Multi-directionally non-linear magnetic equivalence circuit calculation (MACC) of rotational magnetization intensity in transformer cores

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Abstract
This paper puts a novel methodology of ``multi-directionally non-linear magnetic equivalent-circuit calculation''(MACC) for discussion. It models transformer cores of Goss texture through local elements that are represented by non-linear magnetic resistances. From its concept, it allows for 2D or 3D distributions of induction components, considering arbitrary degrees of non-linearity and anisotropy. The present work describes modelling of rotational magnetization by means of a network of elements for flux in three different directions, the rolling direction(RD), the transverse direction (TD) and the diagonal direction (DD) in overlaps. Other directions are assumed to be ``hard'', thus being neglected. A 3-phase core package is modelled by 41 elements, assuming two main flux paths. Three sets of nonlinear permeability functions are attributed to the individual elements, starting with roughly estimated induction distributions. The corresponding system of Kirchhoff equations is solved in well known ways. Step-wise approximations of the set of induction components are performed until they correspond with the set of permeability values in acceptable grades. The resulting local distribution of induction components indicates maximum values of TD-components in the T-joint region and the adjoining yoke regions corresponding to maximum rotational magnetization. In comparison with experimental findings, the results of modelling show similar tendencies. However, as a specific advantage of MACC-modelling, it allows flexible and rapid checks of consequences of changes of material parameters and geometric parameters, respectively.

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