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Small-scale renewable energy sources (RESs) have transformed from traditional energy consumers into energy prosumers. However, the problem of grid-connected power fluctuation deteriorated by rooftop photovoltaic has always been the main obstacle restricting the widespread application of distributed energy resources in demand-side users. In this paper, a rolling optimal dispatch strategy of energy prosumer, which considers the grid-connected power fluctuation suppression and the energy storage degradation cost, is developed to achieve economic and stable operation. The complementary characteristics of hybrid energy storage (HES) can not only play role in economic dispatch, but also smooth grid-connected power fluctuation. We build a mathematical model of the PV-HES-load system for the prosumer. Furthermore, the real-time power fluctuation suppression method with the trigger mechanism and based on the uncertainty interval is originally designed. Finally, to ensure the economic and stable operation of the system, a rolling optimal dispatch strategy is proposed. Numerical results show that the designed dispatch strategy for the prosumer can effectively mitigate the grid-connected power fluctuation and reduce total operation cost.