Full Text:   <4124>

CLC number: TM75

On-line Access: 

Received: 2008-08-12

Revision Accepted: 2008-10-20

Crosschecked: 2009-06-10

Cited: 0

Clicked: 4286

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.8 P.1191~1198


Earth return path impedances of underground cable for three-layer earth


Affiliation(s):  Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

Corresponding email(s):   vahidi@aut.ac.ir

Key Words:  Underground cables, Earth return path impedance, Earth stratification, Finite element method (FEM)

B. HEMMATIAN, B. VAHIDI, S. H. HOSSEINIAN. Earth return path impedances of underground cable for three-layer earth[J]. Journal of Zhejiang University Science A, 2009, 10(8): 1191~1198.

@article{title="Earth return path impedances of underground cable for three-layer earth",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Earth return path impedances of underground cable for three-layer earth
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 8
%P 1191~1198
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820598

T1 - Earth return path impedances of underground cable for three-layer earth
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 8
SP - 1191
EP - 1198
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820598

One of the factors that affect the parameters of an underground cable is earth return path impedance. Pollaczek developed a formula for the case of one-layer (homogenous) earth. But in practice the earth is composed of several layers. In this study we develop a new formula for earth return path impedance in the case of a three-layer earth. To check the accuracy of the obtained results, a comparison has been made with the finite element method (FEM). A comparison between the results of the Pollaczek formula and results of the obtained formula for a three-layer earth has been made, showing that the use of the Pollaczek formula instead of the actual formula can cause serious errors.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Alvarado, F.L., Betancourt, R., 1983. An accurate closed-form approximation for ground return impedance calculations. Proc. IEEE, 71(2):279-280.

[2] Ametani, A., 1980. A general formulation of impedance and admittance of cables. IEEE Trans. Power Appar. Syst., PAS-99(3):902-910.

[3] Ametani, A., Schinzinger, R., 1976. Equations for surge impedance and propagation constant of transmission lines above stratified earth. IEEE Trans. Power Appar. Syst., PAS-95(3):773-781.

[4] Carson, J.R., 1926. Wave propagation in overhead wires with ground return. Bell Syst. Tech. J., 5:539-554.

[5] Cheng, D.K., 2001. Field and Wave Electromagnetics (2nd Ed.). Addison-Wesley Publishing Co., Boston.

[6] Davies, A.E., Tong, Y.K., Lewin, P.L., German, D.M., 1995. Frequency-independent circuit model of earth return effects in transmission system. IEE Proc.-Gener. Transm. Distrib., 142:143-148.

[7] Dommel, H.W., 1986. Electromagnetic Transients Program Reference Manual, Chapter 5. Bonneville Power Administration, Portland, OR, p.1-23.

[8] Lagace, P.J., Fortin, J., Crainic, E.D., 1996. Interpretation of resistivity sounding measurements in n-layer soil using electrostatic images. IEEE Trans. Power Del., 11(3):1349-1354.

[9] Nakagawa, M., Iwamoto, K., 1976. Earth-return impedance for multilayer case. IEEE Trans. Power Appar. Syst., PAS-95(2):671-676.

[10] Nguyen, T.T., 1998a. Earth return path impedances of underground cables—Part 1: numerical integration of infinite integral. IEE Proc.-Gener. Transm. Distrib., 145(6):621-626.

[11] Nguyen, T.T., 1998b. Earth return path impedances of underground cables—Part 2: evaluations using neural networks. IEE Proc.-Gener. Transm. Distrib., 145(6):627-633.

[12] Noda, T., 2006. A double logarithmic approximation of Carson’s ground-return impedance. IEEE Trans. Power Del., 21(1):472-479.

[13] Papagiannis, G.K., Triantafyllidis, D.G., Labridis, D.P., 2000. A one step finite element formulation for the modeling of single and double circuit transmission lines. IEEE Trans. Power Syst., 15(1):33-38.

[14] Papagiannis, G.K., Tsiamitros, D.A., Andreou, G.T., Labridis, D.P., Dokopoulos, P.S., 2003. Earth Return Path Impedances of Underground Cables for the Multi-layer Case— A Finite Element Approach. Proc. IEEE Bologna Power Tech Conf., 3:1005-1011.

[15] Papagiannis, G.K., Tsiamitros, D.A., Labridis, D.P., Dokopoulos, P.S., 2005a. Direct numerical evaluation of earth path impedances of underground cables. IEE Proc.-Gener. Transm. Distrib., 152(3):321-327.

[16] Papagiannis, G.K., Tsiamitros, D.A., Labridis, D.P., Dokopou-los, P.S., 2005b. A systematic approach to the evaluation of the influence of multilayered earth on overhead power transmission lines. IEEE Trans. Power Del., 20(4):2594-2601.

[17] Pollaczek, F., 1926. Uber das Feld einer unendlich langenwechselstrom durchflossenen einfachleitung. Elektriche Nachrichtentechnik, 3:339-359 (in German).

[18] Robert, C.P., Casella, G., 2004. Monte Carlo Statistical Methods. Springer, New York.

[19] Saad, O., Gaba, G., Giroux, M., 1996. A closed-form approximation for ground return impedance of underground cables. IEEE Trans. Power Del., 11(3):1536-1545.

[20] Sadiku, M.N.O., 2004. Numerical Technique in Electromagnetics. CRC Press, New York.

[21] Satsios, K.J., Labridis, D.P., Dokopoulos, P.S., 1998. Finite element computation of field and eddy currents of a system consisting of a power transmission line above conductors buried in nonhomogeneous earth. IEEE Trans. Power Del., 13(3):876-882.

[22] Sunde, E.D., 1968. Earth Conduction Effects in Transmission Systems (2nd Ed.). Dover, New York, p.1-30, 98-140.

[23] Tsiamitros, D.A., Papagiannis, G.K., Labridis, D.P., Doko-poulos, P.S., 2005. Earth return path impedance of underground cables for the two layer case. IEEE Trans. Power Del., 20(3):2174-2181.

[24] Wedepohl, L.M., Wilcox, D.J., 1973. Transient analysis of underground power-transmission systems—system-model and wave propagation characteristics. IEE Proc.-Gener. Transm. Distr., 120:253-260.

[25] Xu, X.B., Liu, G., Chow, P., 2002. A finite-element method solution of the zero-sequence impedance of underground pipe-type cable. IEEE Trans. Power Del., 17(1):13-17.

[26] Zhang, B., Cui, X., Li, L., He, J., 2005. Parameter estimation of horizontal multilayer earth by complex image method. IEEE Trans. Power Del., 20(2):1394-1401.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE