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 $O\left(n_m{n}_s{n}_l\right)$ and $O\left(1\right)$, 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.

虚假数据注入 (FDI) 攻击是一种针对电力系统状态估计器的恶意网络攻击。在本文中，提出了一种动态贝叶斯博弈论方法来分析具有不完整信息的 FDI 攻击。在这种方法中，根据提出的双层优化模型确定玩家的收益，并且根据历史资料和测量值之间的关系不断更新攻击者类型的先验信念。证明了类型信念和贝叶斯纳什均衡是收敛的。这种方法的稳定性和可靠性可以通过大数定律和中心极限定理来保证。时间复杂度和空间复杂度分别为$哦\left(n_{米}{n}_{秒}{n}_{升}\right)$ 和 $哦\left(1\right)$， 分别。数值结果表明，识别风险负载测量的平均成功率为 98%。防御者可以使用动态贝叶斯博弈论方法有效地将资源分配给风险负载测量。