Multi-time scale optimization scheduling of microgrid considering source and load uncertainty

•A multi-time scale optimal scheduling framework is proposed for microgrid scheduling to deal with the uncertainty of source and load.•A two-stage distributionally robust model is constructed to improve the robustness of the day-ahead scheduling plan.•The distributed model prediction control method is used to maintain the smooth power of contact lines.•The proposed multi-time scale scheduling method can achieve robust and economic operation of the microgrid.