From Cycle Space to Cycle Manifold: Limits and Achievability of Blind False Data Injection Attacks

2026-09-09

AI Summary

本文解决了盲虚假数据注入攻击的隐蔽性和最小信息需求问题，通过利用加权循环空间和循环流形方法来实现，并提出了测量重构方法。

Abstract

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.

Problem

• false data injection attack
• bad data detector
• weighted cycle space
• stealthy attack
• grid state

Innovation

• weighted cycle space
• stealthy attack space
• measurement-only reconstruction
• topology-assisted manifold fitting
• GPU