To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring that the grid can be effectively monitored. This optimization problem motivates the graph theoretic power dominating set problem. In this paper, we propose a method for computing minimum power dominating sets via a set cover IP formulation and a novel constraint generation procedure. The set cover problem's constraints correspond to neighborhoods of zero forcing forts; we study their structural properties and show they can be separated with delayed row generation. In addition, we offer several computation enhancements which be be applied to our methodology as well as existing methods. The proposed and existing methods are evaluated in several computational experiments. In many of the larger test instances considered, the proposed method exhibits an order of magnitude runtime performance improvement.

中文翻译：

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权力支配集问题的新计算方法：集覆盖和迫零堡垒的邻域

为了监控整个电网的电气活动并减少中断，可以安装称为相量测量单元的传感器。由于实施成本，希望最小化部署的传感器数量，同时确保可以有效监控电网。这个优化问题激发了图论功率支配集问题。在本文中，我们提出了一种通过集合覆盖 IP 公式和新的约束生成过程来计算最小功率支配集合的方法。集覆盖问题的约束对应于迫零堡垒的邻域；我们研究了它们的结构特性，并表明它们可以通过延迟行生成来分离。此外，我们提供了一些计算增强功能，可应用于我们的方法以及现有方法。在几个计算实验中评估了所提出的和现有的方法。在考虑的许多较大的测试实例中，所提出的方法表现出一个数量级的运行时性能改进。