A QUBO Formulation for Minimum Loss Network Reconfiguration

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 formulated as QUBO, taking advantage of the relationship between several model variables in order to reduce the overall losses expression. Finally, these terms are added to the model as the objective function to minimize. In order to achieve the best possible 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.