Battery energy storage (BES) system gained more attention during integration in distribution system due to rapid development in its technology. Therefore, the best allocations and sizes of BES in radial distribution system (RDS) are determined by a recent proposed hybrid methodology combining the arithmetic optimization algorithm and sine cosine approach (AOA-SCA). The proposed approach incorporates sine cosine approach in the arithmetic algorithm to improve the exploitation phase of AOA. In this work, BES is considered in discharging state when the load demand is high and in charging state as long as the demand is low, this is managed via the proposed approach to improve the reliability of RDS. The proposed approach is applied on two different networks, modified 30-bus and IEEE 69-bus systems. The target considered in this work is minimizing the whole active power loss of the network. Other algorithms of AOA, SCA, COOT, dynamic programming (DP), and gray wolf optimizer (GWO) are implemented and compared with the proposed method. The simulation results proved the superiority of the presented AOA-SCA in identifying the best allocations and sizes of BESs in RDS. The network loss is minimized via installing one, five, ten, and sixteen BESs in IEEE 69-bus by 1.43%, 6.71%, 11.32% and 16.45%, and for modified 30-bus system by 0.42%, 2.02%, 3.33% and 4.26%, respectively.