Optimal Defense Resources Allocation for Power System Based on Bounded Rationality Game Theory Analysis

Power utility allocates defense resources to prevent unscheduled load shedding due to transmission line failure caused by the malicious physical attacks. Game theory explains the interaction between the defender and the attacker, overcoming the shortage of unilateral vulnerability analysis. Different from previous researches typically assuming the players are rational and the total defense resources are fixed, this paper investigates the bounded rationality and allows variable total defense resources aiming for a higher level of practicability. Stochastic response to strategies of the bounded rational attacker is described by the Quantal Response Equilibrium (QRE) model. A two-layer defense resources allocation optimization framework is established to obtain both optimal total defense resources and optimal resource distribution, and we design a combined power-of-two and dichotomy (CPTD) algorithm for solution. We also explore the multiple properties of bounded rational behaviors in the attack-defense game. Besides, a unified resources allocation framework of bilateral players is established, which advantages in both cost and reward calculations. To the knowledge of the authors, this work is more general and more practical than previous relevant publications. The experimental studies on the IEEE 14-bus system and the IEEE 118-bus system empirically justify the improvements by our modeling and solution approaches.