A fast stochastic solution method for the Blade Element Momentum equations for long‐term load assessment

Unsteady power output and long‐term loads (extreme and fatigue) drive wind turbine design. However, these loads are difficult to include in optimization loops and are typically only assessed in a post‐optimization load analysis or via reduced‐order methods. Both alternatives yield suboptimal results. The reason for this difficulty lays in the deterministic approaches to long‐term loads assessment. To model the statistics of lifetime loads they require the analysis of many unsteady load cases, generated from many different random seeds—a computationally expensive procedure. In this paper, we present an alternative: a stochastic solution for the unsteady aerodynamic loads based on a projection of the unsteady Blade Element Momentum (BEM) equations onto a stochastic space spanned by chaos exponentials. This approach is similar to the increasingly popular polynomial chaos expansion, but with 2 major differences. First, the BEM equations constitute a random process, varying in time, while previous polynomial chaos expansion methods were concerned with random parameters (ie, random but constant in time or initial values). Second, a new, more efficient basis (the exponential chaos) is used. This new stochastic method enables us to obtain unsteady long‐term loads much faster, enabling unsteady loads to become accessible inside wind turbine optimization loops. In this paper we derive the stochastic BEM solution and present the most relevant results showing the accuracy of the new method.