Analysis of false data injection attacks in power systems: A dynamic Bayesian game-theoretic approach

False data injection (FDI) attack is a malicious kind of cyber attack that targets state estimators of power systems. In this paper, a dynamic Bayesian game-theoretic approach is proposed to analyze FDI attacks with incomplete information. In this approach, players' payoffs are identified according to a proposed bi-level optimization model, and the prior belief of the attacker's type is constantly updated based on history profiles and relationships between measurements. It is proven that the type belief and Bayesian Nash equilibrium are convergent. The stability and reliability of this approach can be guaranteed by the law of large numbers and the central limit theorem. The time complexity and space complexity are O(n_mn_sn_l) and O(1), respectively. Numerical results show that the average success rate to identify at-risk load measurements is 98%. The defender can efficiently allocate resources to at-risk load measurements using the dynamic Bayesian game-theoretic approach.