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This paper presents a model predictive control strategy for an induction machine fed by a three-level flying capacitor converter. In order to reduce the calculation effort (64 different switching possibilities for one prediction step) in a first step the best one of the 19 voltage vectors is determined. After that the best switching state which delivers this voltage vector is determined regarding the flying capacitor voltage balancing and the switching effort, making use of a hysteresis-based algorithm. The proposed control algorithm is verified by several simulations which clearly verify that an effective control of speed, torque, flux and of the flying capacitor voltages is possible.