Physically Consistent Null Space Alignment for Detection of Low-Magnitude False Data Injection Attacks

2026-06-07

AI Summary

This work addresses the challenge posed by low-magnitude false data injection attacks, which evade conventional detection mechanisms by aligning with the system’s pseudo-null space, thereby severely compromising state estimation accuracy. To counter this, the authors propose the Physically Consistent Null-Space Alignment (PCNSA) framework, which introduces a Pseudo-Null Space Preserving (PSCP) preprocessing method. This approach maintains the geometric correspondence between the physical residual space and the measurement pseudo-null space without requiring knowledge of the system matrix H, thereby overcoming the subspace distortion caused by standard normalization. By integrating power system physics with data-driven techniques—through physical-coordinate preprocessing, SVD-based subspace extraction, and residual analysis—the method significantly outperforms baseline detectors such as XTM, LSTM, autoencoders, and Isolation Forest on IEEE 14/30/57/118 bus systems, achieving higher F1 scores and detection accuracy while remaining robust under partial observability and realistic PMU noise conditions.

Abstract

False data injection attacks (FDIAs) introducing small measurement perturbations can still cause large deviations in power system state estimation when the injected signals align with the pseudo-null space of the system model. Existing model- and data-driven detectors may fail to identify such low-magnitude but high-impact attacks because residual tests ignore changes hidden in the pseudo-null space, while subspace learning methods capture correlation patterns without enforcing physical consistency. This paper proposes Physically Consistent Null Space Alignment (PCNSA), a framework that detects stealthy FDIAs by preserving, through preprocessing, the geometric correspondence between the physical null space and the measurement-derived pseudo-null space. The key point is a Pseudo-null Space Conserved data Preprocessing (PSCP) step that re-expresses measurements in the physical coordinate frame before subspace extraction. We prove that PSCP preserves the separation between row space and its orthogonal complement, a property that conventional per-feature standardization violates. This keeps the singular value decomposition (SVD)-derived pseudo-null subspace aligned with the physical residual space without explicit knowledge of H. Experiments on IEEE 14-, 30-, 57-, and 118-bus systems confirm this principle in practice: stealthy attacks that evade XTM, LSTM, AE and Isolation Forest baselines appear as clear deviations in the aligned subspace, yielding higher F1-score and detection accuracy while remaining robust under partial observability and realistic PMU noise.

Problem

• False Data Injection Attacks
• Null Space Alignment
• State Estimation
• Power Systems
• Stealthy Attacks

Innovation

• Physically Consistent Null Space Alignment
• Pseudo-null Space Conserved Preprocessing
• False Data Injection Attacks
• Subspace Alignment
• Power System State Estimation