Control of modular multilevel converters based on time-scale analysis and orthogonal functions

Modular multilevel converter (MMC) is a promising multilevel topology for high-voltage applications that has been developed in recent years. The control of MMCs has been analyzed in detail in many papers, showing that the converter capacitors can be kept charged and balanced by controlling the circulating current of each leg. The set-point signal of the circulating current is probably the most difficult variable to choose. Typically, it is chosen in such a way to control the total energy and the energy unbalance of each leg. Although several theories are available, the control of the circulating current is still a complex task and cannot be fully tackled with traditional linear control techniques. In this paper a multiple time-scale analysis is proposed to determine an approximated model of the MMC that can be used to solve the control problem of the capacitor voltages. In addition, it is shown that the reference signal of the circulating current can be built by combining orthogonal functions of the measured voltages and currents. Numerical simulations are used to test the feasibility of the developed approach.