Robust ${H_\infty }$ Control of Doubly Fed Wind Generator via State-Dependent Riccati Equation Technique

Abstract

A novel approach on the robust ${H_\infty }$ controller design for the doubly fed induction generator (DFIG)-based wind generation systems through the state-dependent Riccati equation (SDRE) technique is proposed in this paper. The control objective is to mitigate the impact of grid voltage dips to enhance the fault-ride-through capability of the wind generation system. A robust ${H_\infty }$ control problem using the fifth-order detailed DFIG model is formulated to mitigate the impact of voltage dips for the DFIG riding through the faults. The SDRE technique performs extended linearization of nonlinear systems, and the robust ${H_\infty }$ control problem can be solved through an algebraic Riccati equation like approach with state-dependent coefficient (SDC) matrices. The pointwise stabilizability and controllability of the extended linearized system are guaranteed by using the input-to-state stability theory. Accordingly, weighting matrices as well as the SDC matrices are designed with fully studied principles. The notion of controllability Gramian is used to optimize the choice of SDC matrices. The control performance of the proposed robust ${H_\infty }$ controller is verified through case studies. Comparisons with the proportional-integral controllers, the sliding mode control, and the exact linearization-based nonlinear control are performed, which demonstrate better dynamic performances and disturbance attenuation through the proposed controller.