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

arXiv:2606.08473v1 Announce Type: new 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.