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Severity-Aware Minimum Security Sets for Accelerated Preventive SCOPF Using Machine Learning

Mohammad Iman Alizadeh, Saeed Zeynali, Salah Ghamizi, Sylvain Kubler

arXiv:2610.19750v1eess.SYcs.SY

TL;DR

Preventive AC-PSCOPF can become computationally burdensome, while existing filtering leaves gaps in jointly screening contingencies and constraints and controlling residual severity. The paper constructs severity-aware MSS labels and trains a model to predict them from operating states. Tests on IEEE 60-bus and 118-bus systems report substantial computation reductions with preventive solutions close to full PSCOPF.

  • Problem

    Existing reduced AC-PSCOPF approaches give limited attention to jointly screening relevant contingencies and constraints while controlling residual post-contingency severity.

    Source: §I · p. 2

  • Method

    The framework constructs severity-aware, operating-point-dependent MSS labels using assessment and screening, then trains a supervised model to predict them from pre-contingency states.

    Source: §I · p. 2, D. Two-Stage Graph Attention Screening… · p. 6

  • Results

    For the IEEE 118-bus system, solution time fell by 89.5%, with variables reduced by 39.2% and constraints by 48.4%.

    Source: §V · p. 10

  • Takeaways & Limitations

    On the IEEE 60-bus and 118-bus systems, filtering substantially reduced computation while keeping the preventive operating point close to full PSCOPF.

    Source: §V · p. 10

Abstract

from arXiv · show

This paper proposes a severity-aware machine learning framework for reducing the computational burden of preventive AC security-constrained optimal power flow (PSCOPF). The central idea is to identify a compact minimum security set (MSS) containing only the non-dominated contingencies and associated post-contingency constraints that materially influence the preventive operating point while satisfying a prescribed severity tolerance. An offline procedure combines AC security assessment, severity-based ranking, non-dominated screening, and iterative reduced PSCOPF. After each reduced PSCOPF solution, exhaustive security assessment over all credible contingencies identifies additional contingency--constraint pairs whose residual severity exceeds the specified threshold. Severity is characterized using the normalized number, accumulated magnitude, maximum magnitude, and average magnitude of post-contingency violations. The resulting operating-point-dependent MSSs are used as labels for a supervised multi-label learning model that predicts the security elements required to construct the reduced PSCOPF directly from the pre-contingency state. The proposed framework therefore focuses the optimization on the contingencies and constraints that affect preventive control decisions, reducing problem size and computation time while explicitly controlling residual post-contingency severity. Results on the IEEE 60-bus and 118-bus systems, the latter having an approximately seven-times-larger PSCOPF formulation, demonstrate substantial computational reductions with limited impact on the preventive operating solution.

I. INTRODUCTION

AC-PSCOPF captures post-contingency security but grows costly with network size and contingency count. The paper addresses limits of binary and contingency-only screening with a severity-aware, operating-point-dependent minimum security set and a learned predictor.

I. INTRODUCTION

  • The AC-PSCOPF’s nonlinear, non-convex formulation becomes computationally burdensome as the network and credible-contingency set grow.It models pre-contingency and post-contingency states simultaneously,.Source: §I · p. 1
  • Existing filtering often screens contingencies or constraints from a predefined representation without controlling residual post-contingency severity.Binary relevance can retain both a marginal violation and a severe state, while contingency-level selection may leave many associated constraints in the model.Source: §I · p. 2
  • The severity-aware MSS retains the minimum contingencies and associated constraints needed to meet a prescribed post-contingency severity level.Its severity criterion combines normalized violation count, accumulated magnitude, maximum magnitude, and average magnitude.Source: §I · p. 2
  • The MSS is operating-point-dependent because the same outage can have different security relevance under different loading, generation, flow, and voltage conditions.Non-dominance screening removes contingencies whose violated constraints and magnitudes are covered by a more severe contingency.Source: §I · p. 2
  • An offline construction procedure combines severity prioritization, non-dominance screening, iterative reduced PSCOPF, and exhaustive security assessment to label MSSs for supervised multi-label prediction.The model predicts contingency–constraint elements from the pre-contingency state rather than predicting the PSCOPF solution itself.Source: §I · pp. 2–3

II. SEVERITY-AWARE AC-PSCOPF

The formulation keeps preventive active-power schedules fixed across contingencies while allowing specified post-contingency adjustments. Its severity extension measures violations and uses a threshold to balance optimization size against residual security impact.

A. Generic Preventive AC-PSCOPF Formulation

  • Non-slack generators retain their pre-contingency active-power schedules after an outage, while the slack generator and reactive outputs can adjust within their stated roles and limits.The AC formulation enforces power balance, generator capability, voltage, and branch thermal constraints across pre- and post-contingency states.Source: A. Generic Preventive AC-PSCOPF… · p. 3
  • A severity-aware MSS can omit marginal security elements below the prescribed tolerance, reducing PSCOPF size while keeping the preventive objective value almost unchanged.Exhaustive post-optimization security assessment checks residual violations across the complete contingency set against that tolerance.Source: A. Generic Preventive AC-PSCOPF… · p. 3

B. Severity-Aware Risk Extension

  • Four normalized indices characterize post-contingency violations by their number and magnitude, and a weighted aggregation forms each contingency’s severity index.The components are normalized total count, accumulated magnitude, maximum magnitude, and average magnitude.Source: B. Severity-Aware Risk Extension · p. 3
  • The severity threshold β prioritizes contingencies for further assessment and selection, while below-threshold contingencies may be excluded unless later security evaluations identify a problem.Source: B. Severity-Aware Risk Extension · p. 4

III. MINIMUM SECURITY SET CONSTRUCTION AND ML APPROXIMATION

Because severity indices require AC security assessment and the full constraint set is too large, the framework learns which security elements belong in the reduced model. Offline MSS labels train a supervised predictor that maps operating states to those elements.

III. MINIMUM SECURITY SET CONSTRUCTION AND ML APPROXIMATION

  • The framework learns the minimum contingency–constraint representation satisfying the severity criterion, rather than approximating the PSCOPF solution.The stated aim is to reduce explicitly modelled contingencies and constraints while preserving the original problem’s AC-feasible operating point.Source: §III · p. 4

A. Overview

  • For each operating sample, offline AC OPF, security assessment, severity screening, non-dominance selection, and iterative reduced PSCOPF construct an MSS label for supervised multi-label learning.Source: A. Overview · p. 4
  • Online, the trained model maps pre-contingency operating features x(s) to MSS M(s), which can be regrouped by contingency and associated active constraints.The regrouped representation identifies the samples in which a contingency belongs to the MSS and the active post-contingency constraints associated with it.Source: A. Overview · p. 4

B. Initial Screening

Initial screening ranks contingencies by aggregate post-contingency severity and removes dominated cases. This yields a compact, severity-representative candidate set for iterative MSS construction.

B. Initial Screening

  • For each sample, exhaustive security assessment returns constraint-violation vectors for credible contingencies, which are summarized by aggregate severity and ranked from highest to lowest.Source: B. Initial Screening · p. 4
  • A contingency is dominated when another covers all its violated constraints and has at least the same aggregate severity, so retaining it adds no new violated constraint or more severe condition.Source: B. Initial Screening · p. 4
  • The non-dominated candidates provide a compact, severity-representative initialization for the iterative MSS construction.Source: B. Initial Screening · p. 4

C. Iterative Construction of the MSS

The MSS is built iteratively from initially screened non-dominated contingency–constraint pairs. Reduced PSCOPF solutions are checked against the full contingency set, and additional pairs are added until the severity budget or another stopping condition is reached.

C. Iterative Construction of the MSS

  • The initial candidate set comprises violated constraint pairs from non-dominated contingencies selected through severity-based screening.Algorithm 2 refines the candidates from Algorithm 1, which runs AC security assessment, records violated constraints, ranks contingencies by severity, and screens dominated cases.Source: C. Iterative Construction of the MSS · pp. 4–5
  • Each reduced PSCOPF solution is assessed against the complete contingency set to find violated pairs not yet represented in the MSS.These unresolved pairs are collected when their constraints remain violated after the current reduced PSCOPF.Source: C. Iterative Construction of the MSS · p. 5
  • If every contingency’s updated severity is within β, the procedure terminates and retains the current MSS.Otherwise, unresolved pairs are prioritized by violation magnitude and severity contribution, then added before resolving the reduced PSCOPF; iteration also stops if no unresolved pairs remain or Nmax is reached.Source: C. Iterative Construction of the MSS · p. 5
  • The final MSS labels supervised learning, while its iterative growth avoids unnecessary security elements and preserves the original problem’s AC-feasibility and severity-aware risk characteristics.Only pairs revealed as unresolved by full security assessment are added during the process.Source: C. Iterative Construction of the MSS · pp. 5–6

D. Two-Stage Graph Attention Screening Model

The screening model maps a pre-contingency operating state to an MSS using a two-stage graph attention network. It represents the grid explicitly and predicts retained contingencies followed by their binding post-contingency limits.

D. Two-Stage Graph Attention Screening Model

  • A two-stage graph attention network maps the pre-contingency operating point to an MSS, using buses as nodes and branches as edges.Its graph structure reflects the network topology over which post-contingency stress propagates.Source: D. Two-Stage Graph Attention Screening… · p. 6
  • The model distributes the base-case AC OPF state over bus nodes, with node features including demand, generation, voltage magnitude and angle, and incident-branch flows.Features are standardized using training-set statistics, and the edge set reproduces branch topology.Source: D. Two-Stage Graph Attention Screening… · p. 6
  • Stage A predicts binding probabilities for candidate contingencies, and conditioned on retained contingencies, Stage B predicts probabilities for monitored post-contingency limits.The two heads decode a shared sample embedding into contingency and constraint predictions.Source: D. Two-Stage Graph Attention Screening… · p. 6
  • The two prediction heads are jointly trained with a summed binary cross-entropy loss, while their thresholds trade true-MSS coverage against predicted-set size.The MSS supervision is represented as a multi-hot encoding.Source: D. Two-Stage Graph Attention Screening… · p. 6

IV. NUMERICAL RESULTS

The evaluation uses IEEE 60-bus and 118-bus systems, with comprehensive performance assessment on the smaller system and scalability demonstration on the larger one. It varies the severity threshold and uses sampled operating points with specified contingency screening.

IV. NUMERICAL RESULTS

  • The study evaluates the method on IEEE 60-bus and 118-bus systems, using the former for comprehensive assessment and the latter primarily for scalability.The 118-bus full PSCOPF formulation averages approximately seven times as many variables and constraints as the 60-bus formulation.Source: §IV · p. 6
  • Operating samples allow bus loads to deviate by up to 20% under a uniform distribution, and credible line contingencies exclude islanding, bus disconnection, or conflicting pairs.The NLP problems are implemented in Julia and solved with IPOPT.Source: §IV · p. 6
  • The severity-index thresholds tested are β = 0.0, β = 0.1, and β = 0.3; larger thresholds focus on more critical violations.Smaller β values retain contingencies and constraints associated with even minor violations.Source: §IV · p. 6

A. Comparison with the Full PSCOPF Benchmark

On the IEEE 60-bus system, reduced PSCOPF cuts solution time while leaving objective deviation unchanged. Increasing the severity threshold further reduces problem size, with a small increase in residual post-contingency violations.

A. Comparison with the Full PSCOPF Benchmark

  • Average solution time falls from approximately 6 s for full PSCOPF to 1.5, 1.2, and 1.0 s at severity thresholds 0.0, 0.1, and 0.3, while objective deviation remains unchanged.The corresponding time reductions are 75%, 81%, and 82%.Source: A. Comparison with the Full PSCOPF… · pp. 6–7, Table I · p. 7
  • Retained contingencies decrease by 56% at severity 0.0 to 65.8% at severity 0.3; variable reduction rises from 54.7% to 66.6% and constraint reduction from 61.5% to 71.5%.The full PSCOPF has 50,948 variables and 65,067 constraints; increasing severity thresholds progressively removes marginal contingency–constraint pairs.Source: A. Comparison with the Full PSCOPF… · p. 7
  • At severity 0.0 there are no residual violations; at 0.1 there are 0.25 violations per sample on average with average magnitude 3.5 × 10−4, rising at 0.3 to 0.62 and 1.5 × 10−3.The reported trade-off is greater computational savings at higher thresholds alongside a small increase in residual post-contingency violations.Source: A. Comparison with the Full PSCOPF… · p. 7

B. Performance on a Larger Test System

On the IEEE 118-bus system, the reduced PSCOPF substantially lowers solution time while leaving the preventive objective essentially unchanged. Increasing the severity threshold reduces the security representation but permits residual post-contingency violations, which are checked through exhaustive security assessment.

B. Performance on a Larger Test System

  • Solution time falls from approximately 152 s to 30, 21, and 16 s at severity levels 0.0, 0.1, and 0.3, reductions of 80.3%, 86.2%, and 89.5%.The full PSCOPF contains 356,688 variables and 456,805 constraints.Source: Table II · p. 7, B. Performance on a Larger Test System · p. 7
  • Across 100-sample IEEE 118-bus experiments, the reduced security representation retains 85 contingencies on average; as the severity threshold increases, it retains 128, 69, and 59, corresponding to reductions of 8.5%, 50.7%, and 57.8%.The original credible set contains 140 transmission-line contingencies.Source: B. Performance on a Larger Test System · p. 7
  • Variable reductions rise from 9.3% to 39.2%, while constraint reductions rise from 23.1% to 48.4% as the severity threshold increases.Fewer represented contingencies reduce contingency-dependent variables and constraints.Source: B. Performance on a Larger Test System · p. 7
  • The preventive objective remains essentially unchanged; severity 0.0 yields no residual violations, while 0.1 and 0.3 yield an average of two, with maximum violations of 0.92 and 0.95, respectively.Source: B. Performance on a Larger Test System · p. 7
  • The threshold trades computational burden against residual severity, while exhaustive post-optimization assessment evaluates omitted contingency–constraint pairs and triggers re-solving if severity exceeds the threshold.The corresponding contingency and violated constraints can be added without modifying the PSCOPF formulation.Source: B. Performance on a Larger Test System · pp. 7–8
  • Sample-averaged results need not match the target severity threshold because filtering applies it per contingency, whereas reported metrics aggregate across contingencies and operating samples.Nonlinear PSCOPF can also shift the preventive point toward a more conservative solution, producing smaller residual violations than the threshold.Source: B. Performance on a Larger Test System · p. 8

C. Sparsity and recurrence of retained contingency sets

The retained contingency sets are sparse but recurrent across operating points, while static frequency-ranked labels miss complete-set coverage. On held-out samples, two-stage GAT screening sharply reduces the security representation while maintaining full mean coverage at the conservative threshold.

C. Sparsity and recurrence of retained contingency sets

  • Across 5,000 operating points, 16.08 contingencies are retained on average (60.77% sparsity), and only 27 distinct sets occur; the five most frequent cover 76.12% of samples.The sparsity and recurrence motivate learning contingency selection from operating conditions.Source: Table III · p. 8, C. Sparsity and recurrence of retained… · p. 8
  • A static set of the 15 most frequent labels covers 91.30% of label events but contains the complete exported set in only 35.58% of operating points.Twelve contingency IDs occur at every operating point, while ID 27 appears only three times.Source: Table IV · p. 8, C. Sparsity and recurrence of retained… · p. 8

D. Two-Stage GAT Screening Performance

  • At τ = 0.005 for β ∈ {0, 0.1, 0.3}, Stage B keeps roughly two of 296 monitored limits per retained contingency, spanning about 40.7k scalar slots versus 3.33M full-space slots over the test set—a reduction of close to 99% at full coverage.Source: Table V · p. 9, D. Two-Stage GAT Screening Performance · p. 9
  • Stage A predicts 21.74, 19.07, and 16.02 contingencies for β = 0, 0.1, and 0.3, respectively, versus 41 candidates, with CovMu = 1.000 for each budget.Predicted sets are intentionally larger than true sets under the conservative threshold, favoring retention over false negatives.Source: D. Two-Stage GAT Screening Performance · p. 8, Table V · p. 9
  • Stage B predicts 2.25, 2.48, and 1.46 constraints from 296 candidates for β = 0, 0.1, and 0.3, respectively, with CovMu = 1.000 throughout.Additional predictions act conservatively by adding constraints rather than omitting elements required by the reference MSS.Source: D. Two-Stage GAT Screening Performance · pp. 8–9, Table V · p. 9
  • Across threshold sweeps, both stages retain near-unity coverage over a low-threshold band as predicted set sizes fall, before coverage drops sharply past a knee.Larger severity budgets shift both coverage and predicted-set-size curves downward.Source: D. Two-Stage GAT Screening Performance · p. 9, Figure 1 · p. 9, Figure 2 · p. 9

V. CONCLUSION

The paper introduces a severity-aware framework for constructing minimum security sets and learning to predict relevant contingency–constraint pairs. Tests on IEEE 60-bus and 118-bus systems show substantial computational reductions while keeping the preventive operating point close to full PSCOPF.

  • The severity-aware criterion accounts for the number, accumulated magnitude, maximum magnitude, and average magnitude of post-contingency violations.An offline procedure combines AC security assessment, non-dominated contingency screening, and iterative reduced PSCOPF to construct MSS labels for supervised prediction.Source: §V · p. 10
  • 82.8% lower solution time on the 60-bus system and 89.5% lower solution time on the 118-bus system, with the preventive operating point close to full PSCOPF.For the 60-bus system, variables and constraints fell by 66.7% and 71.5%; for the 118-bus system, they fell by 39.2% and 48.4%, respectively.Source: §V · p. 10
  • The severity threshold controls the trade-off between computational efficiency and residual post-contingency violations.Exhaustive post-optimization assessment can add violations exceeding the threshold back into the reduced PSCOPF if required.Source: §V · p. 10
  • Future work will examine larger systems, alternative machine-learning architectures, and online validation of learned MSS predictions for operational deployment.Source: §V · p. 10
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