maximize the mean expected power depending on the Weibull wind distribution at a specific site because in wind power systems optimization is highly site dependent [1]. This approach avoids assumptions about optimal attack angle related to the ratio between the lift to drag coefficients.

Genetic algorithms are global optimizers that have a wide trade-off between exploration and explotation on the space problem. The geometry definition of a wind blade is a problem with many degrees of freedom being suitable to fall in local optima, which can be surpassed using evolutionary methods. Evolutionary Algorithms are frequently used as powerful optimization methods. They are stochastic methods inspired by the natural process of evolution[2,3], and among their advantages are their global search due to the management of a population of candidate solutions instead only one, and also the only requirement of the knowledge of the fitness function value to perform a evolutionary optimization, without any other consideration such as derivability or continuity of the function. Many different optimum design problems in multiple fields of sciences and engineering have been solved outperforming any other previous results with evolutionary algorithms [4].

To optimize chord and twist distributions, an efficient implementation of the Blade-Element and Momentum (BEM) theory [1,5,6] is used. It is basically a simplified theory that is used routinely by wind power industry because it provides a reasonably accurate prediction of performance. The BEM theory has shown to give good accuracy with respect to time cost, and at moderate wind speeds, it has sufficed for blade geometry optimization.

In the implementation of BEM, the sophistication is dismiss to reduce computational cost. The time required to evaluate the forces in a typical turbine is in the order of milliseconds, which allows massive evaluation of trial turbines. The implementation is validated by comparing power prediction with the experimental data of the Risø test turbine that is one of six experimental turbines widely tested by the IEA. The data are contained in the Annex XVIII report [7] and in the public database of rotor performances at the ECN.

High quality in results is obtained until the stall zone, about wind speed of 13m/s proximately. Predictions are used to compute the mean power that is the fitness function in the genetic algorithm. The mean power, which is proportional to the annual generated energy, is obtained by averaging power predictions with the probability obtained from the Weibull distribution of the specific site. To obtain the optimal blade, the upper and lower limits of chord and twist are needed as well as an optional upper limit of the blade area.

An application is presented to optimize the blades of the Risø test turbine at a site with wind distribution parameters: and . Optimized blades have more torsion and the collective pitch angle is changed from to . A slight redistribution of chord is generated with decreasing values in both external sections. Results show that optimized turbine has better performance for wind speed until 14.5m/s and worse for higher values, but these are less probable.

1

Martin O.L. Hansen. Aerodynamics of Wind Turbines. Rotors, Loads and Structures. James & James, 2000.

2

J. Holland. Adaptation in Natural and Artificial Systems. PhD thesis, University of Michigan, 1975.

3

D. Goldberg. Genetic Algorithms in Search, optimization and Machine Learning. Addison-Wesley, 1989.

4

G. Winter, J. Periaux, M. Galán, and P. Cuesta, editors. Genetic Algorithms in Engineering and Computer Science. John Wiley & Sons, 1995.

5

T. Burton, D. Sharpe, N. Jenkins, and E. Bossanyi. Wind Energy Handbook. Jhon Wiley & Sons, 2001.

6

J. M. Jonkman. Modelling of the UAE wind turbine for refinement of FAST_AD. Technical Report NREL/TP-500-34755, National Renewable Energy Laboratory, December 2003.

7

J.G. Schepers et al. Final report of IEA Annex XVIII: 'Enhanced field rotor aerodynamics database'. Technical Report ECN-C-02-016, Energy research Centre of the Netherlans, February 2002.

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