Solving the capacitor placement problem in radial distribution networks

Abstract

The optimal capacitor allocation problem is suggested in this article. This study purposes to maximize the voltage stability, minimize the power losses, and consolidate the annual net savings. Calculating the optimal locations and sizes of fixed and switched capacitors is done in two steps. The first step is using the fuzzy expert rules in calculating the most candidate buses for capacitor allocation. While the second step is using a nondominated sorting genetic algorithm II (NSGA-II) in determining the list of Pareto optimal solutions and then applying a fuzzy decision maker to pick the most compromise. To emphasize the effectiveness of the proposed method, radial distribution systems are proposed; IEEE 33-bus system and the actual Portuguese IEEE 94-bus system. To demonstrate the strength and applicability of this method, a multiobjective water cycle algorithm (MOWCA), multiobjective grey wolf optimizer (MOGWO), and other optimizers used in the published papers are used. From simulation and analysis, the proposed NSGA-II outperforms other optimizers considered for comparison in achieving the maximum percentages of minimization in a real power loss of 32.369% and 31.1011% for the 33-bus system and 25.6296% and 25.3027% for the 94-bus system, the maximum percentages of minimization in a reactive power loss of 31.7916% and 30.4948% for 33-bus system and 25.9457% and 25.8001% for the 94-bus system, the maximum annual net savings of 23,612 $ and 23,131 $ for the 33-bus system for fixed and switched capacitors, respectively, and boosting the total voltage stability, which show its superior ability to give high-grade solutions.