Dissipativity-Based Stability Analysis for Networked Nonlinear Descriptor Systems and its Application to Power Grids

Abstract

This paper pursues to construct a theoretical framework which can efficiently capture dynamics of large-scale heterogeneous power grids. We formulate a networked nonlinear descriptor system consisting of subsystems and network system as a mathematical generalization of such grids. This descriptor representation of the system enables us to consider efficient analysis and control of the system with preserving its network topology. As a main result, we clarify the disippativity of the systems, and derive a sufficient local asymptotic stability of partial state and synchronization based on the dissipativity. We also apply these dissipativity and stability results to a power grid described by a structure-preserving model.