In this paper, the modeling of distribution network with Doubly Fed Induction Generator (DFIG) is done in a different way where the resistances of the line are considered. Based on this modeling, this paper presents an analysis to investigate the critical parameters for distribution systems stability where DFIG is used as distributed generation. In order to analyze the critical parameters, the system is linearized about an operating point by using Taylor series expansion method. The critical parameters are investigated through the concept of eigenvalues and participation factors. This paper also shows the graphical output for different states by varying the line resistor. Finally, a Linear Quadratic Regulator (LQR) controller is proposed to improve the parameters disturbances in the distribution network with DFIG.