New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem

TL;DR

This paper introduces a new exact formulation and strong MISOCP relaxations for the AC optimal transmission switching problem, addressing inaccuracies of previous DC-based models and improving solution quality and computational efficiency.

Contribution

It presents a novel AC OTS formulation with enhanced MISOCP relaxations and a practical algorithm, advancing the state-of-the-art in transmission switching optimization.

Findings

Efficiently solves IEEE standard and congested instances.

Achieves significant cost reductions with tight bounds.

Provides a practical approach for high-quality solutions.

Abstract

As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that DC approximation may lead to inaccurate flow solutions and also overlook stability issues. In this paper, we focus on the optimal transmission switching problem with the full AC power flow model, abbreviated as AC OTS. We propose a new exact formulation for AC OTS and its mixed-integer second-order conic programming (MISOCP) relaxation. We improve this relaxation via several types of strong valid inequalities inspired by the recent development for the closely related AC Optimal Power Flow (AC OPF) problem. We also propose a practical algorithm to obtain high quality feasible solutions for the AC OTS problem. Extensive computational experiments show that the proposed formulation and algorithms efficiently solve IEEE standard and congested instances and lead to significant cost benefits with provably tight bounds.