Modular multilevel converters (MMCs) play an important role in the power electronics industry due to their many advantages, such as modularity and reliability. In the current research, the simulation method is used to study the system. However, with the increasing number of sub-modules (SMs), it is difficult to model and simulate the system. In order to overcome these difficulties, this paper presents a universal mathematical model (UMM) of MMC using half-bridge cells as SMs. The UMM is a full-scale model with switching state, capacitance, inductance, and resistance characteristics. This method can calculate any number of SMs, and it does not need to build a simulation model (SIM) of physical MMC—in particular, parametric design can be realized. Compared with the SIM, the accuracy of the proposed UMM is verified, and the computational efficiency of the UMM is 8.7 times higher than the simulation method. Finally, by utilizing the proposed UMM method, the influence of the parameters of MMCs is studied, including the arm induction, SM capacitance, SM number, and output current/voltage total harmonic distortion (THD) based on the UMM in the paper. The results offer an engineering insight to optimize the design of MMCs.

Modular multilevel converters (MMCs) play an important role in the power electronics industry due to their many advantages such as modularity and reliability. However, one of the challenges is to suppress fluctuations of circulating current and capacitor voltage and to ensure the quality of the output current. In this paper, the upper and lower arm voltages are employed as control inputs to control the output current and circulating current which are fed back to track the desired value. Based on linear matrix inequality (LMI), the control law of the MMC with multi-input system is designed to optimize the control value. The optimum arm voltage is divided by the SM nominal capacitor voltage to determine the number of SMs inserted into the upper/lower arm. The Voltage Sorting Algorithm (VSA) is then used to suppress the capacitor voltage fluctuation. The proposed tracking control strategy is implemented in MATLAB/Simulink. The results show that even under a small number of SMs (4 per arm), the output current can track the desired values and have better harmonic performance (current THD: 5.42%,voltage THD: 5.67%), and the fluctuations of the circulating current can be suppressed. Furthermore, it has better robustness and three-phase variable load fault tolerance.