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389 IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 2, February 1983 TRANSIENT ANALYSIS OF GROUNDING SYSTEMS A. P. Meliopoulos IEEE, Member M. G. Moharam IEEE, Member School of Electrical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Abstract This paper addresses the problem of computing the ground potential rise of grounding systems during transients. Finite element analysis is employed to model 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 with the method of moments. The other parameters of the finite element, namely inductance and capacitance, are computed from the resistance utilizing Maxwell's equa- tions. This modeling enables the computation of the transient response of substation grounding systems to fast or slow waves striking the substation. The result is obtained in terms of a convolution of the step re- sponse of the system and the striking wave. In this way the impedance of substation systems to 60 cycles is accurately computed. Results demonstrate the depen- dence of the 60 cycle impedance on system parameters. The methodology allows to interface this model of a substation ground mat with the Electromagnetic Trans- ient Analysis Program thus, allowing explicit represen- tation of earth effects in electromagmatic transients computations. 1. INTRODUCTION The transient response characteristics of ground- ing systems play an important role in the protection of electrical installations. For example, the voltage drop along a ground rod connecting a surge arrester and the transformer it is protecting can obtain a value which is a substantial percentage of the basic impulse level of the transformer insulation. Depending on the configuration, 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 this context, analysis procedures predicting the transient response of substation grounding systems are very im- portant. The transient response of grounding structures has been studied many years ago by Rudenberg [1], Bewley [2], Sunde [3] and others. The classical experiments performed by Bewley [21 on counterpoises provide much information about the transient characteristic of 82 SM 369-7 A paper recommended and approved by the IEEE Substations Committee of the IEEE Power Engineer- ing Society for presentation at the IEEE PES 1982 Summer 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 that distributed resistance and inductance models of buried ground wires predict transient response of such systems in agreement with the experiments of Bewley. However, they do not provide any models for practical substation grounding systems. Kostaluk, Loboda and Mukhedkar [15] provide experimental data for transient ground impe- dances. Similarly, Rogers [6] reports on actual system transient response of a large tower footing. Bellashi et al. [8], [91, [10], have given a complete treatment of driven rods characteristics. Gupta and Thapar [7] provide empirical formulae for the impulse impedance of substation ground grids, defined as the ratio of the peak value of the voltage developed at the feeding point to the peak value of the current. This defini- tion of impulse impedance leads to uncertainty because the peak values of voltage and current do not necessar- ily occur at the same time. The so defined impulse impedance strongly depends on the rise time of the wave considered, the mesh size of the grid, soil resistivity and permittivity, the feeding point, etc. This paper presents 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 the problem of transient analysis of practical grounding systems 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, the simple case of an earth embedded conductor is treated. This case is extended to the case of a substation ground mat. These two cases clearly illustrate the methodology. Sample test cases are presented and com- pared to known experimental data. The comparison is favorable. Finally, a methodology is outlined for the interface of the grounding system models of this paper with the EMTP computer program which enables the study of the impact of grounding systems on electromagnetic transients. 2. TRANSIENT RESPONSE OF AN EARTH EMBEDDED CONDUCTOR 2.1 Problem Formulation Development of models of grounding structures suitable for the computation of their transient re- sponse can be demonstrated with the simple system of a single buried conductor. Such a system is illustrated in Figure 1. A small segment of length Q of the conductor of Figure 1, is characterized with a series resistance Ar, a series inductance AL, conductance Ag to remote earth and capacitance AC. This representa- tion is illustrated in Figure 2. These parameters are distributed along the length Q of the segment. The thick solid line signifies the tact. The numerical values of the quantities Ag, AL, AC can be directly computed from two quantities, namely the conductance Ag and the speed of electromagnetic waves in the soil V , as follows. The speed V is 0018-9510/83/0002-0389$01.00 ( 1983 IEEE

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  • 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


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