Phase portrait-based stability region estimation for grid-connected VSC with PLL

Here, the stability region of grid-connected VSC with phase locked loop (PLL) is estimated. First, the conservative stability region is derived via the classical Lyapunov method. Then an energy function is constructed as the general stable condition for the VSC system. Based on the constructed energy function, two estimation methods of the system stability region by approximation of phase trajectory are proposed. The stability regions by the proposed methods are less conservative than that by the classical Lyapunov method. A stability evaluation function for the initial states of the VSC system is further proposed based on the estimated stability region. Time-domain simulations verify the correctness of the proposed methods and the effectiveness of the stability evaluation function.