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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. [ABSTRACT FROM AUTHOR]

DC distribution power systems are vulnerable to instability because of the destabilizing effect of converter-controlled constant power loads (CPLs) and input filters. Standard stability analysis tools based on averaging linearization techniques can be used only when the switching frequency of the converter is significantly higher than the cutoff frequency of the filter. However, dc distribution systems with a reduced size filter, and consequently a high cutoff frequency, are common in transportation applications. Conventional methods fail to detect instabilities in the system because they do not take into account the switching effect. To overcome this drawback, this paper proposes a discrete-time method to analyze the stability of dc distribution systems. This model is applied here to a dc power system with a CPL. The switching effects and the nonlinearities of the system model are taken into account with a simple discretization approach. The proposed method is able to predict the dynamic properties of the system, such as slow-scale and fast-scale instabilities. An active stabilizer is also included in the system model in order to extend the stability margin of the system. Finally, these observations are validated experimentally on a laboratory test bench. [ABSTRACT FROM AUTHOR]