The Complexity of Switching and FACTS Maximum-Potential-Flow Problems

TL;DR

This paper investigates the computational complexity of maximizing load in power networks using switching and FACTS devices, establishing NP-hardness and the absence of efficient approximation schemes.

Contribution

It provides the first comprehensive complexity analysis of FACTS and switching maximum-potential-flow problems in power networks, including various network restrictions.

Findings

The problem is NP-complete.

No fully polynomial-time approximation scheme exists.

NP-hardness persists under network restrictions like planarity and degree constraints.

Abstract

This papers considers the problem of maximizing the load that can be served by a power network. We use the commonly accepted Linear DC power network model and consider wo configuration options: switching lines and using FACTS devices. We present the first comprehensive complexity study of this optimization problem. Our results show hat the problem is NP-complete and that there is no fully polynomial-time approximation scheme. For switching, these results extend to planar networks with a aximum-node degree of 3. Additionally, we demonstrate that the optimization problems are still NP-hard if we restrict the network structure to cacti with a maximum degree of 3.