This paper introduces a distributed economic dispatch strategy for microgrids with multiple energy storage systems. This strategy overcomes the challenges of dynamic couplings among all decision variables and stochastic variables in a centralized dispatching formulation. The proposed strategy can be implemented in the microgrid central controller as multiple problems with simplified and decomposed formulations. It can also be implemented in the local controllers and managed by the central controller. Numerical studies and experimental results illustrate the effectiveness of the proposed dispatching systems.