A Survey of Machine Learning Methods for Detecting False Data Injection Attacks in Power Systems

Motivation

• FDIAs inject false measurements to manipulate State Estimation, and can bypass traditional residual-based Bad Data Detection.The paper frames prompt detection as important to power-system security and reliability.Source: §1 · p. 1

Limits of existing detection

• Several existing techniques miss attacks that match historical measurement distributions or cause only small, bus-specific errors.The surveyed limitations also include difficulty identifying bad leverage points with largest-normalized-residual tests.Source: §1 · p. 1

Machine-learning approaches

• Researchers have studied supervised, semi-supervised, unsupervised, and deep-learning methods for FDIA detection, with reported gains in accuracy and adaptability.The paper situates these methods among machine-learning applications for power-grid control and monitoring.Source: §1 · p. 1

Paper contributions

• The survey covers FDIA settings, impacts, defenses, machine-learning detectors and their limitations, and further research problems.Its stated goal is to inform future directions for machine-learning-based FDIA detection.Source: §1 · pp. 1–2

2.1 Power System State Estimation

• State Estimation uses system inputs and measurement redundancy to estimate grid states, assess anomalous behavior, and inform mitigation decisions.Its inputs include system parameters, collected measurements, and pseudomeasurements when system information is insufficient; the process can be resource-intensive and sensitive to measurement errors.Source: §2.1 · p. 2, §2.2 · p. 2

2.2 Transmission System Modeling for State Estimation

• Transmission estimation includes AC models using voltage magnitudes and phase angles, DC linear approximations that trade accuracy for lower computational burden, and dynamic methods for changing system behavior.Dynamic estimation addresses limitations of low-update-rate steady-state measurements; Kalman-filtering approaches seek to reduce linearization errors and computational overhead.Source: §2.2.1 · p. 2, §2.2.2 · p. 3, §2.2.3 · p. 3

2.3 Distribution System Modeling for State Estimation

• Distribution systems are typically radial, less measured, dynamically changing, and unbalanced, requiring DSSE models that differ from transmission-system assumptions.Three-phase unbalanced estimation can require synchronized phasor measurements, and its modeling complexity limits real-time applicability.Source: §2.3 · p. 4, §2.3.1 · p. 4

2.4 Bad Data Detection and Identification

• Bad Data Detection tests whether measurements contain errors, while Largest Normalized Residual identifies suspect measurements by assuming bad data produce large residuals.The Chi-Square test assumes Gaussian measurements; residual-based methods cannot efficiently detect FDIAs.Source: §2.4.1 · p. 5, §2.4.2 · p. 5

2.5 False Data Injection Attacks in Power Systems

• FDIAs tamper with power-system measurements, and attackers can construct attacks that preserve residuals to bypass BDD in DC and AC state estimation.For DC estimation, an attack vector formed as a linear combination of Jacobian columns leaves the residual unchanged; the AC formulation likewise preserves the residual under its stated condition.Source: §2.5 · p. 5

3.1 FDIAs Settings

• Attackers may have full or partial system knowledge, and attacks can be constrained by accessible meters or by resources limiting how many meters they compromise [13].With partial knowledge, attackers may estimate unknown topology from historical or online measurements and still launch successful attacks [68].Source: §3.1.1 · p. 6, §3.1 · p. 6, §3.1.2 · p. 6
• SVD and PCA approaches use measurements to construct blind FDIA models, while attackers can use the resulting subspace or reduced matrix to form attack vectors [70, 71].The SVD approach constructs a basis for H's column space from the measurement covariance; the PCA-reduced matrix is used to construct the blind attack and tampered measurement vector.Source: §3.1.2 · pp. 6–7

3.2 Impacts of FDIAs on Power Systems

• Load Redistribution attacks corrupt state estimates used by SCED, producing incorrect dispatch solutions and potentially infeasible operation or load shedding [77, 79].Source: §3.2.1 · p. 7
• Energy deceiving attacks spoof routing messages, potentially creating demand-supply imbalances and sharply increasing energy-distribution costs [80].Source: §3.2.2 · p. 7
• FDIAs can manipulate ex-post market nodal prices and generate financial profit for attackers, including under studied limited-sensor threat models [81, 82].The cited study examined the IEEE 14-bus system with one or three congested lines.Source: §3.2.3 · p. 7

• Meter-protection studies seek critical measurements, with a greedy method finding a minimum set and budgeted objectives maximizing minimum or average attack cost [58].Earlier work used brute force to identify measurements requiring protection [13, 83].Source: §4 · pp. 7–8
• Steiner-tree algorithms and MILP can reduce the cost of selecting meters to protect, but protecting a minimum set may reduce redundancy or leave security gaps [85].Source: §4 · p. 8
• PMUs can help protect measurements through synchronized voltage and phase-angle data, but large-scale deployment is costly and GPS spoofing can compromise timestamps [88, 87, 99].Source: §4 · p. 8
• A stochastic game uses attack effects to allocate defensive resources, but its attacker-defender model is described as neither scalable nor realistic [89, 100].Source: §4 · p. 8
• Dummy-measurement detection is limited because attackers may learn or guess its configuration, while PAMA is computationally intensive and encrypted communications can add overhead and latency [96, 97].The communication costs may be impractical in large, densely interconnected systems with limited edge-computing resources.Source: §4 · p. 8

5.1 Performance Metrics

• Evaluation commonly uses Accuracy, Precision, Recall, F1 score, and ROC/AUC; Accuracy suits balanced data, while Precision, Recall, and F1 are used for imbalanced data.ROC curves show true-positive rate against false-positive rate across thresholds, and a curve nearer the upper-left corner (larger AUC) indicates better discrimination between attacked and secured measurements.Source: §5.1 · pp. 8–9

5.2 Supervised Learning Algorithm

• Supervised methods generally outperform residual-based bad-data detection; SVMs achieve the highest accuracy in one comparison [32], while larger-system performance and detection of sophisticated attacks remain uncertain.SVMs outperformed KNN and ENN in most IEEE 30-bus test cases, with accuracy and F1 score increasing in a critical sparsity range [34]. Distributed SVMs converged empirically to centralized SVMs on the IEEE 118-bus system [102]. KNN can fail when sample size is smaller than feature dimension, and simulations do not establish real-deployment performance.Source: §5.2 · pp. 9–10

5.3 Semi-supervised Learning

• Semi-supervised S3VM approaches use unlabeled data, but their reported performance depends on feature-space separation, threshold choice, and data balance.A Gaussian-mixture S3VM achieved a high F1 score against SVMs and perceptrons when attacked and real measurements occupied distinct feature-space regions; a high threshold reduced Recall, while a low threshold reduced Precision. Another S3VM was more robust to sparsity than supervised methods but remained sensitive to unbalanced samples.Source: §5.3 · pp. 10–11

5.4 Unsupervised Learning

• Unsupervised approaches detect attacks through clustering or anomaly detection, with reported high accuracy under specific conditions.FCM with PCA was used to detect and locate attacks, including scenarios with topology changes, and achieved higher detection accuracy than SVMs and KNN [108]. Local outlier factor, isolation forest, and robust covariance estimation achieved high detection rates only when the contamination rate was known and small [107].Source: §5.4 · p. 11

5.5 Deep Neural Network

• Deep-learning studies report strong FDIA detection, while illustrating trade-offs in training speed and the use of temporal information.Four MLP architectures achieved accuracy of around 98% [131], while another MLP study reported higher detection accuracy than other algorithms but slow training [104]. NARX uses correlated measurements and historical values for step-ahead state prediction [109]; RNNs use past events, and LSTM units address vanishing gradients and retain information longer [132].Source: §5.5 · p. 12
• 99% accuracy was reported for Ayad et al.’s RNN classifier on IEEE 30-bus data with 112 measurement vectors [103].The model uses back-propagation through time; its output is thresholded into compromised (1) or normal (0) classes.Source: §5.5 · p. 12
• Yu et al.’s DWT-based RNN achieved a 93% detection rate for AC state estimation using over 200,000 training samples [112].Tests used IEEE 118- and 300-bus cases with complete and incomplete system knowledge; the model leverages temporal and spatial features, but its hyperparameters require tuning.Source: §5.5 · p. 12
• DBNs comprise layers of stochastic latent variables and can be built from RBMs or autoencoders [133].A separate autoencoder-based approach detects FDIAs by leveraging temporal and spatial correlations in sensor data [134].Source: §5.5 · p. 12
• He et al.’s DBN-based model achieved the highest detection accuracy among the compared methods, including MLPs and SVMs [113].It assumes system topology changes little over short intervals and was evaluated on four IEEE 118-bus attack scenarios; its CDBN extracts temporal features, while the SVE thresholds the 2-norm of measurement residuals. DBN training can take weeks even with GPU acceleration [135].Source: §5.5 · p. 12
• 98% accuracy was reported for Wei et al.’s DBN-based FDIA detector [114].Its workflow has preprocessing, training, and testing stages; training uses greedy layer-wise unsupervised pretraining with RBMs followed by back-propagation tuning.Source: §5.5 · p. 13

6 Discussion on the Detection Performance of Machine Learning Algorithms

• Machine-learning detectors do not require exact system-model knowledge, and induced uncertainties such as measurement noise or topology changes do not affect their detection efficacy.Source: §6 · p. 13
• The literature is transmission-heavy, while distribution-system detection remains an ongoing research direction; surveyed attack settings include random, targeted, and stealthy FDIAs.Source: §6 · p. 13
• Evaluation differences in system topology, attack type, dataset size, and metrics make overarching comparisons or a universally optimal detector infeasible.Some studies test hundreds of scenarios across multiple systems, while others use limited datasets or custom metrics.Source: §6 · p. 13
• SVMs report detection rates from 85% to 99% [32, 34, 102] and avoid exhaustive training and large datasets, but kernel choice or sparse systems can degrade performance.The survey also notes SVM susceptibility to adversarial examples, including label-flipped attacks [143, 145].Source: §6 · p. 13
• Deep-learning detectors report detection rates between 90% and 99% with abundant training data [103, 104, 108–112], but require large datasets, costly training, and specialized equipment.One method required more than 3k measurement samples to achieve a 98% detection rate [113].Source: §6 · p. 13
• Machine-learning detectors have been reported to detect FDIAs effectively in real time [113, 128], but extensive historical attack data, overfitting, and adversarial examples challenge generalization and robustness.Source: §6 · p. 13

7 Conclusions and Future Directions

• The survey reviews FDIA impacts and defenses, compares machine-learning detectors, describes their limitations, and identifies further research problems.Source: §7 · p. 13
• The survey concludes that supervised learning and deep-learning methods achieve the highest FDIA detection rates.Source: §7 · p. 13
• Future work will examine detectors in distribution systems incorporating DERs such as microgrids and explore GANs against stealthy, sophisticated attacks.Source: §7 · p. 13