Improved PLL Design for Transient Stability Enhancement of Grid Following Converters Based on Lyapunov Method

Fluctuations in phase angle and frequency under large disturbances can lead to loss of synchronism (LOS) in grid-following (GFL) converters. The power angle and frequency of synchronous generators (SGs) correspond to rotor position and speed, whereas those of converters lack a direct physical counterpart in the real world and can thus be directly adjusted by control methods to prevent loss of synchronization. In this paper, an improved phase-locked loop (PLL) design with reset control for GFL converters is proposed to enhance transient stability. The stability domain (SD) of a GFL converter is first analyzed, and three forms of SD are identified under different short circuit ratios. Secondly, based on the characteristics of the three SD forms, two PLL-reset methods are proposed, including omega reset and omega&delta reset. Thirdly, to provide the triggering conditions for the PLL-reset control, the Lyapunov function of the GFL converter is constructed based on three methods: the approximation-based Lyapunov method, the Zubov method, and the analytical trajectory reversing method. All these methods are immune to the negative damping problem of PLL dynamics, which makes traditional energy-perspective Lyapunov functions invalid. Finally, the estimation accuracy of the three Lyapunov-based methods is analyzed, and the effectiveness of the PLL-reset control is verified in single-machine and multi-machine case studies.