A State-Space Model for Stability Boundary Analysis of Grid-Forming Inverters Considering Grid Conditions

This paper presents a state-space-based stability boundary analysis of a traditional dual-droop-controlled grid-forming inverter under varying grid conditions. A small-signal state-space model is established by incorporating the inverter power stage, output filter, and dual-droop-control dynamics, enabling an explicit characterization of the interaction between inverter control parameters and the external grid. In particular, this study focuses on the influence of the active-power/frequency and reactive-power/voltage droop coefficients on system stability. Based on the developed model, stability boundaries with respect to the droop coefficients are derived under different grid conditions, including variations in grid strength and grid impedance, to identify the stable operating region and the critical parameter limits beyond which oscillatory or unstable behavior emerges. The analysis reveals a strong dependence of the allowable droop-coefficient range on grid conditions, providing important insight into the design and tuning of traditional dual-droop-controlled grid-forming inverters. To validate the proposed approach, the obtained stability boundaries are further verified through detailed switch-model simulations in MATLAB/Simulink. The results confirm the accuracy of the state-space model and the effectiveness of the proposed method in predicting stability limits, offering a useful basis for stability assessment and controller parameter design of grid-forming inverters in practical power systems.