Joint Feeder Routing and Conductor Sizing in Rural Unbalanced Three-Phase Distribution Networks: An Exact Optimization Approach

This paper addresses the simultaneous feeder routing and conductor sizing problem in unbalanced three-phase distribution systems, formulated as a nonconvex mixed-integer nonlinear program (MINLP) that minimizes the equivalent annualized expansion cost—combining investment and loss costs—under voltage, ampacity, and radiality constraints. The model captures nonconvex voltage–current–power couplings, Δ/Y load asymmetries, and discrete conductor selections, creating a large combinatorial design space that challenges heuristic methods. An exact MINLP formulation in complex variables is implemented in Julia/JuMP and solved with the Basic Open-source Nonlinear Mixed Integer programming (BONMIN) solver, which integrates branch-and-bound for discrete variables and interior-point methods for nonlinear subproblems. The main contributions are: (i) a rigorous, reproducible formulation that jointly optimizes routing and conductor sizing; (ii) a transparent, replicable implementation; and (iii) a benchmark against minimum spanning tree (MST)-based and metaheuristic approaches, clarifying the trade-off between computational time and global optimality. Tests on 10- and 30-node rural feeders show that, although metaheuristics converge faster, they often yield suboptimal solutions. The proposed MINLP achieves globally optimal, technically feasible results, reducing annualized cost by 14.6% versus MST and 2.1% versus metaheuristics in the 10-node system, and by 17.2% and 2.5%, respectively, in the 30-node system. These results highlight the advantages of exact optimization for rural network planning, providing reproducible and verifiable decisions in investment-intensive scenarios.