Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems

Xiaojun Zhao; Yuting Zhong; Dawei Guan; Fanhui Meng; Zhiguang Cheng

doi:doi:10.11648/j.ijepe.s.2016050101.15

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Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems

Xiaojun Zhao, Yuting Zhong, Dawei Guan, Fanhui Meng, Zhiguang Cheng

Published in International Journal of Energy and Power Engineering (Volume 5, Issue 1-1)

Received: 21 September 2015 Accepted: 21 September 2015 Published: 15 October 2015

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Abstract

A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.

Published in	International Journal of Energy and Power Engineering (Volume 5, Issue 1-1) This article belongs to the Special Issue Numerical Analysis, Material Modeling and Validation for Magnetic Losses in Electromagnetic Devices
DOI	10.11648/j.ijepe.s.2016050101.15
Page(s)	37-41
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Eddy Current, Fixed-Point, Harmonic solutions, Reluctivity

References

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[2]	X. Zhao, L. Li, J. Lu, Z. Cheng and T. Lu, “Characteristic analysis of the square laminated core under dc-biased magnetization by the fix-point harmonic-balanced mehtod,” IEEE Trans. Magn., vol. 48, no. 2, pp. 747-750, 2012.
[3]	O. Biro and K. Preis, “An efficient time domain method for nonlinear periodic eddy current problems,” IEEE Trans. Magn., vol. 42, no. 4, pp. 695-698, 2006.
[4]	E. Dlala and A. Arkkio, “Analysis of the convergence of the fixed-point method used for solving nonlinear rotational magnetic field problems,” IEEE Trans. Magn., vol. 44, no. 4, pp. 473-478, 2008.
[5]	S. Ausserhofer, O. Biro, and K. Preis, “A strategy to improve the convergence of the fixed-point method for nonlinear eddy current problmes,” IEEE Trans. Magn., vol. 44, no. 6, pp. 1282-1285, 2008.
[6]	G. Koczka, S. Auberhofer, O. Biro and K. Preis, “Optimal convergence of the fixed point method for nonlinear eddy current problmes,” IEEE Trans. Magn., vol. 45, no. 3, pp. 948-951, 2009.
[7]	X. Zhao, J. Lu, L. Li, Z. Cheng and T. Lu, “Analysis of the saturated electromagnetic devices under DC bias condition by the decomposed harmonic balance finite element method”, COMPEL., vol. 31, no. 2, pp. 498-513, 2012.
[8]	F. I. Hantila, G. Preda and M. Vasiliu, “Polarization method for static field” IEEE Trans. Magn., vol.36, no.4, pp. 672-675, 2000.
[9]	X. Zhao, J. Lu, L. Li, Z. Cheng and T. Lu, “Analysis of the DC Bias phenomenon by the harmonic balance finite-element method,” IEEE Trans. on Power Delivery., vol.26, no.1, pp. 475-485, 2011.
[10]	I. Ciric, and F. Hantila, “An efficient harmonic method for solving nonlinear time-periodic eddy-current problmes,” IEEE Trans. Magn., vol. 43, no. 4, pp. 1185-1188, 2007.
[11]	P. Zhou, W. N. Fu, D. Lin, and Z. J. Cendes, “Numerical modeling of magnetic devices,” IEEE Trans. Magn., vol. 40, no. 4, pp. 1803–1809, 2004.

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APA Style

Xiaojun Zhao, Yuting Zhong, Dawei Guan, Fanhui Meng, Zhiguang Cheng. (2015). Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. International Journal of Energy and Power Engineering, 5(1-1), 37-41. https://doi.org/10.11648/j.ijepe.s.2016050101.15

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ACS Style

Xiaojun Zhao; Yuting Zhong; Dawei Guan; Fanhui Meng; Zhiguang Cheng. Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. Int. J. Energy Power Eng. 2015, 5(1-1), 37-41. doi: 10.11648/j.ijepe.s.2016050101.15

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AMA Style

Xiaojun Zhao, Yuting Zhong, Dawei Guan, Fanhui Meng, Zhiguang Cheng. Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. Int J Energy Power Eng. 2015;5(1-1):37-41. doi: 10.11648/j.ijepe.s.2016050101.15

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@article{10.11648/j.ijepe.s.2016050101.15,
  author = {Xiaojun Zhao and Yuting Zhong and Dawei Guan and Fanhui Meng and Zhiguang Cheng},
  title = {Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems},
  journal = {International Journal of Energy and Power Engineering},
  volume = {5},
  number = {1-1},
  pages = {37-41},
  doi = {10.11648/j.ijepe.s.2016050101.15},
  url = {https://doi.org/10.11648/j.ijepe.s.2016050101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijepe.s.2016050101.15},
  abstract = {A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.},
 year = {2015}
}

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TY  - JOUR
T1  - Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems
AU  - Xiaojun Zhao
AU  - Yuting Zhong
AU  - Dawei Guan
AU  - Fanhui Meng
AU  - Zhiguang Cheng
Y1  - 2015/10/15
PY  - 2015
N1  - https://doi.org/10.11648/j.ijepe.s.2016050101.15
DO  - 10.11648/j.ijepe.s.2016050101.15
T2  - International Journal of Energy and Power Engineering
JF  - International Journal of Energy and Power Engineering
JO  - International Journal of Energy and Power Engineering
SP  - 37
EP  - 41
PB  - Science Publishing Group
SN  - 2326-960X
UR  - https://doi.org/10.11648/j.ijepe.s.2016050101.15
AB  - A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.
VL  - 5
IS  - 1-1
ER  -

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Author Information

Xiaojun Zhao

Department of Electrical Engineering, North China Electric Power University, Baoding, China
Yuting Zhong

Department of Electrical Engineering, North China Electric Power University, Baoding, China
Dawei Guan

Department of Electrical Engineering, North China Electric Power University, Baoding, China
Fanhui Meng

Department of Electrical Engineering, North China Electric Power University, Baoding, China
Zhiguang Cheng

Institute of Power Transmission and Transformation Technology, Baobian Electric Co., Ltd, Baoding, China

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Plain Text BibTeX RIS

APA Style

Xiaojun Zhao, Yuting Zhong, Dawei Guan, Fanhui Meng, Zhiguang Cheng. (2015). Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. International Journal of Energy and Power Engineering, 5(1-1), 37-41. https://doi.org/10.11648/j.ijepe.s.2016050101.15

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ACS Style

Xiaojun Zhao; Yuting Zhong; Dawei Guan; Fanhui Meng; Zhiguang Cheng. Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. Int. J. Energy Power Eng. 2015, 5(1-1), 37-41. doi: 10.11648/j.ijepe.s.2016050101.15

Copy | Download

AMA Style

Xiaojun Zhao, Yuting Zhong, Dawei Guan, Fanhui Meng, Zhiguang Cheng. Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems. Int J Energy Power Eng. 2015;5(1-1):37-41. doi: 10.11648/j.ijepe.s.2016050101.15

Copy | Download

@article{10.11648/j.ijepe.s.2016050101.15,
  author = {Xiaojun Zhao and Yuting Zhong and Dawei Guan and Fanhui Meng and Zhiguang Cheng},
  title = {Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems},
  journal = {International Journal of Energy and Power Engineering},
  volume = {5},
  number = {1-1},
  pages = {37-41},
  doi = {10.11648/j.ijepe.s.2016050101.15},
  url = {https://doi.org/10.11648/j.ijepe.s.2016050101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijepe.s.2016050101.15},
  abstract = {A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Fixed-Point Harmonic-Balanced Method for Nonlinear Eddy Current Problems
AU  - Xiaojun Zhao
AU  - Yuting Zhong
AU  - Dawei Guan
AU  - Fanhui Meng
AU  - Zhiguang Cheng
Y1  - 2015/10/15
PY  - 2015
N1  - https://doi.org/10.11648/j.ijepe.s.2016050101.15
DO  - 10.11648/j.ijepe.s.2016050101.15
T2  - International Journal of Energy and Power Engineering
JF  - International Journal of Energy and Power Engineering
JO  - International Journal of Energy and Power Engineering
SP  - 37
EP  - 41
PB  - Science Publishing Group
SN  - 2326-960X
UR  - https://doi.org/10.11648/j.ijepe.s.2016050101.15
AB  - A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.
VL  - 5
IS  - 1-1
ER  -

Copy | Download