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Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networks

Osman Boyaci, Mohammad Rasoul Narimani, Katherine Davis, Muhammad Ismail, Thomas J Overbye, Erchin Serpedin

arXiv:2104.11846v2cs.LGcs.AIcs.CReess.SY

TL;DR

Stealth FDIAs threaten power-system security, while attack localization remains less studied than detection. The paper proposes an ARMA-filter GNN that jointly detects and localizes attacks by exploiting grid topology and measurement correlations, and reports better detection and localization than available methods across IEEE test systems.

  • Problem

    Stealth FDIAs can evade bad-data detection, and prior work has paid less attention to identifying the attacked grid units needed for preventive action.

  • Method

    The paper uses an end-to-end GNN with IIR-type ARMA graph filters to exploit power-grid topology and spatial measurement correlations for joint detection and localization.

  • Results

    The proposed ARMA model outperforms available methods in both FDIA detection and localization across different IEEE test systems.

  • Takeaways & Limitations

    The approach identifies targeted grid areas so operators can take preventive actions before attacks affect the grid.

Abstract

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False data injection attacks (FDIA) are a main category of cyber-attacks threatening the security of power systems. Contrary to the detection of these attacks, less attention has been paid to identifying the attacked units of the grid. To this end, this work jointly studies detecting and localizing the stealth FDIA in power grids. Exploiting the inherent graph topology of power systems as well as the spatial correlations of measurement data, this paper proposes an approach based on the graph neural network (GNN) to identify the presence and location of the FDIA. The proposed approach leverages the auto-regressive moving average (ARMA) type graph filters (GFs) which can better adapt to sharp changes in the spectral domain due to their rational type filter composition compared to the polynomial type GFs such as Chebyshev. To the best of our knowledge, this is the first work based on GNN that automatically detects and localizes FDIA in power systems. Extensive simulations and visualizations show that the proposed approach outperforms the available methods in both detection and localization of FDIA for different IEEE test systems. Thus, the targeted areas can be identified and preventive actions can be taken before the attack impacts the grid.

NOMENCLATURE

The paper frames stealth FDIAs as cyber-physical threats that can mislead power-system state estimation, while emphasizing the need to detect and localize attacks. It introduces graph and power-system notation used to describe these tasks.

  • NOMENCLATURE: The notation defines buses, measurements, system states, attack vectors, graph matrices, graph Fourier quantities, and the normalized graph Laplacian.The listed symbols distinguish original and attacked states and measurements and define the graph-frequency representation.
  • INTRODUCTION: Smart-grid ICT links field measurements from RTUs and PMUs to SCADA and application-level processing, making measurement integrity relevant to power-system reliability.The passage describes measurement acquisition, communication, and operator processing across the smart-grid architecture.
  • INTRODUCTION: Stealth FDIAs can bypass bad-data detection by satisfying power-flow equations, making attack localization important for preventive operator actions.The paper highlights isolating attacked buses and redispatching the system as examples of preventive responses.
  • RELATED WORK: Power-system approaches span model-based methods requiring no historical data and data-driven methods requiring historical data and training.Model-based methods may face detection delays, scalability issues, and threshold-tuning burdens.
  • RELATED WORK: Prior FDIA localization work includes graph-based cluster localization, analytical redundancy, and graph-signal-processing methods, but reported limitations include low resolution and manual tuning.Some prior evaluations also used random, easily detectable attacks that may not comprehensively assess performance.

B. Motivation

Smart-grid measurements have non-Euclidean topology, so graph architectures can model their spatial correlations more naturally than conventional Euclidean processing. The paper therefore proposes an end-to-end ARMA-GNN framework for joint FDIA detection and localization.

  • B. Motivation: Graph topology makes smart-grid signals non-Euclidean: neighboring nodes are unordered and vary in number, unlike pixels in regular images.The paper uses this distinction to motivate graph signal processing and graph neural networks for power-grid data.
  • B. Motivation: GNNs provide an end-to-end alternative to manually designed graph filters and thresholds while exploiting spatial locality learned from historical data.Polynomial graph filters avoid spectral decomposition through localized vertex-domain operations, but remain limited in adapting sharp frequency transitions.
  • B. Motivation: ARMA graph filters are selected because their rational frequency responses can fit sharp spectral changes more flexibly than polynomial Chebyshev filters.The paper reports that ARMA filters better approximate a desired band-pass response than CHEB filters at the same order on IEEE 118- and 300-bus systems.
  • Contributions: The proposed scalable ARMA-GNN jointly predicts grid-level attack presence and bus-level attack locations in a few milliseconds.The architecture automatically learns filter weights and produces predictions for the whole grid and each bus separately.
  • Contributions: The study compares implemented data-driven baselines with systematic Bayesian hyperparameter optimization and evaluates localization using sample-wise and node-wise comparisons.The paper also uses t-SNE to visualize intermediate representations and reports extensive test-system experiments.

II. PROBLEM FORMULATION

The problem formulation models FDIA as manipulation of power-system measurements that can shift the estimated state, then casts joint detection and localization as multi-label classification.

  • State Estimation: The PSSE estimates bus voltage magnitudes and phase angles from noisy complex-power measurements using weighted least squares.The measurements include active and reactive injections and flows, with R representing their error covariance matrix.
  • FDIA Model: An FDIA injects false data into original measurements so the PSSE converges to a different system state, potentially bypassing traditional bad-data detection.The attack construction a = h(ˇx) − h(ˆx) changes the state from the original estimate to an alternative state.
  • FDIA Model: The attacker is modeled as targeting a grid area T, changing connected measurements to spoil the state variables within that area.This constraint links targeted state variables and measurements through the system measurement function.
  • Detection and Localization: Joint detection and localization are formulated as multi-label classification with one binary label per bus plus an additional binary label for whole-grid attack presence.The IEEE 14-bus illustration distinguishes correctly detected attacks from missed attacked buses and falsely alarmed buses.

III. JOINT DETECTION AND LOCALIZATION OF FDIA

The graph formulation represents the smart grid through vertices, edges, and weighted adjacency, then filters graph signals spectrally or with localized polynomial approximations. These operations provide the foundation for graph-based FDIA modeling.

  • Graph Representation: A smart grid is represented as a weighted graph whose vertices are buses, edges are branches or transformers, and weights are line admittances.A graph signal assigns a scalar feature to each vertex, allowing measurements to be modeled over the grid topology.
  • A. Spectral Graph Filters: Spectral graph filtering transforms vertex-domain signals into the graph Fourier domain, scales Fourier components by h(Λ), and transforms them back.The graph Fourier basis comes from the normalized Laplacian eigenvectors, while its eigenvalues represent graph frequencies.
  • B. Polynomial Graph Filters: Polynomial graph filters approximate spectral responses with K-order polynomials and depend only on K-hop neighborhoods, making them localized and computationally efficient.They implement weighted moving-average filtering in finite-impulse-response form.
  • B. Polynomial Graph Filters: Chebyshev filters avoid full eigenvalue decomposition and compute efficiently through recursion, but high-degree polynomials can struggle with sharp spectral transitions.Their response uses the scaled Laplacian and requires approximation of only the largest eigenvalue for the stated implementation.

C. Rational Graph Filters

The paper develops distributed IIR-type ARMA graph filters whose rational responses adapt to sharp spectral changes and whose recursions can be unrolled into neural-network layers.

  • C. Rational Graph Filters: ARMA graph filters use rational filter compositions to approximate sudden frequency-response changes better than FIR-type moving-average filters.The paper motivates distributed IIR-type ARMA filters as more flexible alternatives to polynomial FIR filters.
  • C. Rational Graph Filters: An ARMA1 filter recursively combines the current input with outputs from adjacent nodes, enabling distributed graph filtering.The recursion converges regardless of the initial output and Laplacian values, with a rational frequency response.
  • C. Rational Graph Filters: Unrolling the ARMA1 recursion for T fixed iterations implements the filter as a neural-network layer with trainable coefficients.The trainable parameters include channel-mixing weights for inputs, outputs, and bias terms.
  • C. Rational Graph Filters: An ARMAK filter averages K parallel ARMA1 filters to obtain a higher-order rational graph filter.This construction preserves the distributed implementation while increasing filter order.

D. Frequency Response of Polynomial and Rational GFs

The frequency-response experiment compares ARMA and CHEB graph filters on IEEE 118- and 300-bus systems, showing that ARMA more flexibly approximates sharp ideal-filter transitions.

  • D. Frequency Response of Polynomial and Rational GFs: The experiment designs ideal graph filters for the IEEE 118- and 300-bus test systems to compare ARMA and CHEB approximation capability.The comparison uses numerical empirical frequency responses rather than only theoretical filter forms.
  • D. Frequency Response of Polynomial and Rational GFs: Empirical frequency response ˜h(λi) measures how the graph Fourier component associated with λi scales an input signal to produce the output.The response is estimated from graph-filter input-output pairs and then smoothed across samples.
  • D. Frequency Response of Polynomial and Rational GFs: ARMA graph filters more flexibly fit sudden frequency-response changes than CHEB filters for a fixed filter order.The models are trained on generated input-output pairs and their empirical responses are averaged and plotted.

E. Architecture of the Proposed Joint Detector & Localizer

The proposed ARMA GNN jointly predicts attack presence at the graph level and attack location at individual buses, using ARMAK layers to extract spatial features from power injections.

  • E. Architecture of the Proposed Joint Detector & Localizer: The model jointly outputs node-level attack probabilities for localization and a graph-level probability for detecting whether an attack is present.Its architecture uses an input layer, L−1 hidden ARMAK layers, a dense layer, and an output layer.
  • E. Architecture of the Proposed Joint Detector & Localizer: The GNN represents each bus with [Pi, Qi] inputs and transforms hidden ARMAK-layer outputs into location and presence predictions.The model outputs are Y ∈ R^n for bus locations and S ∈ R for graph-level presence.
  • E. Architecture of the Proposed Joint Detector & Localizer: Each ARMAK layer contains K parallel ARMA1 blocks, matching the filter construction used by the proposed neural architecture.The architecture visualization links each parallel block to the ARMA1 implementation.
  • E. Architecture of the Proposed Joint Detector & Localizer: The dataset is generated from NYISO historical load profiles on IEEE 57-, 118-, and 300-bus systems and includes four simulated FDIA types.The attacks include replay, scale, distribution-based, and constrained-optimization attacks.
  • E. Architecture of the Proposed Joint Detector & Localizer: The data are shuffled, standardized, and divided into training, validation, and testing splits, with the test split containing all four attack methods.Ao and Ad are included in training and validation, while the test split also evaluates the other attack types.

B. Feature Selection, Performance Metrics, and Training

The detector uses active-power and reactive-power measurements as graph features, evaluates predictions with detection and localization metrics, and trains by supervised binary cross-entropy.

  • B. Feature Selection, Performance Metrics, and Training: The models use Pi and Qi power measurements as inputs so attacks can be detected and localized without waiting for PSSE voltage outputs.Voltage magnitude and phase-angle features were not added because their information was highly correlated with the power measurements.
  • B. Feature Selection, Performance Metrics, and Training: The graph structure is weighted with W = |Ybus| to construct the modified Laplacian supplied to the ARMAK layers.Ybus denotes the nodal admittance matrix.
  • B. Feature Selection, Performance Metrics, and Training: Performance is assessed with detection rate, false alarm rate, and F1 score based on true-positive, false-positive, true-negative, and false-negative counts.The evaluation rules assign perfect or zero metric values for the all-correct no-attack case or any mismatch, respectively.
  • B. Feature Selection, Performance Metrics, and Training: The models are trained with multi-label binary cross-entropy using mini-batches, bounded epochs, and early stopping based on validation loss.Training uses mini batches of 256 samples and tolerates 16 epochs without sufficient validation improvement.

C. Joint Detection and Localization Results

The ARMA model achieves the strongest detection and localization performance across the IEEE test systems, while localization is assessed at both sample and node levels.

  • Detection: ARMA reaches the best detection F1 scores—99.81%, 99.44%, and 99.91%—for the 57-, 118-, and 300-bus systems, respectively.Its detection rates are 99.90%, 99.13%, and 99.97%, with false-alarm rates of 0.28%, 0.24%, and 0.14%.
  • Evaluation protocol: Localization is evaluated both sample-wise across buses and node-wise across samples using F1-score distributions and threshold-based ratios.The analysis uses quartiles, whiskers, outliers, and the percentages of samples or buses meeting F1 thresholds.
  • Sample-wise localization: ARMA exceeds CHEB in acceptable sample-wise localization by 5.64%, 8.56%, and 10.07% on the 57-, 118-, and 300-bus systems.Acceptable samples are those with F1 ≥95%.
  • Node-wise localization: ARMA is the only model with at least 80% F1 for every bus and 0% unacceptable node-wise localizations across all test systems.Unacceptable node-wise performance is defined as F1 ≤5%.

D. Joint Detection and Localization Times

The joint detection and localization models are compared on response time and intermediate representations. Most neural and graph models meet the stated real-time timing range, while ARMA produces the cleanest separation in the visualization.

  • Runtime comparison: DT, MLP, CNN, CHEB, and ARMA respond in under 3 milliseconds for every test system, supporting real-time application.DT is fastest at under 0.7 milliseconds, whereas its poor detection and localization performance limits its reliability.
  • Visualization method: t-SNE maps high-dimensional intermediate-layer outputs into two dimensions to compare how models separate attacked and non-attacked samples.The IEEE-300 analysis uses 5,760 test samples, with attacked samples shown as green stars and non-attacked samples as black circles.
  • Intermediate-layer visualization: ARMA produces only 4 false positives and 1 false negative, outperforming CHEB’s visualization with five additional missed attacks and more than five times as many false positives.The authors attribute ARMA’s result to rational graph filters with more flexible frequency responses.

F. Discussions & Theoretical Comparisons

The discussion compares data-driven architectures and localization metrics, finding that topology-aware ARMA-based modeling is especially advantageous on larger power-grid graphs. It also argues that F1 is more informative than accuracy for bus-level FDIA localization.

  • F. Discussions & Theoretical Comparisons: GNNs are better suited than conventional architectures for power-grid measurements because grid topology defines their relevant non-Euclidean spatial correlations.The discussion contrasts this setting with CNNs, whose locality is naturally modeled in Euclidean image space.
  • F. Discussions & Theoretical Comparisons: ARMA outperforms CHEB at the 95% F1 threshold, with localization gains increasing across IEEE 57-, 118-, and 300-bus systems.SW gains are 5.64%, 8.56%, and 10.07%; NW gains are 8.78%, 11.87%, and 14.67%, respectively.
  • F. Discussions & Theoretical Comparisons: ARMA graph filters better adapt to abrupt spectral-domain changes than polynomial filters because they use rational rather than polynomial filter compositions.
  • F. Discussions & Theoretical Comparisons: Higher-order polynomial filters are needed to capture global graph characteristics, but their interpolation and extrapolation limitations make them sensitive to variations.
  • F. Discussions & Theoretical Comparisons: Bus-level localization is a multi-label task, so evaluation should prioritize F1 over accuracy when missed attacks are more consequential than false alarms.The examples show accuracy can remain high while failing to reflect missed attacks, whereas F1 distinguishes samples with different true-positive counts.
  • F. Discussions & Theoretical Comparisons: CHEB detection performance on the IEEE 300-bus system is optimal at filter order K = 4.

V. CONCLUSION

The paper proposes a topology- and spatial-correlation-aware GNN with ARMA graph filters to jointly detect and localize FDIAs. Across IEEE test systems, it improves detection and especially localization relative to CHEB.

  • V. CONCLUSION: The proposed ARMA-GNN jointly detects and localizes FDIAs by integrating grid topology, measurement spatial correlations, and full AC power-flow equations.
  • V. CONCLUSION: Compared with CHEB, detection improves by 0.12%, 0.68%, and 0.38% on IEEE 57-, 118-, and 300-bus systems, respectively.
  • V. CONCLUSION: Compared with CHEB at the 95% F1 threshold, localization improves by 5.64%, 8.56%, and 10.07% for SW and by 8.78%, 11.87%, and 14.67% for NW across the same systems.
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