The increase of power exchanges through long lines makes power systems exhibiting predominant nonlinear inter-area or local oscillations, for which the conventional linear analysis fails to offer an accurate picture. Existing 2nd Order and 3rd Order Normal Form methods make possible to do analytical investigations of the nonlinear interactions by including higherorder terms. However, those methods can only study the power system dynamics under free oscillations, usually used to study the effect of disturbances apply to the state variables, e.g the post-fault cases. When the system is subject to excitation, as variable power references or variable loads, there is no available Normal Form method in the literature making possible to study the higher-order oscillations. In this paper, for the first time to the author's knowledge, a methodology based on the Normal Form theory is proposed to give an analytical description of power system nonlinear dynamic response of excited power systems. The proposed method makes possible to simplify the initial problem by decomposing the complex power system dynamics into a set of simpler normal dynamics. The proposed analytical normal dynamics are validated using time-domain simulations and open the way to new analyzing tools for power grids.