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Scalable and Reliable State-Aware Inference of High-Impact N-k Contingencies

Lihao Mai, Chenhan Xiao, Yang Weng

TL;DR

This work tackles the high computational cost of higher-order $N$-$k$ contingency analysis under dynamic grid conditions by introducing a state-conditioned generative framework that directly samples high-impact outages without exhaustive enumeration. It combines a conditional diffusion model with a topology-aware EVGNN to produce a compact, state-specific shortlist of contingencies and provides a tunable coverage guarantee that a fixed number of AC power-flow evaluations will capture a desired portion of severe events. Theoretical analysis establishes complexity advantages over brute-force and proves a probabilistic tail-coverage bound that scales with the sampling budget and model fidelity, independent of the combinatorial contingency space. Empirical results on IEEE benchmark systems show that the proposed method concentrates evaluations on high-severity, AC-feasible contingencies, achieving higher top-$m$ severities than uniform sampling for the same budget and enabling more reliable risk-aware operation.

Abstract

Increasing penetration of inverter-based resources, flexible loads, and rapidly changing operating conditions make higher-order $N\!-\!k$ contingency assessment increasingly important but computationally prohibitive. Exhaustive evaluation of all outage combinations using AC power-flow or ACOPF is infeasible in routine operation. This fact forces operators to rely on heuristic screening methods whose ability to consistently retain all critical contingencies is not formally established. This paper proposes a scalable, state-aware contingency inference framework designed to directly generate high-impact $N\!-\!k$ outage scenarios without enumerating the combinatorial contingency space. The framework employs a conditional diffusion model to produce candidate contingencies tailored to the current operating state, while a topology-aware graph neural network trained only on base and $N\!-\!1$ cases efficiently constructs high-risk training samples offline. Finally, the framework is developed to provide controllable coverage guarantees for severe contingencies, allowing operators to explicitly manage the risk of missing critical events under limited AC power-flow evaluation budgets. Experiments on IEEE benchmark systems show that, for a given evaluation budget, the proposed approach consistently evaluates higher-severity contingencies than uniform sampling. This allows critical outages to be identified more reliably with reduced computational effort.

Scalable and Reliable State-Aware Inference of High-Impact N-k Contingencies

TL;DR

This work tackles the high computational cost of higher-order - contingency analysis under dynamic grid conditions by introducing a state-conditioned generative framework that directly samples high-impact outages without exhaustive enumeration. It combines a conditional diffusion model with a topology-aware EVGNN to produce a compact, state-specific shortlist of contingencies and provides a tunable coverage guarantee that a fixed number of AC power-flow evaluations will capture a desired portion of severe events. Theoretical analysis establishes complexity advantages over brute-force and proves a probabilistic tail-coverage bound that scales with the sampling budget and model fidelity, independent of the combinatorial contingency space. Empirical results on IEEE benchmark systems show that the proposed method concentrates evaluations on high-severity, AC-feasible contingencies, achieving higher top- severities than uniform sampling for the same budget and enabling more reliable risk-aware operation.

Abstract

Increasing penetration of inverter-based resources, flexible loads, and rapidly changing operating conditions make higher-order contingency assessment increasingly important but computationally prohibitive. Exhaustive evaluation of all outage combinations using AC power-flow or ACOPF is infeasible in routine operation. This fact forces operators to rely on heuristic screening methods whose ability to consistently retain all critical contingencies is not formally established. This paper proposes a scalable, state-aware contingency inference framework designed to directly generate high-impact outage scenarios without enumerating the combinatorial contingency space. The framework employs a conditional diffusion model to produce candidate contingencies tailored to the current operating state, while a topology-aware graph neural network trained only on base and cases efficiently constructs high-risk training samples offline. Finally, the framework is developed to provide controllable coverage guarantees for severe contingencies, allowing operators to explicitly manage the risk of missing critical events under limited AC power-flow evaluation budgets. Experiments on IEEE benchmark systems show that, for a given evaluation budget, the proposed approach consistently evaluates higher-severity contingencies than uniform sampling. This allows critical outages to be identified more reliably with reduced computational effort.
Paper Structure (14 sections, 1 theorem, 24 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 14 sections, 1 theorem, 24 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Methodology
  4. Fast state-conditioned generation of high-impact $N\!-\!k$ contingencies
  5. Coverage-controlled screening with performance guarantees
  6. Offline data preparation and high-risk screening for training
  7. Theoretical Analysis
  8. Computational Complexity Analysis
  9. Sample-Efficient Coverage of High-Severity Contingencies
  10. Experiment
  11. Experimental setup
  12. Top-$m$ screening curves under a fixed AC power-flow evaluation budget
  13. High-severity retention and in-band rates under diffusion screening
  14. Conclusion and Future Work

Key Result

Theorem 1

Under Assumptions assump:severity-region, let $(\mathbf{c}_i,s_i)_{i=1}^{m}$ be $m$ i.i.d. samples drawn from $p_\theta$. the learned generative model assigns probability mass $p_\theta(\mathcal{A}_\delta) \ge \delta - \sqrt{\varepsilon/2}.$ Moreover, for any $\eta\in(0,1)$,

Figures (4)

  • Figure 1: Overview of the proposed sample-efficient $N\!-\!k$ contingency screening framework via conditional diffusion. (a) In large power networks, exhaustive $N\!-\!k$ contingency analysis is computationally intractable due to the combinatorial growth of outage combinations, rendering brute-force AC power-flow evaluation infeasible. (b) Rather than enumerating all contingencies, a conditional graph diffusion model directly samples outage patterns from the upper tail of the severity distribution, generating state-conditioned, high-risk $N\!-\!k$ contingency scenarios without looping over the full combinatorial space. (c) A topology-aware EVGNN, trained once using only base-case and $N\!-\!1$ data, is reused as a fast risk surrogate to score generated $N\!-\!k$ contingency scenarios without additional AC power-flow simulations, enabling the construction of a compact, high-risk dataset through graph-based generalization from single- to multi-line outages.
  • Figure 2: Recommendation curves for convergent $N-k$ contingencies across 200 operating scenarios on four IEEE benchmark systems. Left: uniform random sampling. Right: the proposed conditional diffusion generator. For each system and scenario, $m$ contingencies are produced under the method of the corresponding panel within the specified $k$-range (IEEE 14: $k\in[2,4]$, IEEE 39: $k\in[2,6]$, IEEE 57: $k\in[2,5]$, IEEE 118: $k\in[2,15]$), evaluated by AC power-flow, and only convergent cases are retained. Within each scenario, convergent contingencies are sorted by AC power-flow-severity, and the average severity of the top-$m$ is computed; curves report the average of this quantity over the 200 scenarios. Comparing panels at the same $m$ shows that diffusion-based recommendations concentrate on higher-severity (higher-impact) convergent contingencies than uniform random sampling.
  • Figure 3: AC power-flow severity distributions for sampled $N\!-\!k$ contingencies on the IEEE 14-, 39-, 57-, and 118-bus systems with $k \in [2,4]$, $[2,6]$, $[2,5]$, and $[2,15]$, respectively. For each system, each method generates a fixed number of contingencies per operating scenario, which are evaluated using AC power flow. Left panels show severity distributions on a logarithmic scale, with outcomes categorized as ACPF-convergent in-band, ACPF-convergent out-of-band, or ACPF-nonconvergent. Right panels report the corresponding outcome composition as stacked proportions.
  • Figure 4: Detailed view of the IEEE 14‑bus results from two methods from the four‑system composite figure (14/39/57/118‑bus). ACPF severity distribution for sampled $N\!-\!k$ contingencies and corresponding outcome composition.

Theorems & Definitions (3)

  • Definition 1: High-severity region
  • Theorem 1: Coverage of high-severity contingencies
  • proof