Modeling of Nonlinear Characteristics of Transformers in Harmonic Studies Including Hysteresis

A. Damnjanovic and G.M.J. Parsley (South Africa)


Transformers, Nonlinear characteristic, power system studies, Harmonic Balance, Consuming Function


Power system elements such as transformers and reactors contain iron-cored coils, which have nonlinear voltage current characteristics. To do a study and an analysis of power systems, such as harmonic power flow, ferroresonance, inrush current, and filter design require appropriate modeling of these devices. The nonlinearity of these devices cannot be appropriately taken into account unless a hysteresis is included in the analysis. This paper attempts to create a model for the nonlinear characteristics of transformers that can be used in the steady state analysis of power systems. The model is based on the representation of the hysteresis curve as an orthogonal, orthonormal, polynomial sum of two sets. Fitting a polynomial of the n-th and r-th degree to represent the normalized excitation curve and hysteresis losses called a "consuming function", solves the identification problem. Harmonics of the hysteresis and the excitation current are obtained with the Harmonic Balance Method. This modeling approach can also be applied in the study of the phase-shifted flux harmonics, magnetostriction and their effects on magnetic materials.

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