Phase Dynamics induced by Droop Control in Networks with Uniform Effective Impedances

Phase dynamics of interconnected voltage sources executing active power versus frequency droop control can exhibit balanced, synchronized, and clustered equilibria. Parametric conditions for stability of these equilibria are established for networks that feature uniform effective impedances (pairwise and node-to-ground). The problem setup is motivated by several applications in power systems and power electronics including synchronization of  synchronous generators and grid-forming inverters, and phase balancing of single-phase resources in multi-phase networks. Simulation results for a variety of topologies illustrate the analytical developments.