A harmonic model for the nonlinearities of single-phase transformer with describing functions

In a transformer, the harmonic model is essential for the filter design and analysis of harmonic power flow. Among all of the harmonic analyses of nonlinear devices, the core nonlinearity caused by the transformer hysteresis has received the most interest. Although many harmonic models have been proposed to interpret the nonlinearity of the transformer core, most of them require complex calculations. In this study, we derive the mathematical formulas of the exciting current for a single-phase transformer by the describing function methods. The mathematical expression allows us to obtain the Fourier series for the exciting current; and, then, it provides the various order harmonic magnitudes and phase angles of the exciting current. This work also presents a mathematical model characterized by simple calculation and with high precision for the harmonics of exciting current. The transformer is under no load condition. Actual measuring verifies the effectiveness of the proposed model.