Direct method of Lyapunov applied to synchronization stability of VSC with phase-locked loop

Synchronization stability of one single voltage source converter (VSC) connected to the infinite bus system via transmission lines is studied. Firstly, a second-order system model with damping is obtained under certain reasonable assumptions, which can be written as the classical Liénard system. Then, one Lyapunov function with larger analytical stable region than existing ones is constructed. Subsequently, an oscillatory instability phenomenon is firstly discovered and it is related to the system nonlinear damping. Based on Poincaré Theory, it is indicated that an unstable limit cycle exists between the derived stability boundary and the angle of unstable equilibrium point (UEP). One limit cycle appears when the positive and negative damping effect over one period is mutually balanced. Moreover, one numerical method via backwards starting from UEP is proposed to obtain the exact stability boundary. Numerical results verifies the correctness of the proposed model and the effectiveness of the analysis method.