Large-signal Stability Analysis of Inverter-based Microgrids via Sum of Squares Technique

Increasing the penetration of low inertia inverter-based resources in power systems creates new system stability challenges and requires sophisticated stability assessment tools. One of the practical tools for large-signal stability assessment is determining the system region of stability (ROS)—i.e., the portion of the system state space where variable trajectories converge to a stable equilibrium point. In contrast to time-domain simulation methods, Lyapunov function-based methods are fast and can measure system stability margin from the ROS. This paper proposes a sum of squares (SOS) technique to determine large-signal stability regions of inverter-based microgrids using the Lyapunov function. An accurate dynamic model of grid-connected inverter-based resources is applied for the state-space model of the network. The Lyapunov function is constructed based on the sum of squares method by SOSTOOL. In comparison to Krasovskii’s method, the stability region created by the SOS method is found more accurate. Two scenarios—a changing load event and an adjustment to the inverter control—are analyzed in the stability region assessment.