Resilient power grid state estimation under false data injection attacks

The problem of finding an optimal defense strategy against false data injection attacks on state estimation for power systems is considered in this paper. The state of the art utilizes measurement residuals to filter faulty measurements and to detect data integrity attacks. A carefully designed coordinated attack on sensor measurements can bypass the bad data detector (BDD) and may inject arbitrary additive error to the true state estimations. In this work, we propose an optimal defense strategy by applying perturbations to the impedance of transmission lines by D-FACTS devices and monitoring their effects on the system. The problem of finding the optimal set of target transmission lines for perturbation is formulated as an optimization problem so that to minimize the maximum additive error to the true state estimations. Additionally, we have considered a game theoretic approach to obtain the optimal probability of choosing an action from the actions set for the attacker and the defender. In this case, the attacker actions are defined as targeting any subset of the set of vulnerable system states and the defender actions are defined as changing the particular choice of a set of candidate transmission lines according to the derived optimal probability for the given game. To obtain the optimal defense strategy, the worst case scenario has considered where the knowledge of the set of transmission lines to be perturbed and their level of perturbations are common information between the attacker and the defender. The effectiveness of the proposed approaches are studied through simulations for a 14-bus system.