Large-signal Stability of Phase-balanced Equilibria in Single-phase Grid-forming Inverter Systems

This paper explores the setup where large numbers of single-phase grid-forming inverters with droop control across distribution networks self-organize into a stable and balanced system with $120^\circ$ phase offsets across aggregates in the absence of balanced three-phase generating resources or external communication. A suite of circuit- and system-theoretic notions are leveraged to derive a dynamical model for phase-angle differences across aggregates of inverters connected in the three phases. Focusing on this model, large-signal stability is established and the region of attraction of the phase-balanced equilibria is determined with the aid of a Lyapunov function. Experimental validation for a bench-top prototype network is included to support the analytical developments. Overall, the effort supports the vision of facilitating balanced operation of distribution networks with grid-forming inverters during service disruptions at the bulk transmission network.