Optimal Selection of Angular Input Data for the ODF-Based Model Applied to B–H Magnetization Curves of Grain-Oriented Electrical Steels

Grain-oriented electrical steels (GOES) are widely used in transformers to increase energy efficiency while reducing the volume and weight of such transformers. These GOES are characterized by their strong anisotropy, which leads to different magnetic properties (behavior law and iron losses) depending on the strength and the direction of the applied magnetic field to the rolling direction (RD). To describe the anisotropy of the GOES behavior law, the orientation distribution function (ODF)-based approach shows interesting features regarding ease of identification and implementation. However, a significant oscillation issue in this model at low magnetic field exists. It is recently reported that a high-order ODF-based method can improve the accuracy of the original model. But the high-order ODF-based model implies an important number of experimental data according to different directions of the applied field to RD (different magnetization angles) to build a model with sufficient accuracy. In addition, the accuracy also depends on how the input magnetization angles are selected between the RD and the transverse direction (TD). In this article, an optimal algorithm for input magnetization angle selection is proposed for the high-order ODF-based method. To validate the proposed algorithm, 13 magnetization angles have been measured. A comparative study has been conducted based on the original and high-order ODF-based models built with the proposed selected magnetization angles. It is shown that the proposed algorithm can reduce the number of experimental data needed for the ODF-based model while providing an acceptable global error.