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Symmetry
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2 January 2026

Optimization of Distributed Energy Resources in Distribution Networks Using Multi-Objective Archimedes Optimization Algorithm

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1
Department of Electrical Engineering, COMSATS University Islamabad, Islamabad 45550, Pakistan
2
Directorate of Inspections, National University of Medical Sciences, Islamabad 46000, Pakistan
3
Department of Software Engineering, Foundation University, Islamabad 44000, Pakistan
4
Department of Engineering, Computing and Mathematical Sciences (ECaMS), Lewis University, Romeoville, IL 60446, USA
This article belongs to the Special Issue Symmetry in Energy Systems and Electrical Power

Abstract

Distributed energy resources (DERs) can improve the performance of radial distribution systems. The nonlinear power flow constraints, multi-objective trade-offs, and network reconfiguration scenarios for DER placement and sizing call for the formulation of optimization problems. Most of the times optimization algorithms suffer from premature convergence and poor exploration-exploitation balance. These problems exhibit an inherent internal structural symmetry. In order to overcome the above problem, this study uses the Multi-Objective Archimedes Optimization Algorithm (MAOA) to optimally allocate DERs in the Radial Distribution Networks (RDNs), moreover the performance of the proposed MAOA is compared with the other well established algorithms including Particel Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Shuffled Frog Leaping Algorithm (SFLA), Atom Search Optimization (ASO), and Butterfly Optimization Algorithm (BOA) on the IEEE-33 RDN. The comparison is made for the four cases (S1: DER Only), (S2—Network Reconfiguration Only), (S3—DER Followed by Reconfiguration), and (S4—Reconfiguration Followed by DER) considering factors like voltage profile, network reconfiguration, active and reactive power loss reduction, carbon emission DER utilization and Cost reduction. The MAOA is observed to provide better results among all the other benchmark algorithms. In S3, the active power loss is reduced by 68.41%, whereas the reactive power loss is reduced by 57.44% and the MAOA algorithm improves the voltage by 3.98%. The minimum voltage of the network is also improved by 6.28%. The algorithm improves convergence with a percentage of 18.50% enhancing the system’s operational symmetry and stability, while satisfying all constraints. At Bus 3 and Bus 6 of IEEE-33 bus radial distribution network (Baran–Wu test system), DG capacity is allocated to be 3.8 MW and 2.1 MW, respectively.

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