Abstract: Recently, sub-synchronous oscillation（SSO） is observed in many direct drive permanent magnet synchronous generator（D-PMSG） based wind farms integrated in a weak AC grid in the northwest of China. To investigate the mechanism and characteristics of this emerging issue, firstly, the positive and negative sequence impedance model of a typical D-PMSG based on the harmonic linearization theory was established in this paper. After that, the impedance of the D-PMSG was measured by the method of hardware control in the loop, and the Nyquist stability criterion was used to analyze the stability of the D-PMSG connected to a weak AC grid. In addition, a kind of optimized design method for phase-locked loop control parameters was provided to suppress the sub-synchronous oscillation. Finally, a detailed electromagnetic transient model of a wind farm with 110 units of 1.5 MW D-PMSGs was built on the RT-lab real-time simulation platform. The results of simulation verified the correctness of the theoretical analysis.