Optimal Selection of Conductor Sizes in Three-Phase Asymmetric Distribution Networks Considering Optimal Phase-Balancing: An Application of the Salp Swarm Algorithm

Abstract

This paper presents a new methodology to simultaneously solve the optimal conductor selection and optimal phase-balancing problems in unbalanced three-phase distribution systems. Both problems were represented by means of a mathematical model known as the Mixed-Integer Nonlinear Programming (MINLP) model, and the objective function was the minimization of the total annual operating costs. The latter included the costs associated with energy losses, investment in conductors per network segment, and phase reconfiguration at each node in the system. To solve the problem addressed in this study, a master–slave methodology was implemented. The master stage employs a discrete version of the Salp Swarm Algorithm (SSA) to determine the set of conductors to be installed in each line, as well as the set of connections per phase at each of the nodes that compose the system. Afterward, the slave stage uses the three-phase version of the backward/forward sweep power flow method to determine the value of the fitness function of each individual provided by the master stage. Compared to those of the Hurricane-based Optimization Algorithm (HOA) and the Sine Cosine Algorithm (SCA), the numerical results obtained by the proposed solution methodology in the IEEE 8- and 25-node test systems demonstrate its applicability and effectiveness. All the numerical validations were performed in MATLAB.