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This paper presents a detailed description of finite control set model predictive control (FCS-MPC) applied to power converters. Several key aspects related to this methodology are, in depth, presented and compared with traditional power converter control techniques, such as linear controllers with pulsewidth-modulation-based methods. The basic concepts, operating principles, control diagrams, and results are used to provide a comparison between the different control strategies. The analysis is performed on a traditional three-phase voltage source inverter, used as a simple and comprehensive reference frame. However, additional topologies and power systems are addressed to highlight differences, potentialities, and challenges of FCS-MPC. Among the conclusions are the feasibility and great potential of FCS-MPC due to present-day signal-processing capabilities, particularly for power systems with a reduced number of switching states and more complex operating principles, such as matrix converters. In addition, the possibility to address different or additional control objectives easily in a single cost function enables a simple, flexible, and improved performance controller for power-conversion systems.