Real-Time Stochastic Assessment of Dynamic N-1 Grid Contingencies

TL;DR

The paper develops a real-time dynamic-N-1 screening framework that uses a linearized swing-equation model to quantify transient overload risk after random line faults. It introduces an Overload Indicator and a scalable dynamic-evaluation workflow based on first-order and multi-step eigen perturbations, enabling fast trajectory estimates without full time-domain simulations. Probabilistic risk is computed with Cross-Entropy Adaptive Importance Sampling via a dedicated engine called N1Plus, which efficiently estimates rare-event probabilities (e.g., line overcurrents) and provides operator-ready risk dashboards. The approach is demonstrated on the Israeli transmission grid, achieving sub-second evaluation times for ~10^5 fault trajectories while maintaining strong agreement with exact benchmarks, highlighting its practical value for high-renewable, low-inertia grids. Overall, the work extends static N-1 analysis to dynamic, rare-event screening, offering a scalable, interpretable tool for real-time reliability assessment and planning.

Abstract

Power system operators need tools for rapid, real-time counterfactual assessments of grid security under fast-changing conditions. Traditional N-1 contingency analysis lacks dynamic evaluation, especially of frequency swings from common faults. This paper introduces a real-time dashboard framework to screen dynamic contingencies. It assumes: (a) the grid starts in a balanced state; (b) faults can occur randomly on any transmission line, temporarily de-energizing and then reconnecting it within about one second; and (c) contingencies are flagged if post-fault transients cause line flows to exceed safety thresholds. The key contributions are: (1) Overload Indicator: a system-wide metric quantifying integrated N-1 dynamic risk from a given state; (2) Scalable Fault Evaluation Algorithm: a linear-scaling method to assess dynamic fault impacts without brute-force simulations; and (3) Risk Estimation: a Cross Entropy Adaptive Importance Sampling method estimating the likelihood of low probability by high risk events, e.g. associated with potential transformer over-current. We demonstrate the framework on the Israeli transmission power grid (IG).

Figures (8)

• Figure 1: Single-Phase Fault Example (IG) – Unstable Case. If the faulty line isn’t re-energized quickly, loss of synchronization occurs (system splits). Fault, Clearance, Finish occurs at time: 0.0, 0.5 and 20s respectively.
• Figure 2: Conceptual Dashboard for Dynamic Contingency Screening.
• Figure 3: Fault timeline: system is balanced, pre-fault; fault is cleared, a faulty line is de-energized; line is back in service, post-fault transient.
• Figure 4: Overload indicator vs. fault duration (3-Phase Faults)· Each curve shows line-specific overload vs. fault time $\tau$. Tripped lines$(X_{n,m})$: trigger peak overload Critical lines (associated with transformers)$(i,j)$: accumulate highest total overload. Left: Israel grid with relevant lines highlighted.
• Figure 5: Probabilistic security assessment (3-Phase Faults). For critical lines and fault durations $\tau$ we determine $\mathbb{P}\left[S_{ij}\ge T^{(*)}\right]$. Risk zones by $Q_{ij}(\tau)<5\%$: Safety Zone, $Q_{ij}(\tau)\in [5\%,10\%]$: Warning Zone and $Q_{ij}(\tau)>10\%$: Emergency Zone