Transient Stability Analysis of an SG–VSG Parallel Microgrid: A Comprehensive Study Using Phase Trajectory, Direct Method, and Time‐Domain Simulation

The distinct dynamic characteristics of virtual synchronous generators (VSGs) and synchronous generators (SGs) make the transient behavior of their parallel operation difficult to characterize using a single analytical approach. This paper investigates the transient stability of an SG–VSG parallel microgrid through a cross‐validated framework integrating phase‐trajectory analysis, an energy‐based direct method, and detailed electromagnetic transient (EMT) simulation. First, we develop an equivalent model of the parallel system and characterize its transient instability mechanisms under fault scenarios using the equal‐area criterion (EAC), providing qualitative insights into stability trends. Subsequently, we derive the system’s nonlinear state‐space equations and perform an analysis to evaluate stability boundaries under variations of critical parameters and current‐limiting conditions, thereby quantifying the mechanisms of parametric influence. Furthermore, by constructing the transient energy function via Takagi–Sugeno (TS) fuzzy modeling combined with linear matrix inequalities (LMIs), we comparatively evaluate the geometric properties of attraction domains under diverse parameter configurations. Finally, the EMT simulations verify the consistency between theoretical predictions and dynamic responses, with additional sensitivity assessments under representative operating and network variations and supplementary verification under an asymmetric single‐phase voltage sag. The results further quantify the effects of key parameters and current‐limiting control, as well as the stability differences between SG–VSG and VSG–VSG parallel configurations.