提出物理一致的空域对齐方法，有效检测微小但破坏性强的电力系统数据注入攻击。
Physically Consistent Null Space Alignment for Detection of Low-Magnitude False Data Injection Attacks
- 通过保持物理空域与测量空域几何对应，预处理数据以实现空域对齐。
- 在多个测试系统中，对基线模型无法发现的隐蔽攻击仍能实现高精度检测。
- 无需系统模型参数即可保持空域一致性，适合实际电力系统部署。
虚假数据注入攻击（FDIA）通过引入微小测量扰动，当攻击信号与系统模型的伪零空间对齐时，仍可能导致状态估计出现巨大偏差。现有基于模型或数据驱动的检测方法可能无法识别此类低幅度、高影响的攻击，因为残差检验忽略了伪零空间中的变化，而子空间学习方法虽捕捉相关性模式，却未强制物理一致性。本文提出物理一致的空域对齐（PCNSA）框架，通过预处理步骤——伪零空间保持的数据预处理（PSCP），在物理坐标系下重表达测量值，以保留物理零空间与测量导出的伪零空间之间的几何对应关系。证明了该方法可维持行空间与其正交补之间的分离性，而传统逐特征标准化会破坏此性质。由此得到的奇异值分解（SVD）导出的伪零子空间与物理残差空间自然对齐，且无需显式已知系统矩阵H。在IEEE 14、30、57和118节点系统的实验表明，该原理在实践中有效：基线模型（XTM、LSTM、AE、Isolation Forest）无法识别的隐蔽攻击，在对齐子空间中表现出显著偏离，实现更高F1分数与检测准确率，并在部分可观测性和真实PMU噪声下保持鲁棒性。
原文摘要 · Abstract (English)
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.
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