Analysis of the relationship between switching frequency and sub-module capacitor unbalanced voltage for a modular multilevel converter

With voltage-balancing control, the voltage difference among sub-module (SM) capacitors in a modular multilevel converter can be reduced. However, this comes at the cost of increased device switching frequency. In this paper, the relationship between the switching frequency and SM capacitor unbalanced voltage is investigated. As the relationship depends on the voltage-balancing control schemes, a popular scheme using a modified sorting method is considered. The switching frequency is found to be inversely proportional to the SM capacitor unbalanced voltage due to the voltage-balancing control and an analytical relationship is derived for the first time. As the SM capacitors voltage-unbalance increases the voltage fluctuation for each SM, the impact of switching frequency on the SM capacitance design is further investigated. The developed analytical relationship can thus be used for the SM capacitance design. Finally, the theoretical analysis is verified by simulation.