An Improved Equilibrium Optimizer for Optimal Placement of Distributed Generators in Distribution Systems Considering Harmonic Distortion Limits

Abstract

Abstract This paper proposes an improved equilibrium optimizer (IEO) for determining optimal location and effective size of distributed generation units (DGUs) in the distribution systems in order to minimize the total power loss on distribution branches, investment cost, and operation and maintenance cost. To reach good solutions of DGUs placement, limits regarding voltage, current and harmonic flows are also seriously concerned and they must be satisfied exactly within a predetermined range. Especially, individual harmonic distortion (IHD) and total harmonic distortion (THD) of bus voltage must falls into IEEE Std. 519. The proposed IEO is developed from the original equilibrium optimizer (EO), which was motivated by control volume mass balance models. This novel algorithm can effectively expand the search area and avoid the premature convergence to low quality solution spaces. With the determined solutions from IEO, not only are the voltages well improved, but also the harmonics are mitigated from the offending values down to the allowable values of IEEE Std. 519. Moreover, the total power loss is significantly reduced from 0.2110 MW to 0.0815 MW, 0.2245 MW to 0.07197 MW and 0.3161 MW to 0.1515 MW for IEEE 33-bus, IEEE 69-bus and IEEE 85-bus radial distribution systems, respectively. Not only that, the total cost of DGUs is also more economical and consumes only $3.4753 million, $3.2840 million and $3.0593 million corresponding to the three systems for a 20-year planning period. The performance of the proposed algorithm is compared to three other implemented methods consisting of artificial bee colony (ABC) algorithm, salp swarm algorithm (SSA) and EO, and eight previously published methods for the three test systems. The comparisons of results imply that IEO is better than other methods in terms of performance, stability and convergence characteristic.