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This paper proposes the predictive control with the discrete space-vector modulation (DSVM) for Vienna rectifier connecting to the permanent magnet synchronous generator (PMSG) of the wind turbine system (WTS). Since Vienna rectifier has the special operation principle, Vienna rectifier generates only the feasible eight voltage vectors, which can be a candidate vector for the predictive control, depending on the sign of the input currents. In the proposed predictive control, the feasible voltage vectors are extended from 8 to 19 consisting the 8 original voltage vectors and 11 virtual voltage vectors by using the DSVM for improving the current quality related to the torque ripple, vibration, and noise, and the neutral-point voltage balance with low voltage ripple is guaranteed by using the offset value calculated based on the model of two dc-link capacitors in Vienna rectifier. The scheme for reducing calculation burden is applied in selecting the candidate vector. In addition, the limited operation range for the maximum torque per ampere control of PMSG connected to Vienna rectifier is analyzed. The performance of the proposed predictive control with DSVM for Vienna rectifier with PMSGs is verified in simulation and experiment. [ABSTRACT FROM AUTHOR]