A Unified Framework for Numerically-Stable State Estimation and False Data Injection Attack Detection in Distribution Networks

The integrity of distribution network state estimation is critically challenged by false data injection attacks, whose detection is often hampered by the numerical instability of underlying estimators. Such instability introduces artifacts that can mask an attack’s signature. This article presents a unified framework that achieves robust detection by decoupling these estimator artifacts from malicious data patterns. The framework’s core is a numerically stabilized forecasting aided state estimation employing a U-D factorization cubature Kalman filter (UD-CKF). By ensuring covariance positive-definiteness, it generates high-fidelity state estimates and, crucially, a statistically consistent innovation covariance matrix. This stable foundation enables a novel geometric inconsistency detector (GID). Instead of analyzing temporal patterns, the GID evaluates the geometric alignment between the observed innovation vectors and their expected statistical distribution defined by the UD-CKF. By monitoring the evolution of the innovation subspace, it effectively distinguishes the random orientation of noise from the persistent directional signature of a stealthy attack. This approach is validated on IEEE test feeders, demonstrating exceptional capability in identifying subtle FDIAs that remain undetected by magnitude-based or purely temporal methods.