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Battery storage (BS) sizing problems for grid-connected microgrids (GC<i>&#956;</i>Gs) commonly use stochastic scenarios to represent uncertain natures of renewable energy and load demand in the GC<i>&#956;</i>G. Though taking a large number of stochastic scenarios into consideration can deliver a relatively accurate optimal result, it can also highly deteriorate the computational efficiency of the sizing problem. To make an accuracy-efficiency trade-off, a computationally efficient optimization method to optimize the BS capacities based on the power exchanging process of the GC<i>&#956;</i>G is proposed in this paper. According to the imbalanced power of the GC<i>&#956;</i>G, this paper investigates the power exchanging process between the GC<i>&#956;</i>G, BS and external grid. Motivated by the BS dynamics, a forward/backward sweep-based energy management scheme is proposed based on the power exchanging process. A heuristic two-level optimization model is developed with sizing BS as the upper-level problem and optimizing the operational cost of the GC<i>&#956;</i>G as the lower-level problem. The lower-level problem is solved by the proposed energy management scheme and the objective function of the upper-level is minimized by the pattern search (PS) algorithm. To validate the accuracy and computational efficiency of the proposed method, the numerical results are compared with the mixed integer linear programming (MILP) method. The comparison shows that the proposed method shares similar accuracy but is much more time-efficient than the MILP method.