In this thesis, the application of enhanced predictive control methods with the aim of capacitor voltage balancing in reduced flying capacitor multilevel converters is investigated. Capacitors are one of the main elements in multilevel converter structures which their voltage stabilization is vital for proper converter operation. Although reducing the number of capacitors, with the aim of decreasing the overall volume and cost, has been one of the issues addressed in recent studies, it causes new challenges to capacitor voltage balancing. Finite set model predictive control (FCS-MPC) is one of the most powerful control methods to control power electronic converters. This control method is a reliable way of removing the obstacles caused by reduction the number of capacitors and consequently the number of redundant switching states. However, due to the inherent challenges of this method such as variable switching frequency, heuristic selection of weighting factors and large number of calculations, the desired performance is not achieved. After reviewing different types of capacitors in multilevel converter structures and the factors affecting charging/discharging of capacitors, a few examples of conventional modulation-based balancing methods are mentioned. Then, considering the advantages of predictive control methods and focusing on the FCS-MPC, the general equations associated with the control of ower converters and subsequently the equations needed in the capacitor voltage balancing are presented. Then, the main challenges of this control method are mentioned and the solutions presented so far to improve the performance of this method are reviewed. Next, by focusing on four-level single flying capacitor converter (4L-SFC) as one of the derivatives of flying-capacitor multilevel converter with reduced capacitors and using the concept of phase voltage levels reconstruction, three control methods are proposed in order to fulfill two general goals. The first aim is to eliminate the capacitor voltage balancing constraints in reduced capacitor structures, and the second is to modify the inherent challenges of FCS-MPC and improve system performance while applying this control method. In all the proposed methods, since the capacitor voltage balancing is the task of voltage levels reconstruction, the equations related to capacitor voltage prediction are eliminated, which leads to the required calculations are not increasing due to the changes made, and also the need to determine the appropriate weighting factor in the FCS-MPC method is eliminated. In addition, approaching new control methods to modulation-based methods in terms of concept, current harmonic spectrum is improved compared to the FCS-MPC method. Using Deadbeat Predictive Control (DPC), the third proposed method is also suggested to reduce the computation needed and improve the current harmonic spectrum. In the following, simulation results of three proposed methods and one SVM modulation-based method are compared and the priority of each method in terms of different performance characteristics is evaluated. In order to verify the performance of the proposed control methods, a laboratory-type experimental setup of 4L-SFC Converter is used, and the experimental results of applying the preferred control method to this converter via TMS320F28335 are presented and compared with simulation results to verify the viability of proposed method. Finally, conclusions and suggestions for further researchs are presented.