基于角度的直流最优输电开关闭合问题的面定义不等式
Facet-Defining Inequalities for the Angle-Based DC Optimal Transmission Switching Formulation
AI总结：
本文通过多面体分析，提出了一种基于角度的直流最优输电切换问题的面定义不等式，以收紧电压角度差的界限，从而改进输电网络的优化配置。
摘要：
输电线路的切换可以显著提高电力系统的经济性和运行效率。直流最优输电切换（DC-OTS）问题提供了一个正式框架，通过在线性化功率流模型下重新配置输电网络拓扑结构来最小化发电成本。DC-OTS通常被表述为混合整数线性规划问题，其中包含离散约束以捕捉某些变量之间的必要关系，这些约束通过大M参数来表示。更具体地说，这些参数代表非运行输电线路两端电压角度差的上限。在实践中，过于保守（且任意）的界限往往被使用。人们普遍认为收紧这些值需要解决计算上不可行的最长路径问题。本文通过针对基于角度的DC-OTS问题的新型多面体分析来挑战这一观点。我们为基于角度的松弛的凸包构造了扩展形式，并推导出面定义不等式以收紧角度差界限。
英文摘要：
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.
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