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For medium-voltage drives, model predictive direct torque control (MPDTC) significantly reduces the switching losses and/or the harmonic distortions of the torque and stator currents, when compared to standard schemes, such as direct torque control or pulse width modulation. Extending the prediction horizon in MPDTC further improves the performance. At the same time, the computational burden is greatly increased due to the combinatorial explosion of the number of admissible switching sequences. Adopting techniques from mathematical programming, most notably branch and bound, the number of switching sequences explored can be significantly reduced by discarding suboptimal sequences. This reduces the computation time by an order of magnitude, enabling MPDTC with long prediction horizons to be executed on today's available hardware.