A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem

TL;DR

This paper introduces a graph-based iterative method to improve the efficiency of solving the all-line transmission switching problem by tightening relaxations and using heuristics, leading to faster computation on large power networks.

Contribution

It presents a novel approach combining graph theory and iterative heuristics to enhance solution speed and accuracy for the transmission switching problem.

Findings

Significant reduction in computational time on a 118-bus network.

Tighter big-M values improve optimization relaxation.

Iterative heuristic accelerates finding low-cost feasible solutions.

Abstract

The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M constants that lead to weak relaxations and significant computational challenges, particularly when all lines are switchable. In this paper, we propose a two-fold approach: first, using graph theory to derive tighter big-M values by solving a relaxed longest path problem; second, introducing an iterative algorithm that incorporates a heuristic version of the switching problem to efficiently generate low-cost feasible solutions, thereby accelerating the search for optimal solutions in the integer optimization solver. Numerical results on the 118-bus network show that the proposed methodology significantly reduces the computational burden compared to conventional approaches.