False data injection attacks (FDIAs) pose a persistent challenge to AC power system state estimation. In current practice, detection relies primarily on topology-aware residual-based tests that assume malicious measurements can be distinguished from normal operation through physical inconsistency reflected in abnormal residual behavior. This paper shows that this assumption does not always hold: when FDIA scenarios produce manipulated measurements that remain on the measurement manifold induced by AC power flow relations and measurement redundancy, residual-based detectors may fail to distinguish them from nominal data. The resulting detectability limitation is a property of the measurement manifold itself and does not depend on the attacker's detailed knowledge of the physical system model. To make this limitation observable in practice, we present a data-driven constructive mechanism that incorporates the generic functional structure of AC power flow to generate physically consistent, manifold-constrained perturbations, providing a concrete witness of how residual-based detectors can be bypassed. Numerical studies on multiple AC test systems characterize the conditions under which detection becomes challenging and illustrate its failure modes. The results highlight fundamental limits of residual-based detection in AC state estimation and motivate the need for complementary defenses beyond measurement consistency tests.

翻译：虚假数据注入攻击（FDIAs）对交流电力系统状态估计构成持续挑战。当前实践中，检测主要依赖于基于拓扑感知的残差检验，其假设恶意测量值可通过异常残差行为所反映的物理不一致性而与正常运行数据区分。本文表明这一假设并非总是成立：当FDIA场景产生的受操纵测量值仍保持在由交流潮流关系及测量冗余所诱导的测量流形上时，基于残差的检测器可能无法将其与标称数据区分。这种可检测性局限是测量流形本身的固有属性，并不依赖于攻击者对物理系统模型的详细认知。为使该局限在实践中可观测，我们提出一种数据驱动的构造机制，该机制结合交流潮流的通用函数结构来生成物理一致且受流形约束的扰动，从而为基于残差的检测器如何被规避提供了具体例证。在多个交流测试系统上的数值研究刻画了检测变得困难的条件，并阐明了其失效模式。研究结果揭示了交流状态估计中基于残差检测的根本局限，并表明需要超越测量一致性检验的互补性防御措施。