Optimal Allocation and Sizing of Electrical Substations Using an Improved Black Widow Algorithm

The allocation and sizing of electrical substations are critical for the efficient planning and expansion of distribution networks. This study presents the application of an enhanced Black Widow Algorithm (BWA) to solve this complex problem, considering multiple variables and constraints. The BWA, inspired by the reproductive behavior of black widows, was employed to optimize the placement and sizing of new substations and connection of load centers. Two mutation methods were evaluated: the original BWA mutation and a genetic algorithm-inspired mutation incorporated into the BWA algorithm (GA mutation). Four scenarios with varying load center distributions were tested to assess the algorithm’s adaptability and performance. The results showed that the GA mutation consistently outperformed the original mutation in more complex scenarios, reducing total costs by up to 14.75%. The proposed GA mutation enabled greater flexibility in escaping local optima, leading to improved solutions in scenarios involving numerous new load centers. Additionally, increasing the number of generations and black widows enhanced convergence and solution stability, particularly in challenging cases. This study demonstrates the feasibility of using the enhanced BWA for real-world applications, offering a valuable tool for electrical distribution planning.