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

Michael K. McWilliam, Antariksh C. Dicholkar, Frederik Zahle and Taeseong Kim
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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

Energies, 2022, vol. 15, issue 9, 1-19

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.

Keywords: wind turbines; optimization; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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