Mixed integer nonlinear programming for optimal placement and size of capacitors in RDS

This paper introduces a method that utilizes nonlinear mixed integer programming (MINLP) to determine the best location and size of capacitors in radial distribution systems (RDS) to enhance the voltage profile, decrease active and reactive power losses, and reduce the cost of capacitor installation. The proposed method is divided into two parts: the first part identifies potential bus locations for the capacitors by calculating the modified loss sensitivity index (MLSI), and the second part employs MINLP to calculate the optimal size of capacitors to be placed in the candidate buses. The optimization problem is refined by incorporating constraints. The effectiveness of the proposed approach was evaluated by applying it to 10, 33, and 69 bus RDS and comparing the results to those of six other methods. The simulation results indicate that the proposed method outperforms the others in terms of loss minimization, capacitor costs, and voltage profile improvement.