Two novel methods, digital calculation based on Callahan algorithm and dynamic simulation based on MATLAB/SIMULINK software, are proposed in this paper to study the electromagnetic transient process caused by asynchronous energization of electric power transformer while taking non-linearity into consideration. The effectiveness and accuracy of the results are verified by each other. Then regularity of the inrush current generation is found and harmonics analysis by Fourier transform is done to provide relay protection criterion. Furthermore, different conditions influencing inrush current such as the saturation characteristics, residual flux and switching on time are investigated. Finally, measures to eliminate the inrush current are suggested to avoid similar electrical breakdown accident. This paper is of great value for the studies on the dynamic process within the power system, the precise design and smooth operation of high voltage apparatus, and the proper selection for operation values of relay protection equipment for the electrical facilities