  Electric power systems with growing penetration of renewable generation face
problems of frequency oscillation and increased uncertainty as the operating
point may veer close to instability. Traditionally the stability of these
systems is studied either in terms of local stability or as an angle
synchronization problem under the simplifying assumption that decouples the
amplitude along with all dissipations. Without the simplifying assumption,
however, the steady state being studied is basically a limit cycle with the
convergence of its orbit in question. In this paper we present an analysis of
the orbital stability of a microgrid integrating the proposed type of
distributed generation controller, whose internal reference voltage arises from
the rotation of the reference frame much like a rotating machine. We utilize
the shifted passivity framework to prove that, with sufficient dissipation,
such system is globally convergent to a nontrivial orbit. This is the first
global stability result for the limit cycle of such system in the full state
space, which provides new insight into the synchronization mechanism as well as
how dissipation plays a role in the orbital stability. The proposed controller
is verified with a test microgrid, demonstrating its stability and transient
smoothness compared to the standard droop control.
