Frequency and voltage dynamics, as the focus of power systems, depend more and more on the frequency and amplitude response characteristics of renewable energy devices subjected to power imbalance. The doubly-fed induction generator (DFIG)-based wind turbine (WT) is representative of renewable energy devices and shows different characteristics from those of conventional synchronous generators (SGs). Unfortunately, the individual characteristics of WTs during system frequency and voltage dynamics are not intuitively illustrated by the existing structure-oriented models. Therefore, this paper proposes a function-oriented modeling methodology by representing inertia-controlled DFIG-based WT as an internal voltage frequency and amplitude solely stimulated by active and reactive power imbalance. The individuality of the characteristics is demonstrated by the grid voltage detection-based controls that the internal voltage depends solely on the power imbalance of WTs, just like the case of SGs. Through the infinity gain equivalence of the fast-electromagnetic loops, a simplified analytical model illustrating the electromechanical characteristics of WTs is further proposed. Based on the model, the similarities and differences between the characteristics of WTs and SGs are recognized. Simulation results are also presented for verification.