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Dynamic Impact of Zero-Sequence Circulating Current on Modular Multilevel Converters: Complex-Valued AC Impedance Modeling and Analysis

The stability impacts of the internal control dynamics of the modular multilevel converters (MMCs) have been discussed recently. Yet, the impact of zero-sequence circulating-current (ZSCC) dynamics on the ac-side dynamics of the MMCs is hitherto unaddressed. This article develops the ac impedance model for the grid-connected MMCs by means of complex vectors and harmonic transfer-function matrices, which allows separately characterizing the dynamics of the ZSCC. Then, based on the complex-valued model, a single-input–single-output closed-loop equivalent impedance is derived for grid-connected MMCs, considering both the frequency-coupling dynamics of the MMCs and the interactions with the grid impedance, which enables a design-oriented analysis on the stability impact of the ZSCC. It is revealed that the resonant peaks in the ac impedance of the MMC are yielded due to the absence of the ZSCC control, which tends to destabilize the system in weak grids. A systematic parameter-tuning method of the ZSCC control loop is developed to guarantee the system stability. Case studies in time-domain simulations corroborate the theoretical analysis.