Optimal Selection of Conductors in Three-Phase Distribution Networks using the Newton Metaheuristic

Context: The accelerated growth of cities and rural areas requires the adequate expansion of electrical distribution systems in order to meet the electrical energy requirements with efficiency, reliability, and safety for commercial, residential, and industrial users. To serve the different users of the electrical network, a typical methodology used by network operators corresponds to the optimal assignment of the calibers of the conductors associated with the distribution routes. This selection is made while considering its cost of investment and operation for a determined planning horizon. Method: To solve the problem regarding optimal selection in three-phase distribution networks, the application of an optimization algorithm of the family of combinatorial techniques known as Newton's metaheuristic algorithm (NMA) is proposed. The main advantage of the NMA is that it uses evolution rules based on the first and second derivatives of the objective function, which are applied to each individual in the population. In addition, the evolution rules of the NMA cause this algorithm to have a proper balance between the exploration and exploitation of the solution space as the iterative process advances.Results: Numerical validations in two three-phase distribution systems composed of 8 and 27 nodes with balanced and unbalanced operation scenarios show that the NMA reaches the optimal solution reported in the literature for the 8-node system and improves the scientific reports for the 27-node test system in both test scenarios. Conclusions: The results obtained through the application of the NMA to the problem regarding the optimal selection of conductors in distribution systems demonstrate the effectiveness of the proposed solution methodology for mixed integer nonlinear programming problems in electrical engineering with exponential sizes of the solution space. Furthermore, the reported results for the 8-node and 27-node test systems constitute a benchmark for further research.