A Unified Model for Voltage-Source and Current-Source Virtual Synchronous Generators

The virtual synchronous generator serves as a critical interface between renewable generation systems and the grid, providing inertia to support both active and reactive power. Based on the duality principle, a virtual permanent-capacitor synchronous generator is derived to enhance the inertia of the three-phase current-source inverter, exhibiting dynamic characteristics similar to those of a virtual permanent-magnet synchronous generator. Additionally, this work presents a unified virtual synchronous generator model applicable to both voltage-source and current-source topologies. By constructing a suitable Lyapunov function candidate, the stability criteria of the unified model under standalone operation are established. The Lyapunov function candidate is constructed as a Bregman divergence, whose monotonic decrease characterizes the convergence to synchronous equilibrium. In grid-connected mode, a frequency-locking condition is derived to ensure synchronization of the virtual synchronous generators with the grid. Eigenvalue analysis is employed to assess the stability of the unified model under frequency-locking conditions. The correctness of the derived stability conditions in standalone and grid-connected modes is confirmed through time-domain simulations.