Recently, the installation of Renewable Distributed Generation (RDG) into the Electrical Distribution System (EDS) became one of the best solutions that guarantee the balance between electric energy consumption and production, also show various advantages. In addition to delivering clean energy, they contribute to minimizing power losses, as well as enhancing the voltage profiles. In this paper, the metaheuristic optimization algorithm of the Grey Wolf Optimizer (GWO) is utilized to optimally allocate the RDG based multiple PV and WT units into EDS considering the uncertainty of electrical output energy from the RDGs as well as load demand variation during all seasons. The Multi-Objective Functions (MOF) developed in this paper is considered to minimize simultaneous the indices of the total of Active Power Loss Index (APLI), the Reactive Power Loss Index (RPLI), the Voltage Deviation Index (VDI), the Operation Time Index (OTI) of the overcurrent relay (OCR), and enhance the Coordination Time Interval Index (CTII) of the overcurrent relays installed in the test system which is the IEEE 33-bus EDS.