Abstract: Due to the large order of direct-drive wind farms via VSC-HVDC system, it is difficult to build the detailed model for studying the sub-synchronous oscillation（SSO）. To solve this issue, a simplified model for studying the inside-wind-farm/wind-farm-grid SSO was proposed based on the matrix’ similarity transformation theory. Based on the principle that the similar matrices have the identical eigenvalues, the SSO analysis of multi-machine via VSC-HVDC system was conducted based on two kinds of single-machine systems, and the dynamic mathematical models and physical simplified models of two kinds of single-machine systems were presented after order reduction. The first kind of single-machine system can reflect the inside-wind-farm SSO modes, and the second kind of single-machine system can reflect the wind-farm-grid SSO modes. Finally, the validity of the proposed simplified model was verified through project planning stage, project commissioning stage and practical wind farms cases. The results show that the proposed simplified model has a strict theoretical basis. Although the system order is reduced significantly, the proposed simplified model can still reflect inside-wind-farm/wind-farm-grid SSO modes, which makes up for the deficiency that the output multiplication based equivalent model（OMM） cannot reflect the inside-wind-farm SSO modes. Meanwhile, it is verified theoretically that the OMM is a special case of the second kind of single-machine system and can reflect wind-farm-grid SSO modes.