The energy consumption statistics of buildings have shown that in China, 50%-70% of the annual energy consumption is consumed by cooling and heating systems, the majorities are air conditions and hot water supply. To cut down the investment of BESS, this paper studies the application of Air Source Heat Pump (ASHP) in a photovoltaic/Battery Energy Storage System (PV/BESS) microgrid. Energy dispatching strategy is proposed to take advantage of the thermal storage, and fluctuation stabilization strategy is proposed based on the decouple characteristics between Heat Pumps (HPs) and terminal devices. As the characteristics of fluctuation and the inputted capacity of ASHP should be considered during the stabilization, there are too many input variables for traditional fuzzy logic algorithm. According to this, this paper proposes an improved fuzzy logic algorithm, Double Fuzzy Logic (DFL) algorithm, to involve in all the necessary variables. At last, a case is simulated to verify the feasibility of the energy dispatching and fluctuation stabilization strategy. The results have verified that ASHP can decrease the capacities of PV/ BESS and stabilize the fluctuation effectively. (C) 2016 Elsevier Ltd. All rights reserved.