VP2-12 BH curve normalization method for semi-infinity silicon steel sheets model based on vector magnetic circuit theory
Creators: Wei Qin
Xiang Ma
Ming Cheng
Zhongze Wu
Zheng Wang
Xinkai Zhu
Publisher: name: IEEE
Year: 2025

The BH curve, also known as the magnetization curve, is a essential concept in the study of magnetic materials in the field of electromagnetism. It describes the relationship between the peak magnetic induction Bm and the peak magnetic field strength Hm of magnetic materials [1]. Due to the skin effect of magnetic flux, these magnetic circuit parameters not only vary with the B of the magnetic circuit but also change with the frequency [2]. Therefore, for the same magnetic material, the magnetic circuit parameters corresponding to different frequencies exhibit variations, resulting in BH curves that differ at different frequencies. Currently, research on the measurement and simulation methods of BH curves for magnetic materials at different frequencies is relatively limited. Obtaining BH curves at different frequencies requires sequential measurements at each frequency, which is not only time-consuming but also requires specialized high-frequency experimental equipment. Prof Cheng proposed a method to extrapolate BH curves based on the concept of magductance and experimental analysis. While this method shows some feasibility in practical applications, it lacks reliable theoretical derivation. Therefore, building upon this foundation, this paper conducts a systematic theoretical derivation. It proposes an infinite thickness model for silicon steel sheets and, based on this, a method to extrapolate and deduce BH curves. With this method, given the BH curve at a certain frequency, one can deduce BH curves at different frequencies using vector magnetic circuit theory [3]. The proposed BH curve method not only aligns with theoretical validation from literature references but also conforms to experimental measurement results [4]. The formulae for calculating magnetic reluctance and magductance can be derived based on the semi-infinite model of silicon steel sheets. According to the formulas, it is evident that reluctance is directly proportional to f0.5, while magductance is inversely proportional to f0.5. Based on this relationship, a method for extrapolating BH curves is proposed, as shown in Fig. 1. The reliability of this extrapolation method has been validated through relevant experiments, as depicted in Fig. 2.References: [1] S. K. Sahdev . Electrical machines[M]. Cambridge: Cambridge University Press, 2018. [2]M. K. Kazimierczuk . High-frequency magnetic components, 2nd edition[M]. New York: Wiley, 2014. [3] M. Cheng, W. Qin, X. Zhu , "Magnetic-Inductance: Concept, Definition, and Applications," IEEE Transactions on Power Electronics, vol. 37, no. 10, pp. 12406–12414, Oct. 2022. [4] W. Qin , M. Cheng , Z. Wang , Vector magnetic circuit analysis of silicon steel sheet parameters under different frequencies for electrical machines[J]. IET Electric Power Application. 2024, 1–14.
The BH curve, also known as the magnetization curve, is a essential concept in the study of magnetic materials in the field of electromagnetism. It describes the relationship between the peak magnetic induction Bm and the peak magnetic field strength Hm of magnetic materials [1]. Due to the skin effect of magnetic flux, these magnetic circuit parameters not only vary with the B of the magnetic circuit but also change with the frequency [2]. Therefore, for the same magnetic material, the magnetic circuit parameters corresponding to different frequencies exhibit variations, resulting in BH curves that differ at different frequencies. Currently, research on the measurement and simulation methods of BH curves for magnetic materials at different frequencies is relatively limited. Obtaining BH curves at different frequencies requires sequential measurements at each frequency, which is not only time-consuming but also requires specialized high-frequency experimental equipment. Prof Cheng proposed a method to extrapolate BH curves based on the concept of magductance and experimental analysis. While this method shows some feasibility in practical applications, it lacks reliable theoretical derivation. Therefore, building upon this foundation, this paper conducts a systematic theoretical derivation. It proposes an infinite thickness model for silicon steel sheets and, based on this, a method to extrapolate and deduce BH curves. With this method, given the BH curve at a certain frequency, one can deduce BH curves at different frequencies using vector magnetic circuit theory [3]. The proposed BH curve method not only aligns with theoretical validation from literature references but also conforms to experimental measurement results [4]. The formulae for calculating magnetic reluctance and magductance can be derived based on the semi-infinite model of silicon steel sheets. According to the formulas, it is evident that reluctance is directly proportional to f0.5, while magductance is inversely proportional to f0.5. Based on this relationship, a method for extrapolating BH curves is proposed, as shown in Fig. 1. The reliability of this extrapolation method has been validated through relevant experiments, as depicted in Fig. 2.References: [1] S. K. Sahdev . Electrical machines[M]. Cambridge: Cambridge University Press, 2018. [2]M. K. Kazimierczuk . High-frequency magnetic components, 2nd edition[M]. New York: Wiley, 2014. [3] M. Cheng, W. Qin, X. Zhu , "Magnetic-Inductance: Concept, Definition, and Applications," IEEE Transactions on Power Electronics, vol. 37, no. 10, pp. 12406–12414, Oct. 2022. [4] W. Qin , M. Cheng , Z. Wang , Vector magnetic circuit analysis of silicon steel sheet parameters under different frequencies for electrical machines[J]. IET Electric Power Application. 2024, 1–14.