Theoretical Grid-Forming Extreme of Inverters

Abstract: What are the theoretical and physical limits of a grid-forming inverter? This letter proposes that the extreme grid-forming ability of inverters is limited by their dc-side, ac-side, circuit topology dynamics, but not control. While many papers focus on how to improve grid-forming inverters stability, power sharing, inertia emulation, fault response, few, if any, formally define the fundamental theoretical limits or extremes of grid-forming behavior. It seems that the grid-forming can be improved endlessly. No physical system can support a grid indefinitely without limitations, especially under increasing levels of disturbance or uncertainty. Therefore, this boundary is explicitly shown by a mathematical expression in this letter. Consequently, the results show that relatively low dc-side voltage and high active power injection could damage the grid-forming ability. Poor consideration of dc-side, ac-side, and circuit topology dynamics in real practice will cause jeopardizing oscillation even by the theoretical best grid-forming control strategy.