AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home CSEE Journal of Power and Energy Systems Article
PDF (2.8 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Open Access

Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface

Teng Wen, Xiang Cui, Xuebao Li( ), Hao Ma, Zhibin Zhao
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Show Author Information

Abstract

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic (EQS) field conditions with high accuracy. The proposed method is suitable for both 2-D and 3-D applications. Firstly, the governing equations represented by scalar electric potential are discretized by the nodal finite element method (FEM) in space and the finite difference method in time. Secondly, the transient constrained electric field equation on the boundary (TCEFEB) is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface. Finally, a 2-D numerical example is employed to demonstrate the validity of the proposed method. Furthermore, the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted. The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

Keywords

Electroquasistatic fieldcomposite insulation structuretransient constrained electric field equation on the boundaryfinite element methodinterface chargetime-domain

References

[1]
W. N. Kennedy, C. C. Crichton, D. A. Cillies, W. F. Criffard, H. C. Fischer, C. Hurty, W. Lampe, C. A. Pobbins, W. W. Stein, and E. Yasuda, “Recommended dielectric tests and test procedures for converter transformers and smoothing reactors,”IEEE Transactions on Power Delivery, vol. 1, no. 3, pp. 161–166, Jul. 1986.
Crossref Google Scholar
[2]
P. Y. Fu, Z. B. Zhao, X. B. Li, X. Cui, T. Wen, and S. Y. Mo, “Surface discharge characteristics and initiation mechanism of PEEK in nitrogen under semi-square voltage,”AIP Advances, vol. 8, no. 7, pp. 075322, Jul. 2018.
Crossref Google Scholar
[3]
G. Liu, L. Li, F. Ji, W. P. Li, Y. L. Sun, B. Li, and J. Z. Li, “Analysis of transient electric field and charge density of converter transformer under polarity reversal voltage,”IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 275–278, Feb. 2012.
Crossref Google Scholar
[4]
P. Y. Fu, Z. B. Zhao, X. Cui, T. Wen, H. Y. Wang, X. B. Li, and P. Zhang, “Partial discharge measurement and analysis in high voltage IGBT modules under DC voltage,”CSEE Journal of Power and Energy Systems, vol. 4, no. 4, pp. 513–523, Dec. 2018.
Crossref Google Scholar
[5]
L. Egiziano, V. Tucci, C. Petrarca, and M. Vitelli, “A Galerkin model to study the field distribution in electrical components employing nonlinear stress grading materials,”IEEE Transactions on Dielectrics and Electrical Insulation, vol. 6, no. 6, pp. 765–773, Dec. 1999.
Crossref Google Scholar
[6]
K. C. Wen, Y. B. Zhou, J. Fu, and T. Jin, “A calculation method and some features of transient field under polarity reversal voltage in HVDC insulation,”IEEE Transactions on Power Delivery, vol. 8, no. 1, pp. 223–230, Jan. 1993.
Crossref Google Scholar
[7]
H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy, Englewood Cliffs, NJ: Prentice Hall, 1989.
[8]
H. K. Dirks, “Quasi-stationary fields for microelectronic applications,”Electrical Engineering, vol. 79, no. 2, pp. 145–155, Apr. 1996.
Crossref Google Scholar
[9]
T. Steinmetz, M. Helias, G. Wimmer, L. O. Fichte, and M. Clemens, “Electro-quasistatic field simulations based on a discrete electromagnetism formulation,”IEEE Transactions on Magnetics, vol. 42, no. 4, pp. 755–758, Apr. 2006.
Crossref Google Scholar
[10]
D. Weida, C. Richter, and M. Clemens, “Design of ZnO microvaristor material stress-cone for cable accessories,”IEEE Transactions on Dielectrics and Electrical Insulation, vol. 18, no. 4, pp. 1262–1267, Aug. 2011.
Crossref Google Scholar
[11]
L. Egiziano, V. Tucci, C. Petrarca, and M. Vitelli, “A Galerkin model to study the field distribution in electrical components employing nonlinear stress grading materials,”IEEE Transactions on Dielectrics and Electrical Insulation, vol. 6, no. 6, pp. 765–773, Dec. 1999.
Crossref Google Scholar
[12]
M. Clemens, M. Wilke, G. Benderskaya, H. De Gersem, W. Koch, and T. Weiland, “Transient electro-quasistatic adaptive simulation schemes,”IEEE Transactions on Magnetics, vol. 40, no. 2, pp. 1294–1297, Mar. 2004.
Crossref Google Scholar
[13]
U. Van Rienen, M. Clemens, and T. Weiland, “Simulation of low-frequency fields on high-voltage insulators with light contaminations,”IEEE Transactions on Magnetics, vol. 32, no. 3, pp. 816–819, May 1996.
Crossref Google Scholar
[14]
R. D. Cook and H. Saunders, Concepts and Applications of Finite Element Analysis, 2nd ed., Chichester: John Wiley & Sons, 1981.
[15]
L. Li, F. Ji, and G. Liu. “A state-space finite element method for the calculation of transient electrical field in oil-paper insulation construction,”Proceedings of the CSEE, vol. 30, no. 36, pp. 111–116, Dec. 2010.
Google Scholar
[16]
B. H. Nguyen, X. Zhuang, and T. Rabczuk. “NURBS-based formulation for nonlinear electro-gradient elasticity in semiconductors,”Computer Methods in Applied Mechanics and Engineering, vol. 346, pp. 1074–1095, Apr. 2019.
Crossref Google Scholar
[17]
E. Samaniego, C. Anitescu, S. Goswami, V. M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, and T. Rabczuk, “An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications,”Computer Methods in Applied Mechanics and Engineering, vol. 362, pp. 112790, Apr. 2020.
Crossref Google Scholar
[18]
A. Kurita, E. Takahasi, J. Ozawa, M. Watanabe, and K. Okuyana, “DC flashover voltage characeteristics and their calculation method for oil-immersed insulation systems in HVDC transformers,”IEEE Transactions on Power Delivery, vol. 1, no. 3, pp. 184–190, Jul. 1986.
Crossref Google Scholar
[19]
K. Preis, O. Bíró, P. Supancic, and I. Tičar, “FEM simulation of thermistors including dielectric effects,”IEEE Transactions on Magnetics, vol. 39, no. 3, pp. 1733–1736, May 2003.
Crossref Google Scholar
[20]
H. Singer, H. Steinbigler, and P. Weiss, “A charge simulation method for the calculation of high voltage fields,”IEEE Transactions on Power Apparatus and Systems, vol. PAS-93, no. 5, pp. 1660–1668, Sep. 1974.
Crossref Google Scholar
[21]
J. M. Jin, The Finite Element Method in Electromagnetics, New York: John Wiley & Sons, 2002.
[22]
O. C. Zienkiewicz, The Finite Element Method, 3rd ed., London: McGraw-Hill, 1977.
[23]
J. F. Borges Da Silva and V. M. Machado, “Accurate gradient field evaluation using node potential values obtained by the finite element method,”IEE Proceedings-Science, Measurement and Technology, vol. 152, no. 4, pp. 149–154, Jul. 2005.
Crossref Google Scholar
[24]
M. Kasper and J. Franz, “Highly accurate computation of field quantities and forces by superconvergence in finite elements,”IEEE Transactions on Magnetics, vol. 31, no. 3, pp. 1424–1427, May 1995.
Crossref Google Scholar
[25]
D. Giannacopoulos and S. McFee, “An experimental study of superconvergence phenomena in finite element magnetics,”IEEE Transactions on Magnetics, vol. 33, no. 5, pp. 4137–4139, Sep. 1997.
Crossref Google Scholar
[26]
Z. M. Zhang and A. Naga, “A new finite element gradient recovery method: superconvergence property,”SIAM Journal on Scientific Computing, vol. 26, no. 4, pp. 1192–1213, Mar. 2005.
Crossref Google Scholar
[27]
H. T. Huang, S. L. Chang, C. S. Chien, and Z. C. Li, “Superconvergence of high order FEMs for eigenvalue problems with periodic boundary conditions,”Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 30–32, pp. 2246–2259, Jun. 2009.
Crossref Google Scholar
[28]
X. Cui and X. Xi, “Camplementary variational method for calculating electromagnetic field variables E and B,”Proceedings of the CSEE, vol. 8, no. 2, pp. 22–32, Mar. 1988.
Google Scholar
[29]
P. Zuo, J. Zou, and J. S. Yuan, “Global method of evaluating nodal field intensity based on known nodal potentials by the 3D finite element method,”Proceedings of the CSEE, vol. 35, no. 5, pp. 1243–1249, Mar. 2015.
Google Scholar
[30]
G. Mur, “Edge elements, their advantages and their disadvantages,”IEEE Transactions on Magnetics, vol. 30, no. 5, pp. 3552–3557, Sep. 1994.
Crossref Google Scholar
[31]
D. Boffi, P. Fernandes, L. Gastaldi, and I. Perugia, “Computational models of electromagnetic resonators: analysis of edge element approximation,”SIAM Journal on Numerical Analysis, vol. 36, no. 4, pp. 1264–1290, Jun. 1999.
Crossref Google Scholar
[32]
J. C. Li, P. Liu, and V. Dinavahi, “Massively parallel computation for 3-D nonlinear finite edge element problem with transmission line decoupling technique,”IEEE Transactions on Magnetics, vol. 55, no. 10, pp. 7401908, Oct. 2019.
Crossref Google Scholar
[33]
H. Yamashita, K. Shinozaki, and E. Nakamae, “A boundary-finite element method to compute directly electric field intensity with high accuracy,”IEEE Transactions on Power Delivery, vol. 3, no. 4, pp. 1754–1760, Oct. 1988.
Crossref Google Scholar
[34]
Y. Xie and L. Li, “Finite element method-boundary element method for calculation of nodal electric field intensity in multi-medium electric field,”Journal of North China Electric Power University, vol. 43, no. 4, pp. 21–26, 2016.
Google Scholar
[35]
X. Cui, “Compulation of electric field intensity on the dirichlet’s boundary surface by the finite element method with constrained electric field equation on the boundary,”Proceedings of the CSEE, vol. 7, no. 1, pp. 53–60, Jan. 1987.
Google Scholar
[36]
H. Jeffreys and B. Jeffreys, Methods of Mathematical Physics, 3rd ed., Cambridge: Cambridge University Press, 1999.
Crossref
[37]
J. R. Marti and J. M. Lin, “Suppression of Numerical Oscillations in the EMTP,”IEEE Power Engineering Review, vol. 9, no. 5, pp. 71–72, May 1989.
Crossref Google Scholar
[38]
P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed., New York: Cambridge University Press, 1996.
Crossref
CSEE Journal of Power and Energy Systems
Volume 8 Issue 1,
January 2022
Pages 143-154
DOI: 10.17775/CSEEJPES.2020.02170
Cite this article:
Wen T, Cui X, Li X, et al. Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface. CSEE Journal of Power and Energy Systems, 2022, 8(1): 143-154. https://doi.org/10.17775/CSEEJPES.2020.02170

836

Views

21

Downloads

2

Crossref

N/A

Web of Science

18

Scopus

8

CSCD

Altmetrics
Received: 28 May 2020
Revised: 12 September 2020
Accepted: 25 October 2020
Published: 20 November 2020
© 2020 CSEE
Return