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Centrality-based Structural-Electrical Contingency Screening and Transmission Reinforcement Prioritization

Abanish Tiwari, Chandan Chaudhary, Mekh Raj Joshi, Mohammed Ben-Idris, Joydeep Mitra

arXiv:2610.10999v1eess.SYcs.SY

TL;DR

Full AC contingency analysis is computationally costly for large contingency sets, while structural screening may not capture operating-point-dependent severity or quantify simultaneous-outage interactions and reinforcement benefits. The approach combines dispatch-independent reactance-weighted centrality with LODF-based severity analysis, using synergy and tolerance indices for outage interactions and reinforcement ranking. Using a 5% threshold above unity, 115 of 547 evaluated pairs were super-additive; maximum observed synergy was 7.33, and line 4–13 had a tolerance value of 7.49%.

  • Problem

    Full AC contingency analysis is computationally costly for large contingency sets, while structural screening may not capture operating-point-dependent severity or quantify simultaneous-outage interactions and reinforcement benefits.

    Source: §I · p. 1

  • Method

    The approach combines dispatch-independent reactance-weighted centrality with LODF-based severity analysis, using synergy and tolerance indices for outage interactions and reinforcement ranking.

    Source: §I · p. 2

  • Results

    Using a 5% threshold above unity, 115 of 547 evaluated pairs were super-additive; maximum observed synergy was 7.33, and line 4–13 had a tolerance value of 7.49%.

    Source: §III · p. 5

  • Takeaways & Limitations

    The structural layer can help reduce the contingency search space, but electrical assessment remains necessary to capture operating-condition-dependent severity and power-flow redistribution.

    Source: §IV · p. 6

    Structural metrics alone do not capture operating-condition-dependent severity and power-flow redistribution effects.

    Source: §IV · p. 6

Abstract

from arXiv · show

Rapid contingency screening is essential for secure transmission system operation and planning. Although full AC contingency analysis provides accurate system assessment, it requires high computational effort for large contingency sets. Topology-based screening methods reduce this burden but may not accurately represent operating-point-dependent electrical stress. In addition, conventional single-contingency screening does not quantify interactions among simultaneous outages or provide a direct criterion for reinforcement prioritization. This paper presents a hybrid structural-electrical screening approach that combines a computationally efficient, dispatch-independent structural analysis based on reactance-weighted centrality measures with a flow-based severity assessment using line outage distribution factors. Two indices are evaluated using the flow-based severity: a synergy index to quantify super-additive interactions among simultaneous line outages and a tolerance index to rank reinforcement candidates based on their reduction in aggregate post-contingency severity. The correspondence between structural indicators and electrical severity is evaluated quantitatively. Tests on the IEEE 39-bus system identify 115 super-additive line pairs beyond a 5% threshold, with the most severe interaction exceeding seven times the linear combination of individual outage effects. The highest-ranked reinforcement reduces the mean post-contingency thermal severity by 7.5%. The structural rankings show limited correlation with flow-based severity, with a Spearman coefficient of approximately 0.2. The proposed approach provides an efficient pre-screening method to reduce contingency and reinforcement search spaces before detailed AC and economic evaluations.

I. INTRODUCTION

The introduction motivates efficient contingency screening while identifying gaps in structural-to-electrical severity correspondence, simultaneous-outage interactions, and reinforcement prioritization. It presents a hybrid approach with indices for outage synergy and reinforcement tolerance.

I. INTRODUCTION

  • AC contingency analysis provides accurate electrical information but becomes computationally costly as the number and order of contingencies grow.Screening indicators identify critical events before detailed analysis.Source: §I · p. 1
  • Structural indicators have not been comprehensively quantified against operating-point-dependent severity, and topology-based importance may differ from electrical criticality.Conventional screening also focuses mainly on single outages, although simultaneous outages can compound severity.Source: §I · p. 1
  • The paper combines reactance-weighted centrality with LODF-based severity analysis and statistically evaluates the correspondence between structural indicators and electrical severity.The approach is intended to support detailed AC analysis and expansion planning by reducing the contingency and reinforcement search spaces.Source: §I · p. 2
  • The synergy index quantifies super-additive interactions among simultaneous outages, extending risk screening beyond N-1 assessment.The motivation is that outage effects can compound beyond the sum of individual contingencies.Source: §I · pp. 1–2
  • The tolerance index ranks reinforcement candidates by their reduction in aggregate post-contingency severity.This provides a screening criterion for expansion studies.Source: §I · p. 2

II. METHODOLOGY

The methodology pairs a structural analysis of reactance-weighted network properties with a flow-based analysis of operational severity. It uses the latter to assess outage interactions and reinforcement benefits, and statistically evaluates the relationship between the analyses.

II. METHODOLOGY

  • The framework combines structural analysis based on reactance-weighted network properties with flow-based analysis based on operational severity.The two analyses are complementary rather than treated as interchangeable.Source: §II · p. 2
  • The flow-based layer quantifies outage interactions and reinforcement benefits.Source: §II · p. 2
  • Statistical evaluation measures the correspondence between the structural and flow-based analyses.Source: §II · p. 2

A. System Model, Assumptions, and Notation

The system model represents the transmission network as a weighted graph, using reactance-based structural distances and susceptance-based current-flow calculations. Flow-based severity uses a DC approximation, with AC power flow serving as an independent benchmark.

A. System Model, Assumptions, and Notation

  • The network is modeled as an undirected weighted graph whose vertices are buses and edges are transmission lines.Source: A. System Model, Assumptions, and… · p. 2
  • Line reactance weights distance-based structural metrics, while reciprocal reactance, the line susceptance, weights current-flow calculations.This scheme represents electrical proximity rather than physical connectivity alone.Source: A. System Model, Assumptions, and… · p. 2
  • The flow-based indices use a DC model assuming a predominantly inductive network, near-unity voltage magnitudes, and small phase-angle differences.A Newton–Raphson AC solution is used as an independent benchmark; the method requires branch reactances, thermal limits, and a base operating condition.Source: A. System Model, Assumptions, and… · p. 2

B. Structural Layer

The structural layer uses three reactance-weighted centrality measures to characterize path dependency, electrical proximity, and current redistribution. It screens line contingencies and bus importance while separating islanding cases from valid contingencies.

B. Structural Layer

  • Betweenness identifies buses on many minimum-reactance paths, while closeness measures proximity using minimum-reactance distances within the bus's connected component.Source: B. Structural Layer · p. 2
  • Betweenness, closeness, and current-flow betweenness represent path dependency, electrical proximity, and current redistribution, respectively.Current-flow betweenness accounts for redistribution through multiple paths according to reactances.Source: B. Structural Layer · pp. 2–3
  • The method classifies islanding contingencies separately and excludes them from the valid set so structural distances and centralities remain well-defined.Connectivity is assessed using algebraic connectivity, where positive λ2 indicates a connected network.Source: B. Structural Layer · p. 3
  • Line-wise impacts provide a low-cost structural ranking of contingencies, whereas bus-wise impacts identify locations whose structural importance varies across contingencies.Source: B. Structural Layer · p. 3

C. Flow-Based Severity Layer

The flow-based layer uses base-case dispatch and LODFs to assess post-outage severity, with thermal and voltage measures and checks across operating points.

C. Flow-Based Severity Layer

  • LODFs combine base-case flows with outage effects to estimate post-contingency line flows without repeated power-flow solutions.The analysis uses base-case dispatch and branch parameters.Source: C. Flow-Based Severity Layer · p. 3
  • The quadratic thermal performance index measures thermal stress and increases sensitivity to heavily loaded branches.Line thermal limits are used in the index.Source: C. Flow-Based Severity Layer · p. 3
  • Generalized LODFs calculate post-contingency flows for simultaneous outages when the removed lines do not island the network.Source: C. Flow-Based Severity Layer · p. 3
  • An AC-based voltage severity index benchmarks voltage-related vulnerabilities omitted by the DC formulation, and perturbed operating points test ranking robustness.The AC solution supplies the maximum voltage stability index; load perturbations vary power-flow patterns.Source: C. Flow-Based Severity Layer · p. 3

D. Synergy Index for Compounded Severity

The synergy index compares joint outage severity with the sum of individual severity increments, identifying super-additive interactions among simultaneous outages.

D. Synergy Index for Compounded Severity

  • The synergy index compares the joint severity increment with the sum of individual outage increments on an additive severity scale.The increments are measured relative to the pre-contingency condition.Source: D. Synergy Index for Compounded Severity · p. 3
  • Values greater than unity indicate that a combined outage produces a severity increase larger than the linear contribution of individual outages.Source: D. Synergy Index for Compounded Severity · p. 4
  • The index targets hidden multi-line risks that single-contingency screening cannot reveal, including interactions linked to shared transfer corridors or sequential flow redistribution.A predefined tolerance margin τ is used because most line pairs are weakly coupled and the index generally approaches unity.Source: D. Synergy Index for Compounded Severity · p. 4

E. Tolerance Index for Reinforcement

The tolerance index ranks candidate lines by their reduction in average post-contingency thermal severity, as a preliminary reinforcement-screening measure.

E. Tolerance Index for Reinforcement

  • The tolerance index measures the difference in average thermal severity across valid single-line contingencies between the original network and a network with a candidate line added.Source: E. Tolerance Index for Reinforcement · p. 4
  • A positive tolerance index indicates reduced post-contingency stress, and high-ranked candidates provide alternative transfer paths that mitigate overloads.The contingency set is held identical and the added line is not treated as an outage.Source: E. Tolerance Index for Reinforcement · p. 4
  • The index is intended to screen reinforcement candidates before detailed planning that considers cost, feasibility, right-of-way, voltage constraints, and stability requirements.Source: E. Tolerance Index for Reinforcement · p. 4

F. Coupling and Validation

The paper evaluates structural–electrical correspondence with rank-correlation tests and validates its indices against DC and AC calculations and conventional AC rankings.

F. Coupling and Validation

  • Structural and flow-based rankings for contingencies, synergy, and tolerance are compared using Spearman correlation, bootstrap confidence intervals, and permutation tests.Source: F. Coupling and Validation · p. 4
  • The synergy index is checked against exact DC re-solutions and AC power-flow solutions, while tolerance is checked against full AC re-solutions of reinforced networks.Validation uses maximum deviation from exact solutions and correlation with the AC benchmark.Source: F. Coupling and Validation · p. 4
  • Flow-based severity rankings are compared with conventional AC rankings using rank correlation and critical-event recall to identify when structural screening can reduce the search space.The comparison also identifies cases where the flow-based layer must determine the final ranking.Source: F. Coupling and Validation · p. 4

III. TEST SYSTEM AND RESULTS

On the IEEE 39-bus system, the proposed structural measures highlighted buses 16–17 and corridor 14–17, but their rankings correlated only weakly with flow-based severity. Flow-based synergy and tolerance indices identified super-additive outage pairs and reinforcement candidates, and their rankings agreed closely with AC benchmarks.

III. TEST SYSTEM AND RESULTS

  • The IEEE 39-bus New England test system comprised 39 buses and 46 transmission branches; analysis spanning eight operating points and 75 reinforcement candidates finished in under one minute on a standard eight-core workstation.Of 1,035 possible double-line outage pairs, 562 remained electrically connected and were considered for severity evaluation.Source: §III · p. 4
  • The three reactance-weighted centrality measures consistently identified buses 16 and 17 and the corridor between buses 14–17 as structurally dominant.Fig. 1 shows the normalized bus centrality profiles.Source: §III · p. 4, Figure 1 · p. 5
  • The largest structural redistribution from single-line outages and bus-level centrality changes occurred in the same highly connected corridors.These patterns are shown in the single-outage ranking and bus-impact figures.Source: §III · p. 5, Figure 2 · p. 5, Figure 3 · p. 5
  • Structural-severity correlations were 0.22 ± 0.03 for current-flow betweenness, 0.32 for betweenness, and 0.20 for closeness, versus 0.81 for DC line-flow rankings.The comparison covered eight operating points generated by independently perturbing bus loads within ±30%; AC voltage-stability-index correlation was 0.24.Source: §III · p. 5, Figure 4 · p. 5
  • 115 of 547 valid line pairs exceeded the 5% super-additivity threshold, 26 exceeded 1.5, and the maximum synergy was 7.33 for lines 5–6 and 6–7.Most pairs were close to unity; the highest-ranked synergy pairs are summarized in Table I.Source: §III · p. 5, Table I · p. 5
  • 7.49% tolerance for line 4–13 was the largest reduction in average contingency severity; 65 of 75 candidate additions reduced aggregate severity.The evaluated candidates were generated between two-hop neighboring buses; Table II lists the ten highest-ranked options.Source: §III · p. 5, Table II · p. 6
  • 0.998 Pearson correlation for synergy and 0.95 for tolerance against AC re-solutions; tolerance had approximately 1% mean absolute deviation.The indices were checked against independent DC and AC solutions; Fig. 6 shows the parity plots.Source: §III · p. 6, Figure 6 · p. 6
  • 0.99 Spearman correlation with full AC contingency rankings, with all most critical outages identified; synergy reached 0.83 and identified 83% of highest-ranked pairs, while tolerance reached 0.81 and identified all highest-ranked candidates.These are the LODF-based thermal-severity, N–2 synergy, and reinforcement-ranking comparisons, respectively.Source: §III · p. 6

IV. CONCLUSION

The method combines dispatch-independent, reactance-weighted structural metrics with LODF-based electrical severity analysis. It uses synergy and tolerance indices to assess outage interactions and rank reinforcements while retaining electrical assessment for operating-condition-dependent severity.

IV. CONCLUSION

  • The hybrid method combines dispatch-independent structural metrics with LODF-based electrical severity analysis for contingency screening and reinforcement assessment.The structural layer uses reactance-weighted graph metrics; the electrical layer captures power-flow redistribution effects.Source: §IV · p. 6
  • Structural metrics efficiently identify vulnerable network regions and reduce the contingency search space, but do not replace electrical assessment.Electrical assessment remains necessary to capture operating-condition-dependent severity and power-flow redistribution.Source: §IV · p. 6
  • The synergy and tolerance indices identify compounded outage interactions and rank reinforcement candidates by their impact on system security.The method describes a scalable screening approach to support detailed AC, dynamic, and economic security studies.Source: §IV · p. 6
  • Future work will evaluate larger systems, add injection-aware structural measures and AC and dynamic constraints, and integrate the indices with reliability-based and economic expansion planning.Source: §IV · p. 6
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