The fractional frequency transmission system is an emerging technology for long-distance wind power integration

and the modular multilevel matrix converter (M

3

C) is the keen equipment. Since the M

3

C 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 M

3

C. 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 M

3

C considering the close-loop control is establis

hed

based on which a panoramic harmonic coupling relationship between the system- and the low-frequency side is concluded. Finally

the M

3

C model and harmonic coupling relationship are validated by simulation tests conducted in MATLAB/Simulink environment.