A Mixed Integer Linear Programming Model for the Distribution Network Reconfiguration Problem

This paper proposes a novel model for the Distribution Network Reconfiguration (DNR) Problem. The DNR consists of altering the state of the switches (opening or closing them) in the network to obtain a different topology, thus modifying the flow of power in the network. This optimization problem is often formulated to minimize the losses in the network and can be combined with other objectives as well. Our study introduces a novel Mixed Integer Linear Programming (MILP) model that includes the losses of the lines in the power balance constraints. The efficacy of the proposed model is assessed with the use of two variants of the IEEE-33 bus network, the standard one as well as a modified version where Distributed Generations (DGs) are added, and a simple three-bus network.

I. Introduction

Distribution Network Reconfiguration (DNR) is the process of changing the network's topology by editing the state of the switches of the network. The goal of the reconfiguration in this paper is to minimize power losses while respecting the network's constraints. The DNR problem is known to be challenging due to the non-linearity of the Power Flow (PF) equations. Moreover, the large number of switches in the distribution networks complicates the search for the optimal configuration. DNR is known to be an efficient way to reduce power losses and enhance voltage stability. In addition, the goal is to benefit from decentralized producers while maintaining voltage variation stability and respecting radiality constraints. In this paper, a deterministic model is considered: A Mixed Integer Linear Programming (MILP) model that includes the losses of the lines¹

What is meant here is the (active power /reactive power ) consumed by the (resistance /reactance ) of a line, where is the current flowing through that line.

in the power balance constraints, while taking into account the Distributed Generation (DG) in the model.