Model Predictive Control for Wake Redirection in Wind Farms: a Koopman Dynamic Mode Decomposition Approach

Abstract

Wind farms are high order systems whose dynamics are governed by non linear partial differential equations with no known analytic solution, making the design and implementation of numerical optimal controllers in high fidelity fluid dynamics solvers computationally expensive and unsuitable for real time usage. Reduced order state models provide a possible route to the design and implementation of practical cooperative wind farm controllers. This work makes use of an innovative algorithm in the context of wind farm modelling - Input Output Dynamic Mode Decomposition - to find suitable reduced order models to be used for model predictive control. The contribution of the work in this article resides in deriving a reduced order model from high fidelity simulation data where wake redirection control by yaw misalignment is evaluated. A model based predictive controller is designed and tested. In the present case study it is shown that a reduced order linear state space model with 37 states can accurately reproduce the downstream turbine generator power dynamics with a fit of 88%, reconstruct the upstream turbine wake with an average normalized root mean squared error of 4% and that optimal controllers can be designed for a collective power reference tracking problem.