Abstract: In order to achieve the goal of "double-carbon" and promote energy transformation, achieving safe and reliable transmission of large-scale renewable energy such as offshore wind power has become a key research direction. The flexible low-frequency transmission system improves transmission capacity and saves economic costs by reducing transmission frequency, and gradually becomes a beneficial supplement to the traditional power frequency transmission and DC transmission. However, the stability of flexible low frequency transmission system, especially the stability of large signal, is still a difficult problem in engineering practice. In this paper, the Lyapunov direct method is used to analyze the large signal stability of flexible low-frequency transmission system based on modular multilevel matrix converter (M3C). Firstly, for the high order of the nonlinear state equation of the system makes it difficult to directly construct the energy function through experience or Jacobian matrix method of linear system, a fuzzy model is established by a sector nonlinear method, the system energy function is constructed concisely and quickly, and the large signal domain of attraction (LS-DOA) is calculated. Secondly, the mapping method of multi-dimensional space attraction region is introduced to reveal the influence of main circuit and control system parameters on the large signal stability of system more intuitively from the perspective of frequency difference. Then, combined with the convex optimization theory of linear matrix inequality (LMI), the relevant mechanism of large signal instability of the system is analyzed and an efficient stabilization strategy is given. Finally, the system model is established through MATLAB/Simulink, and the simulation verification of the theoretical analysis is realized, which is an important reference for the engineering practice of the flexible low-frequency transmission system.