Simultaneous Feeder Routing and Conductor Selection in Rural Distribution Networks Using an Exact MINLP Approach

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.