In the study of transients in a grid-forming doubly-fed induction generator (GFM-DFIG), synchronous control and outer loop control over a large time scale are usually retained for transient modeling. To be suitable for the traditional transient stability analysis methods such as the transient energy function method, it is necessary to ignore the dynamic of the integral links of the external ring during the transient change process and to further reduce to the second-order model. This will create some errors. To solve the error problem caused by ignoring integral dynamics, a second order transient model of a GFM-DFIG considering current limiting is established. The transient energy function method is used to calculate the transient limiting voltage (TSLV) and critical clear time (CCT). Then, based on the above indices, the influence of integral dynamics on the error of the second-order transient model is ignored. Finally, an error comparison is made between the simulation results of the second-order system and the full-order model, and quantitative analysis is carried out based on the CCT error to reveal the influence law of system parameters on the relative error, and the applicability range of the second-order model is summarized.