Power grid state estimation after a cyber-physical attack under the AC power flow model

In this paper, we present an algorithm for estimating the state of the power grid following a cyber-physical attack. We assume that an adversary attacks an area by: (i) disconnecting some lines within that area (failed lines), and (ii) obstructing the information from within the area to reach the control center. Given the phase angles of the buses outside the attacked area under the AC power flow model (before and after the attack), the algorithm estimates the phase angles of the buses and detects the failed lines inside the attacked area. The novelty of our approach is the transformation of the line failures detection problem, which is combinatorial in nature, to a convex optimization problem. As a result, our algorithm can detect any number of line failures in a running time that is independent of the number of failures and is solely dependent on the size of the network. To the best of our knowledge, this is the first convex relaxation for the problem of line failures detection using phase angle measurements under the AC power flow model. We evaluate the performance of our algorithm in the IEEE 118- and 300-bus systems, and show that it estimates the phase angles of the buses with less that 1% error, and can detect the line failures with 80% accuracy for single, double, and triple line failures.