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## Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits

## Abstract

This paper presents a high-fidelity finite-element modeling technique for magnetic hysteresis and eddy current losses in toroid inductors. The method is based on the separation of ferromagnetic loss characteristics into two components: a quasi-static hysteresis component and a dynamic eddy current component. The Preisach model is used to describe the quasi-static magnetic hysteresis behavior of the core, providing strong guarantees on the reproducibility of the experimentally measured characteristics. This model is used to represent the magnetic field constitutive relationships within a finite-element framework combining the effects of hysteresis and eddy currents in a unified dynamic simulation. The finite-element model of the toroid is used as a high-order inductor model coupled to a resonant circuit simulation. The modeling technique is validated through experimental measurements on two different series RLC circuits. The first circuit is based on an M19 electrical steel toroid having resonant frequency near 200 Hz. The second circuit is based on a T38 ferrite toroid having a resonant frequency near 10 kHz. The models agree closely with the measured voltages, currents, and losses. The models also successfully predict discontinuities in the measured frequency responses due to the existence of bistable operating regimes.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Karma Automotive LLC, Irvine, CA (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Vehicle Technologies Office (EE-3V)

- OSTI Identifier:
- 1546525

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Journal of Emerging and Selected Topics in Power Electronics

- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 3; Journal ID: ISSN 2168-6777

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Magnetic hysteresis; Integrated circuit modeling; RLC circuits; Current measurement; Inductors; Eddy currents; Frequency measurement; magnetic losses; finite-element methods

### Citation Formats

```
Pries, Jason, Gurpinar, Emre, Tang, Lixin, and Burress, Timothy A. Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits. United States: N. p., 2019.
Web. doi:10.1109/JESTPE.2019.2908894.
```

```
Pries, Jason, Gurpinar, Emre, Tang, Lixin, & Burress, Timothy A. Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits. United States. doi:10.1109/JESTPE.2019.2908894.
```

```
Pries, Jason, Gurpinar, Emre, Tang, Lixin, and Burress, Timothy A. Thu .
"Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits". United States. doi:10.1109/JESTPE.2019.2908894.
```

```
@article{osti_1546525,
```

title = {Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits},

author = {Pries, Jason and Gurpinar, Emre and Tang, Lixin and Burress, Timothy A.},

abstractNote = {This paper presents a high-fidelity finite-element modeling technique for magnetic hysteresis and eddy current losses in toroid inductors. The method is based on the separation of ferromagnetic loss characteristics into two components: a quasi-static hysteresis component and a dynamic eddy current component. The Preisach model is used to describe the quasi-static magnetic hysteresis behavior of the core, providing strong guarantees on the reproducibility of the experimentally measured characteristics. This model is used to represent the magnetic field constitutive relationships within a finite-element framework combining the effects of hysteresis and eddy currents in a unified dynamic simulation. The finite-element model of the toroid is used as a high-order inductor model coupled to a resonant circuit simulation. The modeling technique is validated through experimental measurements on two different series RLC circuits. The first circuit is based on an M19 electrical steel toroid having resonant frequency near 200 Hz. The second circuit is based on a T38 ferrite toroid having a resonant frequency near 10 kHz. The models agree closely with the measured voltages, currents, and losses. The models also successfully predict discontinuities in the measured frequency responses due to the existence of bistable operating regimes.},

doi = {10.1109/JESTPE.2019.2908894},

journal = {IEEE Journal of Emerging and Selected Topics in Power Electronics},

number = 3,

volume = 7,

place = {United States},

year = {2019},

month = {4}

}