Power Grid State Estimation Following a Joint Cyber and Physical Attack

This paper focuses on joint cyber and physical attacks on power grids and presents methods to retrieve the grid state information following such an attack. We consider a model where an adversary attacks a zone by physically disconnecting some of its power lines and blocking the information flow from the zone to the grid's control center. We use tools from linear algebra and graph theory and leverage the properties of the linearized power flow model to develop methods for information recovery. Using information observed outside the attacked zone, these methods recover information about the disconnected lines and the phase angles at the buses. We identify sufficient conditions on the zone structure and constraints on the attack characteristics such that these methods can recover the information. We also show that it is NP-hard to find an approximate solution to the problem of partitioning the power grid into the minimum number of attack-resilient zones. However, since power grids can often be represented by planar graphs, we develop a constant approximation partitioning algorithm for these graphs and numerically demonstrate its performance on real power grids.