Modeling and Quadratic Optimal Control of Three-phase APF Based on Switched System

A new equivalent discrete-time switched linear system (EDSLS) model of the three-phase active power filter (APF) based on the pulse-width modulator (PWM) theory is proposed. Then the EDSLS model is further transformed to a linear equivalent discrete-time switched linear system (LEDSLS) by linearization at some neighborhood of the equilibrium manifold. Finally, a quadratic linear optimal controller is designed with on-time tracking property, where the duty cycle is adopted as the control variables. The proposed control scheme has clearer physical significance and can be easily adopted in practice. The simulation results show that the proposed three-phase APF model and the control strategy are correct and effective.