Numerical Prediction of Rhombic Rotational Magnetization Patterns in a Transformer Core Package

Evaluations of local induction time patterns
$ {B}$
(
$ {t}$
) in transformer cores show high relevance for both losses and magnetostriction. This paper presents numerical calculations for a three-phase core package stacked from grain-oriented SiFe for
$ {B} _{\mathrm { {NOM}}} = 1.7$
T. Modeling is based on a novel multi-directionally non-linear magnetic equivalence circuit calculation (MACC). It considers non-linear permeability functions in rolling direction, transverse direction (TD), and diagonal direction in overlaps. MACC yields instantaneous local values
$ {B}$
, and the corresponding reluctances and permeabilities as a basis for conclusions. Snapshots of induction distributions for important time instants of zero or maximum limb induction reveal dominant roles of anisotropy and multi-directional non-linearity. Small changes of permeability in the TD yield distinct changes of rotational magnetization (RM) and circulating magnetization. Local dynamic magnetization patterns
$ {B}$
(
$ {t}$
) are calculated considering 180 instants of time, for sufficient resolution of dynamics. The results confirm the formation of RM patterns of oblique rhombic (or lozenge) shape, in contrast to elliptic patterns as frequently assumed. They also confirm that the induction vector
$ {B}$
rotates with maximum angular velocity when passing through the TD.