Structural and Multidisciplinary Optimization

, Volume 53, Issue 1, pp 15–27 | Cite as

Multidisciplinary dynamic optimization of horizontal axis wind turbine design

  • Anand P. DeshmukhEmail author
  • James T. Allison


The design of physical (plant) and control aspects of a dynamic system have traditionally been treated as two separate problems, often solved in sequence. Optimizing plant and control design disciplines separately results in sub-optimal system designs that do not capitalize on the synergistic coupling between these disciplines. This coupling is inherent in most actively controlled dynamic systems, including wind turbines. In this case structural and control design both affect energy production and loads on the turbine. This article presents an integrated approach to achieve system-optimal wind turbine designs using co-design, a design methodology that accounts directly for the synergistic coupling between physical and control system design. A case study, based on multidisciplinary simulation, is presented here that demonstrates a promising increase (up to 8%) in annualized wind turbine energy production compared to the results of a conventional sequential design strategy. The case study also revealed specific synergistic mechanisms that enable performance improvements, which are accessible via co-design but not sequential design.


Wind Turbines Structural Design Optimal Control Dynamic Optimization 



Rotor power, W


Instantaneous wind speed, m/s


Cut–in wind speed, m/s


Cut-out wind speed, m/s


Plant design vector


Rotor torque, N ⋅m


Generator torque, N ⋅m


Gear ratio


Rotor inertia, kg ⋅m2


Generator side inertia, kg ⋅m2


Rotor torsional damping, N ⋅m/rad/s


Generator side torsional damping, N ⋅m/rad/s


Rotor speed, RPM


Speed on high-speed side (Generator), RPM


Blade pitch angle, deg


Tower height at the rotor hub, m


Turbine rotor radius, m


Turbine blade hub radius, m


Turbine rotor diameter, m


Turbine blade hub diameter, m


Rotor power coefficient


Rotor torque coefficient


Blade tip–speed ratio


Air density, kg/m3


Annualized energy production, kW ⋅h



This work was partially supported by the Clean Energy Education and Research Fellowship awarded to first author by the Graduate College at the University of Illinois at Urbana-Champaign. This support is gratefully acknowledged.


  1. Allison JT (2013) Plant-limited co-design of an energy-efficient counterbalanced robotic manipulator. ASME J Mech Des 135(10):101,003CrossRefGoogle Scholar
  2. Allison JT, Herber DR (2014) Multidisciplinary design optimization of dynamic engineering systems. AIAA J 52(4):691–710CrossRefGoogle Scholar
  3. Allison JT, Guo T, Han Z (2014) Co-design of an active suspension using simultaneous dynamic optimization. ASME J Mech Des 136(8):081,003CrossRefGoogle Scholar
  4. Ashuri T, Zaaijer MB, Martins JRRA, van Bussel GJW, van Kuik GA (2014) Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy. Renew Energy 68:893–905CrossRefGoogle Scholar
  5. Bajodah AH (2005) Nonminimal kane’s equations of motion for multibody dynamical systems subject to nonlinear nonholonomic constraints. Multibody System Dynamics 14(2):155–187CrossRefMathSciNetzbMATHGoogle Scholar
  6. Benini E, Toffolo A (2002) Optimal design of horizontal-axis wind turbines using blade-element theory and evolutionary computation. Journal of Solar Energy Engineering 124(4):357–363CrossRefGoogle Scholar
  7. Betts JT (2010) Practical methods for optimal control and estimation using nonlinear programming. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  8. Biegler LT (2010) Nonlinear programming: concepts, algorithms, and applications to chemical processes. SIAMGoogle Scholar
  9. Boukhezzar B, Lupu L, Siguerdidjane H, Hand M (2007) Multivariable control strategy for variable speed, variable pitch wind turbines. Renew Energy 32:1273–1287CrossRefGoogle Scholar
  10. Bryson AE, Ho YC (1975) Applied optimal control: optimization, estimation and control. Taylor & FrancisGoogle Scholar
  11. Burnham A (2009) Variable rotor-resistance control of wind turbine generators. In: Power & energy society general meeting. IEEE, pp 1–6Google Scholar
  12. Chen L, MacDonald E (2012) Considering landowner participation in wind farm layout optimization. J Mech Des 134:084,506CrossRefGoogle Scholar
  13. Chen L, MacDonald E (2014) A system-level cost-of-energy wind farm layout optimization with landowner modeling. Energy Convers Manag 77:484–494CrossRefGoogle Scholar
  14. Chowdhury S, Messac A, Zhang J, Castillo L, Lebron J (2010) Optimizing the unrestricted placement of turbines of differing rotor diameters in a wind farm for maximum power generation. In: ASME 2010 international design engineering technical conferences and computers and information in engineering conference, MontrealGoogle Scholar
  15. Chowdhury S, Zhang J, Messac A, Castillo L (2012) Unrestricted wind farm layout optimization (uwflo): investigating key factors influencing the maximum power generation. Renew Energy 38:16–30CrossRefGoogle Scholar
  16. Chowdhury S, Tong W, Messac A, Zhang J (2013a) A mixed-discrete particle swarm optimization algorithm with explicit diversity-preservation. Struct Multidiscip Optim 47(3):367–388CrossRefMathSciNetzbMATHGoogle Scholar
  17. Chowdhury S, Zhang J, Messac A, Castillo L (2013b) Optimizing the arrangement and the selection of turbines for wind farms subject to varying wind conditions. Renew Energy 52:273–282CrossRefGoogle Scholar
  18. Cramer EJ, Dennis JE, Frank PD, Lewis RM, Shubin GR (1993) Problem formulation for multidisciplinary optimization. SIAM J Optim 4:754–776CrossRefMathSciNetGoogle Scholar
  19. Dang DQ, Wu S, Yang W, Cai W (2009) Model predictive control for maximum power capture of variable speed wind turbines. In: IEEE international conference on control and automation, ChristchurchGoogle Scholar
  20. Dang DQ, Wu S, Yang W, Cai W (2010) Ieee international conference on control and automation. In: IPEC2010Google Scholar
  21. DOE (2008) 20 % wind energy by 2030: Increasing wind energy’s contribution to u.s. electricy supply. Tech. Rep. DOE/GO-102008-2567, US Department of Energy,
  22. DuPont BL, Cagan J (2012) An extended pattern search approach to wind farm layout optimization. J Mech Des 134(8):081,002CrossRefGoogle Scholar
  23. Fathy H, Reyer J, Papalambros P, Ulsoy AG (2001) On the coupling between the plant and controller optimization problems. In: 2001 American control conference. IEEE, pp 1864–1869Google Scholar
  24. Forcier LC, Joncas S (2012) Development of a structural optimization strategy for the design of next generation large thermoplastic wind turbine blades. Struct Multidiscip Optim 45(6):889–906CrossRefzbMATHGoogle Scholar
  25. Giguere P, Selig MS, Tangler JL (1999) Blade design trade-offs using low-lift airfoils for stall-regulated hawts. Journal of Solar Energy Engineering:217–223Google Scholar
  26. He Y, Monahan AH, Jones CG, Dai A, Biner S, Caya D, Winger K (2010) Probability distributions of land surface wind speeds over north america. J Geophys Res Atmos 115(D4):1–9CrossRefGoogle Scholar
  27. Holley WE (2003) Wind turbine dynamics and control: Issues and challenges. In: American control conference, DenverGoogle Scholar
  28. Jonkman J (2009) Dynamics of offshore floating wind turbines - model development and verification. Wind Energy:459–492Google Scholar
  29. Jonkman J, Buhl M (2004) New developments for the nwtc’s fast aeroelastic hawt simulator. In: 42nd aerospace sciences meeting and exhibit conference. AIAA, RenoGoogle Scholar
  30. Jonkman JM, Buhl ML (2005) Fast user’s guide. Tech. Rep. NREL/EL-500-38230, National renewable energy laboratoryGoogle Scholar
  31. Jureczko M, Pawlak M, Mezyk A (2005) Optimisation of wind turbine blades. J Mater Process Technol:463–471Google Scholar
  32. Kusiak A, Li W, Song Z (2010) Dynamic control of wind turbines. Renew Energy:456–463Google Scholar
  33. Lu S, Kim HM (2014) Wind farm layout design optimization through multi-scenario decomposition with complementarity constraints. Eng Optim 46(12):1669–1693Google Scholar
  34. Maalawi KY, Negm HM (2002) Optimal frequency design of wind turbine blades. J Wind Eng Ind Aerodyn:961–986Google Scholar
  35. Martins JRRA, Lambe AB (2013) Multidisciplinary design optimization: a survey of architectures. AIAA J 51:2049–2075Google Scholar
  36. Moriarty P, Hansen A (2005) Aerodyn theory manual. Technical Report NREL/TP-500-36881, National Renewable Energy LaboratoryGoogle Scholar
  37. Muljadi E, Butterfield CP (2001) Pitch-controlled variable-speed wind turbine generation. IEEE Trans Ind Appl 37(1):240–246Google Scholar
  38. Munteanu I, Bratcu AI, Cutululis NA, Ceanga E (2008) Optimal control of wind energy systems. Advances in industrial control. Springer, London, pp 76–77Google Scholar
  39. Namik H, Stol K (2011) Performance analysis of individual blade pitch control of offshore wind turbines on two floating platforms. Mechatronics 21(4):691–703CrossRefGoogle Scholar
  40. Negm HM, Maalawi KY (2000) Structural design optimization of wind turbine towers. Comput Struct:649–666Google Scholar
  41. Nicholson JC (2011) Design of wind turbine tower and foundation systems: optimization approach. Master’s thesis. University of Iowa, USAGoogle Scholar
  42. Pontryagin LS (1962) The mathematical theory of optimal processes. InterscienceGoogle Scholar
  43. Quarton DC (1998) The evolution of wind turbine design analysis-a twenty year progress review. Wind Energy 1:5–24Google Scholar
  44. Reyer J, Fathy H, Papalambros P, Ulsoy A (2001) Comparison of combined embodiment design and control optimization strategies using optimality conditions. In: Conferences International Design Engineering Technical, Renaud J E (eds) ASME, pp 1023– 1032Google Scholar
  45. Sale D (2010) Harp-opt user’s guide. Nwtc design codes, National Renewable Energy Laboratory,
  46. Scholbrock A, Fleming P, Fingersh L, Wright A, Schlipf D, Haizmann F, Belen F (2013) Field testing lidar-based feed-forward controls on the nrel controls advanced research turbine. In: 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and AstronauticsGoogle Scholar
  47. Sobieszczanski-Sobieski J, Haftka RT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Structural optimization 14(1):1–23CrossRefGoogle Scholar
  48. Soltani M, Wsniewski R, Brath P, Boyd S (2011) Load reduction of wind turbines using receding horizon control. In: International Conference on Control Applications (CCA), DenverGoogle Scholar
  49. Stotsky A, Egardt B (2013) Individual pitch control of wind turbines: Model-based approach. Proc IMechE Part I J Syst Control Eng 227(7):602–609CrossRefGoogle Scholar
  50. Thiringer T, Linders J (1993) Control by variable rotor speed of a fixed-pitch wind turbine operating in a wide speed range. Transactions on Energy Conversion 8(3):520–526CrossRefGoogle Scholar
  51. Uys P, Farkas J, Jármai K, van Tonder F (2007) Optimisation of a steel tower for a wind turbine structure. Eng Struct 29(7):1337– 1342CrossRefGoogle Scholar
  52. Wan Z, Kothare MV (2003) An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39(5):837–846CrossRefMathSciNetzbMATHGoogle Scholar
  53. Wang Y, Boyd S (2010) Fast model predictive control using online optimization. IEEE Trans Control Syst Technol 18(2):267– 278CrossRefGoogle Scholar
  54. Xudong W, Shen WZ, Zhu WJ, Sorensen JN (2009) Shape optimization of wind turbine blades. Wind Energy:781–803Google Scholar
  55. Yoshida S (2006) Wind turbine tower optimization method using a genetic algorithm. Wind Eng 30(6):453–469Google Scholar
  56. Zakhama R, Abdalla MM (2010) Wind load modeling for topology optimization of continuum structures. Struct Multidiscip Optim 42(1):157–164Google Scholar
  57. Zeid I (1991) CAD/CAM theory and practice. McGraw-Hill series in mechanical engineering, McGraw-HillGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Engineering Systems Design LaboratoryUniversity of Illinois at Urbana–ChampaignUrbanaUSA

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