During non-severe fault conditions, crowbar protection is not activated and the rotor windings of a doubly-fed induction generator (DFIG) are excited by the AC/DC/AC converter. Meanwhile, under asymmetrical fault conditions, the electrical variables oscillate at twice the grid frequency in synchronous dq frame. In the engineering practice, notch filters are usually used to extract the positive and negative sequence components. In these cases, the dynamic response of a rotor-side converter (RSC) and the notch filters have a large influence on the fault current characteristics of the DFIG. In this paper, the influence of the notch filters on the proportional integral (PI) parameters is discussed and the simplified calculation models of the rotor current are established. Then, the dynamic performance of the stator flux linkage under asymmetrical fault conditions is also analyzed. Based on this, the fault characteristics of the stator current under asymmetrical fault conditions are studied and the corresponding analytical expressions of the stator fault current are obtained. Finally, digital simulation results validate the analytical results. The research results are helpful to meet the requirements of a practical short-circuit calculation and the construction of a relaying protection system for the power grid with penetration of DFIGs.