“Wind-fire bundling” is currently one of the important forms of centralized wind power transmission. Studying the transient stability issues of wind-fire bundling systems is of great significance. This paper establishes a time-varying impedance model that covers the dynamic characteristics of doubly-fed wind turbines to consider the impact of the time-varying characteristics of voltage, current, and power after fault clearance on the first swing angle stability of such bundling systems. By applying the extended equal area criterion, an equivalent single-machine infinite bus model of the wind-fire bundling system is constructed. The analysis reveals six different effects of active power restoration on transient power angle curves of wind turbines. This paper also examines the impact of active power restoration rates on the initial swing amplitude in different scenarios, uncovering the influencing rules of first swing stability with varying active power restoration rates for different system parameters. Based on the theoretical analysis, a control strategy for improving the first swing stability of doubly-fed wind turbines through active power restoration is proposed. Finally, the correctness of the theoretical analysis is verified through simulation.