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

arXiv: https://arxiv.org/abs/2606.08473 · HTML: https://mlsanity.com/paper/2606.08473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networks](https://mlsanity.com/paper/2104.11846/) (2021)
- [Detection of False Data Injection Attacks Using the Autoencoder Approach](https://mlsanity.com/paper/2003.02229/) (2020)
- [Subspace Methods for Data Attack on State Estimation: A Data Driven Approach](https://mlsanity.com/paper/1406.0866/) (2014)
- [Modeling and performance evaluation of stealthy false data injection attacks on smart grid in the presence of corrupted measurements](https://mlsanity.com/paper/1605.06180/) (2016)
- [False Data Injection Attack Against Power System Small-Signal Stability](https://mlsanity.com/paper/2102.10587/) (2021)

## Abstract (arXiv)

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.