Journal Article

A Mixed-Integer Convex Optimization Framework for Cost-Effective Conductor Selection in Radial Distribution Networks While Considering Load and Renewable Variations

Montoya, Oscar Danilo, Florez-Cediel, Oscar David, Gil-González, Walter, Giral-Ramírez, Diego Armando, Grisales-Noreña, Luis Fernando

2025

Overview

The optimal selection of conductors (OCS) in radial distribution networks is a critical aspect of system planning, directly impacting both investment costs and energy losses. This paper proposed a mixed-integer convex (MI-Convex) optimization framework to solve the OCS problem under balanced operating conditions, integrating the costs of conductor investment and energy losses into a single convex objective. This formulation leveraged second-order conic constraints and was solved using a combination of branch-and-bound and interior-point methods. Numerical validations on standard 27-, 33-, and 85-bus test systems confirmed the effectiveness of the proposal. In the 27-bus grid, the MI-Convex approach achieved a total cost of$550,680.25, outperforming or matching the best results reported by state-of-the-art metaheuristic algorithms, including the vortex search algorithm (VSA), Newton’s metaheuristic algorithm (NMA), the generalized normal distribution optimizer (GNDO), and the tabu search algorithm (TSA). The MI-Convex method demonstrated consistent and repeatable results, in contrast to the variability observed in heuristic techniques. Further analyses considering three-period and daily load profiles led to cost reductions of up to 27.6%, and incorporating distributed renewable generation into the 85-bus system achieved a total cost of $ 705,197.06—approximately 22.97% lower than under peak-load planning. Moreover, the methodology proved computationally efficient, requiring only 1.84 s for the 27-bus and 12.27 s for the peak scenario of the 85-bus. These results demonstrate the superiority of the MI-Convex approach in achieving globally optimal, reproducible, and computationally tractable solutions for cost-effective conductor selection.

• Publisher: MDPI AG
• Subject: Accuracy / Approximation / Convex analysis / Costs / Efficiency / electric distribution networks / energy losses costs / Genetic algorithms / Heuristic / investment costs in conductors / Linear programming / Methods / mixed-integer convex programming / optimal selection of conductors / Optimization techniques / radial distribution grids / Reproducibility / Simulation / Test systems