  The small-signal impedance modeling of modular multilevel converter (MMC) is
the key for analyzing resonance and stability of MMC-based ac power electronics
systems. MMC is a converter system with a typical multi-frequency response due
to its significant steady-state harmonic components in the arm currents,
capacitor voltages, and control signals. Therefore, traditional small-signal
modeling methods for 2-level voltage-source converters (VSCs) cannot be
directly applied to the MMC. In this paper, the harmonic state-space (HSS)
modeling approach is introduced to characterize the harmonic coupling behavior
of the MMC. On this basis, the small-signal impedance models of the MMC are
developed according to the harmonic linearization principle, which can include
all the steady-state harmonic effects of the state variables, leading to the
accurate impedance models. Furthermore, in order to reveal the impact of the
internal dynamics and closed-loop control on the small-signal impedance of the
MMC, three cases are considered in this paper, i.e., open-loop control, ac
voltage closed-loop control, and circulating current closed-loop control.
Finally, the analytical impedance models are verified by both simulation and
experimental results.
