Cycle-Space Informed Detection of Autoencoded Blind False Data Injection Attacks on Power Systems

A false data injection attack (FDIA) can change the estimated grid state while evading a residual-based bad data detector (BDD). Existing blind attacks learn a low-rank measurement subspace, but this algebraic view does not state the physical grid constraints that make an attack stealthy or the minimum information needed to recover the complete attack space. Under the connected direct-current (DC) branch-flow model, we show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Its orthogonal complement is therefore the complete stealthy attack space, making weighted cycle-space knowledge both necessary and sufficient for complete blind FDIA. This space identifies the topology only up to 2-isomorphism and the relative cycle-edge parameters only up to one scale per biconnected component; bridge parameters are neither identified nor required. We then formulate a computationally unconstrained benchmark and a tractable measurement-only reconstruction method. Experiments on IEEE systems compare BDD bypass rate at a 95% nominal-acceptance threshold against state impact. As a compact alternating-current (AC) extension, we characterize feasible branch P/Q measurements by a cycle manifold and demonstrate topology-assisted manifold fitting and measurement generation on a graphics processing unit (GPU). In the lossless fixed-voltage small-angle limit, the normal space of the active-power slice reduces to the DC weighted cycle space.

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.

Training and evaluating false data injection attack (FDIA) detectors for power systems is constrained by data scarcity. Operational grid measurements are commercially sensitive, and hand-crafted attacks fail to capture complex distributional structures imposed by network physics. We present \textsc{GenAI-FDIA}, a framework benchmarking a pool of $P{=}20$ architectures for physics-compliant FDIA synthesis, spanning Wasserstein GANs, MMD-VAEs, normalising flows, diffusion models, and cross-family hybrids. These are evaluated across three IEEE testbeds (14-bus DC, 30-bus DC, and 14-bus AC) under a 60/20/20 chronological split using data-driven Bad Data Detection (BDD) threshold calibration. Our empirical results verify that these models generate high-fidelity attacks, with all architectures achieving evasion rates of $ε_{\text{BDD}} \ge 86.6\%$ on the 14-bus network; additionally, limiting an attacker's topological knowledge induces a measurable degradation in stealthiness ($p \le 0.0022$). Crucially, we identify a previously unreported failure mode: applying affine physics projections directly in normalised feature spaces critically displaces the attack vector, collapsing BDD evasion from ${\sim}55\%$ to $<\!2\%$ on the 30-bus testbed. We resolve this via a novel inference-time harmoniser, restoring full stealthiness ($ε_{\text{BDD}}{=}100\%$) across all physics-informed variants without retraining. Finally, we isolate a covariance-collapse phenomenon ($κ\approx {-}0.076$) within advanced hybrid architectures and rectify it through 50-epoch warm-up schedules ($κ\to 0.785$, $Δ\text{MMD}={-}3.1\%$). Ultimately, \textsc{GenAI-FDIA} delivers a robust recovery blueprint applicable to any physics-constrained generative model deployed for power-system security.