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Graph Neural Networks Based Detection of Stealth False Data Injection Attacks in Smart Grids

Osman Boyaci, Amarachi Umunnakwe, Abhijeet Sahu, Mohammad Rasoul Narimani, Muhammad Ismail, Katherine Davis, Erchin Serpedin

arXiv:2104.02012v2eess.SPcs.AIcs.LGcs.SYeess.SY

TL;DR

Stealth FDIAs can mislead state estimation and evade bad-data detection, and prior work had not explored GNNs for FDIA detection. The paper develops a generic localized stealth-FDIA generation technique and a scalable detector that combines grid topology with spatially correlated measurements in GNN layers. The detector surpasses currently available methods in literature by 3.14%, 4.25%, and 4.41% in F1 score, respectively.

  • Problem

    Stealth FDIAs can mislead state estimation and evade bad-data detection, and prior work had not explored GNNs for FDIA detection.

    Source: §I · p. 1

  • Method

    The paper develops a generic localized stealth-FDIA generation technique and a scalable detector that combines grid topology with spatially correlated measurements in GNN layers.

    Source: §I · p. 2, §V · p. 10

  • Results

    The detector surpasses currently available methods in literature by 3.14%, 4.25%, and 4.41% in F1 score, respectively.

    Source: §V · p. 11

  • Takeaways & Limitations

    The work makes labeled attack data available and tests a scalable, real-time detector on standard AC power-grid test systems.

    Source: §V · p. 10

Abstract

from arXiv · show

False data injection attacks (FDIAs) represent a major class of attacks that aim to break the integrity of measurements by injecting false data into the smart metering devices in power grids. To the best of authors' knowledge, no study has attempted to design a detector that automatically models the underlying graph topology and spatially correlated measurement data of the smart grids to better detect cyber attacks. The contributions of this paper to detect and mitigate FDIAs are twofold. First, we present a generic, localized, and stealth (unobservable) attack generation methodology and publicly accessible datasets for researchers to develop and test their algorithms. Second, we propose a Graph Neural Network (GNN) based, scalable and real-time detector of FDIAs that efficiently combines model-driven and data-driven approaches by incorporating the inherent physical connections of modern AC power grids and exploiting the spatial correlations of the measurement. It is experimentally verified by comparing the proposed GNN based detector with the currently available FDIA detectors in the literature that our algorithm outperforms the best available solutions by 3.14%, 4.25%, and 4.41% in F1 score for standard IEEE testbeds with 14, 118, and 300 buses, respectively.

NOMENCLATURE

Power-grid measurements feed critical state estimation and downstream operations, while stealth FDIAs can mislead that process and evade conventional bad-data detection. The paper motivates topology-aware detection by identifying limits in existing models and proposes a GNN approach for the grid’s correlated measurements.

I. INTRODUCTION

  • Stealth FDIAs can mislead state estimation while bypassing conventional bad-data detection, leaving operators to act on a false operating point.PSSE outputs feed multiple Energy Management System functions, including forecasting, contingency analysis, and economic dispatch.Source: §I · p. 1
  • Prior FDIA detectors often use DC approximations that omit voltage magnitudes and reactive power, limiting validation of stealthiness under AC models.Some topology-aware methods also rely on manually designed filters, while many detectors target small systems.Source: §I · pp. 1–2
  • Model-based detectors avoid historical training data, whereas data-driven detectors require historical data and training to reduce detection time and improve scalability.The paper also notes that learned models may miss the underlying physical system and overfit.Source: §I · p. 2
  • The paper proposes a GNN that incorporates grid topology and spatially correlated measurements, addressing a gap in GNN-based FDIA detection.The authors also describe stealth-attack generation and a detector intended to scale across grid sizes.Source: §I · p. 2

A. Power System State Estimation

  • Power-system state estimation uses noisy RTU or PMU measurements to estimate bus voltage magnitude and phase angle through iterative weighted least squares.Measurements include active and reactive power injections and branch flows; R denotes measurement error covariance.Source: NOMENCLATURE · p. 1, A. Power System State Estimation · p. 3

B. False Data Injection Attacks

An FDIA changes measurements so state estimation converges to a misleading state. The section also describes how normalized residuals support conventional bad-data detection and why stealth attacks can evade it.

B. False Data Injection Attacks

  • An FDIA constructs attacked measurements that lead state estimation to a different, misleading state.The attack vector relates the original and attacked measurements and their corresponding estimated states.Source: B. False Data Injection Attacks · p. 3

C. Bad Data Detection

  • The largest normalized residual test flags measurements whose normalized residual exceeds an operator-set sensitivity threshold.Residuals are observed measurements minus calculated measurements; the process uses the Jacobian and measurement error covariance to compute residual sensitivity.Source: C. Bad Data Detection · p. 3
  • A stealth attack keeps the maximum normalized residual below the bad-data detection threshold, allowing it to evade that test.The threshold is specified by the grid operator.Source: C. Bad Data Detection · p. 3

III. GNN BASED DETECTION OF FDIA

The attack scenario places an attacker between the meters and operator, while a defender uses a GNN to assess attacked measurements. The attack-generation method models a locally reachable region and balances stealth against attack strength.

A. False data injection attack scenario

  • The operator receives attacked measurements while the defender runs the GNN detector on those measurements to predict attack probability.The attacker seeks measurements that evade the operator’s bad-data detection mechanism while retaining enough strength to cause intended effects.Source: A. False data injection attack scenario · p. 3, Figure 1 · p. 3
  • The attack model limits manipulation to a local target area reachable from a compromised entry point within a chosen neighborhood radius.The method is intended to represent limited access to grid measurements rather than access across the entire system.Source: A. False data injection attack scenario · p. 3
  • The attacker skips generator buses and avoids changing flows that would violate Kirchhoff’s current law at connected buses.In the IEEE 14-bus example, bus 6 and the line between buses 6 and 11 are excluded.Source: A. False data injection attack scenario · p. 4, Figure 2 · p. 4
  • The attack objective trades off measurement similarity against deviation of targeted state variables, so stronger attacks carry greater detection risk.The attacker searches for a false state using stochastic gradient descent, updates only variables in the active insecure area, and injects data depending on the final loss.Source: A. False data injection attack scenario · p. 4

B. Graph Neural Network Modeling of Smart Grids

The paper represents the grid as a graph and applies graph convolution to signals defined on its buses. Chebyshev approximation makes these filters localized and computationally efficient.

B. Graph Neural Network Modeling of Smart Grids

  • Buses, branches, transformers, and line admittances map respectively to graph vertices, edges, and edge weights.A graph signal is represented by a vector whose entries correspond to values at individual buses.Source: B. Graph Neural Network Modeling of… · p. 4
  • The normalized graph Laplacian is diagonalized into eigenvectors and eigenvalues that define the graph Fourier basis and frequencies.The paper defines the normalized Laplacian using the identity matrix and degree-normalized adjacency matrix.Source: B. Graph Neural Network Modeling of… · p. 4
  • Graph convolution transforms signals to the spectral domain, multiplies their spectral components, and transforms the result back to the vertex domain.The paper describes this as the graph analogue of convolution, using the graph Fourier transform and its inverse.Source: B. Graph Neural Network Modeling of… · pp. 4–5
  • Chebyshev polynomial filters replace nonlocalized spectral filters, yielding K-localized convolution with O(K|E|) computational complexity.The paper gives the non-parametric filter's complexity as O(n^2) and notes that Chebyshev terms are computed recursively.Source: B. Graph Neural Network Modeling of… · p. 5

C. Detection of Attacks Using Graph Neural Network

The detector processes bus power injections through Chebyshev graph-convolution layers and a dense output layer. Its training data are generated from normalized load profiles for IEEE test systems.

C. Detection of Attacks Using Graph Neural Network

  • The detector uses one input layer for bus power injections, L Chebyshev graph-convolution layers for spatial features, and an output layer for attack probability.The input tensor contains active and reactive bus injections, while the hidden layers successively transform feature tensors.Source: C. Detection of Attacks Using Graph… · p. 5
  • Each Chebyshev layer applies graph convolution, adds a bias, and uses ReLU; the dense layer produces a scalar through a sigmoid.The hidden-layer coefficients and biases are learned parameters.Source: C. Detection of Attacks Using Graph… · p. 5

A. Data Generation

  • Synthetic data for IEEE 14-, 118-, and 300-bus systems are generated using normalized ERCOT load profiles and Pandapower.Load and generation scaling is bounded between 0.7 and 1.3, followed by AC power-flow solutions and measurements modeled with 1% noise.Source: A. Data Generation · pp. 5–6

B. Attack Generation

The attack-generation method selects a time, entry bus, and local target area, then optimizes altered state variables to produce false measurements. The illustrated IEEE 300-bus outcomes quantify attack success and resulting measurement and state deviations.

B. Attack Generation

  • The attack-generation procedure labels honest and malicious samples separately and returns attacked measurements and state variables with their sample labels.The label vector uses 0 for honest samples and 1 for malicious samples.Source: B. Attack Generation · p. 6
  • Attacks occur when a sampled frequency exceeds its threshold and target measurements and state variables within a radius of a randomly selected bus.The target area is formed by breadth-first search, excluding generator and zero-injection buses; the frequency threshold is selected for roughly 15% of time steps on average.Source: B. Attack Generation · p. 6
  • The attacker optimizes altered complex state variables to create a fake operating point, using measurement and state-variable errors in its loss.The described optimization uses root mean squared measurement error and mean absolute state error; the altered voltage magnitude is constrained to 0.9–1.1 p.u. and angle to −π–π.Source: B. Attack Generation · pp. 6–7
  • 83.4% of attempts succeeded while seizing up to 30% of meters, with maximum 2% voltage-magnitude and 1.2-degree angle deviations.The figure reports that attacks added a maximum of 30 MW or 30 MVAR to measurement devices.Source: Figure 5 · p. 7

C. Attack Detection

The detector uses active and reactive bus injections with graph-convolution layers to predict attacks, and its predicted probabilities separate honest and malicious test samples.

C. Attack Detection

  • The model uses only Pi and Qi as inputs so it can predict attack probability without waiting for PSSE; their node values represent branch values by summation.PSSE and BDD continue to receive every available measurement.Source: C. Attack Detection · p. 7
  • The training, validation, and test splits use the first 60%, next 20%, and last 20% of samples, respectively, and each split is standardized separately.The output labels mark honest samples as 0 and malicious samples as 1.Source: C. Attack Detection · p. 7
  • The GNN detector uses a multi-layer Chebyshev graph convolution layer and a dense output layer, with the grid’s Ybus matrix magnitude defining node relations.The graph Laplacian is derived from that weighted adjacency matrix and scaled for the model.Source: C. Attack Detection · p. 7
  • The GNN’s predicted class probabilities separate honest and malicious test samples, whereas normalized residues make them almost impossible to separate.Fig. 6 shows the distributions for the 14-, 118-, and 300-bus test systems.Source: Figure 6 · p. 8, C. Attack Detection · p. 8

D. Model Scalability

The proposed models scale linearly with bus count under the examined configuration; their parameter count is independent of bus count except for the final dense layer.

D. Model Scalability

  • The models scale linearly with bus count n in prediction time and total parameters when K = 3, L = 3, and each layer has 32 channels.Fig. 7 presents prediction time t [ms] and parameter count p.Source: D. Model Scalability · p. 8, Figure 7 · p. 8
  • Except for the final dense layer, GNN parameter count is independent of bus count n and scales with neighborhood order K and adjacent layer filter sizes.Each Chebyshev layer has K × c_(l−1) × c_l coefficients and c_l bias terms; the dense layer has n × c_L weights and a bias.Source: D. Model Scalability · p. 8
  • To compare scalability as n increases, the study fixes K = 3, L = 3, and c_l = 32 for every layer.Prediction delays and total parameter counts are measured for each system.Source: D. Model Scalability · p. 8

E. Visualization of how information spreads through layers

The visualization traces how a point-wise attack propagates through K-localized Chebyshev layers before the dense layer produces an attack classification.

E. Visualization of how information spreads through layers

F. Comparison with Other Methods

The comparison finds topology-aware GNN detection strongest among the tested methods, while showing that detector architecture affects performance. The baselines were retrained on the paper’s dataset because the original studies’ datasets were unavailable.

F. Comparison with Other Methods

  • The authors retrained DTC, SVC, MLP, RNN, and CNN on their dataset because they could not access the datasets used by the corresponding studies.They trained, validated, and tested these models similarly to the proposed detector.Source: F. Comparison with Other Methods · p. 9
  • On each test system, BDD predicts every sample as malicious, yielding a 100% false-alarm rate; DTC and SVM perform better than BDD, with F1 scores ranging from 67.91% to 85.97%.Source: F. Comparison with Other Methods · p. 9
  • 3.14%, 4.25%, and 4.41% F1-score gains over CNN on IEEE 14-, 118-, and 300-bus systems, respectively; only CNN and GNN reach the 90% F1 range.The detector comparison is reported in Table I.Source: Table I · p. 9, F. Comparison with Other Methods · p. 9
  • The authors attribute performance differences to architecture: GNN models graph adjacency, whereas CNN’s regular-grid representation cannot capture power-grid topology except in trivial cases.The paper argues that topology-aware GNNs better reflect measurement adjacency relations.Source: F. Comparison with Other Methods · p. 9

G. Impact of Different Weights in the Attack Generation

The attack-generation weights set cautious, balanced, or aggressive attack power, affecting state-variable deviations and detector performance. GNN outperforms the best available solutions across all three settings and test-system sizes.

G. Impact of Different Weights in the Attack Generation

  • Setting λz = 10 and λx = 1 creates cautious DSc attacks, λz = 1 and λx = 10 creates aggressive DSa attacks, and λz = λx = 1 defines balanced DSb.The cautious setting lowers attack power to reduce detection risk; the aggressive setting raises attack power at higher detection risk.Source: G. Impact of Different Weights in the… · p. 9
  • The ratio of weighting factors λx and λz, defined in (5), directly affects the attack power on the state variables.Source: G. Impact of Different Weights in the… · p. 10
  • 4.31%, 3.46%, and 4.48% (cautious), 3.14%, 4.25%, and 4.41% (balanced), and 3.19%, 3.43%, and 3.88% (aggressive) are GNN’s F1-score gains over the best available solutions for 14-, 118-, and 300-bus systems, respectively.Across models and test systems, detection performance increases from cautious to aggressive attacks; the authors attribute this to more separable honest and malicious sample distributions.Source: G. Impact of Different Weights in the… · p. 10
  • GNN performs better on larger cases, which the authors associate with stronger spatial correlation between adjacent measurements as node count increases.They report that denser topology translates into more spatial correlation and improves GNN accuracy.Source: G. Impact of Different Weights in the… · p. 10

H. Tuning Model Hyperparameters

The paper tunes model hyperparameters using Bayesian optimization and evaluates the resulting models on test splits. Its conclusion reports that the GNN detector outperforms available methods on IEEE testbeds and combines grid topology with spatially correlated measurements.

H. Tuning Model Hyperparameters

  • For the proposed GNN, F1 performance increases with larger systems and more aggressive attacks.Figure 10 summarizes the effects of attack power and grid size on detector F1 scores.Source: Figure 10 · p. 10
  • Bayesian optimization uses past trial performance to guide parameter selection; each model’s parameters were tuned in 200 trials using validation data, then assessed on test splits.Model fitting used training splits; Table II lists hyperparameter spaces and selected values.Source: H. Tuning Model Hyperparameters · p. 10

V. CONCLUSION

  • The conclusion describes a generic, locally applied stealth-FDIA generation method using SGD to solve a nonlinear non-convex optimization problem, with labeled data made publicly available.The paper also proposes a scalable, real-time GNN detector for modern AC power grids.Source: §V · p. 10
  • 3.14%, 4.25%, and 4.41% F1-score gains over currently available methods are reported for the IEEE 14-, 118-, and 300-bus testbeds, respectively.The conclusion presents the detector as scalable and real-time, fusing grid topology and spatially correlated measurements in GNN layers.Source: §V · pp. 10–11

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