An accurate MINLP formulation for selecting conductors in three-phase asymmetric networks: A computational implementation in the Julia software

The increasing global demand for electricity, driven by population growth and technological advancements, has necessitated the expansion of power generation, transmission, and distribution systems. Consequently, grid operators are focused on redesigning networks to enhance energy supply efficiency, with special emphasis on selecting conductors for unbalanced three-phase systems to minimize costs. This paper introduces a computational implementation of a mathematical model in the complex variable domain, addressing the conductor selection problem. The primary aim is to offer a comprehensive tutorial that guides readers through the formulation of three-phase power flow in distribution networks and the computational implementation of the conductor selection problem in both single-hour and multi-period scenarios using the Julia programming language. The mathematical models were implemented and solved using the JuMP optimization environment alongside the Bonmin solver. Validation was performed on academic test systems with different network configurations to assess the impact of conductor selection under balanced and unbalanced operating conditions. The results confirm that the proposed exact optimization methodology outperforms metaheuristic algorithms commonly found in the literature, achieving lower total costs and improved computational efficiency.