Approximate method for AC transmission switching based on a simple relaxation for ACOPF problems

Transmission switching planning under an AC power flow model is a challenging mathematical problem, incorporating nonlinearities, nonconvexities, and discrete variables. An effective solution methodology would develop an appropriate relaxation and then rely on methods from discrete optimization to simultaneously refine the relaxation, and perform enumeration, so as to obtain a sequence of narrowing lower and upper bounds to the problem. In this paper we discuss a formulation and experiments for the AC power flow transmission switching problem that relies on a simple but relatively accurate relaxation for AC OPF which is easily adapted to discrete optimization methods.

I. Introduction

In the AC transmission switching problem (ACTS for short) a planner seeks to switch off transmission lines with the goal of reducing transmission cost, improving congestion, carrying out line maintenance, or a number of other reasons. In addition, the planner may seek to enforce additional constraints on the set of switched off lines, such as only allowing a specific subset of lines to be switched off and placing upper or lower bounds on the quantity of switched off lines. See [4], [7]. Network modeling relies on an AC power flow model; thus ACTS is a nonlinear, nonconvex, mixed-integer optimization problem.