Traditional phasor representation of sinusoidal signals, the standard analytical tool for power system stability analysis, is limited by the quasistationary assumption on the speeds of the phasor states. This paper provides a rigorous formulation of a time-varying phasor representation for the balanced three-phase large power system with no restrictions on the speeds. Power balance equations become a set of differential equations in the phasor dynamic states and singularly perturbed behavior of the resulting dynamics is explored.