A Mixed-Integer Linear Programming Formulation for Distribution Network Reconfiguration

The Distribution Network Reconfiguration (DNR) problem is a well-known problem in the field of power system optimization. It consists of altering the state of the switches in Distribution Networks (DNs), resulting in a topology that is optimal with respect to certain criteria, such as minimizing active power losses (APL), while satisfying network constraints. The choice of the formulation plays an important role in the DNR problem, as both accuracy and runtime are affected by it. This paper proposes a Mixed-Integer Linear Programming (MILP) formulation for the DNR problem that includes the APL and reactive power losses (RPL) in the Power Balance Equations (PBEs) through a piecewise-linear (PWL) approximation, without additional binary variables in the formulation beyond those used to model the state of the switches. A domain truncation (DT) method is also assessed. The proposed formulation is evaluated using the IEEE 33-bus and the IEEE 69-bus networks. Furthermore, it is analyzed (i) in the presence or absence of DGs in the network, (ii) when loads are modeled as constant power demands and also as voltage dependent loads, and (iii) for static (single-time-period) and dynamic (multiple-time-period) DNR. Results show that the proposed PBE-loss-aware formulation leads to an increase in runtime when compared with an MILP formulation in which losses are not included in the PBEs, but achieves higher modeling accuracy. Furthermore, the use of the DT method results in a significant gain in the precision of the formulation.