Small-Signal Stability Analysis and Parameters Optimization of Virtual Synchronous Generator for Low-Inertia Power System

The stable operation of converter-interfaced generation (CIG) units is paramount for ensuring resilience in low-inertia power systems. This paper presents a comprehensive small-signal modeling and stability analysis framework for grid-connected virtual synchronous generators (VSGs), integrating: an LCL-filter interfaced power converter, active/reactive power loop (APL/RPL) controllers, and dual-loop PI-based current and voltage control. Through systematic eigenvalue analysis and parameter sensitivity studies, complemented by time-domain verification in MATLAB/SIMULINK, we demonstrate the decisive influence of VSG control parameters on low-frequency oscillation (LFO) damping characteristics, transient frequency stability metrics, including the rate of change of frequency (ROCOF), maximum frequency deviation (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f_nadir</i>), overshoot, and settling time. We further propose a hybrid Particle Swarm Optimization (PSO) algorithm with a multi-objective cost function to optimize VSG controller gains. The optimized design achieves an 83% reduction in ROCOF, a 90% improvement in frequency deviation, and a non-oscillatory power response. These results quantitatively validate that proper VSG gain tuning can significantly enhance dynamic performance and frequency stability in inertia-constrained grids. The proposed methodology offers practical insights for designing resilient CIG-dominated power systems.