Computation of Self-impedance and Mutual Impedance of Transformer Winding Considering the Frequency-dependent Losses of the Iron Core

Abstract

To study electromagnetic transients in transformers, it is necessary to compute the impedance matrix of windings considering the frequency-dependent behavior of the iron core. In this article, a new method based on the application of the surface impedance boundary condition is presented by which the impedances of windings at high frequencies can be computed accurately inside and outside the core window. The idea of using the surface impedance boundary condition stems from the fact that the depth of penetration of leakage flux into the iron core decreases considerably at enough high frequencies (above some kilohertz), motivating the use of this condition for core walls to take the iron core's eddy current losses into account. As a result of this representation, the problem of impedance calculation inside the core window is converted to a Sturm–Liouville eigenvalue problem. The accuracy of the proposed method has been verified by finite-element method simulations. The results of this study make a noteworthy contribution to the calculation of transformer impedance matrix inside the core window through finding a way for considering the effects of eddy currents in the yokes on impedance values, a subject thus far not appropriately addressed in previous studies.