In applications of the dual-active bridge (DAB) converters, minimizing circulating current and maximizing zero-voltage switching (ZVS) capability are crucial to ensure high efficiency and reliable operation. To address these challenges, this article proposes an optimal triple-phase-shift modulation scheme for the DAB converter. The proposed scheme minimizes rms current and achieves ZVS with minimal increase in circulating current across the entire load range. Building on previous modulation strategies, this article introduces a comprehensive ZVS analysis. It establishes precise ZVS criteria by rigorously accounting for the nonlinear voltage characteristics of parasitic MOSFET capacitances and the dynamic circuit behavior during the dead time, factors often simplified or overlooked in prior approaches. Using nonlinear optimization constrained by these precise ZVS criteria, the proposed modulation scheme guarantees a wide ZVS range without requiring excessive circulating current for complete ZVS, significantly reducing both switching and conduction losses. For experimental validation, a 20 kW/50 kHz SiC-based DAB converter was built, where the converter achieved a peak efficiency of 98.8%, thereby confirming the effectiveness of the proposed method.