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Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades

Author

Listed:
  • Michael K. McWilliam

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Antariksh C. Dicholkar

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Frederik Zahle

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Taeseong Kim

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

Abstract

Post-Optimum Sensitivity Analysis (POSA) extends numerical design optimization to provide additional information on how the design and performance would change if various parameters and constraints were varied. POSA is challenging since it typically requires accurate gradients and gradient-based optimization problems that provide Lagrange multipliers. To overcome this problem, this paper introduces a technique to automatically tune gradients with statistical methods and algorithms to calculate the Lagrange multipliers after an optimization. This allows these methods to be applied to problems with noisy gradients or problems solved with gradient-free optimization algorithms. These methods have been applied to swept wind turbine blades. Swept blades can reduce wind turbine loads by twisting out of the wind when the wind speed increases. The methods have shown that introducing design freedom in the sweep, blade root flap-wise bending moments and blade tip deflection has a weaker influence on the design. Instead, blade root torsion moment and material failure become the driving constraints.

Suggested Citation

  • Michael K. McWilliam & Antariksh C. Dicholkar & Frederik Zahle & Taeseong Kim, 2022. "Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades," Energies, MDPI, vol. 15(9), pages 1-19, April.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:9:p:2998-:d:797666
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    References listed on IDEAS

    as
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    2. E. Castillo & A. J. Conejo & C. Castillo & R. Mínguez & D. Ortigosa, 2006. "Perturbation Approach to Sensitivity Analysis in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 49-74, January.
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    4. Ashuri, T. & Zaaijer, M.B. & Martins, J.R.R.A. & van Bussel, G.J.W. & van Kuik, G.A.M., 2014. "Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy," Renewable Energy, Elsevier, vol. 68(C), pages 893-905.
    5. Larwood, Scott & van Dam, C.P. & Schow, Daniel, 2014. "Design studies of swept wind turbine blades," Renewable Energy, Elsevier, vol. 71(C), pages 563-571.
    6. Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
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