Impedance modeling and analysis of modular multilevel converters

This paper presents impedance modeling of modular multilevel converters (MMC) for stability and resonance analysis of HVDC transmission, renewable energy, STATCOM and other systems that increasingly rely on MMC as the hardware building block. The basis of the modeling method is harmonic linearization, which has been applied to other types of converters and converter systems, but a new formulation is presented to allow the inclusion of harmonic effects. This generalization, called multi-harmonic linearization, is necessary for MMC because of the significant second harmonic in the arm currents, module capacitor voltages, and control signals. To accommodate multiple harmonics in the linearization process, a matrix formulation is also introduced and used to model both the converter and its control. The developed impedance models are validated in the frequency-domain by point-by-point simulation of detailed converter circuit models, and used to characterize MMC impedance under different conditions.