The benefits of transmission line switching are well-known in terms of reducing operational cost and improving system reliability of power systems. However, finding the optimal power network configuration is a challenging task due to the combinatorial nature of the underlying optimization problem. In this work, we identify a certain “node-based” set that appears as substructure of the optimal transmission switching problem and then conduct a polyhedral study of this set. We construct an extended formulation of the integer hull of this set and present the inequality description of the integer hull in the original space in some cases. These inequalities in the original space can be used as cutting-planes for the transmission line switching problem. Finally, we present the results of our computational experiments using these cutting-planes on difficult test cases from the literature.

传输线切换的好处在降低运营成本和提高电力系统的系统可靠性方面是众所周知的。然而，由于潜在优化问题的组合性质，找到最佳电力网络配置是一项具有挑战性的任务。在这项工作中，我们确定了某个“基于节点”的集合，它作为最优传输切换问题的子结构出现，然后对该集合进行多面体研究。我们构造了这个集合的整数包的扩展公式，并在某些情况下给出了整数包在原始空间中的不等式描述。原始空间中的这些不等式可以用作传输线切换问题的切割平面。最后，