Accurate Steady-State Mathematical Models of Arm and Line Harmonic Characteristics for Modular Multilevel Converter

The analysis of circulating current in modular multilevel converter (MMC) has aroused extensive research interests recently. Most studies on the derivation of harmonic components of circulating current neglect the harmonics in the line currents, but the harmonics evidently distort the line currents in many MMC applications where a circulating path for the dominant third-order harmonic current exists. So far, little research has been done on the model of the harmonics in line currents of MMC and neglecting them inevitably causes large error in the previous analytical expressions of circulating current. To solve these problems, this paper proposes a novel accurate steady-state mathematical model of harmonic components existing both in arm and line currents, and presents the detailed relations between the inner and outer harmonic characteristics of MMC. Thus, the derived instantaneous voltages and currents both in arm and line from the proposed models are far more accurate than the present research. What's more, each existing higher order harmonic is precisely calculated for the first time, filling up the blank of the conventional studies, and providing a better reference for the understanding, designing, and controlling of the MMC engineering applications. The correctness and high accuracy of the proposed models are verified by simulation results in PSCAD/EMTDC.