With the increasing proportion of wind power in the power grid, the stability of wind power grid connection under the weak grid has attracted more and more attention. In view of the stability of wind power grid connection, the existing research usually decouples the generator side and grid side to simplify and analyze the stability of both sides, but from the perspective of time scale, there is coupling between the generator-side and grid -side dynamics, which is ignored in the existing modeling. In this paper, a unified model of converter control for machine side and grid side is established in view of the stability of grid-connected wind turbines. The stability analysis method considering machine side and grid side converter control is given. Compared with the traditional impedance analysis method, the analysis method adopted in this paper is more accurate. Finally, Simulink simulation is used to verify the analysis results.