Grid-Forming Control of Power Converters: Equivalence Proof through Simplified Models

This work establishes the equivalence of selected grid-forming control algorithms within the context of simplified theoretical models. Considered algorithms are droop control, Virtual Synchronous Machine (VSM) and matching control. It is shown that nodal and network dynamics under those regulators boil down to the same equations near the selected (trivial) nominal operating point. Finally, some practical insights on each regulator dynamics and an outlook are provided.