An optimal modulation scheme with triple-phase-shift (TPS) control could increase the efficiency in the entire load range for a dual-active-bridge (DAB) converter under wide output voltage range conditions. Therefore, this study proposes a convergent approach to TPS mode selection, coupled with an optimal modulation scheme, ensuring the circuit’s efficiency over the entire range in the realm of a high-power and high-efficiency battery charger for electric vehicles. The convergent approach to TPS mode selection also reduces the numerous cases for small-signal analysis through general average modeling. After verifying the small-signal models under various voltage transfer ratios and load conditions to verify the stability, a converter prototype with a rated power of 15 kW is built and tested. Thus, a peak efficiency of 97.7% can be achieved.