Conditions of Existence and Uniqueness of Limit Cycle for Grid-Connected VSC With PLL

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to infinite bus system through transmission line. One conservative stable region is obtained via direct method Lyapunov. Based on Poincaré Theorem, it interesting find there might exist limit cycle between boundary and angle unstable equilibrium point (UEP). Accordingly, nonlinear damping effect defined, one exists when positive negative over period mutually balanced. A existence condition further derived by constructing a proper piece-wise curve approximate specified trajectory. The analytical can directly predict without numerical simulations. Finally, also proves that studied dynamic has at most cycle, if exists, unstable.