Abstract: The oscillation analysis of the grid-connected converter system（GCS） can be transformed into a stability analysis of a single-input single-output（SISO） system via both sequence-impedance model and generalized-impedance model. Then the oscillation mechanism of GCS can be explained from the perspective of circuit resonance. However, the existing research lacks applicability evaluation for the stability criteria. The mathematical principle of the SISO system obtained from the two impedance models was first analyzed. Then, the process was uniformly illustrated based on the primal-dual complex circuit. Secondly, it is found that sequence-impedance-based stability criterion（SISC） is inaccurate when neglecting the frequency coupling（FC）. Although the FC in SISC is manageable with Schur complement method, the corresponding transfer function may have unstable poles, resulting in irrationality to explain the oscillation mechanism with a circuit. The aforementioned problem can be generally avoided by using generalized-impedance-based stability criterion（GISC）. Furthermore, to evaluate the applicability of the impedance-based analysis methods, the index, condition number, was proposed from the perspective of considering the uncertainty. This study shows that GISC takes more advantages for intermediate frequency oscillation problems, such as sub-super-synchronous oscillations, in which the dynamic of the phase-locked loop（PLL） plays a significant role. Finally, the rationality of the proposed method and conclusion were validated by simulation.