Comparative frequency- and time-domain analysis of four grid-forming inverters: Droop, VSM, matching, and dVOC

The increasing integration of inverter-based resources (IBRs) challenges conventional power system stability, especially in weak grid conditions. Grid-forming inverters (GFMIs) have emerged as a solution, offering voltage and frequency regulation at the point of common coupling (PCC). While prior studies have primarily focused on active power control (APC) and reactive power control (RPC), they often overlook the implications of voltage regulation strategies under varying grid strengths. This paper addresses this gap by conducting a comprehensive comparative analysis of four GFMI control strategies — droop control, virtual synchronous machine (VSM), matching control, and dispatchable virtual oscillator control (dVOC) — with a specific emphasis on PCC voltage regulation and fault response. The primary control loops in these GFMIs regulate active power injection via the APC and maintain PCC voltage through a voltage regulator that mimics the behavior of an automatic voltage regulator (AVR) in synchronous machines. The analysis includes both frequency-domain small-signal stability assessment using Bode and Nyquist plots and time-domain EMT simulations under a wide range of grid conditions, including grid short-circuit ratio ( SCR ), grid impedance ratio ( X g / R g ), and voltage sag scenarios. Unlike previous works, this study evaluates the impact of primary voltage regulation — beyond APC and RPC — on system dynamics. Furthermore, it presents new insights into the fault ride-through performance and transient voltage overshoots of each GFMI, particularly in very weak/strong grids. Additional sensitivity analysis case studies for VSM-based GFMIs are conducted under varying virtual inertia, highlighting its significant impact on frequency response, time-domain dynamics, and transient stability during fault ride-through. The findings provide a clearer understanding of the trade-offs among existing and emerging GFMI strategies. Practical guidance is offered for deployment in evolving power systems. Finally, future research directions are highlighted, including adaptive GFMI functions, advanced control, multi-GFMI interactions, impedance modeling, high-IBR stability, wide-area performance, and standardized grid codes.