To study very fast transients in transformers, it is required to compute the inductance matrix of windings at very high frequencies (MHz). The core acts as a flux barrier at very high frequencies, affecting the values of the self and mutual inductances of windings. In the previous work by the authors, analytical methods for computation of the inductance matrix at very high frequencies, using a 2-D planar approximation of the transformer geometry, were presented. The purpose of this paper is to present analytical methods for the same problem in cylindrical coordinates which do not suffer from the previous approximations in geometry.
A method based on the Fourier integral transform is described for the calculation of inductance outside the core window. For the region inside the core window, inductance formulas are extracted using the Fourier series analysis.
The final expressions are accurate and fast convergent. Comparisons with FEM simulations and previous 2-D planar formula prove the excellent accuracy of the proposed inductance formulas.
The value of the presented formulas accounts for considering the effect of iron core on inductances in transformer very fast transient analysis.
Eslamian, M. and Vahidi, B. (2014), "Computation of the inductance matrix of axisymmetric windings for very fast transients studies in transformers", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 6, pp. 2082-2100. https://doi.org/10.1108/COMPEL-05-2013-0168
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