Reconfiguration of Distribution Systems using the Newton Method in Quadratic Formulations

The distribution system reconfiguration problem is concerned with finding the state of all switches in a set of primary distribution feeders so that a given objective function is optimised, typically the minimisation of the total electrical loss. Constraints such as Kirchhoffpsilas Current Law (KCL) and branch capacity are usually enforced. An additional and important constraint is also imposed so that the obtained solutions are all radial. This optimisation problem is a mixed-integer non-linear optimisation problem, in which the integer variables represent the state of the switches and the continuous variables represent the current flowing through the branches. The paper develops new quadratic formulations for the continuous part of the problem. It is shown that all the formulations lead to convex problems, which guarantees that the global minimum is unique and hence allows an efficient application of the standard Newton Method. The paper also presents a new integer search based on the well-known branch-and-bound method. Results from the application of the proposed approaches to three different distribution systems are presented and discussed.