Trajectory sensitivity analysis-based systematic Q-matrix of DFIG with LQR auxiliary voltage and power compensation for oscillation damping

Abstract

This study proposes a systematic method to define the weighting Q-matrix of the linear quadratic regulator (LQR) for doubly fed induction generators (DFIGs) through auxiliary voltage and power compensation for oscillation damping. Trajectory sensitivity analysis (TSA) is applied to define the Q-matrix. The TSA solves the system dynamics to obtain the sensitivity of states to DFIG primary voltage control reference and primary wind power reference. The Q-matrix is determined as the infinity norm of TSA sensitivity. Stability criteria of the LQR are analyzed with the proposed Q-matrix. The combined LQR voltage and power compensation loops are designed, and the LQR compensation gains are applied to a modified two-area power system and then tested at different disturbances and wind power penetration levels (WPLs). Simulation results show the capability and robustness of the designed process in damping the oscillation with designing the Q-matrix under major fault conditions. Moreover, the proposed method is robust at different WPLs.