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)能够提供高精度、高保真的测量数据，用于监测电网状态并支持各项控制与规划任务。然而，PMU高昂的安装成本限制了其大规模部署。在保持网络完全可观性的前提下，需尽可能减少PMU安装数量。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决策出现偏差。本文提出一种基于双层随机非合作博弈的配置模型，用于在存在网络攻击风险时的PMU布点优化。第一层模型在考虑电网运营商与攻击者各自资源约束条件下，研究网络中单个PMU的保护策略。第二层模型中，攻击者通过观测PMU布点位置实施攻击，旨在最大化状态估计误差并降低网络可观性。该技术在IEEE-9节点测试系统中进行验证，结果表明在考虑网络风险时，电网运营商部署PMU的成本降低了9%。