Synchronization Stability of Grid-Connected VSC With Limits of PLL

Limits of phase locked loop (PLL) are necessary to make sure the transient converter frequency bounded in a safety range. This leads to the grid-connected voltage source converter (VSC) with limits of PLL as one switched system. Stability of switched dynamic system is fully discussed in this paper. One conservative analytical stable region of the unbounded autonomous system is derived by Lyapunov method. It is proved that when bounds are touched, any trajectory of the studied switched system deviates from these bounds at two fixed switching Points. Moreover, the switched system energy is non-increasing when trajectories lie inside the derived analytical stable region. Based on these properties of switched system, it is proved that to ensure the globally asymptotically stability, the fixed switching Points should be placed inside the derived stable region of the unbounded autonomous system. Finally, stabilization method is proposed via placement of the fixed switching Points so that the globally asymptotically stability is ensured.