Harmonic domain modeling of transformer nonlinear characteristic with piece-wise approximation

Power system devices such as transformers, generators, and reactors have nonlinear characteristics because of the magnetic material used for their construction. Hence, understanding how the harmonics affect the power system requires explorations of the harmonic characteristics of each nonlinear component including the transformers. Thus, particular models need to be developed for the power system and machines design, and harmonic power flow analysis. Regarding the modeling of transformer nonlinearity, including hysteresis, there are many numerical methods that have been applied and many models have been developed. The nonlinearity of these devices cannot be correctly represented unless the hysteresis is included. Although the developed model can be used for other devices such as reactors, generators and motors, we are primarily focused on modeling of the transformers. There are many models developed for nonlinear transformer characteristics from various aspects, but none address the influences of the actual mechanical stresses on the magnetic materials. Mechanical stress modifies the nonlinear characteristics of the transformer and consequentially influences the operation of the transformers generating higher level of harmonics, increasing both losses and transformer noise. Our goal was to develop an accurate model and expressive formulas that can be used for practical engineering applications in transformer design and power system analysis based on minimal measured data requirements. The excitation characteristics of the transformer are presented with two piecewise approximated functions. The Harmonic Balance Method - Describing Function is used to obtain the harmonic magnitude and phase angles of the excitation current. The proposed model has been verified with experimentally obtained results for the transformer excitation current.