This paper presents a novel unipolar SPWM-oriented modulation for the isolated bi-directional DC-to-three-phase-AC converter with high-frequency-link (HFL) using SiC MOSFETs. The converter consists of a full bridge (FB) stage and a single-to-three-phase matrix converter with high frequency transformer isolation. Under the proposed modulation, zero voltage switching (ZVS) is realized for the full bridge and zero voltage zero current switching (ZVZCS) is realized for the switches operating in the selected modes in the matrix converter for all load range. Synchronous Rectification (SR) is implemented for switches operating in the complimentary and synchronous modes. The proposed modulation technique takes advantages of the manifest merits of SiC devices such as the low turn-on resistance and ultra-fast reverse recovery characteristic. Moreover, the voltage spike induced by the transformer leakage inductance is mitigated with the proposed modulation technique without additional snubber circuits or components. The simulation results provided well validate the functionality and effectiveness of soft-switching of the proposed modulation. For the experimental results, the proposed modulation with SiC devices is implemented to improve the efficiency from 88.0% to 94.1% at 1.3kW compared to traditional modulation in matrix converter.