Nonlinear Transient Stability Analysis of Phased-Locked Loop-Based Grid-Following Voltage-Source Converters Using Lyapunov's Direct Method

In this article, using Lyapunov's stability theorem, the transient stability conditions for a grid-following voltage-source converter (VSC) are found. These conditions take into account both the grid specifications and the VSC's dynamics. The derived conditions are based on a well-known nonlinear model of the VSC's phase-locked loop. To evaluate the stability of the nonlinear system, Lyapunov's direct method is employed. To this end, a new Lyapunov's function is proposed, and its characteristics are analyzed. Using this Lyapunov's function, the domain of attraction of the system's equilibrium point is calculated. In addition, a novel system strength index based on the domain of attraction of the system is proposed. The privileges of this index over the conventional indices are absoluteness, VSC's dynamics consideration, and comparability of different VSCs with each other from a stability point of view. In the end, the correctness of the proposed stability analysis is validated via simulation in MATLAB/PLECS and experiment.