  The integration of microgrids that depend on the renewable distributed energy
resources with the current power systems is a critical issue in the smart grid.
In this paper, we propose a non-cooperative game-theoretic framework to study
the strategic behavior of distributed microgrids that generate renewable
energies and characterize the power generation solutions by using the Nash
equilibrium concept. Our framework not only incorporates economic factors but
also takes into account the stability and efficiency of the microgrids,
including the power flow constraints and voltage angle regulations. We develop
two decentralized update schemes for microgrids and show their convergence to a
unique Nash equilibrium. Also, we propose a novel fully distributed PMU-enabled
algorithm which only needs the information of voltage angle at the bus. To show
the resiliency of the distributed algorithm, we introduce two failure models of
the smart grid. Case studies based on the IEEE 14-bus system are used to
corroborate the effectiveness and resiliency of the proposed algorithms.
