Abstract
Small-signal models (SSM) of modular multilevel converter (MMC) based HVDC grid under unbalanced grid conditions in recent literatures do not consider interactions between MMC and dc network. Therefore, it is necessary to correctly model the double-fundamental-frequency zero-sequence circulating currents (DFF-ZSCC) existing under unbalanced grid conditions, although they can be suppressed to avoid penetrating into dc side. In view of that, a general and modular small-signal modeling method of MMC-HVDC grid under unbalanced grid condition is developed. Firstly, a general d-q transformation process for multi-sequence and multi-frequency components is introduced to build the state-space model of MMC electric part in d-q frame. Secondly, the SSM of dc network, which is divided into dc- and double-fundamental-frequency parts, is developed based on the existing frequency-dependent-cascaded-pi (FDC-PI) cable model. Then, to interface MMC stations with dc network under unbalanced grid conditions, a general method to synchronize the variables of double fundamental frequency at dc side of each MMC station is introduced to compose the SSM of the entire HVDC grid from SSMs of each MMC and dc network. Finally, taking a three-terminal MMC-HVDC grid as an example, two SSMs of the MMC-HVDC grid with FDC-PI cable model and single-PI cable model are developed in Matlab, respectively. The small-signal dynamics and stability of both SSMs of the grid under unbalanced grid conditions are compared to validate the accuracy and stability of the proposed SSM of the whole HVDC grid. The simulation results validate the correctness and effectiveness of the proposed modular modeling method.
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