The Maximum Transmission Switching Flow Problem

Abstract

The Maximum Transmission Switching Flow (MTSF) is the problem of maximizing the power flow of a power grid by switching off lines. This static transmission design problem is known to be NP-hard even on strongly restricted graph classes. In this paper, we study the combinatorial structure of the MTSF problem and its relationship to familiar problems. We tackle the problem by exploiting the structure of the power grid leading to the first algorithms for MTSF having provable performance guarantees. We decrease the theoretical gap not only by developing algorithms with guarantees, but also by proving that the decision problem of MTSF is NP-hard even when the network contains only one generator and one load. In this context, we introduce the Dominating Theta Path, which is an exact algorithm on certain graph structures and can be used as a switching metric in general. Our simulations show that the algorithms provide very good results (in many cases near-optimal) on the NESTA benchmark cases that provide realistic thermal line limits.