Further Improvements in Topological Transformer Model Covering Core Saturation

This paper is devoted to improvements of the low-frequency topological model of a three-legged stacked-core transformer. It is shown that
$B-H$
hysteresis loops employed in the transformer model and
$\Psi -i$
curves measured at transformer terminals are quite different in shape. A distinction is made between transformer modeling at moderate and deep saturations, separated conditionally by the level of technical saturation (near 2 Tesla) typical for grain-oriented steels. In the former case, in addition to the magnetic coupling of different phase windings through the core, an important part is played by air gaps at core joints. It is found that the effective gap length depends on the instantaneous magnetic flux and this dependence is proposed to implement by a variable inductance. It is shown that regardless of the core saturation depth, an important role in the transformer modeling belongs to the distribution of the zero-sequence path between all three phases. In addition to accurate replications of the special purpose saturation test, the modeled results are in a close agreement with positive- and zero sequence data measured on a 50 kVA transformer, as well as with the measured inrush currents.