The switching of transmission lines can significantly improve the economic and operational efficiency of power systems. The Direct-Current Optimal Transmission Switching (DC-OTS) problem provides a formal framework for minimizing power generation costs by reconfiguring the transmission network topology under a linearized power flow model. DC-OTS is typically formulated as a mixed-integer linear program that incorporates disjunctive constraints to capture the required relationships between certain variables via big-M parameters. More specifically, these parameters represent upper bounds on voltage angle differences across non-operational transmission lines. In practice, overly conservative (and arbitrary) bounds tend to be used. The belief is that tightening these values requires the solution of the computationally intractable longest path problem. This work challenges that view through a novel polyhedral analysis of the angle-based DC-OTS formulation. We construct an extended formulation for the convex hull of an angle-based relaxation and derive facet-defining inequalities that tighten angle-difference bounds.

翻译：输电线路的切换能显著提升电力系统的经济与运行效率。直流最优输电切换（DC-OTS）问题提供了一个在直流潮流模型下通过重构输电网络拓扑来最小化发电成本的正式框架。DC-OTS通常被表述为一个混合整数线性规划，其中包含通过大M参数捕捉特定变量间必要关系的析取约束。更具体地说，这些参数表示非运行输电线路两端电压相角差的上界。在实践中，往往采用过于保守（且任意）的边界值。普遍观点认为，收紧这些值需要求解计算上难以处理的最长路径问题。本研究通过对基于角度的DC-OTS模型进行新颖的多面体分析，挑战了这一观点。我们为基于角度的松弛模型的凸包构建了一个扩展模型，并推导出能够收紧相角差边界的面定义不等式。