Data Injection Attacks on Smart Grids With Multiple Adversaries: A Game-Theoretic Perspective

Data injection attacks have emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the surge of existing literature on data injection, most such works assume the presence of a single attacker and assume no cost for attack or defense. In contrast, in this paper, a model for data injection attacks with multiple adversaries and a single smart grid defender is introduced. To study the interactions between the defender and the attackers, two game models are considered. In the first, a Stackelberg game is proposed in which the defender acts as a leader that can anticipate the actions of the adversaries, that act as followers, before deciding on which measurements to protect. The existence and properties of the Stackelberg equilibrium of this game are studied. To find the equilibrium, a distributed learning algorithm that operates under limited system information is proposed and shown to converge to the game solution. In the second proposed game model, it is considered that the defender cannot anticipate the actions of the adversaries. To this end, a hybrid satisfaction equilibrium-Nash equilibrium game is proposed. To find the equilibrium of this hybrid game, a search-based algorithm is introduced. Numerical results using the IEEE 30-bus system are used to illustrate and analyze the strategic interactions between the attackers and defender. The results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system. Moreover, the results also show how, at equilibrium, multiple attackers can play a destructive role toward each other by choosing to carry out attacks that cancel each other out, leaving the system unaffected. In addition, the obtained equilibrium strategies under the Stackelberg and the hybrid models are compared while characterizing the amount of loss that the defender endures due to its inability to anticipate the attackers' actions.