A novel modeling technique via coupled magnetic equivalent circuit with vector hysteresis characteristics of laminated steels

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This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developed MEC model is coupled with both the single-valued B-H curve (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAM problem 32. The induced voltage calculated by the MEC model with the VHM demonstrates a good agreement with the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

Original languageEnglish
Article number9933897
Pages (from-to)1481-1491
Number of pages11
JournalIEEE Transactions on Industry Applications
Issue number2
Publication statusPublished - Mar 2023


  • Ferromagnetic laminations
  • Finite element analysis
  • Integrated circuit modeling
  • Magnetic hysteresis
  • Magnetostatics
  • Perpendicular magnetic anisotropy
  • Saturation magnetization
  • Static VAr compensators
  • fixed-point method
  • iron loss estimation
  • magnetic equivalent circuit
  • magnetic vector hysteresis


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