The dynamics of network power response play a crucial role in system stability. However, the integration of power electronic equipment leads to amplitude and angular frequency (abbreviated as “frequency”) time-varying characteristics of the node voltage during dynamic processes. As a result, traditional calculation methods for and characteristics of the power response of the network based on phasor and impedance lose their validity. Therefore, this paper undertakes mathematical calculations to reveal the power response of a network under excitation by voltage with time-varying amplitude and frequency (TVAF), relying on the original mathematical relationships and superimposed step response. Then, the multi-timescale characteristics of both the active and reactive power of the network are explored physically. Additionally, this paper reveals a new phenomenon of storing and releasing the active and reactive power of the network. To meet practical engineering requirements, a simplified power expression is presented. Finally, the theoretical analysis is validated through time-domain simulations.