Link State Estimation Under Cyber-Physical Attacks: Theory and Algorithms

Effective defense against cyber-physical attacks in power grids requires accurate damage assessment. While some solutions have been proposed to recover the line states within the attacked area, existing solutions are limited by the assumption of a connected post-attack grid and the lack of verifiable performance guarantees. To fill this gap, we study the recovery of line states under a cyber-physical attack that disconnects lines while blocking information from the attacked area. In contrast to existing solutions assuming a connected post-attack grid or known post-attack power injections, we consider a more challenging scenario where the attack may partition the grid into islands, which causes unknown changes in power injections. To address this problem, under the DC model we (i) propose a linear programming-based algorithm to recover the line states within the attacked area under unknown post-attack power injections, (ii) characterize the accuracy of the proposed recovery algorithm under certain conditions, and (iii) develop efficient algorithms to verify the recovery results using observable information. Then, we extend the DC-based algorithms to AC model. Our numerical evaluations demonstrate that the proposed recovery algorithm is highly accurate in localizing failed lines, most of which can be successfully verified by the proposed verification algorithms.