一种用于模块化多电平矩阵变换器的新型谐波状态空间建模方法及耦合分析

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 pro-posed 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.