Fast Hybrid Approach for Calculation of Losses in Outer Packages of Transformer Core Due to Perpendicular Stray Flux

Stray flux in a transformer enters the outer packages of a core perpendicularly and induces significant eddy currents that cause ohmic losses. Local thermal conditions near the core are affected by these losses that are dissipated as heat and can cause local overheating in the oil near the outer packages. Stray losses in the outer packages should be considered during the power transformer design process, and it is, therefore, important to model them properly. This type of loss can be solved using 3-D FEM; however, that approach is time-consuming, which makes it impractical for the loss calculation in real time. Another approach is 2-D modeling, which is faster, but it is limited to axisymmetric and planar geometries only. Due to its complex geometry, a transformer cannot be modeled using a single 2-D model. Instead, each quantity of interest, such as a magnetic field or eddy currents, can be obtained from a suitable model. These models include certain simplifications, which should not affect the accuracy of the results. In this article, a hybrid approach that utilizes various 2-D models for the calculation of stray losses in the outer packages is proposed. The advantage of the proposed methodology is in obtaining the same level of accuracy while considerably reducing the calculation time when comparing to the 3-D FEM approach. The estimation of the temperature rise of the outer packages, based on the calculated losses, will be a part of further research.