Matching Control in Grid-Forming Converter Connected to Grid with Synchronous Generator: Lyapunov Stability Analysis and ROA Estimation

Matching control represents one of the promising strategies proposed for grid-forming converters (GFCs). However, Lyapunov stability analysis of matching control in the context of its interaction with grids comprising synchronous generators (SGs) under realistic assumptions has hardly been explored in the literature. This paper conducts such an analysis on a two-bus system with one GFC equipped with matching control and one SG. More specific, we derive analytical conditions that guarantee the asymptotic stability of a generic two bus systems of this configuration and establish the region of attraction around the equilibrium using three analytical methods, highlighting merits and limitations of each. Numerical simulation results are presented in support of our analytical findings.