With the increasing penetration of power electronics, grid-forming modular multilevel converters (MMCs) have attracted great attention in the upcoming MMC-based high-voltage direct current transmission (HVDC) projects. Power synchronization control (PSC) and direct power control (DPC) are two typical grid-forming control schemes for MMCs. This paper sets out to investigate the impedance-based stability characteristics of PSC-MMC and DPC-MMC. Utilizing the harmonic state space (HSS), equivalent impedance models of PSC-MMC and DPC-MMC are developed with the consideration of complete controllers and MMC internal dynamic characteristics. Impedance shaping effects of the major controllers are further analyzed to identify the frequency bands where the MMCs have negative resistive impedance characteristics. Finally, potential instability phenomena of the interconnected system are shown through the case studies, and the virtual impedance method is introduced as the stabilization control scheme. The electromagnetic transient simulation results based on PSCAD/EMTDC verify the accuracy of the impedance models and the effectivity of the stabilization control scheme.

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