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The implementation of finite-control-set model predictive control (FCS-MPC) in voltage source inverters (VSIs) can make the system suffer from poor current harmonics performance, which may complicate the design of the required AC filter. To overcome this shortcoming, a carrier-based modulated model predictive control (CB-MMPC) strategy is proposed in this paper. This method enables the utilization of existing PWM modulation techniques with FCS-MPC, where a modulation waveform with zero-sequence signal injection is generated and compared to a triangular carrier wave, while optimizing the selection of the switching states. As it is shown, the studied CB-MMPC strategy not only considerably improves the current total harmonic distortion (THD) but also attains the performance of fast current dynamic response and robustness as the traditional FCS-MPC. Herein, the detailed implementation of the CB-MMPC control strategy is given, while considering its application to the current feedback control loop of a three-phase three-wire two-level VSI modulated at constant switching frequency. Finally, PLECS circuit simulation and a 3-kW VSI prototype are used to verify the superiority and the effectiveness of the presented CB-MMPC strategy. This is also benchmarked to the FCS-MPC and dead-beat based controllers. [ABSTRACT FROM AUTHOR]