In this paper we present a direct model predictive control (MPC) scheme, which combines control and modulation in one computational stage. The MPC problem is formulated as a current control problem. By utilizing a fixed modulation cycle akin to pulse width modulation (PWM) that allows for one switching transition per phase and half-cycle a constant switching frequency and a discrete current harmonic spectrum result. Thus, the issues that relate to the variable switching frequency and current interharmonics of direct MPC schemes are resolved. To verify the effectiveness of the proposed method a variable speed drive system, which consists of a two-level voltage source inverter and a medium-voltage induction machine, serves as a case study.