Stochastic Games for Power Grid Protection Against Coordinated Cyber-Physical Attacks

Due to the global reliance on the power grid, coordinated cyber-physical attacks on its critical infrastructure can lead to disastrous human and economic losses. In this paper, a stochastic game-theoretic approach is proposed to analyze the optimal strategies that a power grid defender can adopt to protect the grid against coordinated attacks. First, an optimal load shedding technique is devised to quantify the physical impacts of coordinated attacks. Taking these quantified impacts as input parameters, the interactions between a malicious attacker and the defender are modeled using a resource allocation stochastic game. The game is shown to admit a Nash equilibrium and a novel learning algorithm is introduced to enable the two players to reach their equilibrium strategies while maximizing their respective minimum rewards in a sequence of stages. The convergence of the proposed algorithm to a Nash equilibrium point is proved and its properties are studied. Simulation results of the stochastic game model on the WSCC 9-bus system and the IEEE 118-bus system are contrasted with those of static games, and show that different defense resources owned lead to different defense strategies.