Optimum arrangement of high-voltage transmission line conductors by utopian Pareto swarm intelligence

The best arrangement of overhead high voltage transmission line conductors is determined in order to satisfy the following six objectives simultaneously: maximize power capacity, avoid corona, and minimize power losses, cost, electric field, and magnetic field. To that end, in this paper, a new method is proposed, namely, utopian Pareto particle swarm optimization (UPPSO) that combines particle swarm optimization (PSO) and multi-objective Pareto algorithm. Incorporating Pareto algorithm with PSO enables efficient handling of complex problems and producing many alternative optimal solutions; thus, the designer can choose any suitable solution according to his preferences. The global best of UPPSO is determined in each iteration using the weighted Euclidean distance between the utopian point and each particle best solution. An algorithm is devised to check whether the current global best is dominated or nondominated as compared with an archive of the previous Pareto nondominated global best solutions. The utopian point is extracted from the ideal optimized point. Modified cost equations are presented. Examples are given to show the usability and usefulness of the method. Furthermore, the two cases of separation between the line conductors are considered, i.e., with and without considering the effects of ice and wind. A MATLAB computer code is written to implement the algorithm. The computed electric and magnetic fields are compared with measured data to check the validity of the calculations. New configurations of overhead transmission line conductors are obtained that satisfy all the objectives. Finally, the results obtained from UPPSO are compared to those of Ant lion optimization and PSO algorithms, thereby demonstrating the superiority of UPPSO approach.