Abstract: Current research on the sub-synchronous oscillation (SSO) characteristics of grid-connected direct-drive wind farms based on matching control primarily focuses on wind farm-grid interactions, while neglecting the internal interactions within the wind farm. To address this issue, this study investigates the SSO characteristics of a direct-drive wind farm grid-connected system based on matching control, accounting for both internal and external interactions. Firstly, a small-signal model of a two-unit grid-connected system with matching-control-based permanent magnetic synchronous generators (MC-PMSG) is developed. The dominant oscillation modes of the system are analyzed using the eigenvalue method, and two distinct types of SSO modes, namely, intra-farm and farm-grid interaction modes, are identified. On this basis, the impacts of various parameters on the damping of these two types of SSO modes are investigated, and the parameter sensitivities of the damping and the stability regions across different operating conditions are analyzed. Furthermore, the effects of parameter differences and unit scale on the SSO characteristics of the system are investigated. Finally, the correctness of the theoretical analysis is validated through MATLAB/Simulink simulation.