Optimal allocation and sizing of capacitors to minimize the transmission line loss and to improve the voltage profile

In this paper, a modified discrete particle swarm optimization is presented to find the optimal placement and size of capacitors in a distribution system. The objective function is composed of the line loss and the capacitors investment cost. The bus voltage and the feeder current as constraints are included in the objective function by a constraint penalty factor.To validate the proposed method, the 18-bus IEEE distribution system and the semi-urban distribution system which is connected to bus 2 of the Roy Billinton test system are used. The proposed method is applied to the problem and its robustness and accuracy are studied. The results are compared with pure DPSO, genetic algorithm, and nonlinear programming. It is illustrated in two examples that the proposed optimization method is more accurate and particularly more robust than others for the planning of capacitors.