Persistence-Based Identification of Structurally Critical Transmission Lines Under N − 1 Contingencies

Voltage stability assessment under transmission contingencies is traditionally performed using severity-based indices evaluated on isolated outage scenarios. While effective for identifying extreme events, such approaches provide limited insight into which transmission corridors structurally govern voltage-stress behavior across the full contingency space. This paper introduces a persistence-based diagnostic framework for voltage stability assessment under exhaustive N−1 line contingencies, using the Fast Voltage Stability Index (FVSI) as a base indicator. Rather than ranking lines by instantaneous severity, the proposed methodology identifies dominant transmission lines—defined as those attaining the maximum FVSI in each convergent contingency—and aggregates these outcomes statistically to quantify dominance persistence, conditional severity, and dispersion. A dominance concentration metric (k90) is introduced to measure how many transmission corridors are sufficient to explain the majority of dominant voltage-stress events. The framework is applied to IEEE 14, 30, and 118-bus benchmark systems under exhaustive N−1 enumeration. Results reveal a clear phenomenon of dominance collapse: as system size increases, dominant voltage-stress outcomes concentrate onto an extremely small set of transmission corridors. While IEEE 14 exhibits partial dominance dispersion (k90=2), both IEEE 30 and IEEE 118 demonstrate near-total dominance collapse (k90=1), where a single corridor governs more than 90% of dominant FVSI events. The proposed approach is fully deterministic, scalable, and independent of control or optimization assumptions, making it well-suited for planning-stage screening, monitoring prioritization, and pre-filtering of large-scale contingency studies. By shifting voltage stability analysis from severity-only screening to persistence-based structural diagnosis, this work provides new insight into vulnerability concentration in modern transmission networks.