Survey of current research papers reveals the continued interest in application of advanced techniques for accurate estimation and control of stray losses in transformers. This paper gives an overview of research, development and application of various computational tools for stray loss analysis, based on over 50 published papers. All landmark papers are systematically classified. Practicality of application of methods by transformer designers is discussed. The report concludes with critical comments on efficacy of all approaches and directions for pursuing further research.

Stray loss evaluation in power transformers-a review

It is noted that the modelling of transformers by the finite-element method makes it necessary to consider the lamination of steels, whose thicknesses are very small compared to those of the transformers. In the present work, techniques of homogenization are used to solve Maxwell's equations in stratified media such as cores. These methods are based on the substitution of a magnetically inhomogeneous structure by a simpler homogeneous equivalent one. The proposed approach leads to a macroscopic homogenized permeability tensor expressing the global properties of a laminated anisotropic material. >

A technique of homogenization applied to the modelling of transformers

In this paper, an important discussion of transformer design and modeling is given. Anisotropy effects of the transformer laminations have been stressed in the light of the investigation of a three-phase three-limb transformer T-joint. Three simple T-joint modeling schemes accounting for the lamination anisotropy are proposed. The fundamental result is that the flux lines remain almost parallel to the rolling direction (RD), except in a small area around the T-joint. Therefore, transformer yokes and limbs have been divided into longitudinal elements according to the RD. Reluctances related to these elements are connected according to the magnetic circuit coupling and yield a new transformer circuit model. A good agreement is obtained between computed and measured transient currents. Furthermore, the new transformer model enables some localized analysis. The computed localized fluxes and loci of flux density vectors near to the T-joint exhibit a satisfactory agreement with many results based on FEM or experimental investigations.

Anisotropy in three-phase transformer circuit model

Theoretical predictions were made for the dynamic performance of a tangential flux magnetic thrust bearing. A prototype bearing was built with the stators and rotors made from tape wound strip. The performance of this bearing was measured and compared to the theoretical predictions and also to the performance of a radial flux thrust bearing. Tangential flux bearings are intrinsically amenable to construction from tape wound cores. Tape wound cores come in high saturation alloys like supermenduer which can give the bearing a high force to size ratio. The thin tape laminates give the bearing a broad frequency bandwidth. By comparison the paper shows that it is difficult to make a laminated rotor magnetically efficient for radial flux bearings. A test rig is described that was built to measure the performance of the tangential flux bearing. A power amplifier with current feedback provides DC and harmonic currents to the coils. A load cell was built into the test rig to measure the axial thrust, an inductive/Hall sensor was included to measure the coil current, and a Hall probe was used to measure the gap flux.

Comparison of the dynamic response of radial and tangential magnetic flux thrust bearings

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.

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

The prediction of fields and stray loss levels in laminated magnetic steel parts poses a difficult problem for the field analyst. A method is proposed by which the effect of the laminations on the flux paths is simulated by a solid block with anisotropic magnetic permeability. This method is validated by a comparison of calculated flux patterns for the two cases and is applied to the prediction of stray loss in the laminated clamping rings of a power transformer by a high-order, anisotropic, finite element field computation. An example is cited to show that the reaction field due to the eddy currents in the laminated ring need not be calculated.

M. L. Barton

Papers

Loss Calculation in Laminated Steel Utilizing Antisotropic Magnetic Permeability