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AI-Enhanced Resilience in Power Systems: Adversarial Deep Learning for Robust Short-Term Voltage Stability Assessment under Cyber-Attacks

Yang Li, Shitu Zhang, Yuanzheng Li

arXiv:2504.02859v1eess.SYcs.SY

TL;DR

The paper addresses the limited attention given to STVSA robustness under multiple attacks, particularly DoS and adversarial attacks. It proposes an adversarial deep-learning framework with an L-GAT model and reports effectiveness in complex attack environments.

  • Problem

    Investigation of STVSA model stability and robustness under multiple attacks has received insufficient attention, particularly for classical DoS and adversarial attacks.

    Source: §1.1 · p. 2

  • Method

    The framework uses adversarial deep learning and an L-GAT model to capture relationships between time-series data and electrical grid topology.

    Source: §7 · p. 23

  • Results

    The approach demonstrates effectiveness and superiority in complex attack environments, advancing resilience against composite cyber-attacks.

    Source: §7 · p. 23

  • Takeaways & Limitations

    The L-GAT integration supports simultaneous optimization of temporal and spatial analyses in STVSA.

    Source: §7 · p. 23

    The paper identifies a literature gap: multi-attack STVSA robustness, especially against DoS and adversarial attacks, has received insufficient attention.

    Source: §1.1 · p. 2

Abstract

from arXiv · show

In the era of Industry 4.0, ensuring the resilience of cyber-physical systems against sophisticated cyber threats is increasingly critical. This study proposes a pioneering AI-based control framework that enhances short-term voltage stability assessments (STVSA) in power systems under complex composite cyber-attacks. First, by incorporating white-box and black-box adversarial attacks with Denial-of-Service (DoS) perturbations during training, composite adversarial attacks are implemented. Second, the application of Spectral Normalized Conditional Wasserstein Generative Adversarial Network with Gradient Penalty (SNCWGAN-GP) and Fast Gradient Sign Method (FGSM) strengthens the model's resistance to adversarial disturbances, improving data quality and training stability. Third, an assessment model based on Long Short-Term Memory (LSTM)-enhanced Graph Attention Network (L-GAT) is developed to capture dynamic relationships between the post-fault dynamic trajectories and electrical grid topology. Experimental results on the IEEE 39-bus test system demonstrate the efficacy and superiority of the proposed method in composite cyber-attack scenarios. This contribution is pivotal to advancing AI-based resilient control strategies for nonlinear dynamical systems, marking a substantial enhancement in the security of cyber-physical systems.

1 Introduction

The section motivates resilient short-term voltage stability assessment in digital power systems facing complex cyber-attacks, outlining temporal and topological modeling, adversarial training, and generated training data. It also describes normalized CWGAN-GP training and rare-fault synthetic data to improve training stability, generalization, and robustness to unseen adversarial attacks.

1 Introduction

  • Digital transformation increases the information and data in power systems and the possibility and complexity of cyber-attacks.Source: §1 · p. 1

1.1 Advances and Limitations of STVSA

  • Time-domain simulation is computationally expensive, direct-method accuracy and applicability in complex systems need work, and data-driven methods face interpretability, data-dependence, and model-selection challenges.Source: §1.1 · p. 2
  • Robustness under multiple attacks, especially DoS and adversarial sample attacks originating in image processing, remains underexplored in STVSA.Source: §1.1 · p. 2

1.2 Research Gaps of Existing Research

  • STVSA research often overlooks resilience under cyber-attacks and explicit grid topology, while topology-focused graph Transformers can neglect temporal dynamics.Source: §1.2 · p. 3
  • SNCWGAN-GP generates diverse training data to improve model generalizability and resilience against unseen attacks.Source: §1.2 · p. 3
  • The proposed L-GAT combines LSTM temporal modeling and GAT structural reasoning to capture post-fault dynamics and grid topology for robust STVSA.Source: §1.2 · p. 3
  • Adversarial training combines white-box and black-box attacks with DoS perturbations, strengthening robustness and generalization across cyber-attack scenarios.Source: §1.2 · p. 4
  • Discriminator weight normalization in the normalized CWGAN-GP enforces Lipschitz continuity, stabilizes adversarial training, and accelerates convergence.Source: §1.2 · p. 4
  • Synthetic data covering rare grid faults improves generalization and strengthens robustness against unseen adversarial attacks.Source: §1.2 · p. 4

2 Modeling and Implementation of Cyber-Attacks

This section models compromised PMU and device data as a stability risk by describing white- and black-box adversarial sample generation, including FGSM and an iterative strategy, alongside Poisson-based DoS simulation. It also covers composite attacks that combine adversarial and DoS perturbations, including scenarios where attackers lack access to model internals.

2 Modeling and Implementation of Cyber-Attacks

  • PMU-data tampering and attacks on dynamic devices can destabilize power systems, while interconnected stages allow attacks to trigger cascading failures.Source: §2 · pp. 4–5

2.1 Adversarial Sample Attacks

  • Adversarial sample attacks apply usually imperceptible input perturbations that can make deep-learning models decide incorrectly, exposing data-processing vulnerabilities.Source: §2.1 · p. 5

2.1.1 Fast Gradient Sign Method

  • FGSM generates adversarial samples in one step by adding a bounded perturbation in the sign direction of the input-loss gradient.Source: §2.1.1 · p. 6

2.1.2 Adversarial Sample Attack Generation Strategy

  • The training set comes from time-domain simulations processed for diversity; FGSM adds slight loss-maximizing perturbations, then samples are evaluated and regenerated iteratively to desired efficacy.Source: §2.1.2 · pp. 6–7
  • In white-box generation, the model’s loss gradient determines a small input perturbation, and iterations continue until prediction moves toward the target label.The process updates the input with each generated adversarial sample unless the prediction has shifted from the original label toward the target.Source: §2.1.2 · pp. 7–8
  • For black-box attacks, a surrogate model approximates the target model to generate samples, an approach described as less effective but more indicative of real-world power-system threats.The attacker lacks knowledge of the target model’s internal structure and parameters.Source: §2.1.2 · p. 8
  • FGSM examples may fail to disrupt as intended, necessitating further iterations to refine effective attack samples.Source: §2.1.2 · p. 8

2.2 Denial of Service Attacks

  • DoS severity is simulated by zeroing parts of data samples according to probabilities derived from a Poisson distribution.Adjusting its λ parameter models attacks of varying intensities.Source: §2.2 · p. 8

2.3 Composite Adversarial Attacks

  • Composite adversarial attacks combine adversarial perturbations with DoS attacks in white-box and black-box variants.The DoS mask nullifies data segments probabilistically.Source: §2.3 · p. 9

3 Data Clustering and Augmentation

This section describes semi-supervised clustering and SNCWGAN-GP augmentation to address scarce, imbalanced STVSA simulation data and produce a large, balanced dataset for AI training. It outlines the generator–discriminator workflow, including conditional label processing, discriminator feedback, Wasserstein loss, gradient penalty, and spectral normalization.

3 Data Clustering and Augmentation

  • SNCWGAN-GP augmentation is proposed to address limited scale, homogenization, and category imbalance in simulation datasets and support training on larger, balanced data.The stated goal is an AI model with superior performance and robustness.Source: §3 · p. 9

3.1 Semi-supervised Fuzzy C-Means Clustering

  • Semi-supervised Fuzzy C-Means uses a limited labeled subset to guide fuzzy clustering, improving the accuracy and reliability of dataset clustering.It combines supervised information with unsupervised clustering for settings where most data remain unlabeled.Source: §3.1 · p. 10

3.2 Advantages of SNCWGAN-GP

  • SNCWGAN-GP extends CWGAN-GP with spectral normalization in the discriminator while using Wasserstein loss and gradient penalty to support stable training and higher-quality data generation.The gradient penalty restrains discriminator gradients, and spectral normalization constrains layer weights to satisfy the 1-Lipschitz condition.Source: §3.2 · p. 11

3.3 Principle and Structure of the SNCWGAN-GP

  • The SNCWGAN-GP generator uses noise and controlled variables to create diverse synthetic samples, which are combined with real data in the workflow.The model comprises a generator and discriminator.Source: §3.3 · p. 12
  • Spectral normalization constrains discriminator weights, while discriminator-loss feedback and gradient penalty update the generator under Wasserstein loss in an iterative refinement cycle.The discriminator may need self-updates to adapt to changing controlled variables; the iterative process is described as improving generated-data quality.Source: §3.3 · p. 12
  • The generator embeds category labels and uses transposed convolutions to synthesize data, while the discriminator uses convolutional features and spectral normalization to assess sample authenticity.Discriminator feedback helps refine the generator; spectral normalization is described as curbing gradient explosions and maintaining training stability.Source: §3.3 · pp. 12–13

4 LSTM-enhanced Graph Attention Network

The section motivates L-GAT as a way to combine graph-topology learning with temporal modeling for power-system state assessment. Its mechanisms compress node time series, weight neighboring features, and aggregate them through multi-head attention.

4 LSTM-enhanced Graph Attention Network

  • Conventional GCNs rely on static adjacency-based aggregation and can neglect differences among neighbors, while GATs do not adequately capture changing system states over time.The section also notes that GCNs may disregard connectivity and local node structure, and that Transformers were not inherently designed for graph-structured data.Source: §4 · p. 14

4.1 Basic Principles of LSTM-enhanced Graph Attention Networks

  • L-GAT adds LSTM processing of each node’s time series to GAT’s topology learning and neighbor weighting, capturing temporal dependencies and evolving system states.The paper says it adapts graph-attention layers for graph-structured data rather than adopting the complete traditional Transformer architecture.Source: §4.1 · p. 14

4.2 Core Mechanisms of L-GAT

  • L-GAT’s graph-attention layers model complex node interactions to interpret dynamic graph data and handle intricate graph structures.Figure 5 depicts the model’s graph-attention functionality.Source: §4.2 · p. 14

4.2.1 Temporal Features Aggregation

  • LSTM gating compresses each node’s time series into h_t, a compact representation that retains pertinent historical information for later graph attention.The gates selectively preserve or discard input information.Source: §4.2.1 · p. 15

4.2.2 Linear Transformation of Node Features

  • A trainable weight matrix transforms each node’s compressed features into a new feature space before graph attention.The text says this transformation enhances and normalizes representations in preparation for processing inter-node relationships.Source: §4.2.2 · p. 15

4.2.3 Calculation of Attention Coefficients

  • Attention coefficients determine each neighbor’s importance during aggregation, with normalized α_ij weights from node j to node i summing to 1 across neighbors.A learnable attention vector weighs feature importance between nodes; LeakyReLU introduces nonlinearity.Source: §4.2.3 · pp. 15–16

4.2.4 Feature Aggregation

  • Each node’s new feature is a weighted sum of its neighbors’ features, followed by an activation function such as Sigmoid.The weights are the attention coefficients calculated for neighboring nodes.Source: §4.2.4 · p. 16

4.2.5 Multi-Head Attention Aggregation and Averaging

  • L-GAT repeats attention aggregation with different parameter sets; it concatenates heads in intermediate layers and averages them in the final layer or for smoother outputs.The text says averaging across heads supports generalization and helps prevent overfitting.Source: §4.2.5 · p. 16

5 Proposed Methodology

The proposed methodology uses mixed adversarial training with L-GAT for short-term voltage stability assessment under cyber-attacks. It prepares and trains the model, then applies it to online PMU data and post-fault trajectories.

5 Proposed Methodology

  • The proposed L-GAT methodology combines white-box and black-box composite adversarial attacks in mixed training for real-time short-term voltage stability assessment.The workflow comprises data preparation, robust model training, and online assessment.Source: §5 · p. 17

5.1 Data Preparation

  • Data preparation resolves ambiguous labels with semi-supervised clustering, balances and enlarges the dataset, then mixes FGSM-generated white-box and black-box adversarial samples with clean data.The mixed dataset is used for adversarial training.Source: §5.1 · pp. 17–18

5.2 Model Training

  • Robust training iteratively updates model parameters from forward predictions and back-propagated loss gradients, optimizing hyperparameters and retaining the selected configuration for deployment.The listed hyperparameters include learning rate, batch size, number of layers, and number of attention heads.Source: §5.2 · p. 18

5.3 Online Assessment

  • Online assessment uses real-time PMU data and post-fault trajectories to evaluate stability after large disturbances, triggering emergency controls if instability is detected.If stability is confirmed, monitoring continues without manual intervention.Source: §5.3 · p. 18

6 Case Analysis

The case analysis examines L-GAT and SNCWGAN-GP performance in IEEE 39-bus experiments across composite attacks, extreme system states, measurement noise, and observation-window lengths.}

6 Case Analysis

  • Experiments used the IEEE 39-bus test system, and results were validated with 5-fold cross-validation.Simulations were run through PSD-BPA.Source: §6 · p. 18

6.1 Dataset Generation

  • The pipeline simulated an initial dataset of 3,400 samples, applied semi-supervised clustering to classify boundary samples into a fully labeled dataset, then expanded it to 12,000 using SNCWGAN-GP.The 12,000 samples were split into training and testing sets at a 4:1 ratio; FGSM and DoS attack simulation methods created adversarial samples.Source: §6.1 · p. 19
  • SNCWGAN-GP outperformed LSGAN across all three evaluated metrics on the study’s high-dimensional dataset.The comparison assesses generated-data similarity and diversity, with lower metric values indicating better performance.Source: Table 3 · p. 20, §6.1 · p. 20

6.2 Performance Analysis of STVSA under Cyber-attacks

  • Under white-box composite attacks, L-GAT reached 96.66% accuracy, beating alternatives by 1.28–9.48 percentage points while meeting the ACC >95% engineering requirement.DT and SVM fell below 88% accuracy.Source: Table 4 · p. 20, §6.2 · p. 20
  • Under black-box attacks, L-GAT’s accuracy fell only 2.53% (94.13% vs. 96.66% in white-box scenarios), while SVM and DT lost more than 4%.The reported results concern attacks with incomplete adversarial information during training.Source: Table 5 · p. 20, §6.2 · pp. 20–21

6.3 Performance Analysis of STVSA under Varying Noise Environments

  • Increasing Gaussian noise degraded model performance, with the most severe degradation at the lowest tested SNR, 30 dB.Noise was tested at 50 dB, 40 dB, and 30 dB; performance was optimal without noise.Source: Table 6 · p. 22, §6.3 · p. 22

6.4 Impact of Different Observation Time Windows on Evaluation Performance

  • Across observation time windows, L-GAT consistently outperformed Transformer, LSTM, SVM, and DT; increasing window length correlated positively with improved accuracy for all models.Source: §6.4 · pp. 22–23
  • The proposed L-GAT sustains accuracy above 95% under extreme system states for real-time grid stability monitoring during rapid transients.Source: §6.4 · p. 23

7 Conclusions

The study proposes an AI-based control framework to enhance short-term voltage stability assessment under cyber-attacks. It combines an LSTM-enhanced GAT with adversarial learning and reports effective performance in complex attack environments, while identifying limits in attack generation and evaluation scope.

7 Conclusions

  • The L-GAT model captures dynamic relationships between time-series data and grid topology, enabling simultaneous temporal and spatial analysis in STVSA.It integrates LSTM networks with GAT.Source: §7 · p. 23
  • The adversarial deep-learning approach demonstrates effectiveness and superiority in complex attack environments.The conclusion describes its evaluation under composite cyber-attack scenarios.Source: §7 · p. 23
  • Spectral normalization of CWGAN-GP is reported to improve training stability, convergence, data quality, and model generalization and robustness.The study builds on CWGAN-GP-based data augmentation techniques.Source: §7 · p. 23
  • The evaluation uses consistent perturbation strength, but differences in attack-generation mechanisms may influence results.The authors propose broader attack strategies, more complex-system scalability, and real-time data analytics as future directions.Source: §7 · p. 23
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