Multi-Objective Optimization for Distributed Generator and Shunt Capacitor Placement Considering Voltage-Dependent Nonlinear Load Models

This paper aims to optimize the placement and sizing of distributed generator (DG) and shunt capacitor (SC) to minimize various single and multi-objective problems. Initially, three single objectives are addressed: minimizing active power loss, minimizing total operating cost, and minimizing total voltage deviation. A new mathematical expression for total operating cost, based on installation, maintenance, and operation costs of DG and SC, is developed. The Competitive Swarm Optimizer (CSO) algorithm is utilized to solve the optimization problem. The results obtained using CSO are compared with several other algorithms, including Cuckoo Search, Jaya, Teaching Learning Based Optimization, Particle Swarm Optimization, and Genetic Algorithm. The comparative results demonstrate that the CSO algorithm outperforms these methodologies. Subsequently, three multi-objective problems are formulated: simultaneous minimization of active power loss and total voltage deviation, simultaneous minimization of active power loss and total operating cost, simultaneous minimization of active power loss, total voltage deviation, and total operating cost. Multi-objective CSO is used to obtain a set of non-dominated optimal solutions, providing more realistic results. The R-method is then applied to select the best compromise solution from these non-dominated solutions. The developed model demonstrates its ability to find optimal placements of DG and SC, offering superior results compared to existing approaches. The proposed methodology is validated on six different non-linear loads such as constant power, constant current, constant impedance, industrial, commercial, and residential loads, highlighting its effectiveness and tested on the IEEE-34 bus radial distribution system.