Abstract: Bidirectional full-bridge DC-DC（dual active bridge DC-DC converter,DAB）converter,as the energy transmission link of renewable power supply and energy storage equipment,can significantly improve the performance of DAB converter by realizing zerovoltage switching（zero-voltage switch,ZVS）and minimum backflow power,so as to improve the stability of DC microgrid. However,the simultaneous realization of ZVS and minimum reflux power control is mutually restricted in theory. In order to solve this problem,this paper proposes a minimum reflux power dual phase shift control strategy based on ZVS. By segmenting the transmission power under double phase shift,the first section takes ZVS as a constraint condition to obtain the minimum backflow power control strategy under ZVS condition,and the second section realizes the minimum backflow power control strategy under given transmission power by（Karush-Kuhn-Tucker,KKT）condition method. By comparing the proposed control strategy with the traditional dual phase shift control,it is found that the proposed control strategy has less backflow power and current stress,and improves the performance of the converter.Finally,an experimental prototype is built based on the proposed control strategy to verify the correctness and effectiveness of the control strategy.