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Battery energy storage (BES) and demand response (DR) are considered to be promising technologies to cope with the uncertainty of renewable energy sources (RES) and the load in the microgrid (MG). Considering the distinct prediction accuracies of the RES and load at different timescales, it is essential to incorporate the multi-timescale characteristics of BES and DR in MG energy management. Under this background, a hierarchical energy management framework is put forward for an MG including multi-timescale BES and DR to optimize operation with the uncertainty of RES as well as load. This framework comprises three stages of scheduling: day-ahead scheduling (DAS), hour-ahead scheduling (HAS), and real-time scheduling (RTS). In DAS, a scenario-based stochastic optimization model is established to minimize the expected operating cost of MG, while ensuring its safe operation. The HAS is utilized to bridge DAS and RTS. In RTS, a control strategy is proposed to eliminate the imbalanced power owing to the fluctuations of RES and load. Then, a decomposition-based algorithm is adopted to settle the models in DAS and HAS. Simulation results on a seven-bus MG validate the effectiveness of the proposed methodology.