Weighted Least Squares Approach for an Adaptive Aerodynamic Engineered Structure With Twist Transformation

Abstract

A design concept for a wind turbine blade with an adaptive twist transformation is presented. The design improves partial-load wind capture by adapting the twist distribution in relation to wind speed. Structural adaptability is enabled by actuating a series of compliant sections that are mounted on a relatively rigid spar. The sections are assumed to have a unique stiffness that is achievable through additive manufacturing technology. The authors' prior work employed an aerodynamic model to establish the theoretical blade twist distribution as a function of wind speed. The work in this paper focuses on a method to optimize the stiffness of each blade section that has been previously defined. A mathematical model is proposed to support design optimization. The model is parameterized in terms of actuator locations and the torsional stiffness ratios of each blade section. These parameters are optimized to allow the blade to adapt its twist distribution to match the prescribed configurations. The optimization is completed using a weighted-least squares approach that minimizes the error between the theoretical and practical design. The selected solution is based upon the configuration that maximizes production. Weights are assigned to bias the performance of the blade toward different operating regimes. Our results indicate that quadratically penalizing twist angle errors toward the blade tip increases power capture. A Rayleigh distribution is used to create three sets of wind data, which vary in average speed. These sets of data are used to evaluate the performance of the proposed blade and design technique.