A Novel Harmonic State-space Modelling Method on the Modular Multilevel Matrix Converter and Coupling Analysis

The fractional frequency transmission system is an emerging technology for long-distance wind power integration, and the modular multilevel matrix converter (M³C) is the keen equipment. Since the M³C directly connects two ac grids with different frequencies, the external and internal harmonics have complex coupling relationships with a unique dual-fundamental-frequency spectrum, which has not been properly investigated due to a lack of an effective method. To address this issue, a novel harmonic state-space method is proposed to achieve comprehensive modelling of the harmonic dynamics of the M³C. Based on the principle of two-dimensional Fourier transform, the decomposition of the dual-fundamental-frequency harmonics is realized, and the multiplicative coupling between time-domain variables is modelled through double-layer convolution on the frequency domain. Besides, the general expression of the proposed method is provided, which highlights a modularized matrix with easy scalability to meet different truncation requirements. Then, the HSS model of M³C considering the close-loop control is established, based on which a panoramic harmonic coupling relationship between the system- and the low-frequency side is concluded. Finally, the M³C model and harmonic coupling relationship are validated by simulation tests conducted in MATLAB/Simulink environment.