Recent advances in using renewable energy resources make them more accessible and prevalent in microgrids (MGs) and nano grids (NGs) applications. Accordingly, much attention has been paid during the past few years to design and operate MGs with high renewable energy sources (RESs) penetration. Energy storage (ES) is the crucial enabler for reliable MG operation to help MGs become more resistant to disruptions, particularly with the increased penetration of RESs. In this regard, this paper formulates a two-stage optimization framework to improve a grid-connected MG performance. Firstly, the optimal allocation decisions of the battery ES systems (BESSs) are provided to enhance the self-consumption rate of the RESs and the hosting capacity (HC) of the MG. Secondly, an operation strategy with the results (number, location, and capacity) of the BESSs obtained from the first stage is handled as an objective function to minimize the MG’s total operation cost. The IEEE 33-bus radial system is modified to act as the MG with high RESs penetration. The problem is solved using a recent swarm intelligence optimization algorithm called the Harris hawks optimization (HHO) algorithm. The proposed optimal operation strategy considers numerous constraints, such as the charge-discharge balance, number and capacity limitations of the BESSs, and the different technical performance constraints of the MG. The results obtained verify the proposed optimization framework’s effectiveness for grid-connected MGs and validate the benefits gained from the appropriate allocation of BESSs. The results also indicate that oversized storage or using many unneeded storage units may adversely influence the MG’s total power losses.