Abstract: As an interface between new energy power generator units and a power grid, the grid-side converter plays an important role in maintaining the safe and stable operation of power system. Based on the grid-side converter of direct-drive wind turbines, a math model of grid-side converter and its control including the phase-locked loop (PLL) and voltage feed-forward control is established in the paper using the small disturbance mathematic modelling method, and the dynamic impedance analytical expression under dq axis is derived. It is found that the impedance has the features of negative resistance (negative real part) in the subsynchronous frequency band and is unstable in subsynchronous frequency band when connected with weak power grid. The key control parameters that influence the system stabilities are analyzed. The results indicate that the subsynchronous oscillation risks can be reduced to some extent through enhancing the power grid strength, optimizing the PLL control parameters and increasing the voltage feed-forward filtering frequency. Finally, the above analytical results were verified by electromagnetic transient simulation.