A QUBO Formulation for Minimum Loss Spanning Tree Reconfiguration Problems in Electric Power Networks

TL;DR

This paper presents a new QUBO formulation for optimizing distribution grid reconfiguration to minimize electrical losses, enabling efficient solution search using classical and quantum methods.

Contribution

The paper introduces a novel QUBO model for the minimum loss spanning tree problem in power networks, optimized for quantum and hybrid solvers.

Findings

Successfully formulated the problem as a QUBO model.

Validated the model on a 33-node test network.

Obtained and verified the optimal solution.

Abstract

We introduce a novel quadratic unconstrained binary optimization (QUBO) formulation for a classical problem in electrical engineering -- the optimal reconfiguration of distribution grids. For a given graph representing the grid infrastructure and known nodal loads, the problem consists in finding the spanning tree that minimizes the total link ohmic losses. A set of constraints is initially defined to impose topologically valid solutions. These constraints are then converted to a QUBO model as penalty terms. The electrical losses terms are finally added to the model as the objective function to minimize. In order to maximize the performance of solution searching with classical solvers, with hybrid quantum-classical solvers and with quantum annealers, our QUBO formulation has the goal of being very efficient in terms of variables usage. A standard 33-node test network is used as an illustrative example of our general formulation. Model metrics for this example are presented and discussed. Finally, the optimal solution for this example was obtained and validated through comparison with the optimal solution from an independent method.