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Grain-oriented electrical steels (GOES) are extensively utilized in power transformers to enhance energy efficiency and reduce their size and weight. GOES are characterized by their strong magnetic anisotropy, leading to distinct magnetic characteristics (behavior law and iron losses) according to the direction and the intensity of the applied field with respect to the rolling direction (RD). The Orientation Distribution Function (ODF) based approach is a convenient method for describing the anisotropy of the GOES behavior law owing to its ease of identification and implementation. However, it exhibits a significant oscillation issue at low magnetic fields. To address this issue, a high-order ODF-based method has been proposed in the literature. In this article, the ODF-based model, initially stress-free, is extended to include the effects of mechanical tensile stress on the first magnetization curves of a conventional GOES. An ODF-based model considering both magnetic anisotropy and mechanical tensile stress is then proposed. The results are discussed and compared with experimental data.

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 exits. 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 the 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.