# Efficient evaluation of the earth return mutual impedance of overhead conductors over a horizontally multilayered soil

Jae-bok Lee (Electrical Environment Group, Korea Electrotechnology Research Institute, Changwon, Korea)
Jun Zou (State Key Lab of Control and Simulation of Power Systems and Generation Equipment and Department of Electrical Engineering, Tsinghua University, Beijing, P.R. China)
Benliang Li (State Power Economic Research Institute, Beijing, P.R. China)
Munno Ju (Electrical Environment Group, Korea Electrotechnology Research Institute, Changwon, Korea)

ISSN: 0332-1649

Article publication date: 1 July 2014

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## Abstract

### Purpose

The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils.

### Design/methodology/approach

The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands.

### Findings

The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors.

### Originality/value

The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

## Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant No. 51177087.

## Citation

Lee, J.-b., Zou, J., Li, B. and Ju, M. (2014), "Efficient evaluation of the earth return mutual impedance of overhead conductors over a horizontally multilayered soil", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 4, pp. 1379-1395. https://doi.org/10.1108/COMPEL-08-2013-0265

## Publisher

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Emerald Group Publishing Limited