Harmonic State-Space Based Small-Signal Impedance Modeling of a Modular Multilevel Converter With Consideration of Internal Harmonic Dynamics

The small-signal impedance modeling of a modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based power electronic systems. The MMC is a power converter with a multifrequency response due to its significant steady-state harmonic components in the arm currents and capacitor voltages. These internal harmonic dynamics may have great influence on the terminal characteristics of the MMC, which, therefore, are essential to be considered in the MMC impedance modeling. In this paper, the harmonic state-space (HSS) modeling approach is first introduced to characterize the multiharmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC are then developed based on the proposed HSS model of the MMC, which are able to include all the internal harmonics within the MMC, leading to accurate impedance models. Besides, different control schemes for the MMC, such as open-loop control, ac voltage closed-loop control, and circulating current closed-loop control, have also been considered during the modeling process, which further reveals the impact of the MMC internal dynamics and control dynamics on the MMC impedance. Furthermore, an impedance-based stability analysis of the MMC-high-voltage direct current connected wind farm has been carried out to show how the HSS-based MMC impedance model can be used in practical system analysis. Finally, the proposed impedance models are validated by both simulation and experimental measurements.