Probabilistic Voltage Stability Screening Under Stochastic Load Allocation at Weak Buses Using Stability Index

Voltage security assessment is increasingly challenged by stochastic demand growth and localized stress patterns that are not well represented by deterministic, single-snapshot analyses. This paper proposes a fully steady-state probabilistic stress-testing framework based on Monte Carlo simulation and Newton–Raphson AC power flow, jointly evaluating the minimum bus voltage magnitude Vmin (voltage-floor adequacy) and the scenario maximum Fast Voltage Stability Index FVSImax (worst-case line stress). Stress is injected selectively on screened weak buses by sampling a random stress footprint and intensity across three progressive levels (L1–L3), while preserving the local power factor. The approach is demonstrated on IEEE 14-, 30-, and 118-bus benchmark systems using N=2000 realizations per level, with 100% convergence across all cases. Across all systems, results show a consistent, monotone degradation of the voltage floor and a systematic increase in violation risk as stress intensifies. For the IEEE 14 system, the voltage-risk profile escalates rapidly, with P(Vmin<0.90) rising from 0.16 (L1) to 0.54 (L3), while the worst-case FVSI tail strengthens markedly (p95 increasing from 0.1455 to 0.2081), indicating a growing likelihood of severe voltage-stress events. In contrast, the IEEE 30 and IEEE 118 systems exhibit milder shifts in central voltage levels but maintain substantial exposure relative to the 0.95 pu planning threshold, with P(Vmin<0.95) reaching 0.79 and 0.74 at L3, respectively. Beyond risk magnitudes, the framework reveals a nontrivial structural phenomenon in worst-case line stress: as system size increases, stochastic stress outcomes become increasingly concentrated into a small number of dominant transmission corridors. Recurrence analysis at the highest stress level shows fragmented criticality in IEEE 14 (Top-3 lines sharing criticality), near-total dominance by a single corridor in IEEE 30 (>92% of cases), and complete dominance collapse in IEEE 118 (one corridor governing 100% of FVSImax events). These results demonstrate that probabilistic stress-testing can simultaneously quantify voltage-risk escalation and expose hidden structural bottlenecks that remain invisible under deterministic screening, providing a scalable diagnostic tool for planning-stage monitoring and reinforcement prioritization.