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For medium-voltage high-power drives fed by current-source converters (CSCs), a transformerless configuration has benefits in both cost and volume. Removing the isolation transformer necessitates a common-mode choke to undertake the major portion of the drive's common-mode voltage (CMV) stress, which would otherwise cause premature failure of the motor insulation system. On the other hand, as device switching frequency in high-power CSCs is normally limited to a few hundred hertz, improving harmonic performance via modulation has always been a challenge. Selective harmonic elimination (SHE) is a preferred modulation scheme in such a system owing to its ability to eliminate several unwanted low-order harmonic currents. Alternatively, conventional space vector modulation (SVM) provides continuous modulation index adjustment capability, but its output current contains low-order harmonics with high magnitudes that may arouse harmful resonances in the system. Aiming at reducing CMV and improving harmonic performance at the same time, this paper proposes a new SVM-based modulation strategy for high-power CSCs using synthesized reference trajectory on the hexagon in the αβ plane. Along with the proposed strategy, two methods of reference trajectory optimization (RTO) are investigated. By introducing a coefficient to the duty-cycle function for RTO, the first method can remove an extra low-order harmonic component, or minimize the weighted total harmonic distortion. The second method, with a different approach of RTO, eliminates the unwanted low-order harmonics by combining the proposed SVM with the SHE. The proposed concepts are verified by both simulation and experimental results. [ABSTRACT FROM AUTHOR]