Mathematical description of power is deduced under the condition of distorted signals according to a simplified model for the electrical network. A rational measuring method of electric energy for distorted signals is proposed on the basis of an analysis of the power flow. The wavelet sub-band measuring method is employed for measuring the electric energy in the condition of unsteady distorted signals. The accurate measurement of the power consumed by the distorted signals is realized in theory while the correctness of this method is verified by the simulation results. The method will enable the electric power measurement theory to get closer to perfection by providing technical guidance for the development of a wattmeter with a broader scope and more rational measurement.