Transient stability analysis of virtual synchronous generator with current saturation by multiple Lyapunov functions method

Abstract

This paper demonstrates that the switching of one grid-connected virtual synchronous generator (VSG) between two control modes, namely constant voltage control (CVC) and current limiting control (CLC) happens at the derived two switching lines. Based on the current limiting inequality, the traditional current-switched model is transferred to the angle-switched model proposed here, and the system can be studied as one switched dynamic system. Based on this model, the transient stability of VSG with controller limits is investigated. This is achieved by constructing Lyapunov functions for each subsystem and deriving the relationship between the values of Lyapunov functions constructed under different conditions at the switching moment. The stability of the system is ensured when the Lyapunov function of each subsystem presents a decreasing trend in two consecutive switching intervals. On this basis, the stability boundary of the switching system is derived. Further analysis shows that optimal adjustment of the saturation current angle can make the system reach the maximum stability boundary. Finally, the numerical simulations and experimental tests verify the correctness of the proposed analysis.