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Recently cascade multilevel converters have attracted attention for many applications in medium voltage levels, such as STATCOMs and active power filters. The main challenges in these applications are limitation of the switching frequency of semiconductor devices and low harmonic distortion requirement of the current supplied by the current injection device. In this paper a new modulation method is proposed which produces total harmonic distortion of less than 4% with low switching frequency of 300 Hz. The proposed method has very fast dynamic response and can change the supplied current from nominal capacitive to inductive mode in less than 5 msec. The sensitivity of the method in producing a low current distortion to the ripple of the dc capacitors is low, so the current distortion is low even during transient states. Predictive current control is used in current injection loop to determine the required reference value for voltage source converter. A sample design for a 6.6-kV 12-MVAr STATCOM is presented. Simulation results show the feasibility and superiority of the proposed method.