| Summary: | Fractional frequency transmission is a promising technology for medium distance offshore wind power transmission. The key component in the fractional frequency transmission system (FFTS) is the modular multilevel matrix converter (M<sup>3</sup>C). It is regarded as the next generation AC/AC converter for high voltage and high power applications due to various advantages such as high-quality waveforms, scalability, and controllability. It is important to fully study its impact on the power network. The key to the understanding and impact is the development of a suitable model, which is the focus of this paper. A small signal model of the M<sup>3</sup>C taking into account the dynamics of the capacitor voltage, AC currents, and the control system is developed. Electrical quantities from both AC sides at different frequencies couple in the M<sup>3</sup>C since there is no DC link. The complicated nonlinear terms in ABC frame are isolated and transformed in DQ frame. The model is convenient to interface with the control system and external AC systems. Small signal analysis is carried out on the influence of the controller parameters and sub-module capacitance. The correctness of the proposed model is verified by comparing to a detailed electromagnetic transient model of the M<sup>3</sup>C simulated in RTDS.
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