A Gaussian Belief Propagation-Based Cyber-Attack Detection Approach for State Estimation Model in Unbalanced Distribution Networks

Belief propagation (BP)-based algorithms, typified by their efficient probabilistic inference abilities, are widely used for distributed reasoning in complex systems. However, BP has seldom been studied by the existing literature on unbalanced power distribution networks (PDNs), where state estimation (SE) is faced with exacerbated cybersecurity threats posed by malicious adversaries. To this end, the Gaussian BP (GaBP) with superior efficiency and interpretability is employed in this paper, making it the first attempt to propose a GaBP-based detection approach for unbalanced PDNs against various cyber-attacks. In the proposed approach, the nonlinear SE model is emulated by factor graphs and iteratively solved by GaBP, which is further enhanced using message and factor damping techniques to improve algorithm convergence. By analyzing the belief update procedure in a local factor graph, the measurement update term (MUT) corresponding to the local measurement data is designated as the preliminary attack detection variable. To make the attack-induced temporal shape distortion more perceptible, the proposed approach defines the multivariate derivative dynamic time warping (DDTW) distance between the baseline MUT and the latest MUT sequences as the test statistic. Finally, a generalized likelihood ratio test (GLRT) is accordingly designed to detect potential cyber-attacks. Extensive case studies on two modified IEEE test feeders validate the efficacy and superiority of the proposed detection approach.