When a wind farm crosses a low-voltage fault, due to unreasonable system protection design, the fault cannot be quickly removed, there is a problem with reactive power compensation control strategy or the fan does not have high voltage ride-through capability, resulting in a sudden rise after a low voltage ride through fault. In this working condition, this paper considers whether the crowbar circuit will affect the double-fed wind turbine under the premise of taking into account the recovery stage of the voltage sag. Therefore, this paper first establishes a transient mathematical model that considers the voltage dip recovery phase and the crowbar circuit, and derives the stator and rotor current expressions for both the crowbar circuit and the input crowbar circuit. And then it analyzes two situations whether or not the crowbar circuit is put into have influence on the secondary voltage swell fault ride-through characteristics, and obtains the input condition of the crowbar circuit and the optimal input resistance of the crowbar resistance. Finally, simulation verification shows the rationality of derived stator and rotor currents expression, the input conditions and the optimal resistance of the crowbar and illustrates the correctness of the transient model, which can provide an accurate model for the analysis of the secondary catastrophic failure traversal characteristics.