In this paper, a novel modulation function-based method including analyses of the\nmodulation index and phase is proposed for operation of modular multilevel converters (MMCs) in\nhigh voltage direct current (HVDC) transmission systems. The proposed modulation function-based\ncontrol technique is developed based on thorough and precise analyses of all MMC voltages and\ncurrents in the a-b-c reference frame in which the alternating current (AC)-side voltage is the first\ntarget to be obtained. Using the AC-side voltage, the combination of the MMC upper and lower\narm voltages is achieved as the main structure of the proposed modulation function. The main\ncontribution of this paper is to obtain two very simple new modulation functions to control MMC\nperformance in different operating conditions. The features of the modulation function-based control\ntechnique are as follows: (1) this control technique is very simple and can be easily achieved in a-b-c\nreference frame without the need of using Park transformation; and (2) in addition, the inherent\nproperties of the MMC model are considered in the proposed control technique. Considering these\nproperties leads to constructing a control technique that is robust against MMC parameters changes\nand also is a very good tracking method for the components of MMC input currents. These features\nlead to improving the operation of MMC significantly, which can act as a rectifier in the HVDC\nstructure. The simulation studies are conducted through MATLAB/SIMULINK software, and the\nresults obtained verify the effectiveness of the proposed modulation function-based control technique
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