Boundary analysis of damping methods for virtual synchronous generators

Virtual synchronous generators (VSGs) imitate traditional synchronous generators to provide virtual inertia and damping for inverter-based resources. The emulated damping relates to the power synchronization, therefore, has a major impact on system stability. Although various damping methods exist, phase-locked loop (PLL) integration is particularly concerning, as it is a key component in grid-following (GFL) control but now is being applied to grid-forming (GFM). This paper analyzes the typical VSG control and PLL damping unit by mapping stability boundaries and feasibility range. The boundaries are mapped in two dimensions to determine the relationship between the control parameters and the grid impedance. A comprehensive sensitivity analysis of controller parameters for VSG stability is conducted, drawing parallels with the equivalence of droop-based GFM stability. Finally, the boundary analysis is verified by time-domain simulation results and demonstrates the reliability of damping-switching method.