The medium-voltage (MV) dual active bridge (DAB) converter with series-connected SiC (S-SiC) MOSFETs is a promising solution for high-power-density isolated dc/dc converter. To improve the voltage sharing and reliability of S-SiC, relatively large snubber capacitors are connected in parallel with S-SiC. However, this narrows the zero voltage switching-ON (ZVS-ON) range of S-SiC and even reduces the efficiency and reliability of the entire converter. Adding a nonoptimized internal phase shift angle to the low-voltage (LV) side switching unit will result in excessive circulating power and still lead to low efficiency. In this article, the phase shift angle segmentation modulation (PSSM) scheme featuring soft-switching performance is proposed for an MV DAB converter with S-SiC. The proposed modulation scheme is based on a detailed derivation of the ZVS-ON range and operation modes. Then, the changes in operation characteristics and the advantages brought by the proposed modulation scheme are analyzed in terms of transmission power, state transition process, switching current, and device losses. Moreover, the introduced modes and ZVS-ON characteristics are verified on the 4-/1-kV 200-kW experimental prototype. As a result, the converter's loss can be decreased by up to 75% under light load, validating the efficiency advantage of the proposed modulation scheme.