Motivated by the recent and growing interest in microgrids, we study the operation of droop-controlled DC/AC inverters in an islanded inductive microgrid. We present a necessary and sufficient condition for the existence of a synchronized steady state that is unique and locally exponentially stable. We discuss a selection of controller gains which leads to a sharing of power among the generators, and show that this proportional selection enforces actuation constraints for the inverters. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Finally, we present experimental results validating our controller design, along with simulations of extended scenarios. Our results hold without assumptions on uniform line admittances, inverter power ratings, or voltage magnitudes.
