Direct model predictive control (DMPC) is an attractive control method, in particular, for multilevel converters. However, the computation time for classical DMPC schemes increases exponentially with the number of switching states and, compared to modulation-based controllers, real-time implementation may not be feasible. In this paper, two computationally efficient DMPC schemes with hexagon candidate region (HCR) and triangle candidate region (TCR) for torque and power control of three-level neutral-point clamped back-to-back converters in wind turbine systems with permanent-magnet synchronous generator are proposed. By an appropriate selection of the candidate regions, the number of reasonable switching states is drastically reduced which saves computation time up to 55% for HCR and up to 83% for TCR, respectively. The computational efficiency improvements and the control performances of the proposed DMPC schemes are compared and validated by real-time implementations on an field programmable gate array (FPGA) system and by measurement results at a lab-constructed test bench. The achieved control performance of the proposed methods is comparable with that of the classical DMPC, while the computation times are drastically reduced.