389IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 2, February 1983

TRANSIENT ANALYSIS OF GROUNDING SYSTEMS

A. P. MeliopoulosIEEE, Member

M. G. MoharamIEEE, Member

School of Electrical EngineeringGeorgia Institute of Technology

Atlanta, Georgia 30332

Abstract

This paper addresses the problem of computing theground potential rise of grounding systems duringtransients. Finite element analysis is employed tomodel the constituent parts of a grounding system.Short lengths of earth embedded electrodes are charac-terized as transmission lines with distributed induc-tance, capacitance and leakage resistance to earth.Leakage resistance to earth is accurately computed withthe method of moments. The other parameters of thefinite element, namely inductance and capacitance, arecomputed from the resistance utilizing Maxwell's equa-tions. This modeling enables the computation of thetransient response of substation grounding systems tofast or slow waves striking the substation. The resultis obtained in terms of a convolution of the step re-sponse of the system and the striking wave. In this waythe impedance of substation systems to 60 cycles isaccurately computed. Results demonstrate the depen-dence of the 60 cycle impedance on system parameters.The methodology allows to interface this model of asubstation ground mat with the Electromagnetic Trans-ient Analysis Program thus, allowing explicit represen-tation of earth effects in electromagmatic transientscomputations.

1. INTRODUCTION

The transient response characteristics of ground-ing systems play an important role in the protection ofelectrical installations. For example, the voltagedrop along a ground rod connecting a surge arrester andthe transformer it is protecting can obtain a valuewhich is a substantial percentage of the basic impulselevel of the transformer insulation. Depending on theconfiguration, the surge arrester experiences an over-voltage which is less than the one reaching the trans-former. Thus system protection is reduced. The intro-duction of solid state arresters and the every shrink-ing safety margins demand more accurate analysis proce-dures for substation design and protection. In thiscontext, analysis procedures predicting the transientresponse of substation grounding systems are very im-portant.

The transient response of grounding structures hasbeen studied many years ago by Rudenberg [1], Bewley[2], Sunde [3] and others. The classical experimentsperformed by Bewley [21 on counterpoises provide muchinformation about the transient characteristic of

82 SM 369-7 A paper recommended and approved by theIEEE Substations Committee of the IEEE Power Engineer-ing Society for presentation at the IEEE PES 1982Summer Meeting, San Francisco, California, July 18-23,1982. Manuscript submitted February 4, 1982; made avail-able for prinfting April 19, 1982.

grounding systems. Verma and Mukhedkar [51 showed thatdistributed resistance and inductance models of buriedground wires predict transient response of such systemsin agreement with the experiments of Bewley. However,they do not provide any models for practical substationgrounding systems. Kostaluk, Loboda and Mukhedkar [15]provide experimental data for transient ground impe-dances. Similarly, Rogers [6] reports on actual systemtransient response of a large tower footing. Bellashiet al. [8], [91, [10], have given a complete treatmentof driven rods characteristics. Gupta and Thapar [7]provide empirical formulae for the impulse impedance ofsubstation ground grids, defined as the ratio of thepeak value of the voltage developed at the feedingpoint to the peak value of the current. This defini-tion of impulse impedance leads to uncertainty becausethe peak values of voltage and current do not necessar-ily occur at the same time. The so defined impulseimpedance strongly depends on the rise time of the waveconsidered, the mesh size of the grid, soil resistivityand permittivity, the feeding point, etc. This paperpresents data which further illustrate the point.Thus, the definition of impulse impedance of reference[71 is at best ambiguous.

The work reported in this paper addresses theproblem of transient analysis of practical groundingsystems consisting of ground mats, ground rods, etc.The developed models are in good agreement with experi-mental results.

The paper is organized as follows. First, thesimple case of an earth embedded conductor is treated.This case is extended to the case of a substationground mat. These two cases clearly illustrate themethodology. Sample test cases are presented and com-pared to known experimental data. The comparison isfavorable. Finally, a methodology is outlined for theinterface of the grounding system models of this paperwith the EMTP computer program which enables the studyof the impact of grounding systems on electromagnetictransients.

2. TRANSIENT RESPONSE OF AN EARTH EMBEDDED CONDUCTOR

2.1 Problem Formulation

Development of models of grounding structuressuitable for the computation of their transient re-sponse can be demonstrated with the simple system of asingle buried conductor. Such a system is illustratedin Figure 1. A small segment of length Q of theconductor of Figure 1, is characterized with a seriesresistance Ar, a series inductance AL, conductance Agto remote earth and capacitance AC. This representa-tion is illustrated in Figure 2. These parameters aredistributed along the length Q of the segment. Thethick solid line signifies the tact.

The numerical values of the quantities Ag, AL, ACcan be directly computed from two quantities, namelythe conductance Ag and the speed of electromagneticwaves in the soil V , as follows. The speed V is

0018-9510/83/0002-0389$01.00 ( 1983 IEEE