LQR with integral action to enhance dynamic performance of three-phase three-wire shunt active filter

This paper presents the design of a Linear Quadratic Regulator (LQR) with Integral action (LQIR) to improve dynamic performance of a three-phase three-wire shunt active power filter (SAF). The integral action is added to cancel the steady state errors knowing that the standard LQR provides only proportional gains. The controller is designed to achieve DC bus voltage regulation, harmonics and reactive power compensation. The converter model is set in the dq rotating reference frame augmented with the integral of q component of the SAF currents and DC bus voltage. The performance of the controller depends on the weightening matrix which is chosen to guaranty satisfactory responses. The converter is controlled as a whole and a fixed PWM at 2.34 kHz is used to generate the gating signals of the power devices. The system is tested for both active and reactive power variations of the combined linear and non-linear load, for a distorted/unbalanced voltage source, and for unbalanced loads. The Simulation results obtained show good performance in terms of the DC bus voltage regulation (small overshoot and very fast time response) and low total harmonic distortion (THD) of ac line currents.