Abstract Recently, explanations of the sub-synchronous oscillation (SSO) caused by wind farms based on direct-driven wind generators (DDWGs) have been published in the literatures, in which the controller parameters of DDWGs and the system equivalent parameters play an important role. However, more than one set of parameters can cause weakly damped sub-synchronous modes. The most vulnerable and highly possible scenario is still unknown. To find scenarios that have potential oscillation risks, this paper proposes a small disturbance model of wind farms with DDWGs connected to the grid using a state-space modeling technique. Taguchi’s orthogonal array testing is introduced to generate different scenarios. Multiple scenarios with different parameter settings that may lead to SSOs are found. A probabilistic analysis method based on the Gaussian mixture model is employed to evaluate the consistency of these scenarios with the actual accidents. Electromagnetic transient simulations are performed to verify the findings.