Node-based valid inequalities for the optimal transmission switching problem

TL;DR

This paper introduces node-based valid inequalities derived from a polyhedral study to improve the solution process for the optimal transmission switching problem, which is a complex combinatorial optimization challenge in power systems.

Contribution

It identifies a specific node-based substructure, develops an extended formulation, and derives cutting-plane inequalities to enhance optimization efficiency.

Findings

Inequalities improve computational performance on test cases.

Extended formulation tightens the integer hull representation.

Cutting-planes reduce solution time for complex instances.

Abstract

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.