Abstract: Due to the strong nonlinearity and coupling of the grid-connected converter, its transient characteristics in the electromagnetic transient processes are usually complicated and difficult to be identified. In this paper, the dominant transient unstable variables and characteristics are analyzed in a single-converter infinite-bus system. First, the dominant unstable variable of the grid-connected converter is identified as the phase-locked loop angle θ_pll, based on the equivalent time constant analysis. Then, the model is compared with the fifth-order model of the synchronous generator (SG), and the transient characteristics of the fast and slow time scale separation of the grid-connected converter are revealed. In addition, it is found that there exists multi-swing instability during the fault process. It is revealed that this phenomenon is caused by the negative damping which is induced by the terminal voltage control loop. Hence, it is fundamentally different with the multi-swing instability in the multi-SG system. Finally, the effectiveness of the theoretical analysis is verified by Matlab/Simulink simulation.