Sustainable Metaheuristic-Based Planning of Rural Medium- Voltage Grids: A Comparative Study of Spanning and Steiner Tree Topologies for Cost-Efficient Electrification

Lina María Riaño-Enciso, Brandon Cortés-Caicedo, Oscar Danilo Montoya (), Luis Fernando Grisales-Noreña and Jesús C. Hernández ()
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Lina María Riaño-Enciso: Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, Colombia
Brandon Cortés-Caicedo: Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, Colombia
Oscar Danilo Montoya: Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, Colombia
Luis Fernando Grisales-Noreña: Grupo de Investigación en Alta Tensión—GRALTA, Escuela de Ingeniería Eléctrica y Electrónica, Facultad de Ingeniería, Universidad del Valle, Cali 760015, Colombia
Jesús C. Hernández: Department of Electrical Engineering, Universidad de Jaén, Campus Lagunillas s/n, Edificio A3, 23071 Jaén, Spain

Sustainability, 2025, vol. 17, issue 18, 1-39

Abstract: This paper presents a heuristic methodology for the optimal expansion of unbalanced three-phase distribution systems in rural areas, simultaneously addressing feeder routing and conductor sizing to minimize the total annualized cost—defined as the sum of investments in conductors and operational energy losses. The planning strategy explores two radial topological models: the Minimum Spanning Tree (MST) and the Steiner Tree (ST). The latter incorporates auxiliary nodes to reduce the total line length. For each topology, an initial conductor sizing is performed based on three-phase power flow calculations using Broyden’s method, capturing the unbalanced nature of the rural networks. These initial solutions are refined via four metaheuristic algorithms—the Chu–Beasley Genetic Algorithm (CBGA), Particle Swarm Optimization (PSO), the Sine–Cosine Algorithm (SCA), and the Grey Wolf Optimizer (GWO)—under a master–slave optimization framework. Numerical experiments on 15-, 25- and 50-node rural test systems show that the ST combined with GWO consistently achieves the lowest total costs—reducing expenditures by up to 70.63% compared to MST configurations—and exhibits superior robustness across all performance metrics, including best-, average-, and worst-case solutions, as well as standard deviation. Beyond its technical contributions, the proposed methodology supports the United Nations Sustainable Development Goals by promoting universal energy access (SDG 7), fostering cost-effective rural infrastructure (SDG 9), and contributing to reductions in urban–rural inequalities in electricity access (SDG 10). All simulations were implemented in MATLAB 2024a, demonstrating the practical viability and scalability of the method for planning rural distribution networks under unbalanced load conditions.

Keywords: distribution network planning; unbalanced three-phase systems; conductor sizing; metaheuristic optimization; routing selection; rural electrification; cost minimization; energy losses; Minimum Spanning Tree; Steiner Tree (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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