On Balancing Phase Angles with Droop Control

We establish topological and parametric conditions under which phase angles across three identical impedances can be balanced with small-signal stability guarantees when served from three single-phase sources executing active-power frequency droop control. All standard topologies involving Delta and Wye interconnections of sources and loads are examined. The equilibria of phase-angle dynamics are shown to include the desired phase-balanced state, but in addition, they also exhibit an undesirable phase-synchronized state and bi-cluster synchronous state (in which two of the phase angles coincide). The aforementioned analytical conditions for asymptotic stability of phase-balanced equilibria are uncovered by examining the spectral properties of the Jacobian of the linearized dynamics. Simulation results validate the analytical findings.