Common Lyapunov Function Based Stability Analysis of VSC With Limits of Phase Locked Loop

Abstract

The stability of the grid-connected voltge source converter (VSC) with limits of phase locked loop (PLL) is investigated in this letter. The studied system is a nonlinear switched system that consists of three subsystems and a switching rule that connects switching between these subsystems. It is proved that the three subsystems share one common Lyapunov function, and the derivation of the constructed Lyapunov function for each subsystem with respect to time is negative. As a result, one conservative stability region for the studied switched system is derived, and the system can be asymptotically stable under arbitrary switching within the derived stability region. Numerical results show that implementing limits of PLL is one simple and effective approach to enhance the system stability of VSCs.