Nonlinear network dynamics for interconnected micro-grids

This paper deals with transient stability in interconnected micro-grids. The main challenge is to understand the impact of the connectivity of the graph and model nonlinearities on transient and steady-state behavior of the system as a whole. The contribution of this paper is three-fold. First, we provide a robust classification of transient dynamics for different intervals of the parameters for a single micro-grid. We prove that underdamped dynamics and oscillations arise when the damping coefficient is below a certain threshold which we calculate explicitly as function of the product between the inertia coefficient and the synchronization parameter. Second, for interconnected micro-grids, under the hypothesis of homogeneity, we prove that the transient dynamics mimics a consensus dynamics. We provide bounds on the damping coefficient characterizing underdamped and overdamped consensus. Third, we extend the study to the case of disturbed measurements due to hackering or parameter uncertainties. We introduce model nonlinearities and prove absolute stability.