Abstract
The optimal expansion of unbalanced three-phase distribution networks in non-interconnected zones requires the simultaneous resolution of two highly complex planning decisions: the selection of feeder routes and the sizing of conductors. This problem, formulated as a non-convex mixed-integer nonlinear program (MINLP), poses significant computational challenges due to the combinatorial explosion of radial topologies, discrete conductor choices, and the nonlinearity of three-phase power-flow equations. While metaheuristics offer flexible exploration, they lack optimality guarantees and repeatability, whereas exact MINLP solvers provide rigorous solutions but become computationally intractable for systems of realistic size. To overcome these limitations, this paper introduces a novel hybrid exact–metaheuristic framework that synergistically combines the global exploration capabilities of the Equilibrium Optimizer (EO) with the rigorous evaluation power of an exact MINLP model. In this cascade architecture, EO efficiently navigates the discrete space of radial topologies, while the exact MINLP stage, solved using BONMIN with an interior-point branch-and-bound scheme, optimizes conductor selection and evaluates the full annualized cost, rigorously enforcing voltage, ampacity, and physical constraints. The proposed methodology was validated on 10-, 30-, 50-, and 110-node test systems derived from real Colombian non-interconnected zones (Nuquí, Leticia, San Andrés, and a large-scale urban case). Comparative analysis against pure metaheuristics (SSA, GWO, VSA) and standalone MINLP demonstrates that EO-MINLP consistently yields the lowest total annualized costs, achieving savings of up to 0.42%, 0.71%, and 1.36% over the best pure metaheuristic for the 10-, 30-, and 50-node systems, respectively. Crucially, the hybrid strategy dramatically enhances scalability, reducing the standalone MINLP computational time by 15.79%, 78.68%, and 88.95% for these cases, while preserving solution quality and improving repeatability (standard deviation reduced from over 1.2% to as low as 0.11%). For the challenging 110-node system, where the standalone MINLP proved computationally infeasible, the proposed method successfully delivered a feasible, high-quality solution with a standard deviation of just 0.43%, confirming its practical applicability to large-scale planning. These results demonstrate that the EO-MINLP framework provides a robust, scalable, and economically superior tool for the cost-effective design of unbalanced distribution networks, effectively bridging the gap between the flexibility of stochastic search and the rigor of mathematical programming.
