Nonlinear Damping Property and Limit Cycle of VSC

The synchronization stability of the system that one single VSC is connected to an infinite source via the line is studied in this letter. Based on Bendixson criterion, closed orbit (limit cycle) does not exist in the derived stable region, while may exist in the region between the conservative stable boundary and the unstable equilibrium point (UEP). Nonlinear damping effect on the system stability is analytically defined, and an unstable limit cycle appears when the positive and negative damping effect of the system over one period is mutually balanced. Numerical results verify the existence of limit cycle and nonlinear damping property of VSC.