In this paper, two metaheuristic techniques are used for optimal allocation of Distributed Generations (DGs) to reduce the power losses in Radial Distribution Systems (RDS). These techniques are the adaptive Particle Swarm Optimization (APSO) and the modified Gravitational Search Algorithm (MGSA). Single, as well as multiple DGs, are optimized for the optimal size and site with unity- and optimal-PFs. Besides the reduction of power losses, the voltage stability and the total voltage deviation are considered as a multi-objective optimization (MOO) problem. For MOO operation, Pareto-optimal solution, aggregated sum, and ε-constrained techniques are used for determining the DG optimal size and site. The proposed algorithms have been applied to different RDSs, including the IEEE 69-bus and the 85-bus systems. The obtained results are matched favorably with those in the literature. The operation of the DG at optimal-PF is more effective than the UPF in the reduction of power losses. Besides, installing more DGs results in better performance of the systems. The MGSA and APSO algorithms, they are compared to the AEO algorithm according to different performance metrics. The results show that the MGSA and APSO outperform the AEO algorithm. Moreover, the obtained results are significantly approved by using a t-test.

在本文中，两种元启发式技术用于分布式发电（DG）的最佳分配，以减少径向配电系统（RDS）的功率损耗。这些技术是自适应粒子群优化（APSO）和改进的引力搜索算法（MGSA）。针对单个和多个DG，使用统一和最佳PF对最佳大小和位置进行了优化。除了减少功率损耗外，电压稳定性和总电压偏差也被视为多目标优化（MOO）问题。对于MOO操作，使用帕累托最优解，总和和ε约束技术确定DG的最佳大小和位置。所提出的算法已应用于不同的RDS，包括IEEE 69总线和85总线系统。所得结果与文献中的结果相吻合。DG在最佳功率因数下的运行在降低功率损耗方面比UPF更有效。此外，安装更多的DG可以提高系统性能。MGSA和APSO算法根据不同的性能指标与AEO算法进行比较。结果表明，MGSA和APSO优于AEO算法。此外，使用 结果表明，MGSA和APSO优于AEO算法。此外，使用 结果表明，MGSA和APSO优于AEO算法。此外，使用t检验