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The switching frequency of power semiconductor devices in high-power medium voltage drives is limited due to high switching losses. These drives often comprise an LC output filter. The filter introduces a resonant circuit that may be excited, for instance, by fast control transients. One option to avoid such oscillations is to apply damping control methods, which on the other hand usually require switching frequencies well above the filter resonance. This paper presents a predictive stator current controller that avoids the excitation of the filter resonance, realizes active damping and enables fast current control while maintaining low switching frequency. Feasibility and good dynamic performance of the proposed control method is demonstrated by simulation results of a 2.4 kV induction motor drive and by experimental results obtained from a 55 kW prototype ac drive.