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The transient responses and stability followed by grid faults of the modern power systems experience diverse changes and have created concerns, especially for those dominated by doubly fed induction generator (DFIG) based wind turbines (WTs), since the transient characteristics of the DFIG-based WT are totally different from those of a synchronous generator (SG). To physically understand the transient response and theoretically analyze the transient stability of DFIG-based WT, this paper proposes a magnitude/phase dynamical model with synthetical consideration on the controllers in the rotor speed control timescale (around seconds). The proposed model physically explains the relationship between the imbalanced active power as well as the output active/reactive powers themselves and the DFIG-based WT's internal voltage vector, whose form is similar to that of the SG. By comparing with the SG, the distinctive transient phase characteristics of the DFIG-based WT are illustrated. An additional phase limitation is found, exceeding which the operation point does not exist. Based on the proposed model, the transient stability of a simple DFIG-based WT-dominated system is theoretically analyzed, and a new instability phenomenon different from that in an SG-dominated system is identified. Furthermore, some key factors influencing the transient stability are discussed.