Accurate mathematical steady-state models of arm and line harmonic characteristics for modular multilevel converter

The analysis of circulating current in Modular Multilevel Converter (MMC) has been greatly developed in recent years. However, most researches on the derivation of harmonic components of circulating current are based on the premise that no harmonic distortion is contained in the line current, but many MMC applications are against the premise. Hence, the harmonics in the line current inevitably cause large error in the previous analytical expressions of circulating current. Therefore, this paper proposes a more accurate mathematical steady-state model of harmonic components existed both in arm and line, and presents a more detailed relation between the inner and outer characteristics of MMC. Hence, the calculated instantaneous voltages and currents both in arm and line from the proposed models are much more accurate than existed researches, providing a great reference and improving the understanding for MMC engineering applications. The simulation results in PSCAD/EMTDC verify the correctness and high accuracy of the proposed models.