Title: Synchronization and distributed integral control in microgrids

Abstract: Motivated by the recent interest in smart grid technology,
we study the operation of DC/AC inverters in a lossless micro grid. We
show that an interconnection of DC/AC inverters equipped with
power-frequency droop controllers can be cast as a Kuramoto model of
coupled phase oscillators. This novel description, together with
results from the theory of coupled oscillators, allows us to
characterize the behavior of the network of inverters. Specifically,
we provide a necessary and sufficient condition for the existence of a
synchronized solution that is unique and locally exponentially
stable. We propose a distributed integral controller based on
averaging algorithms which dynamically regulates the system frequency
to a nominal value in the presence of a time-varying load. This
distributed controller has the additional property that it maintains
the power sharing properties of the primary droop controller. Our
results hold without assumptions on identical line characteristics or
voltage magnitudes.