Constraint-Aware Framework for Inertia–Security Boundary Extraction in Grid-Forming Inverter-Dominated Power Systems

The transition toward low-inertia power systems has increased interest in grid-forming (GFM) inverters as sources of power system voltage and frequency stability support. However, existing studies in the literature evaluate frequency performance metrics without explicitly extracting system-level inertia–security boundaries under selected converter operating constraints. This paper proposes a disturbance-consistent, constraint-aware boundary extraction methodology to quantify inertia–security limits in GFM-dominated systems. The IEEE-39 bus system is implemented in Python (3.10.19)-based ANDES (1.9.3), and 3682 non-linear root-mean-square (RMS) time-domain simulations are conducted across four operating regimes, namely REGCP1 grid-following baseline, REGF1 droop control true GFM without inertia emulation, REGF2 true GFM with idealized inertia emulation, and REGF2 true GFM with system-level realism constraints, comprising headroom, current limits, and weak grid conditions. Only N-1 generator-trip contingencies are considered to ensure disturbance consistency. Results show that true GFM substantially improves frequency security in relation to the baseline regime. REGF2 true GFM generally improves the initial center-of-inertia (COI) frequency but does not uniformly improve frequency nadir or maximum mean-BusFreq-derived RoCoF relative to REGF1 under matched matched cases. All nominal and broad-stress cases satisfied the predefined primary inertia–security limits of 1.0 Hz/s RoCoF and a 49.5 Hz frequency nadir. Additional boundary-targeted cases exposed finite frequency–security boundaries with both RoCoF and frequency nadir security limits. RoCoF was the more frequently binding security metric, while frequency nadir became binding under severe disturbance conditions and low headroom constraints. Confidence intervals (CI), statistical tests, and expanded threshold sensitivity analysis are used to quantify uncertainty and security classification. The proposed methodology provides a systematic approach to assessing frequency–security limits for future inverter-dominated power systems.