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In order to meet the demands of the bidirectional transmission of electric vehicle charger power, a series-resonant dual-active-bridge (DAB) converter is investigated in this paper. Firstly, the active and reactive power and zero voltage switching (ZVS) conditions of the full-bridge arm under extended phase-shift modulation, dual phase-shift modulation and triple phase-shift modulation are analyzed. Secondly, with the minimum reactive power as the optimization objective, the extended phase shift (EPS) is finally selected as the modulation method after comparing the minimum reactive power under various modulation methods when the normalized value of active power is varied in the range of 0–1. By constructing the objective function and determining the constraints, an off-line reactive power–minimization control strategy is proposed to achieve the ZVS of the full-bridge arm and, finally, the feasibility of the proposed control strategy is verified by simulation and experiment.