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This paper presents a dual active bridge (DAB) converter with reactive power control capability (Q-capability) for a battery energy storage system (BESS) or an electric vehicle (EV) to deliver vehicle-to-home (V2H) and vehicle-to-grid (V2G) services. The DAB topology is preferable for EV charging systems due to its galvanic isolation and bidirectional power flow capabilities. However, this topology increases reactive current peak and loses zero voltage switching (ZVS) operation at light loads if it is not controlled with improved modulation strategies and proper Q control. This paper proposes a mixed modulation method and a reactive power optimization (RPO) algorithm based on power system load flow concepts. Due to the complexities associated with the analytical solution using time domain analysis, this paper develops detailed universal expressions of a DAB converter using the harmonic analysis method. Analytical identification of ZVS boundaries and DSP implementation of the RPO algorithm become easier with these universal expressions. Multiple modes analysis for different operational states is no longer required. Simulation results have been shown for different modulation strategies of the DAB converters. The theoretical analysis of modulation strategies, RPO algorithm and ZVS operation are validated by experimental results on a DAB prototype. Results show that the proposed control strategy reduces the reactive power and provide ZVS operation over a wide ranges of voltages. [ABSTRACT FROM AUTHOR]