Quasi-3D Calculation of Stray Losses in Outer Lamination Stack of Power Transformer Core

This paper presents a quasi-3D method for calculating stray losses in the outer lamination stacks of a power transformer core. The method uses multiple 2D FEM models in several steps to capture the 3D nature of the problem. This paper builds on a previous study that presented a quasi-3D calculation of the magnetic field on the surface of the outer stack. Here, the focus is on the magnetic field and eddy currents within the stack. The magnetic field penetration is analyzed in two distinct regions. To analyze the first region, located at the stack edges where magnetic field penetration is significant, a magnetostatic 2D FEM model with non-linear and anisotropic material properties is used. This model incorporates the concept of equivalent permeability to capture the impact of eddy currents on the field distribution. The equivalent permeability is derived from a 1D analytical model of a metallic plate subjected to a time-varying magnetic field. For the second region, near the surface of the stack where eddy currents strongly affect the field, a basic 1D analytical model is used. This model describes the field behavior using an exponentially decaying function characterized by the skin depth parameter, and its linearization is based on the results of the previous model. The magnetic field distributions serve as inputs to two additional 2D FEM models used to calculate the distribution of eddy currents. By combining the results from these models, the total stray losses in the stack are obtained. The calculation results are then validated experimentally. The experimental setup consists of an analyzed lamination stack, excitation windings, a U-shaped core, and thermal insulation. Typically, magnetically induced losses are evaluated by comparing losses in a system with and without the analyzed metallic component. However, this conventional approach cannot isolate losses in a single metallic component when other metallic components are present. The presented experimental evaluation, based on temperature measurements, overcomes this limitation. Thermal insulation is used to minimize the losses needed to reach a target temperature range and to improve temperature distribution uniformity, facilitating more accurate average temperature measurements. In all test cases, the deviation between the calculated and experimentally evaluated losses remains within the expanded uncertainty of approximately 7%, corresponding to a 95% confidence level.