Abstract: Aiming at the stability judgement of the low-frequency side with the connection of the wind turbines to the grid through the fractional frequency transmission system, this paper realizes the judgment of the low-frequency side stability of the system combined with the stability criterion based on the impedance matrix k-norm by using the impedance analysis. Firstly, based on the mathematical model of the modular multilevel matrix converter (M3C), the corresponding passive controller and filter circuit were designed for the typical scenario of the M3C low-frequency side-connected wind turbine, and the model of the wind turbine was simplified. Secondly, the dq-axis impedance model of the M3C low-frequency side and the wind turbine was derived, and the correctness of the impedance modeling was verified by using the frequency sweeping method. Then, a fast discrimination method based on the impedance matrix norm was designed. Finally, the stability of the low-frequency side with the connection of the wind turbines to the grid through the fractional frequency transmission system was judged in the MATLAB, and the effectiveness of this method is verified on the PSCAD.