Abstract: The existing incomplete mathematical model, incomplete working mode, single optimization goal and inability to optimize online are the main obstacles for further improving the performance of extended-phase-shift（EPS） control strategy on dual active bridge（DAB） converter. The whole EPS working modes are analyzed and the mathematical models of transmission power, backflow power and current stress of each mode are established. On the basis of the integrated mathematical models, a compounded EPS optimization control strategy for minimizing backflow power and current stress is proposed. Specifically, the goal is to optimize the current stress under the premise of ensuring the minimum backflow power. For this goal, some appropriate modes are selected according to the analysis and comparison of the performance of each mode. After selecting the better modes, the constrained extreme value solution method is adopted to further obtain the optimal control path. A closed-loop controller is designed. Finally, the proposed control strategy is verified through experiments. The experimental results show that, the lowest backflow power and lower current stress of the DAB converter could be ensured under the proposed control strategy. Consequently, the efficiency is enhanced.