Power flow studies in traditional power systems aim to uncover the stationary relationship between voltage amplitude and phase and active and reactive powers; they are important for both stationary and dynamic power system analysis. With the increasing penetration of large-scale power electronics devices including renewable generations interfaced with converters, the power systems become gradually power-electronics-dominant and correspondingly their dynamical behavior changes substantially. Due to the fast dynamics of converters, such as AC current controller, the quasi-stationary state approximation, which has been widely used in power systems, is no longer appropriate and should be reexamined. In this paper, for a better description of network characteristics, we develop a novel concept of dynamic power flow and uncover an explicit dynamic relation between the instantaneous powers and the voltage vectors. This mathematical relation has been well verified by simulations on transient analysis of a small power-electronics-based power system, and a small-signal frequency-domain stability analysis of a voltage source converter connected to an infinitely strong bus. These results demonstrate the applicability of the proposed method and shed an improved light on our understanding of power-electronics-dominant power systems, whose dynamical nature remains obscure.