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

In this part of the paper, we focus on implementation of a hierarchical multiscale approach for modeling high-frequency electromagnetic processes in power transformers. We present a large-scale 3D computer model for calculating magnetic fields in a transformer and evaluating effective parameters (inductance and resistance) of its windings and losses. The model accounts for complex, anisotropic, and frequency-dependent effective diamagnetic properties of the windings, which are obtained by solving small-scale 2D field problems as described in Part I of the paper. Results of the computations performed for a test transformer are analyzed in the frequency range 10 Hz-10 MHz. We discuss effects of windings conditions (open and short-circuited) and their location on the transformer core.

I. Introduction

Computer modeling of electromagnetic processes in power transformers has become a popular method for analyzing their performance, interpreting results of diagnostic measurements, and defining ways for design improvements. In particular, computer simulations are widely used today for studying high-frequency phenomena in power transformers during transients [1], [2], for better understanding results of frequency response analysis (FRA) measurements [3]–[5], for designing transformers for switched-mode power supplies [6], etc. This method is especially useful when the quantities of interest cannot be measured directly. Such situations appear, for example, when evaluating inductances of transformer windings at their first resonance frequencies, which are necessary for interpretation of FRA data.