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The common-mode voltage (CMV) produced from a converter system is a source of many problems. E.g. in the motor drive system, CMV might appear at the neutral point of the motor stator windings with respect to the ground and induce destructive bearing current. Reduced common-mode voltage space vector modulation (RCMV SVM) methods have been proposed in both voltage source converter (VSC) and current source converter (CSC) systems. The available RCMV SVMs reduce the CMV by avoiding using zero-state vectors. However, this will lead to some negative effects, such as shrink of modulation index range, increase of switching frequencies, bipolar line-to-line voltage pulse patterns in VSCs, and power quality performance deterioration. In this paper, a RCMV SVM method for CSCs is proposed. By allowing the use of zero-state vectors, the proposed RCMV SVM still produces much lower CMV. However, its other performance indices, such as switching frequency and harmonic performance, are unaffected and comparable to the conventional SVMs. The effectiveness of the proposed RCMV SVM for CSCs is verified in the simulations and experiments.