Evolutionary computing methodology for small wind turbine supporting structures

  • Jakub Bukala
  • Krzysztof Damaziak
  • Hamid Reza Karimi
  • Jerzy MalachowskiEmail author
  • Kjell Gunnar Robbersmyr
Open Access


The paper presents a comprehensive, complex, numerical, optimization methodology (computational framework) dedicated for supporting structures of small-scale wind turbines. The small wind turbine (SWT) supporting structure is one of the key components determining the cost of such a device. Therefore, the supporting structure optimization will allow cost reduction and, hence, popularization of these devices around the world. The presented methodology is based on the following: single-objective (aggregation-approach to multi-objective problem) evolutionary algorithm driven optimization, finite-element structural analyses, estimation of wind energy capture efficiency (coupled aero-servo-elastic numerical simulations), and economic evaluation (based on real meteorological data). Then, the methodology is proposed for a guy-wired mast structure of an arbitrary chosen SWT model. The optimization of chosen design features of the structure is performed and as a result the optimal solution for given assumptions is presented and scaling factor for that case is identified (total mass of the foundations). The successful use of combined numerical methods (genetic algorithms, FE method analyses, coupled aero-servo-elastic numerical simulations, pre-/post-processing scripts, and economic evaluation models) is the main novelty of this work.


Small wind turbine Optimization Finite element method Genetic algorithm Evolutionary algorithm 


Funding information

The study was supported by the Polish-Norwegian Research Programme operated by the National Centre for Research and Development under the Norwegian Financial Mechanism 2009–2014 in the frame of Project Contract No. Pol-Nor/200957/47/2013.


  1. 1.
    Gsänger S, Pitteloud JD (2015) Small wind world report summary 2015. WWEA. Accessed 20 July 2015
  2. 2.
    Grijalva S, Umer Tariq M (2011) Prosumer-based smart grid architecture enables a flat, sustainable electricity industry 978-1-61284-220-2/11/$26.00 ©2011 IEEEGoogle Scholar
  3. 3.
    International Electrotechnical Commission (2013) IEC 61400-2: wind turbines—part 2: small wind turbines. ISBN 978-2-8322-1284-4Google Scholar
  4. 4.
    Bukala J, Damaziak K, Kroszczynski K, Krzeszowiec M, Malachowski J (2015) Investigation of parameters influencing the efficiency of small wind turbines. J Wind Eng Ind Aerodyn 146:29–38. CrossRefGoogle Scholar
  5. 5.
    Gasch R, Twele J (2012) Wind power plants: fundamentals, design, construction and operation, 2nd edn. Springer, Berlin ISBN 978-3-642-22937-4CrossRefGoogle Scholar
  6. 6.
    Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248. CrossRefGoogle Scholar
  7. 7.
    Chehouri A, Younes R, Ilinca A, Perron J (2016) Wind turbine design: multi-objective optimization. Wind turbines—design, control and applications, edited by Abdel Ghani Aissaoui and Ahmed Tahor. InTech, Rijeka, Croatia, Chapter 6:121–147.
  8. 8.
    Schwefel H-PP (1993) Evolution and optimum seeking: the six generation. Wiley, Hoboken ISBN 0471571482Google Scholar
  9. 9.
    Hajela P, Lin C-Y (1992) Genetic search strategies in multicriterion optimal design. Struct Optim 4(2):99–107. CrossRefGoogle Scholar
  10. 10.
    Alexandrov NM, Hussaini MY (1997) Multidisciplinary design optimization: state of the art. 80, SIAM, United States. ISBN 978-0898713596Google Scholar
  11. 11.
    Deb K (2001) Multi-objective optimization using evolutionary algorithms, vol 16. Wiley, Hoboken ISBN 047187339XzbMATHGoogle Scholar
  12. 12.
    Muskulus M, Schafhirt S (2014) Design optimization of wind turbine support structures—a review. J Ocean Wind Energy 1:12–22Google Scholar
  13. 13.
    Chehouri A, Younes R, Ilinca A, Perron J (2015) Review of performance optimization techniques applied to wind turbines. Appl Energy 142:361–388. CrossRefGoogle Scholar
  14. 14.
    Negm HM, Maalawi KY (2000) Structural design optimization of wind turbine towers. Comput Struct 74:649–666. CrossRefGoogle Scholar
  15. 15.
    Uys PE, Farkas J, Jarmai K, van Tonder F (2007) Optimisation of a steel tower for a wind turbine structure. Eng Struct 29:1337–1342. CrossRefGoogle Scholar
  16. 16.
    Nicholson JC, Arora JS, Goyal D, Tinjum JM (2013) Multi-objective structural optimization of wind turbine tower and foundation systems using isight: a process automation and design exploration software. 10th World Congress on Structural and Multidisciplinary Optimization, 19–24 May 2013, Orlando, Florida, USAGoogle Scholar
  17. 17.
    Yoshida S (2006) Wind turbine tower optimization method using a genetic algorithm. Wind Eng 30:453–470. CrossRefGoogle Scholar
  18. 18.
    Yıldırım S, Özkol I (2010) Wind turbine tower optimization under various requirements by using genetic algorithm. Engineering 2:641–647. CrossRefGoogle Scholar
  19. 19.
    Blachowski B, Gutkowski W (2016) Effect of damaged circular flange-bolted connections on behaviour of tall towers, modelled by multilevel substructuring. Eng Struct 111:93–103. CrossRefGoogle Scholar
  20. 20.
    Bottasso CL, Campagnolo F, Croce A (2012) Multi-disciplinary constrained optimization of wind turbines. Multibody Syst Dyn 27(1):21–53. MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Wang L, Wang T, Wu J, Chen G (2017) Multi-objective differential evolution optimization based on uniform decomposition for wind turbine blade design. Energy 120:346–361. CrossRefGoogle Scholar
  22. 22.
    Barnes RH, Morozov EV (2016) Structural optimisation of composite wind turbine blade structures with variations of internal geometry configuration. Compos Struct 152:158–167. CrossRefGoogle Scholar
  23. 23.
    Fagan EM, Flanagan M, Leen SB, Flanagan T, Doyle A, Goggins J (2017) Physical experimental static testing and structural design optimisation for a composite wind turbine blade. Compos Struct 164:90–103. CrossRefGoogle Scholar
  24. 24.
    Kusiak A, Zhang ZJ, Li MY (2010) Optimization of wind turbine performance with data-driven models. IEEE Trans Sustain Energy 1(2):66–76. CrossRefGoogle Scholar
  25. 25.
    Chen J, Shen WZ, Wang Q, Pang X, Li S, Guo X (2013) Structural optimization study of composite wind turbine blade. Mater Des 46:247–255. CrossRefGoogle Scholar
  26. 26.
    Huang J, Yuan Y, Wang Z, Qi Z, Xing C, Gao J (2018) A global-to-local registration and error evaluation method of blade profile lines based on parameter priority. Int J Adv Manuf Technol 94:3829–3839. CrossRefGoogle Scholar
  27. 27.
    Pourrajabian A, Afshar PAN, Ahmadizadeh M, Wood D (2016) Aero-structural design and optimization of a small wind turbine blade. Renew Energy 87:837–848. CrossRefGoogle Scholar
  28. 28.
    Vucina D, Marinic-Kragic I, Milas Z (2016) Numerical models for robust shape optimization of wind turbine blades. Renew Energy 87:849–862. CrossRefGoogle Scholar
  29. 29.
    Tang X, Huang X, Peng R, Liu X (2015) A direct approach of design optimization for small horizontal axis wind turbine blades. Procedia CIRP 36:12–16. CrossRefGoogle Scholar
  30. 30.
    Vitale AJ, Rossi AP (2008) Computational method for the design of wind turbine blades. Int J Hydrog Energy 33:3466–3470. CrossRefGoogle Scholar
  31. 31.
    Olasek K, Karczewski M, Lipian M, Wiklak P, Jozwik K (2016) Wind tunnel experimental investigations of a diffuser augmented wind turbine model. Int J Numer Methods Heat Fluid Flow 26:2033–2047. CrossRefGoogle Scholar
  32. 32.
    Asl HJ, Yoon J (2016) Power capture optimization of variable-speed wind turbines using an output feedback controller. Renew Energy 86:517–525. CrossRefGoogle Scholar
  33. 33.
    Gao R, Gao Z (2016) Pitch control for wind turbine systems using optimization, estimation and compensation. Renew Energy 91:501–515. CrossRefGoogle Scholar
  34. 34.
    Ayadi M, Derbe N (2017) Nonlinear adaptive backstepping control for variable-speed wind energy conversion system-based permanent magnet synchronous generator. Int J Adv Manuf Technol 92:39–46. CrossRefGoogle Scholar
  35. 35.
    Akbar MA, Mustafa V (2016) A new approach for optimization of vertical axis wind turbines. J Wind Eng Ind Aerodyn 153:34–45. CrossRefGoogle Scholar
  36. 36.
    Kear M, Evans B, Ellis R, Rolland S (2016) Computational aerodynamic optimisation of vertical axis wind turbine blades. Appl Math Model 40:1038–1051. MathSciNetCrossRefGoogle Scholar
  37. 37.
    Marinic-Kragic I, Vucina D, Milas Z (2018) Numerical workflow for 3D shape optimization and synthesis of vertical-axis wind turbines for specified operating regimes. Renew Energy 115:113–127. CrossRefGoogle Scholar
  38. 38.
    Clifton-Smith MJ, Wood DH (2010) Optimisation of self-supporting towers for small wind turbines. Wind Eng 34:561–578CrossRefGoogle Scholar
  39. 39.
    Deb K (2014) Multi-objective optimization. Search methodologies. Introductory tutorials in optimization and decision support techniques. Springer, Boston, pp 403–449Google Scholar
  40. 40.
    Stander N, Roux W, Basudhar A, Eggleston T, Goel T, Craig K (2014) LS-OPT® user’s manual. A Design optimization and probabilistic analysis tool for the engineering analyst. Copyright© LIVERMORE SOFTWARE TECHNOLOGY CORPORATIONGoogle Scholar
  41. 41.
    MSC.Software Corporation (2003) MSC.Nastran 2004—reference manual. Printed in USA, ©2003Google Scholar
  42. 42.
    Buhl ML, Manjock A (2006) A comparison of wind turbine aeroelastic codes used for certification. American Institute of Aeronautics and Astronautics. Accessed 19 March 2015
  43. 43.
    Brusca S, Lanzafame R, Messina M (2014) Flow similitude laws applied to wind turbines through blade element momentum theory numerical codes. Int J Energy Environ Eng 5:313–322. CrossRefGoogle Scholar
  44. 44.
    Moriarty PJ, Hansen AC (2015) AeroDyn theory manual. National Renewable Energy Laboratory. Accessed 20 March 2015
  45. 45.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, Chichester, pp 317–337 ISBN 978-1-118-63270-3zbMATHGoogle Scholar
  46. 46.
    Bilir L, Imir M, Devrim Y, Albostan A (2015) Seasonal and yearly wind speed distribution and wind power density analysis based on Weibull distribution function. Int J Hydrog Energy 40:15301–15310. CrossRefGoogle Scholar
  47. 47.
    Drew DR, Barlow JF, Cockerill TT, Vahdati MM (2015) The importance of accurate wind resource assessment for evaluating the economic viability of small wind turbines. Renew Energy 77:493–500. CrossRefGoogle Scholar
  48. 48.
    Holland JH (1975) Adaptation in natural and artificial systems. Univ. Michigan, Ann ArborGoogle Scholar
  49. 49.
    Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Publishing Company, BostonzbMATHGoogle Scholar
  50. 50.
    Bendsoe MP, Mota Soares CA (1992) Topology design of structures. Proceedings of the NATO Advanced Research Workshop on Topology Design of Structures, SesimbraGoogle Scholar
  51. 51.
    Mitsuo G, Runwei C (2000) Genetic algorithms and engineering optimization. Wiley, HobokenGoogle Scholar
  52. 52.
    Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidisc Optim 26:369–395. MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Lagaros ND, Papadrakakis M, Kokossalakis G (2002) Structural optimization using evolutionary algorithms. Comput Struct 80:571–589. CrossRefGoogle Scholar
  54. 54.
    Grefenstette JJ (1986) Optimization of control parameters for genetic algorithms. IEEE Trans Syst Man Cybern 16(1):122–128. CrossRefGoogle Scholar
  55. 55.
    Somers DM (2005) The S833, S834, and S835 Airfoils. Subcontract report. National Renewable Energy Laboratory.,S834,S835_Design.pdf. Accessed 20 May 2016
  56. 56.
    Bukala J, Damaziak K, Karimi HR, Malachowski J (2016) Aero-elastic coupled numerical analysis of small wind turbine—generator modeling. Wind Struct 23(6):577–594. CrossRefGoogle Scholar
  57. 57.
    Grierson DE, Pak WH (1993) Optimal sizing, geometrical and topological design using a genetic algorithm. Struct Optim 6:151–159. CrossRefGoogle Scholar
  58. 58.
    Bukala J, Damaziak K, Karimi HR, Kroszczynski K, Krzeszowiec M, Malachowski J (2015) Modern small wind turbine design solutions comparison in terms of estimated cost to energy output ratio. Renew Energy 83:1166–1173. CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Jakub Bukala
    • 1
  • Krzysztof Damaziak
    • 1
  • Hamid Reza Karimi
    • 2
  • Jerzy Malachowski
    • 1
    Email author
  • Kjell Gunnar Robbersmyr
    • 3
  1. 1.Department of Mechanics and Applied Computer Science, Faculty of Mechanical EngineeringMilitary University of TechnologyWarsawPoland
  2. 2.Department of Mechanical EngineeringPolitecnico di MilanoMilanItaly
  3. 3.Department of Engineering SciencesUniversity of AgderGrimstadNorway

Personalised recommendations