AU-05 A Frequency Independent Excess Loss Modeling for Arbitrary Waveforms
Creators: Takashi Yamada
Kazuki Semba
Tomohisa Sato
Hiroyuki Sano
Publisher: name: IEEE
Year: 2025

Accurate prediction of excess loss has become critical in electric machine design as the driving frequency of machines increases. A commonly used approach is employing the Bertotti model(1). Although the Bertotti model is generic, the resulting model’s validity is limited by measurements that determine the model parameters as a function of magnetic flux density B and frequency(2)(3) and are difficult, especially in the high-frequency range. This is inconvenient for machine design, where complex fields with multiple frequency components and minor loops need to be dealt with. The limitation can be relaxed by removing the frequency dependency from the parameters. We investigated the possibility of a model that does not have frequency dependency and is applicable to arbitrary waveforms. The results showed the possibility. The proposed model shares the general form of the Bertotti model, and excess loss Pex is expressed as C*(dB/dt)^p. The key difference is that C depends not on frequency but only on B. Sets of C and p are identified to satisfy the measurement results changing frequency. If they do not have a frequency dependency, the resulting sets must coincide. The measurements are conducted on a ring core under biased AC fields with multiple frequencies (Fig.1). The target Pex is carried out by subtracting hysteresis loss Phy and classical eddy current loss Pcl from the measured loss Pmes. Phy and Pcl are calculated using the Play model(4)(5) and 1D FEA method(6) to reproduce minor loops and skin effects in the steel sheet. We found that a set of C and p exists that has a weak dependency on frequency when the shape of the steel sheet's magnetic susceptibility is used as C with an appropriate p (Fig.2). This was also observed with another steel sheet.References: (1) G. Bertotti, “General properties of power losses in soft ferromagnetic materials,” IEEE Trans. Magn., vol. 24, no. 1, pp. 621–630(1988) (2) D. Ionel, M. Popescu, and C. Cossar, “A General Model of the Laminated Steel Losses in Electric Motors with PWM Voltage Supply,” IEEE Industry Applications Society Annual Meeting, pp. 1–7(2008) (3) T. Yoshioka, T. Tsuge,and Y. Takahashi, “Iron Loss Estimation Method for Silicon Steel Sheet Taking Account of DC-Biased Conditions,” IEEE Tran. on Magn., vol. 55, no. 6, pp. 1–4(2019) (4) T. Matsuo, D. Shimode, Y. Terada, and M. Shimasaki, “Application of stop and play models to the representation of magnetic characteristics of silicon steel sheet,” IEEE Tran. on Magn., vol. 39, no. 3, pp. 1361–1364(2003) (5) M. A. Krasnosel’skii and A. V. Pokrovskii, Systems with Hysteresis. Berlin, Heidelberg: Springer(1989) (6) O. Bottauscio, M. Chiampi, and D. Chiarabaglio, “Advanced model of laminated magnetic cores for two-dimensional field analysis,” IEEE Trans. on Magn., vol. 36, no. 3, pp. 561–573(2000)
Accurate prediction of excess loss has become critical in electric machine design as the driving frequency of machines increases. A commonly used approach is employing the Bertotti model(1). Although the Bertotti model is generic, the resulting model’s validity is limited by measurements that determine the model parameters as a function of magnetic flux density B and frequency(2)(3) and are difficult, especially in the high-frequency range. This is inconvenient for machine design, where complex fields with multiple frequency components and minor loops need to be dealt with. The limitation can be relaxed by removing the frequency dependency from the parameters. We investigated the possibility of a model that does not have frequency dependency and is applicable to arbitrary waveforms. The results showed the possibility. The proposed model shares the general form of the Bertotti model, and excess loss Pex is expressed as C*(dB/dt)^p. The key difference is that C depends not on frequency but only on B. Sets of C and p are identified to satisfy the measurement results changing frequency. If they do not have a frequency dependency, the resulting sets must coincide. The measurements are conducted on a ring core under biased AC fields with multiple frequencies (Fig.1). The target Pex is carried out by subtracting hysteresis loss Phy and classical eddy current loss Pcl from the measured loss Pmes. Phy and Pcl are calculated using the Play model(4)(5) and 1D FEA method(6) to reproduce minor loops and skin effects in the steel sheet. We found that a set of C and p exists that has a weak dependency on frequency when the shape of the steel sheet's magnetic susceptibility is used as C with an appropriate p (Fig.2). This was also observed with another steel sheet.References: (1) G. Bertotti, “General properties of power losses in soft ferromagnetic materials,” IEEE Trans. Magn., vol. 24, no. 1, pp. 621–630(1988) (2) D. Ionel, M. Popescu, and C. Cossar, “A General Model of the Laminated Steel Losses in Electric Motors with PWM Voltage Supply,” IEEE Industry Applications Society Annual Meeting, pp. 1–7(2008) (3) T. Yoshioka, T. Tsuge,and Y. Takahashi, “Iron Loss Estimation Method for Silicon Steel Sheet Taking Account of DC-Biased Conditions,” IEEE Tran. on Magn., vol. 55, no. 6, pp. 1–4(2019) (4) T. Matsuo, D. Shimode, Y. Terada, and M. Shimasaki, “Application of stop and play models to the representation of magnetic characteristics of silicon steel sheet,” IEEE Tran. on Magn., vol. 39, no. 3, pp. 1361–1364(2003) (5) M. A. Krasnosel’skii and A. V. Pokrovskii, Systems with Hysteresis. Berlin, Heidelberg: Springer(1989) (6) O. Bottauscio, M. Chiampi, and D. Chiarabaglio, “Advanced model of laminated magnetic cores for two-dimensional field analysis,” IEEE Trans. on Magn., vol. 36, no. 3, pp. 561–573(2000)