A revised theoretical analysis of aerodynamic optimization of horizontal-axis wind turbines based on BEM theory

Abstract

This article presents a revised theoretical analysis of aerodynamic optimization of horizontal-axis wind turbines, including drag effects, based on Blade Element-Momentum theory. It is demonstrated that horizontal-axis wind turbines can never reach Betz limit, even in the absence of drag effects. Formulating the optimization problem as a nonlinear programming problem with equality and inequality constraints, it is confirmed that, in order to reach maximum performance, all blade sections have to operate under maximum lift-to-drag ratio condition. This condition has been adopted in the literature, but without a mathematical proof that is indeed true. The optimal distributions of axial and tangential induction factors are determined adopting a different approach from those found in the literature. The results include a diagram where both, the optimal operating tip speed ratio and the maximum power coefficient, can be quickly found as functions of the maximum airfoil lift-to-drag ratio.