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This paper establishes a small-signal impedance model of the doubly fed induction generator (DFIG) system under weak grid faults taking the dynamic of controller and impedance controller into account. Based on the impedance model, the instability mechanism of the DFIG system during LVRT is analyzed using the generalized Nyquist criterion (GNC). The analysis result shows that the small-signal instability of the DFIG system is due to the DFIG-based wind turbines (WTs) in account of the control showing the negative damping characteristics during grid fault. The small-signal stability of the DFIG system can be improved by changing the bandwidth of the phase-locked loop (PLL). The Simulation results verify the correctness of the analysis.

In} this paper, the small signal state space model of the DFIG system taking into account the phase-locked loop (PLL) under the weak grid fault is established. Based on the small signal model, the dynamic behavior of the DFIG-based wind turbines during LVRT is investigated. Moreover, the impacts of voltage dips degree, operating conditions, bandwidth of the PLL and control parameters of the RSC etc. on the dynamic behavior of the DFIG-based wind turbines under weak grid symmetrical faults are revealed in detail. Finally, the simulation for the DFIG-based wind turbine system is carried out using Matlab/Simulink, and the simulation results are presented to verify the correctness of the theoretical analysis.