A data-driven flow model for wind-farm control based on Koopman mode decomposition of large-eddy simulations*

The promise of increasing farm performance through turbine control has caused significant interest in wind farm control research in recent years. However, an incompatibility between control model adequacy and computational cost persists up to date: standard engineering models fail to account for relevant nonlinear flow physics on the one hand, yet accurate nonlinear models such as large-eddy simulations (LES) are still too costly for real-time control purposes on the other hand. In the current work, we present a data-driven linear flow model for wind-farm control based on Koopman theory, in which observables of the underlying nonlinear flow dynamics are lifted into a space on which they evolve linearly through the Koopman operator. By approximating this operator using extended dynamic mode decomposition of LES data, we can incorporate nonlinear flow dynamics into a computationally efficient linear model. Performance of the Koopman model is compared to a nonlinear LES for an array of aligned wind turbines. Finally, opportunities and challenges for application in model-predictive control are discussed.