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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Aerodynamics and rotor design' taking place on Wednesday, 12 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Fernando Echeverria ACCIONA WINDPOWER, Spain

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This paper presents an evolutionary algorithm design tool to optimize the blade design in a wind turbine.
The objective of the optimization is to minimize the COE (cost of energy) of a wind turbine. This COE is evaluated for a wind turbine model using an aerodynamic/aero-elastic code. Every optimization cycle updates the following parameters:
-Blade geometry. Change in chord, twist and master profile (Airfoil section) per blade station.
-Blade structural properties. Change of mass and stiffness matrixes using an AW structural code.

The main restraints considered in the optimization process are:


The optimization algorithm is implemented using two complementary techniques. First procedure consists on a ‘rough’ optimization process, scanning the non-linear response surface in order to provide a candidate solution that neighbors the minimum. Last step is a ‘fine’ searching process where the start point is given in the previous ‘rough’ process.
The optimization surface response is multi-modal intrinsically, as a result of solving several coupled non-linear problems, and discontinuous owing to the fact that some design variables are discrete (master airfoils). In this context GA’S (genetic algorithms) arise as proper candidates to circumvent a potential stacking in a local minimum and in order to handle either continuous or discrete design variables at the same time. Finally, to refine or improve the GA’S better solution (Goldberg 20) a simplex search (Nelder-Mead algorithm ref 23) is used.

Genetic Algorithm (GA)
Genetic algorithms are meta-heuristic optimization search algorithms based on evolutionary and nature selection methods. These algorithms make use of a population of solution instances and improve the overall solution through different generations. The transition rules from one generation through the next one are stochastic and the algorithm does not use any gradient information, performing a robust direct search through the surface optimization response.
A simple GA algorithm (Goldberg 20) consists on the following steps: initialization, fitness evaluation, selection, crossing and mutation.
The GA was developed internally in AW using MATLAB (ref 16) routines and using an adaptive scheme in every optimization cycle instead of adopting fixed values for the probabilities assigned to either mutation or crossing operators. These probabilities are updated per iteration (See sirinivas paper 22)

Nelder-Mead algorithm
The best solution reached with the GA algorithm is the starting point for the simplex algorithm in the “fine” optimization search stage.
The Nelder-Mead ref(23) makes use of the simplex concept. This algorithm is heuristic and does not use any gradient information (direct search), giving accurate results for non-linear uni-modal optimization response surfaces. Since NM can be trapped in any local-minimun is important the work done previously with the GA algorithm which moves closer the previous solution to the global minimum.

Main body of abstract

Blade design constitutes a challenge in every wind turbine design conceptual stage. Due to the fact that it involves a multidisciplinary knowledge (i.e. the structural, aeroelastic, control disciplines).
Traditionally this activity is accomplished following a multi-step schedule. The final target is achieved using a “divide” and conquer strategy due to the difficulties of facing the global optimization problem. As a consequence this global objective is split in several sub-objectives. The first step is devoted to optimize the airfoil master sections according to some aerodynamic criteria (see references 4-8). Secondly, the blade twist and chord are set up in order to minimize the COE (see Benini 3). This last step should be carried out using an aerolastic code that takes into account the change in structural properties in every optimization cycle.
In spite of the difficulties mentioned, the optimum global search that “moves” all blade design variables (either airfoil or twist and chord) simultaneously arises as another alternative to the aforementioned traditional strategy. The results obtained in this paper indicate that an improvement is succeeded following this global search unlike the blade optimization that uses as a main driver either the maximum ‘Cl’ or the maximum ‘Cl/Cd’ ratio (see references 4-8).
A survey of this global search approach is performed in Fulang and Xudong papers. Thus in Fulang the airfoil variables are described using lift and drag coefficients. More specifically in this study either the minimum drag or lift curve slope are fixed and the maximum extrapolated (from NACA profiles) lift coefficient is used as degree of freedom. This assures that results are according to well-known profiles (tested profiles). In Xudong, airfoils are controlled by their respective relative thickness.

In this paper, instead of using lift and drag coefficients, a library of “master” profiles (NACA, DELFT…) is used in a straightforward way (its real tested polar curves are used), therefore a high fidelity degree is attained by using such tested profiles. These airfoils are placed at some distance from blade root (blade station) and an interpolation scheme is used in order to obtain intermediate profiles. It has to be emphasized that different “master” sections may be chosen in every optimization cycle. These “master” airfoils are used as discreet variable designs in combination with twist and chord continuous design variables for the global search approach as it will be shown. As a consequence, a mixed non-linear integer and continuous optimization problem is find out in this paper. Mixed non-linear programming (refs 9-10) can be chosen as optimizer “engine” however due to the non-linearity and the problem complexity a specific hybrid genetic algorithm (GA) in combination with a simplex algorithm was developed in AW to tackle the problem. Simulations are carried in time domain and in every optimization cycle the optimizer engine calls to either an aerolastic or a structural codes.
It has to be remarked that such codes are the ones used in AWP either for load set certification (BLADED) or for structural integrity assessment (FAROB), unlike Fulang and Xudong works where a prior structural validation is performed due to the fact that structural responses are developed by their own non-standardized codes. As a consequence, such previous corroborations are not prescribed in this case since either BLADED (see reference 14) or FAROB (see reference 15) code are well probed and used in the wind turbine industry.

The results obtained with AWP tool highlights that a COE minimization can be achieved.


A new blade design tool was developed using time domain simulations in a complete turbine (Bladed environment).
In addition to chord and twist the possibility of choosing a library of well probed profiles was introduced in the algorithm.
As a consequence an optimization that uses mixed variables (either integer or continuous variables) has to be tackled. This fact linked to surface response lack of awareness leads to the use of an evolutionary algorithm.

In this paper a blade design optimization is carried in a two-step scheme. The first one is a rough estimation as starting point to a well-known simplex algorithm use a final refinement.
This paper shows that both algorithms (Genetic and simplex) are complementary and a good approach to improve the blade design using the COE criteria as optimization driver. It is not guaranteed that the best aerodynamic profiles in terms of ‘Cl’ or ‘Cd’ gives the best COE ratio because the complete turbine has to be considered for this reason the engine optimizer launches an aerolastic code (Bladed) per iteration. In addition such code makes use of the mechanical blade features updating using a well-known structural software (FAROB).
The results obtained illustrates that the proposed blade designs improve the first selection based only in aerodynamic criteria.
In order to circumvent the “curse” of dimensionality a variable reduction study is carried in this work in order to speed up the whole optimization process.
In this paper it is also remarked the fact that a structural updating is necessary in every optimization cycle combining either aerolastic (Bladed) or structural devoted codes (FAROB).

Learning objectives
It can be concluded that the as learning objectives achieved the combination of different nature algorithms can be combined to provide the best response.
It has been analyzed how traditional optimization techniques are enriched with new evolutionary procedures.
The simulation environment and the interaction between different codes and disciplines involved have been studied carefully.

and Industrial Aerodynamics 80 (1999) 191Ð206
1-Optimization method for wind turbine rotors
P. Fuglsang*, H.A. Madsen
Ris~ National Laboratory, DK-4000 Roskilde, Denmark
Received 10 December 1996; accepted 21 May 1998

2-Shape Optimization of Wind Turbine
Wang Xudong, State Key Laboratory of Mechanical Transmission, ChongQing University, Chongqing,
China; Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Lyngby,
Wen Zhong Shen*, Wei Jun Zhu and Jens Nørkær Sørensen, Department of Mechanical Engineering,
Technical University of Denmark, DK-2800 Lyngby, Denmark
Chen Jin, State Key Laboratory of Mechanical Transmission, ChongQing University, Chongqing,

3-Optimal Design of Horizontal-Axis
Wind Turbines Using
Blade-Element Theory and
Evolutionary Computation
Ernesto Benini
e-mail: [email protected]
Andrea Toffolo
e-mail: [email protected]
Dipartimento di Ingegneria Meccanica,
Universita` di Padova,
Via Venezia 1, 35131 Padova, Italy

4-Development of the Risø Wind
Turbine Airfoils
Peter Fuglsang, Christian Bak, Wind Energy Department, Risø National Laboratory, P.O. Box 49, DK-
4000 Roskilde, Denmark, Phone: +45 4677 5071, Fax: +45 4677 5960, e-mail: [email protected]
Wind Energ. 2004; 7:145–162 (DOI: 10.1002/we.117)

5-Improvement of airfoil design using smooth curvature technique
Jin Chen, Quan Wang*, Xiaoping Pang, Songlin Li, Xiaofeng Guo
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China
Renewable Energy 51 (2013) 426e435

6-Airfoil inverse design and optimization
by means of viscous-inviscid techniques
A. Filippone ~
The Test Station for Wind Turbines, Ris~ National Laboratory, Roskilde, Denmark
Journal of Wind Engineering
and Industrial Aerodynamics 56 (1995) 123-136

7-A practical approach for selecting optimum
wind rotors
K.Y. Maalawi, M.A Badr
Mechanical Engineering Department, National Research Center, Dokki, Cairo, Egypt
Renewable Energy 28 (2003) 803–822

8-Modification of the NACA 632-415
Leading Edge for Better
Aerodynamic Performance
Christian Bak
e-mail: [email protected]
Peter Fuglsang
e-mail: [email protected]
Wind Energy Department,
Risø National Laboratory,
P.O. Box 49, DK-4000 Roskilde, Denmark
@DOI: 10.1115/1.1506324#

9-Evolutionary algorithms approach to the solution of mixed integer non-linear programming problems
Lino Costa,
Pedro Oliveira Corresponding author contact information, E-mail the corresponding author
Department of Production and Systems Engineering, University of Minho, 4710 Braga, Portugal
Received 7 January 2000
Revised 25 October 2000
Accepted 25 October 2000
Available online 6 April 2001, How to Cite or Link Using DOI

Department of Industrial and Systems Engineering, Asbikaga Institute of Technology,
Ashikaga 326, Japan

11. D. E. Goldberg. Genetic Algorithms in Search, Optimization & Machine Learning. Addison Wesley, Reading, MA

12. Z. Michalewicz. Generic Algorithms + Data Structures = Evolution Programs, 2nd Edition. Springer, Berlin (1994).

13. M. Gen and R. Cheng. Genetic Algorithms and Engineering Design. Wiley, New York (1996




17-GL 2010

18- DNV

19-IEC 61400

20-D.E.Goldberg, “Genetic Algorithms in Search, Optimization and Machine learning”. Reading, MA: Addison Wesley.1989.

21-K.A. DeJong, “An analysis of the behavior of a class genetic adaptative systems” PhD. Dissertation, University of Michigan.1975.

22-M. Srinivas, and L.M. Patnaik. “Adaptative Probabilities of Crossover and Mutation in Genetic Algorithms”. IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL.24, NO.4. APRIL 1994.

23- Nelder, John A.; R. Mead (1965). "A simplex method for function minimization". Computer Journal 7: 308–313. doi:10.1093/comjnl/7.4.308.