To address the issue of low transmission efficiency in dual active bridge (DAB) converters during electric vehicle charging and discharging processes, a minimum current stress optimization control strategy combining the differential extremum method with segmented control is proposed. This strategy effectively optimizes current stress and suppresses backflow power under soft-switching constraints, thereby significantly improving transmission efficiency. Firstly, taking forward power transmission as an example, the conditions for achieving zero voltage soft-switching for all switches in two operation modes under extended phase shift (EPS) control are derived, and the mechanism of backflow power generation is analyzed, elucidating how reducing current stress contributes to its suppression. Subsequently, the optimization phase-shift combinations for minimum current stress are derived using the differential extremum method, and a segmented control scheme is implemented based on the soft-switching ranges of different modes. Finally, experimental results demonstrate that when the voltage conversion ratio is greater than 1, the proposed strategy achieves soft-switching for all switches across the full power range, while effectively reducing current stress and suppressing backflow power, leading to a significant improvement in transmission efficiency. However, when the voltage conversion ratio is less than 1, while current stress is still reduced, zero voltage switching cannot be achieved for all switches.