Multiscale Computations of Parameters of Power Transformer Windings at High Frequencies. Part I: Small-Scale Level

We propose a hierarchical multiscale approach to modeling of high-frequency phenomena in power transformers. The method is based on considering high-frequency effects on two spatial levels. Part I of the paper focuses on a small-scale level where eddy-current as well as geometrical and proximity effects in conductors of transformer windings are examined. It develops a computer model that accounts for anisotropic frequency-dependent diamagnetic properties of transformer windings, which are represented as composite media with periodic structure. Calculations of effective characteristics of the laminated transformer core take into account anisotropic magnetic properties of steel sheets. The frequency-dependent parameters of transformer elements thus obtained will be further used in Part II for computing effective inductances and resistances of windings and integral losses on a large-scale level, i.e., for the whole transformer.