Abstract

Highlights What are the main findings? A novel MINLP model was developed to simultaneously solve the feeder routing and conductor sizing problem in rural distribution networks, ensuring radial topology and minimizing total system costs. Compared to metaheuristic methods based on the minimum spanning tree and tabu search, the proposed approach achieved a reduction in total planning costs of up to 65.28% and energy loss costs of over 61% in the 25-node test feeder. What is the implication of the main finding? The integration of route and conductor selection into a unified MINLP framework enables globally optimal and long-term cost-effective solutions for rural electrification. This model provides a scalable and reliable methodology for utility companies and planners aiming to expand distribution networks under geographical, economic, and technical constraints.Highlights What are the main findings? A novel MINLP model was developed to simultaneously solve the feeder routing and conductor sizing problem in rural distribution networks, ensuring radial topology and minimizing total system costs. Compared to metaheuristic methods based on the minimum spanning tree and tabu search, the proposed approach achieved a reduction in total planning costs of up to 65.28% and energy loss costs of over 61% in the 25-node test feeder. What is the implication of the main finding? The integration of route and conductor selection into a unified MINLP framework enables globally optimal and long-term cost-effective solutions for rural electrification. This model provides a scalable and reliable methodology for utility companies and planners aiming to expand distribution networks under geographical, economic, and technical constraints.Abstract This article addresses the optimal network expansion problem in rural distribution systems using a mixed-integer nonlinear programming (MINLP) model that simultaneously performs route selection and conductor sizing in radial distribution systems. The proposed methodology was validated on 9- and 25-node test systems, comparing the results against approaches based on the minimum spanning tree (MST) formulation and metaheuristic approaches (the sine-cosine and tabu search algorithms). The MINLP model significantly reduced the total costs. For the nine-node system, the total cost decreased from USD 131,819.33 (MST-TSA) to USD 77,129.34 (MINLP), saving USD 54,689.99 (41.48%). Similarly, the costs of energy losses dropped from USD 111,746.73 to USD 63,764.12, a reduction of USD 47,982.61 (42.94%). In the 25-node system, the total costs fell by over 65% from USD 371,516.59 to USD 128,974.72, while the costs of energy losses decreased by USD 210,057.16 (61.06%). Despite requiring a higher initial investment in conductors, the MINLP model led to substantial long-term savings due to reduced operating costs. Unlike previous methods which separate network topology design and conductor sizing, our proposal integrates both aspects, ensuring globally optimal solutions. The results demonstrate its scalability and effectiveness for long-term distribution planning in complex power networks. The experimental implementation was carried out in Julia (v1.10.2) using JuMP (v1.21.1) and BONMIN.