In a microgrid, an efficient energy storage system is necessary to maintain a balance between uncertain supply and demand. Distributed energy storage system (DESS) technology is a good choice for future microgrids. However, it is a challenge in determining the optimal capacity, location, and allocation of storage devices (SDs) for a DESS. This paper proposes a two-stage approach to solve these SD decision-making problems in a microgrid. In the first stage, a continuous approximation approach was used to formulate the SD location, capacity, and renewable energy investment problems from a long-term perspective. In the second stage, the dispatch quantity problems are addressed to minimize the operational cost based on the results of Stage 1. Some examples and real data are used to illustrate the model and solution approaches. The results show that our approach can achieve the cost minimization. The optimal SD location and capacity strategy and the renewable energy investment level are close to the real data obtained from Liu et al. (2018) after 20 runs. • Designing a two-stage approach to solve these SD decision-making problems in a microgrid. • A continuous approximation approach is used to formulate the SD location, capacity, and renewable energy investment problems from a long-term perspective at the first stage. • The dispatch quantity problems are addressed to minimize the operational cost based on the results of Stage 1 at Stage 2. [ABSTRACT FROM AUTHOR]