Model Predictive Active Power Control for Optimal Structural Load Equalization in Waked Wind Farms

Abstract

In this article, we propose a model predictive active power control (APC) enhanced by the optimal coordination of the structural loadings of wind turbines (WTs) operating with fully developed wind farm (WF) flows that have extensive interactions with the atmospheric boundary layer. In general, the APC problem, that is, distributing a WF power reference among the operating WTs, does not have a unique solution; this fact can be exploited for structural load alleviation of the individual WTs. Therefore, we formulated a constrained optimization problem to simultaneously minimize the WF power reference tracking errors and the structural load deviations of the WTs from their mean value. The wind power plant is represented by a dynamic 3-D large-eddy simulation model, whereas the predictive controller employs a simplified, computationally inexpensive model to predict the dynamic power and load responses of the turbines that experience turbulent WF flows and wakes. An adjoint approach is an efficient tool used to iteratively compute the gradient of the formulated parameter-varying optimal control problem over a finite prediction horizon. We have discussed the applicability, key features, and computational complexity of the controller by using a WF example consisting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 4$ </tex-math></inline-formula> turbines with different wake interactions for each row. The performance of the proposed adjoint-based model predictive control for APC was evaluated by measuring power reference tracking errors and the corresponding damage equivalent fatigue loads of the WT towers; we compared our proposed control design with recently published proportional–integral-based APC approaches.