documentb

389IEEE

Transactionson

PowerApparatus

andSystems,

Vol.PAS-102,

No.2,

February1983

TRANSIENTANALYSIS

OFGROUNDING

SYSTEMS

A.P.

MeliopoulosIEEE,

MemberM.

G.Moharam

IEEE,Member

Schoolof

ElectricalEngineering

GeorgiaInstitute

ofTechnology

Atlanta,Georgia

30332

Abstract

Thispaper

addressesthe

problemof

computingthe

groundpotential

riseof

groundingsystems

duringtransients.

Finiteelement

analysis

isemployed

tomodel

theconstituent

partsof

agrounding

system.Short

lengthsof

earth

embedded

electrodesare

charac-terized

astransmission

lineswith

distributedinduc-

tance,capacitance

andleakage

resistanceto

earth.

Leakageresistance

toearth

isaccurately

computed

withthe

method

ofmoments.

Theother

parametersof

thefinite

element,namely

inductanceand

capacitance,

are

computed

fromthe

resistanceutilizing

Maxwell'sequa-

tions.This

modelingenables

thecomputation

ofthe

transientresponse

ofsubstation

groundingsystems

tofast

orslow

waves

strikingthe

substation.The

result

isobtained

interms

ofa

convolution

ofthe

stepre-

sponseof

thesystem

andthe

strikingwave.

Inthis

way

theimpedance

ofsubstation

systemsto

60cycles

isaccurately

computed.Results

demonstratethe

depen-dence

ofthe

60cycle

impedanceon

systemparameters.

Themethodology

allowsto

interfacethis

model

ofa

substationground

mat

withthe

ElectromagneticTrans-

ientAnalysis

Programthus,

allowingexplicit

represen-

tationof

earth

effectsin

electromagmatictransients

computations.

1.INTRODUCTION

Thetransient

response

characteristicsof

ground-ing

systemsplay

an

importantrole

inthe

protectionof

electricalinstallations.

Forexample,

thevoltage

dropalong

aground

rodconnecting

asurge

arrester

and

thetransformer

itis

protectingcan

obtaina

value

whichis

asubstantial

percentageof

thebasic

impulselevel

ofthe

transformerinsulation.

Dependingon

theconfiguration,

thesurge

arrester

experiencesan

over-

voltagewhich

isless

thanthe

one

reachingthe

trans-former.

Thussystem

protectionis

reduced.

Theintro-

ductionof

solidstate

arresters

and

theevery

shrink-ing

safetymargins

demandmore

accurate

analysis

proce-dures

forsubstation

designand

protection.In

thiscontext,

analysisprocedures

predictingthe

transientresponse

ofsubstation

groundingsystems

are

very

im-portant.

Thetransient

response

ofgrounding

structureshas

beenstudied

many

yearsago

byRudenberg

[1],Bewley

[2],Sunde

[3]and

others.The

classicalexperiments

performedby

Bewley[21

on

counterpoisesprovide

much

informationabout

thetransient

characteristicof

82SM

369-7A

paperrecommended

and

approvedby

theIEEE

SubstationsCommittee

ofthe

IEEEPower

Engineer-ing

Societyfor

presentationat

theIEEE

PES1982

SummerMeeting,

SanFrancisco,

California,July

18-23,1982.

Manuscriptsubmitted

February4,

1982;made

avail-

ablefor

prinftingApril

19,1982.

groundingsystems.

Vermaand

Mukhedkar[51

showedthat

distributedresistance

and

inductancemodels

ofburied

groundwires

predicttransient

response

ofsuch

systemsin

agreementwith

theexperiments

ofBewley.

However,they

donot

provideany

models

forpractical

substationgrounding

systems.Kostaluk,

Lobodaand

Mukhedkar[15]

provideexperimental

datafor

transientground

impe-dances.

Similarly,Rogers

[6]reports

on

actualsystem

transientresponse

ofa

largetower

footing.Bellashi

etal.

[8],[91,

[10],have

givena

completetreatment

ofdriven

rods

characteristics.Gupta

andThapar

[7]provide

empiricalformulae

forthe

impulseimpedance

ofsubstation

groundgrids,

definedas

theratio

ofthe

peakvalue

ofthe

voltage

developedat

thefeeding

pointto

thepeak

value

ofthe

current.

Thisdefini-

tionof

impulseimpedance

leadsto

uncertainty

becausethe

peakvalues

ofvoltage

and

current

donot

necessar-

ilyoccur

atthe

same

time.The

sodefined

impulseimpedance

stronglydepends

on

therise

timeof

thewave

considered,the

mesh

sizeof

thegrid,

soilresistivity

and

permittivity,the

feedingpoint,

etc.This

paperpresents

datawhich

furtherillustrate

thepoint.

Thus,the

definitionof

impulseimpedance

ofreference

[71is

atbest

ambiguous.

Thework

reportedin

thispaper

addressesthe

problemof

transientanalysis

ofpractical

groundingsystems

consistingof

groundmats,

groundrods,

etc.The

developedmodels

are

ingood

agreementwith

experi-mental

results.

Thepaper

isorganized

as

follows.First,

thesimple

case

ofan

earth

embedded

conductor

istreated.

Thiscase

isextended

tothe

case

ofa

substationground

mat.

Thesetwo

cases

clearlyillustrate

themethodology.

Sampletest

cases

are

presentedand

com-

paredto

knownexperimental

data.The

comparison

isfavorable.

Finally,amethodology

isoutlined

forthe

interfaceof

thegrounding

systemmodels

ofthis

paperwith

theEMTP

computer

programwhich

enables

thestudy

ofthe

impactof

groundingsystems

on

electromagnetictransients.

2.TRANSIENT

RESPONSEOF

ANEARTH

EMBEDDEDCONDUCTOR

2.1Problem

Formulation

Developmentof

models

ofgrounding

structuressuitable

forthe

computationof

theirtransient

re-

sponsecan

bedemonstrated

withthe

simplesystem

ofa

singleburied

conductor.

Sucha

systemis

illustratedin

Figure1.

Asmall

segment

oflength

Qof

theconductor

ofFigure

1,is

characterizedwith

aseries

resistanceAr,

aseries

inductanceAL,

conductance

Agto

remote

earth

and

capacitanceAC.

Thisrepresenta-

tionis

illustratedin

Figure2.

Theseparameters

are

distributedalong

thelength

Qof

thesegment.

Thethick

solidline

signifiesthe

tact.

Thenumerical

values

ofthe

quantitiesAg,

AL,AC

can

bedirectly

computedfrom

twoquantities,

namelythe

conductance

Agand

thespeed

ofelectromagnetic

waves

inthe

soilV

,as

follows.The

speedV

is

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

1983IEEE