Phasor measurement units (PMUs) provide accurate and high-fidelity measurements in order to monitor the state of the power grid and support various control and planning tasks. However, PMUs have a high installation cost prohibiting their massive deployment. Minimizing the number of installed PMUs needs to be achieved while also maintaining full observability of the network. At the same time, data integrity attacks on PMU measurements can cause mislead power system control and operation routines. In this paper, a bi-level stochastic non-cooperative game-based placement model is proposed for PMU allocation in the presence of cyber-attack risks. In the first level, the protection of individual PMU placed in a network is addressed, while considering the interaction between the grid operator and the attacker with respective resource constraints. In the second level, the attacker observes the placement of the PMUs and compromises them, with the aim of maximizing the state estimation error and reducing the observability of the network. The proposed technique is deployed in the IEEE-9 bus test system. The results demonstrate a 9% reduction in the cost incurred by the power grid operator for deploying PMUs while considering cyber-risks.

翻译：相量测量单元（PMU）能够提供精确、高保真的量测数据，以监测电网状态并支持各类控制与规划任务。然而，PMU的安装成本高昂，限制了其大规模部署。因此，需要在保持网络完全可观性的同时，最小化PMU的安装数量。与此同时，针对PMU量测的数据完整性攻击可能导致电力系统控制与运行程序出现误导。本文提出一种基于双层随机非合作博弈的部署模型，用于在存在网络攻击风险的情况下进行PMU分配。在第一层中，模型考虑了电网运营商与攻击者分别在资源约束下的博弈互动，从而解决网络中单个PMU的保护问题。在第二层中，攻击者观察PMU部署位置并对其进行攻击，旨在最大化状态估计误差并降低网络可观性。所提技术在IEEE-9节点测试系统上进行了验证。结果表明，在考虑网络风险的情况下，电网运营商部署PMU的成本降低了9%。