Novel Analytical Solution to Fundamental Ferroresonance—Part I: Power Frequency Excitation Characteristic

Abstract

This paper has highlighted a major problem with the traditional excitation characteristic (TEC) of nonlinear inductors, in that the TEC contains harmonic voltages and/or currents, and has been used the way as if it were made up of pure fundamental voltage and current. In comparison to the TEC, a new concept, namely the power frequency excitation characteristic (PEC), which contains no harmonics, has been put forward. Two methods have been presented in obtaining the PEC. The first method is based on Electromagnetic Transients Program simulation, resulting in discrete voltage and current pairs. This method essentially acts as a reference to validate the second one. The second method employs Fourier and Maclaurin series approximation techniques, and brings forth a simple yet effective analytical expression. The expression is proven to have satisfactory precision in the saturated region of the PEC, especially in the extremely saturated region.