Real-time Model Predictive Control for Wind Farms: A Koopman Dynamic Mode Decomposition Approach

Abstract

This work demonstrates the application of Koopman-based system identification to wind farm control, where wake interactions are highly nonlinear in nature. The linear models identified using measurements and signals available in real-time, i.e effective wind speed at the turbine rotors and control signals, show more than 85 % variance-accounted-for (VAF). Different Koopman lifting function combinations, motivated by the 2D Navier-Stokes equations, governing the underlying wake interaction, are compared. The obtained Koopman models are used in closed-loop in the WFSim environment. The design of the qLMPC wind farm controller is provided and it is shown that the underlying quadratic programming (QP) converges in milliseconds thus making this design applicable in real-time to small wind farms. Finally, the results for power reference tracking obtained with qLMPC are shown based on estimated wind. It is demonstrated that using Koopman extended dynamic mode decomposition (EDMD) for wind estimation can lead to high-quality farm level control in the absence of wind measurements.