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This paper presents a predictive strategy for current control of a three-phase flying capacitor converter. Future values of the load current and flying capacitor voltages are predicted with discrete-time system models. An offline solution for obtaining the best one of the 19 possible voltage vectors is combined with a hysteresis-based voltage balancing algorithm which makes use of the redundancy of the 64 switching possibilities of the converter. With few modifications this principle can easily be extended to inverters with a higher number of voltage levels.