The brushless doubly-fed induction generator (BDFIG) realizes the induction excitation because of the special structure design such as double stators, and eliminates the brushes and slip rings, and thus has obvious advantages in the grid-connected power generation application in harsh environment. However, the special designed double-stator structure also leads to higher-order and multi-parameter machine model, and further leads to the complicated mathematical model of the grid-connected system. The complexity of the grid-connected system model often check the symbolic operation upper limit of MATLAB, MathCAD and other softwares. Therefore, most of the existing brushless doubly-fed grid-connected studies simplify the mathematical model by ignoring some or all of the resistance parameters, but the impact of the simplified method on the accuracy of the modeling is not assessed, and the applicable conditions are not clear. In view of this, aiming at the port admittance model reflecting grid-connected stability, this paper fully considers the difficulty of grid-connected modeling caused by the high-order and multi-parameter characteristics of BDFIG, and systematically carries out the simplification and accuracy verification from open-loop modeling to closed-loop modeling. Finally, the simplified admittance model ensuring accuracy is obtained. Based on it, the control parameters are designed and applied to the simulation system and experimental platform. The waveforms under different load and grid strength conditions prove the accuracy of the proposed simplified admittance model and the effectiveness of the designed parameters.