Steady-State Analysis for Modular Multilevel Converters With Considering the Modified Arm DC Reference and Average Capacitor Voltage

For modular multilevel converters (MMCs), it is generally considered that both the arm dc reference and average capacitor voltage are constant values, which are equal to $U_{\mathrm {dc}}$ /2 and $U_{\mathrm {dc}}$ /N, respectively. However, it is identified in this article that these two voltages do not have such a simple constant value relationship as claimed in most of the published studies. The research is conducted based on an enhanced MMC model, where a detailed expression describing their relationship is derived with a high precision of 0.02%. Based on the research, some newfound conclusions can be drawn. First, the average capacitor voltage is composed of the well-known major component and the minor component neglected in most of the present studies. Second, the average capacitor voltage has a downtrend with the arm dc reference increasing due to its major component; meanwhile, influenced by the minor component, their exact relationship highly depends on the practical power condition of MMCs. Third, the average capacitor voltage control is requisite for an MMC, but the conventional strategy has negative effects when the MMC provides reactive power for ac systems. Finally, the conclusions in this article were proved through simulations and experiments.