Optimized conductor selection and phase balancing in unbalanced distribution networks: Economic optimization via the vortex search algorithm

The inherent characteristics of unbalanced three-phase distribution networks can have negative technical and financial effects. In this vein, optimal conductor size selection and phase balancing are among the most common strategies for improving these indicators, which involves dealing with complex optimization problems. This article presents a mixed-integer nonlinear programming model to address conductor selection and phase balancing in distribution systems. Given the complexity of the model, a leader-follower methodology based on the vortex search algorithm (VSA) is employed to determine the conductor caliber and load phase configuration, in conjunction with the three-phase successive approximations power flow method to compute the objective function. This methodology is compared against the hurricane optimization algorithm, the sine cosine algorithm, and the salp swarm optimization algorithm. Simulation results demonstrate that the proposed methodology provides the best solution for unbalanced distribution systems comprising eight and 25 nodes. The VSA yielded the best response, with values of 125,348.4870 USD and 94,475.1477 USD in the two test feeders, respectively, as well as the lowest standard deviation (0.1948% and 0.2147%) while requiring reasonable computational times, within the average for the 8-node system and the best time for the 25-node system. The VSA demonstrated superior performance in terms of cost minimization and solution consistency with a reasonable computational effort, which makes it a valuable tool for optimizing unbalanced distribution systems and enhancing their overall efficiency.