Passivity-based H∞ control for APF in three-phase four-wire distribution power systems

Active power filter (APF) based on voltage source inverter (VSI) is one of the important measures to deal with the power quality problem. Mathematically, the APF model in a power grid is a typical nonlinear one. The idea of passivity is a powerful tool to study the stabilization of such a nonlinear system. In this paper, a state-space model of the four-leg APF is derived, based on which a new H-infinity controller for current tracking is proposed from the passivity point of view. It can achieve not only asymptotic tracking, but also disturbance attenuation in the sense of L-2-gain. Subsequently, a sufficient condition to guarantee the boundedness and desired mean of the DC voltage is also given. This straightforward condition is consistent with the power-balancing law of electrical circuits. Simulation and experimental results verify the validity of the new approach.