The efficiency of wide-bandgap (WBG) power converters can be greatly improved using high-frequency modulation techniques. This article proposes using single-loop and double-loop hexagonal sigma-delta (H-S¿ and DH-S¿, respectively) modulations for voltage source converters (VSC) that use silicon carbide (SiC) semiconductors. These allow high switching frequencies to operate more efficiently than silicon devices. Thus, S¿ modulations are excellent candidates for taking advantage of WBG devices. The proposed modulation techniques allow working with a variable switching frequency, thus producing an extreme reduction in switching losses and mitigating the low-order harmonics in comparison with the classical space vector pulsewidth modulation (SVPWM) technique, and with the innovative variable switching frequency pulse-width modulation (VSFPWM). The performance and losses of both S¿ techniques are analyzed here using MATLAB/Simulink and PLECS, and then compared with SVPWM and VSFPWM.Furthermore, the frequency spectrum and the total harmonic distortion are evaluated. Experimental results performed on a VSC converter that uses SiC MOSFETs show how H-S¿ and DH-S¿ greatly improve efficiency and generate fewer low-order harmonics than the SVPWM and VSFPWM strategies do.