Calculation of spatial loss distribution in stacked power and distribution transformer cores

This paper describes an analytical solution to use a generic 2D finite difference method to accurately calculate the Quasi 3D spatial distribution, components, and total core losses in transformer cores. The solution takes into account 1) Magnetic anisotropy and nonlinearity of the cole material, 2) All components of iron losses of the core material; including losses in directions other than the rolling direction, and 3) joint model & localized losses due to the distorted flux distribution in the joint regions (due to core gaps) across the core-stack. With above attributes considered in the analysis, one is able to use the results to 1) calculate very accurately the total core losses of a transformer at the design stage every time; for all care materials, at all operating inductions, for all core geometries, and for both 50 Hz and 60 Hz, 2) Understand the contribution of cross losses, harmonics, and joints to the total losses of a core, 3) Evaluate the impact of various joint attributes, such as, type of joint, number of steps, number of laminations per step, size of gaps, and lamination thickness on the total performance of the core, and 4) improve the core loss performance of transformers by optimizing core design and core material parameters. This paper presents the analysis as applied to 3-phase, 3-limb cores. Other 1-phase and 3-phase core geometries will be the subject of a subsequent paper. The paper also presents the results of the extensive experimental/test verification performed on a number of model cores in the lab as well as on a large number of actual commercial transformer cores with excellent agreements. The results of this analysis have been used in developing the new design practice at ABB worldwide to calculate core Losses of stacked power and distribution transformers with consistent accuracy.