Power electronic (PE)-dominated power systems with energy storage and control loops of varying timescales exhibit dynamic processes across different timescales. However, the cross-timescale dynamic between different timescales have not received sufficient attention in previous analyses. This paper focuses on a two-machine two-area system composed of doubly-fed induction generator (DFIG)-based wind turbines (WTs) and utilizes modal analysis along with time-domain numerical simulation to elucidate the cross-timescale influence. Firstly, the cross-timescale impacts of current control timescale on rotor speed control timescale, DC-voltage control timescale on rotor speed control timescale, and AC-current control timescale on DC-voltage control timescale are explained using modal analysis. Finally, the main findings of modal analysis were validated using simulation.