The problem of optimal phase-balancing in three-phase asymmetric distribution networks is addressed in this research from the point of view of combinatorial optimization using a master–slave optimization approach. The master stage employs an improved sine cosine algorithm (ISCA), which is entrusted with determining the load reconfiguration at each node. The slave stage evaluates the energy losses for each set of load connections provided by the master stage by implementing the triangular-based power flow method. The mathematical model that was solved using the ISCA is designed to minimize the annual operating costs of the three-phase network. These costs include the annual costs of the energy losses, considering daily active and reactive power curves, as well as the costs of the working groups tasked with the implementation of the phase-balancing plan at each node. The peak load scenario was evaluated for a 15-bus test system to demonstrate the effectiveness of the proposed ISCA in reducing the power loss (18.66%) compared with optimization methods such as genetic algorithm (18.64%), the classical sine cosine algorithm (18.42%), black-hole optimizer (18.38%), and vortex search algorithm (18.59%). The IEEE 37-bus system was employed to determine the annual total costs of the network before and after implementing the phase-balancing plan provided by the proposed ISCA. The annual operative costs were reduced by about 13% with respect to the benchmark case, with investments between USD 2100 and USD 2200 in phase-balancing activities developed by the working groups. In addition, the positive effects of implementing the phase-balancing plan were evidenced in the voltage performance of the IEEE 37-bus system by improving the voltage regulation with a maximum of 4% in the whole network from an initial regulation of 6.30%. All numerical validations were performed in the MATLAB programming environment.

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

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