Line Failure Detection After a Cyber-Physical Attack on the Grid Using Bayesian Regression

We study the problem of line failure detection following a cyber-physical attack. Since such attacks can result in line trippings (by remotely activating switches) as well as loss of measurement feeds, we consider an attack model in which an adversary attacks an area by: (i) disconnecting some lines within the attacked area, and (ii) blocking the measurements coming from inside the attacked area from reaching the control center. Hence, after the attack, voltage phase angles of the buses and status of the lines inside the attacked area become unavailable to the grid operator. We build upon a recently introduced convex optimization method for detecting line failures and exploit Bayesian regression to develop the novel PROBER Algorithm for probabilistically detecting line failures after an attack using partial noisy measurements. The PROBER Algorithm provides the probability that each line is failed inside the attacked area in a running time which is independent of the number of line failures. Hence, these probabilities can be efficiently computed and used to make the existing brute force search methods tractable (for detecting multiple-line failures) by significantly reducing their search space. We numerically demonstrate that such an approach hits a sweet spot in accuracy and efficiency.