Convergence and efficiency of global bases using proper orthogonal decomposition for capturing wind turbine wake aerodynamics

Abstract

Wind turbine wakes affect power production and loads but are highly turbulent and therefore complex to model. Proper orthogonal decomposition (POD) has often been applied for reduced-order models (ROMs), as POD yields an orthogonal basis optimal in terms of capturing the turbulent kinetic energy content. POD is typically used to understand flow physics and reconstruct a specific flow case. However, reduced-order models have been proposed for predicting wind turbine wake aerodynamics by applying POD on multiple flow cases with different governing parameters to derive a global basis intended to represent all flows within the parameter space. This article evaluates the convergence and efficiency of global POD bases covering multiple cases of wind turbine wake aerodynamics in large wind farms. The analysis shows that the global POD bases have better performance across the parameter space than the optimal POD basis computed from a single dataset. The error associated with using a global basis across the parameter space of reconstructions decreases and converges as the dataset is expanded with more flow cases, and there is a low sensitivity as to which datasets to include. It is also shown how this error is an order of magnitude smaller than the truncation error for 100 modes. Finally, the global basis has the advantage of providing consistent physical interpretability of the highly turbulent flow within wind farms.