NetworkProtection&AutomationGuideFirst edition July 2002Previously called Protective Relays Application GuideFirst printed June 1966Reprinted January 1967August 1968November 1970September 1971February 1973January 1974Second editionFirst printed March 1975Reprinted November 1977December 1979November 1982October 1983October 1985Third editionFirst printed June 1987Reprinted September 1990March 1995All rights reserved Copyright AREVA 2005AREVA T&D - 1, Place de la Coupole - 92084 Paris La Dfense - France.www.areva-td.comAREVA T&D Worlwide Contact Centre:http://www.areva-td.com/contactcentre/Tel.: +44 (0) 1785 250 070ISBN : 2-9518589-0-6Layout by Flash Espace, Montpellier, France - Printed by Cayfosa, Barcelona, SpainNet workProtec t i on & Aut omat i onGui deThis book is the result of the co-operation and teamworkofthemanyspecialistengineersemployedbyAREVAT&D Automation & Information Systems. The Company would like to acknowledge their assistancein producing this edition.AREVAT&Dwouldalsoliketoacknowledgegratefullythe co-operation of the following companies in providingmaterial for this edition.ALSTOM PowerAREVA T&D TransformersAREVA T&D Instrument TransformersAREVA T&D Distribution SwitchgearAREVA T&D Network PlanningALSTOM Electrical MachinesALSTOM Transport/Virgin TrainsTheinvaluablecontributionsofPBPowerwithinthereview process are also acknowledged gratefully.Peter RushAcknowledgementsN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eAc knowl edgement s1 Introduction . . . . . . . . . . . . . . . . . . . . p22 Fundamentals of Protection Practice . . . . . . . . . . . . . . . . . . . . p43 Fundamental Theory. . . . . . . . . . . . . . . . p164 Fault Calculations . . . . . . . . . . . . . . . . . p305 Equivalent Circuits and Parametersof Power System Plant . . . . . . . . . . . . . . . . . p466 Current and Voltage Transformers . . . . . . . . . . . . . . . . . p787 Relay Technology . . . . . . . . . . . . . . . . . p988 Protection:Signalling and Intertripping. . . . . . . . . . . . . . . p1129 Overcurrent Protection for Phaseand Earth Faults . . . . . . . . . . . . . . p12210 Unit Protection of Feeders . . . . . . . . . . . . . . p15211 Distance Protection . . . . . . . . . . . . . . p17012 Distance Protection Schemes . . . . . . . . . . . . . . p19213 Protection of Complex Transmission Circuits . . . . . . . . . . . . . . p20214 Auto-Reclosing . . . . . . . . . . . . . . p21815 Busbar Protection . . . . . . . . . . . . . . p23216 Transformer and Transformer-Feeder Protection . . . . . . . . . . . . . . p25417 Generator andGenerator-Transformer Protection . . . . . . . . . . . . . . p28018 Industrial and CommercialPower System Protection . . . . . . . . . . . . . . p31619 A.C. Motor Protection . . . . . . . . . . . . . . p33620 Protection of A.C. Electrified Railways . . . . . . . . . . . . . . p35221 Relay Testing and Commissioning . . . . . . . . . . . . . . p37022 Power System Measurements . . . . . . . . . . . . . . p39823 Power Quality . . . . . . . . . . . . . . p41024 Substation Control and Automation . . . . . . . . . . . . . . p42225 Distribution System Automation . . . . . . . . . . . . . . p442Appendix 1 Terminology . . . . . . . . . . . . . . p454Appendix 2 ANSI/IEC Relay Symbols . . . . . . . . . . . . . . p466Appendix 3 Application Tables . . . . . . . . . . . . . . p468Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p476C o n t e n t s 1 I n t r o d u c t i o nRelayhardwareisbecomingevenmorestandardised,tothepointatwhich versions of a relay may differ only by the software they contain.ThisaccuratepredictionintheprefacetotheThirdEditionoftheProtectiveRelayApplicationGuide(PRAG),1987,hasbeenfollowedbytherapiddevelopmentofintegratedprotectionandcontroldevices.Thechangeintechnology,togetherwithsignificantchangesinUtility,IndustrialandCommercial organisations, has resulted in new emphasis on Secondary SystemsEngineering.In addition to the traditional role of protection & control, secondary systemsare now required to provide true added value to organisations.When utilised to its maximum, not only can the integration of protection &control functionality deliver the required reduction in life-time cost of capital,but the advanced features available (Quality of Supply, disturbance recordingand plant monitoring) enable system and plant performance to be improved,increasing system availability.Theevolutionofallsecondaryconnecteddevicestoformdigitalcontrolsystems continues to greatly increase access to all information available withinthe substation, resulting in new methodologies for asset management.In order to provide the modern practising substation engineer with referencematerial, the Network Protection &Automation Guide provides a substantiallyrevised and expanded edition of PRAG incorporating new chapters on all levelsof network automation.The first part of the book deals with the fundamentals,basictechnology,faultcalculationsandthemodelsofpowersystemplant,includingthetransientresponseandsaturationproblemsthataffectinstrument transformers.Thetypicaldataprovidedonpowersystemplanthasbeenupdatedandsignificantly expanded following research that showed its popularity.Thebookthenprovidesdetailedanalysisontheapplicationofprotectionsystems.ThisincludesanewChapterontheprotectionofa.c.electrifiedrailways.Existing chapters on distance, busbar and generator protection havebeencompletelyrevisedtotakeaccountofnewdevelopments,includingimprovementsduetonumericalprotectiontechniquesandtheapplicationproblemsofembeddedgeneration.TheChapteronrelaytestingandcommissioninghasbeencompletelyupdatedtoreflectmoderntechniques.Finally,newChapterscoveringthefieldsofpowersystemmeasurements,power quality, and substation and distribution automation are found, to reflectthe importance of these fields for the modern Power System Engineer.The intention is to make NPAG the standard reference work in its subject area- while still helping the student and young engineer new to the field.We trustthat you find this book invaluable and assure you that any comments will becarefully noted ready for the next edition. 1 Int roduc t i onN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 3 Introduction 2.1Protection equipment 2.2Zones of protection 2.3Reliability 2.4Selectivity 2.5Stability 2.6Speed 2.7Sensitivity 2.8Primary and back-up protection 2.9Relay output devices2.10Relay tripping circuits2.11Trip circuit supervision 2.12 2 F u n d a m e n t a l so f P r o t e c t i o n P r a c t i c eN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 5 2. 1I NTRODUCTI ONThe purpose of an electrical power system is to generateandsupplyelectricalenergytoconsumers.Thesystemshouldbedesignedandmanagedtodeliverthisenergytotheutilisationpointswithbothreliabilityandeconomy.Severedisruptiontothenormalroutineofmodern society is likely if power outages are frequent orprolonged,placinganincreasingemphasisonreliabilityand security of supply.As the requirements of reliabilityandeconomyarelargelyopposed,powersystemdesignis inevitably a compromise.A powersystemcomprisesmanydiverseitemsofequipment.Figure2.2showsahypotheticalpowersystem;thisandFigure2.1illustratesthediversityofequipment that is found. 2 Fundamental sof Protec t i onPrac t i c eFigure 2.1:Power stationN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 2 Fundamentals ofProtection Practice 6 Figure 2.Figure 2.2:Example power systemFigure 2.1:Example power systemR1R2G1G2T1T2TR3R4G3G4T10T11T14T16T17T15T12T13R5R6G5G6T7T8TR7G7T9T9T5T T6T3T T4TL2L3L4L1AL7AL5L6L8L7BL1BA 380kV380kV 380kV110kVHydro power stationB CB' 33kV C'380kVCCGT power stationE D 220kVSteam power stationGridsubstationF33kV D' 110kV380kVG'GGrid380kVF'N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 7 2 Fundamentals ofProtection PracticeMany items of equipment are very expensive, and so thecompletepowersystemrepresentsaverylargecapitalinvestment.Tomaximisethereturnonthisoutlay,thesystemmustbeutilisedasmuchaspossiblewithintheapplicableconstraintsofsecurityandreliabilityofsupply.Morefundamental,however,isthatthepowersystem should operate in a safe manner at all times.Nomatter how well designed, faults will always occur on apowersystem,andthesefaultsmayrepresentarisktolife and/or property.Figure 2.3 shows the onset of a faulton an overhead line.The destructive power of a fault arccarrying a high current is very great; it can burn throughcopper conductors or weld together core laminations inatransformerormachineinaveryshorttimesometensorhundredsofmilliseconds.Evenawayfromthefault arc itself, heavy fault currents can cause damage toplant if they continue for more than a few seconds.Theprovisionofadequateprotectiontodetectanddisconnect elements of the power system in the event offaultisthereforeanintegralpartofpowersystemdesign. Only by so doing can the objectives of the powersystem be met and the investment protected.Figure 2.4provides an illustration of the consequences of failure toprovide appropriate protection.Thisisthemeasureoftheimportanceofprotectionsystems as applied in power system practice and of theresponsibility vested in the Protection Engineer.2. 2PROTECTI ONEQUI PMENTThe definitions that follow are generally used in relationto power system protection:a. ProtectionSystem:acompletearrangementofprotection equipment and other devices required toachieve a specified function based on a protectionprincipal (IEC 60255-20)b. ProtectionEquipment:acollectionofprotectiondevices(relays,fuses,etc.).Excludedaredevicessuch as CTs, CBs, Contactors, etc.c. ProtectionScheme:acollectionofprotectionequipmentprovidingadefinedfunctionandincludingallequipmentrequiredtomakethescheme work (i.e. relays, CTs, CBs, batteries, etc.)In order to fulfil the requirements of protection with theoptimumspeedforthemanydifferentconfigurations,operating conditions and construction features of powersystems, it has been necessary to develop many types ofrelaythatrespondtovariousfunctionsofthepowersystemquantities.Forexample,observationsimplyofthe magnitude of the fault current suffices in some casesbutmeasurementofpowerorimpedancemaybenecessary in others.Relays frequently measure complexfunctions of the system quantities, which are only readilyexpressible by mathematical or graphical means.Relaysmaybeclassifiedaccordingtothetechnologyused:a. electromechanicalb. staticc. digitald. numericalThe different types have somewhat different capabilities,due to the limitations of the technology used.They aredescribed in more detail in Chapter 7.Figure 2.3:Onset of an overhead line faultFigure 2.4:Possible consequence of inadequate protection N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eInmanycases,itisnotfeasibletoprotectagainstallhazardswitharelaythatrespondstoasinglepowersystemquantity.Anarrangementusingseveralquantitiesmayberequired.Inthiscase,eitherseveralrelays,eachrespondingtoasinglequantity,or,morecommonly,asinglerelaycontainingseveralelements,eachrespondingindependentlytoadifferentquantitymay be used.Theterminologyusedindescribingprotectionsystemsand relays is given in Appendix 1.Different symbols fordescribingrelayfunctionsindiagramsofprotectionschemesareused,thetwomostcommonmethods(IECand IEEE/ANSI) are provided in Appendix 2.2. 3ZONESOFPROTECTI ONTolimittheextentofthepowersystemthatisdisconnected when a fault occurs, protection is arrangedin zones.The principle is shown in Figure 2.5.Ideally, thezones of protection should overlap, so that no part of thepower system is left unprotected.This is shown in Figure2.6(a), the circuit breaker being included in both zones.Figure 2.52.6For practical physical and economic reasons, this ideal isnotalwaysachieved,accommodationforcurrenttransformers being in some cases available only on onesideofthecircuitbreakers,asinFigure2.6(b).ThisleavesasectionbetweenthecurrenttransformersandthecircuitbreakerA thatisnotcompletelyprotectedagainst faults.In Figure 2.6(b) a fault at F would causethebusbarprotectiontooperateandopenthecircuitbreaker but the fault may continue to be fed through thefeeder.Thefeederprotection,ifoftheunittype(seesection2.5.2),wouldnotoperate,sincethefaultisoutsideitszone.Thisproblemisdealtwithbyintertripping or some form of zone extension, to ensurethat the remote end of the feeder is tripped also.The point of connection of the protection with the powersystem usually defines the zone and corresponds to thelocationofthecurrenttransformers.Unittypeprotectionwillresultintheboundarybeingaclearlydefinedclosedloop.Figure2.7illustratesatypicalarrangement of overlapping zones.Figure 2.7Alternatively, the zone may be unrestricted; the start willbedefinedbuttheextent(orreach)willdependonmeasurement of the system quantities and will thereforebesubjecttovariation,owingtochangesinsystemconditions and measurement errors. 2 Fundamentals ofProtection Practice 8 Figure 2.7:Overlapping zonesof protection systemsFigure 2.7:Overlapping zones of protection systems~~Figure 2.5: Division of power system into protection zonesFigure 2.5: Division of power system into protection zonesFeeder 2 Feeder 1 Feeder 3Zone 6Zone 5 Zone 7Zone 4Zone 3Zone 2Zone 1Figure 2.6:CT LocationsAAFFFeeder FeedprotectionFeeder FeedprotectionBusbarprotection rotectionBusbarprotection rotection(a) CT's on both sides of circuit breaker(b) CT's on circuit side of circuit breakerFigure 2.6:CT LocationsN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 9 2. 4RELI ABI LI TYTheneedforahighdegreeofreliabilityisdiscussedinSection 2.1.Incorrect operation can be attributed to oneof the following classifications:a. incorrect design/settingsb. incorrect installation/testingc. deterioration in service2.4.1 DesignThedesignofaprotectionschemeisofparamountimportance.Thisistoensurethatthesystemwilloperateunderallrequiredconditions,and(equallyimportant)refrainfromoperatingwhensorequired(including,whereappropriate,beingrestrainedfromoperatingforfaultsexternaltothezonebeingprotected).Dueconsiderationmustbegiventothenature,frequencyanddurationoffaultslikelytobeexperienced, all relevant parameters of the power system(includingthecharacteristicsofthesupplysource,andmethodsofoperation)andthetypeofprotectionequipment used.Of course, no amount of effort at thisstage can make up for the use of protection equipmentthat has not itself been subject to proper design.2.4.2 SettingsItisessentialtoensurethatsettingsarechosenforprotectionrelaysandsystemswhichtakeintoaccounttheparametersoftheprimarysystem,includingfaultand load levels, and dynamic performance requirementsetc.Thecharacteristicsofpowersystemschangewithtime, due to changes in loads, location, type and amountofgeneration,etc.Therefore,settingvaluesofrelaysmayneedtobecheckedatsuitableintervalstoensurethattheyarestillappropriate.Otherwise,unwantedoperation or failure to operate when required may occur.2.4.3 InstallationThe need for correct installation of protection systems isobvious,butthecomplexityoftheinterconnectionsofmany systems and their relationship to the remainder ofthe installation may make checking difficult.Site testingisthereforenecessary;sinceitwillbedifficulttoreproduce all fault conditions correctly, these tests mustbe directed to proving the installation.The tests shouldbelimitedtosuchsimpleanddirecttestsaswillprovethecorrectnessoftheconnections,relaysettings,andfreedomfromdamageoftheequipment.Noattemptshouldbemadeto'typetest'theequipmentortoestablish complex aspects of its technical performance.2.4.4 TestingComprehensivetestingisjustasimportant,andthistestingshouldcoverallaspectsoftheprotectionscheme,aswellasreproducingoperationalandenvironmentalconditionsascloselyaspossible.Typetesting of protection equipment to recognised standardsfulfilsmanyoftheserequirements,butitmaystillbenecessary to test the complete protection scheme (relays,currenttransformersandotherancillaryitems)andthetests must simulate fault conditions realistically.2.4.5 Deterioration in ServiceSubsequenttoinstallationinperfectcondition,deteriorationofequipmentwilltakeplaceandmayeventuallyinterferewithcorrectfunctioning.Forexample, contacts may become rough or burnt owing tofrequentoperation,ortarnishedowingtoatmosphericcontamination;coilsandothercircuitsmaybecomeopen-circuited,electroniccomponentsandauxiliarydevices may fail, and mechanical parts may seize up.The time between operations of protection relays may beyearsratherthandays.Duringthisperioddefectsmayhave developed unnoticed until revealed by the failure ofthe protection to respond to a power system fault.Forthis reason, relays should be regularly tested in order tocheck for correct functioning.Testingshouldpreferablybecarriedoutwithoutdisturbing permanent connections.This can be achievedby the provision of test blocks or switches.Thequalityoftestingpersonnelisanessentialfeaturewhenassessingreliabilityandconsideringmeansforimprovement.Staff must be technically competent andadequately trained, as well as self-disciplined to proceedin a systematic manner to achieve final acceptance.Importantcircuitsthatareespeciallyvulnerablecanbeprovidedwithcontinuouselectricalsupervision;sucharrangementsarecommonlyappliedtocircuitbreakertripcircuitsandtopilotcircuits.Moderndigitalandnumericalrelaysusuallyincorporateself-testing/diagnosticfacilitiestoassistinthedetectionoffailures.With these types of relay, it may be possible toarrange for such failures to be automatically reported bycommunicationslinktoaremoteoperationscentre,sothatappropriateactionmaybetakentoensurecontinuedsafeoperationofthatpartofthepowersystemandarrangementsputinhandforinvestigationand correction of the fault.2.4.6 Protection PerformanceProtectionsystemperformanceisfrequentlyassessedstatistically.For this purpose each system fault is classed 2 Fundamentals ofProtection PracticeN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d easanincidentandonlythosethatareclearedbythetrippingofthecorrectcircuitbreakersareclassedas'correct'.The percentage of correct clearances can thenbe determined.This principle of assessment gives an accurate evaluationoftheprotectionofthesystemasawhole,butitissevereinitsjudgementofrelayperformance.Manyrelaysarecalledintooperationforeachsystemfault,and all must behave correctly for a correct clearance tobe recorded.Completereliabilityisunlikelyevertobeachievedbyfurtherimprovementsinconstruction.Ifthelevelofreliability achieved by a single device is not acceptable,improvementcanbeachievedthroughredundancy,e.g.duplicationofequipment.Twocomplete,independent,mainprotectionsystemsareprovided,andarrangedsothat either by itself can carry out the required function.If the probability of each equipment failing is x/unit, theresultantprobabilityofbothequipmentsfailingsimultaneously, allowing for redundancy, is x2.Where xis small the resultant risk (x2) may be negligible.Where multiple protection systems are used, the trippingsignalcanbeprovidedinanumberofdifferentways.The two most common methods are:a. all protection systems must operate for a trippingoperationtooccur(e.g.two-out-of-twoarrangement)b. only one protection system need operate to causea trip (e.g. one-out-of two arrangement)Theformermethodguardsagainstmaloperationwhilethelatterguardsagainstfailuretooperateduetoanunrevealedfaultinaprotectionsystem.Rarely,threemainprotectionsystemsareprovided,configuredinatwo-out-of three tripping arrangement, to provide bothreliabilityoftripping,andsecurityagainstunwantedtripping.Ithaslongbeenthepracticetoapplyduplicateprotectionsystemstobusbars,bothbeingrequiredtooperatetocompleteatrippingoperation.Lossofabusbarmaycausewidespreadlossofsupply,whichisclearly undesirable.In other cases, important circuits areprovided with duplicate main protection systems, eitherbeing able to trip independently.On critical circuits, usemayalsobemadeofadigitalfaultsimulatortomodelthe relevant section of the power system and check theperformance of the relays used.2. 5SELECTI VI TYWhenafaultoccurs,theprotectionschemeisrequiredtotriponlythosecircuitbreakerswhoseoperationisrequiredtoisolatethefault.Thispropertyofselectivetripping is also called 'discrimination' and is achieved bytwo general methods.2.5.1 Time GradingProtectionsystemsinsuccessivezonesarearrangedtooperate in times that are graded through the sequence ofequipmentssothatupontheoccurrenceofafault,althoughanumberofprotectionequipmentsrespond,onlythoserelevanttothefaultyzonecompletethetrippingfunction.Theothersmakeincompleteoperationsandthenreset.Thespeedofresponsewilloftendependontheseverityofthefault,andwillgenerally be slower than for a unit system.2.5.2 Unit SystemsItispossibletodesignprotectionsystemsthatrespondonlytofaultconditionsoccurringwithinaclearlydefined zone.This type of protection system is known as'unitprotection'.Certaintypesofunitprotectionareknown by specific names, e.g. restricted earth fault anddifferentialprotection.Unitprotectioncanbeappliedthroughout a power system and, since it does not involvetime grading, is relatively fast in operation.The speed ofresponse is substantially independent of fault severity.Unit protection usually involves comparison of quantitiesat the boundaries of the protected zone as defined by thelocationsofthecurrenttransformers.Thiscomparisonmaybeachievedbydirecthard-wiredconnectionsormaybeachievedviaacommunicationslink.Howevercertainprotectionsystemsderivetheir'restricted'property from the configuration of the power system andmaybeclassedasunitprotection,e.g.earthfaultprotection applied to the high voltage delta winding of apowertransformer.Whichevermethodisused,itmustbe kept in mind that selectivity is not merely a matter ofrelaydesign.Italsodependsonthecorrectco-ordinationofcurrenttransformersandrelayswithasuitable choice of relay settings, taking into account thepossiblerangeofsuchvariablesasfaultcurrents,maximumloadcurrent,systemimpedancesandotherrelated factors, where appropriate.2. 6STABI LI TYThetermstabilityisusuallyassociatedwithunitprotectionschemesandreferstotheabilityoftheprotectionsystemtoremainunaffectedbyconditionsexternal to the protected zone, for example through loadcurrent and external fault conditions.2. 7SPEEDThe function of protection systems is to isolate faults onthepowersystemasrapidlyaspossible.Themainobjectiveistosafeguardcontinuityofsupplybyremoving each disturbance before it leads to widespreadlossofsynchronismandconsequentcollapseofthepower system. 2 Fundamentals ofProtection Practice 1 0 N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 1 Astheloadingonapowersystemincreases,thephaseshiftbetweenvoltagesatdifferentbusbarsonthesystemalsoincreases,andthereforesodoestheprobabilitythatsynchronismwillbelostwhenthesystemisdisturbedbyafault.Theshorterthetimeafault is allowed to remain in the system, the greater canbetheloadingofthesystem.Figure2.8showstypicalrelationsbetweensystemloadingandfaultclearancetimesforvarioustypesoffault.Itwillbenotedthatphase faults have a more marked effect on the stabilityofthesystemthanasimpleearthfaultandthereforerequire faster clearance.Figure 2.8 System stability is not, however, the only consideration.Rapid operation of protection ensures that fault damageisminimised,asenergyliberatedduringafaultisproportional to the square of the fault current times thedurationofthefault.Protectionmustthusoperateasquicklyaspossiblebutspeedofoperationmustbeweighedagainsteconomy.Distributioncircuits,whichdo not normally require a fast fault clearance, are usuallyprotected by time-graded systems.Generating plant andEHVsystemsrequireprotectiongearofthehighestattainablespeed;theonlylimitingfactorwillbethenecessityforcorrectoperation,andthereforeunitsystems are normal practice.2. 8SENSI TI VI TYSensitivityisatermfrequentlyusedwhenreferringtotheminimumoperatinglevel(current,voltage,poweretc.) of relays or complete protection schemes.The relayor scheme is said to be sensitive if the primary operatingparameter(s) is low.Witholderelectromechanicalrelays,sensitivitywasconsideredintermsofthesensitivityofthemeasuringmovement and was measured in terms of its volt-ampereconsumptiontocauseoperation.Withmoderndigitaland numerical relays the achievable sensitivity is seldomlimitedbythedevicedesignbutbyitsapplicationandCT/VT parameters.2. 9PRI MARYANDBACK-UPPROTECTI ONThereliabilityofapowersystemhasbeendiscussedearlier,includingtheuseofmorethanoneprimary(ormain)protectionsystemoperatinginparallel.Intheeventoffailureornon-availabilityoftheprimaryprotection some other means of ensuring that the faultisisolatedmustbeprovided.Thesesecondarysystemsare referred to as back-up protection.Back-upprotectionmaybeconsideredaseitherbeinglocal or remote.Local back-up protection is achievedbyprotectionwhichdetectsanun-clearedprimarysystem fault at its own location and which then trips itsown circuit breakers, e.g. time graded overcurrent relays.Remoteback-upprotectionisprovidedbyprotectionthatdetectsanun-clearedprimarysystemfaultataremotelocationandthenissuesalocaltripcommand,e.g. the second or third zones of a distance relay.In bothcases the main and back-up protection systems detect afaultsimultaneously,operationoftheback-upprotectionbeingdelayedtoensurethattheprimaryprotectionclearsthefaultifpossible.Normallybeingunit protection, operation of the primary protection willbefastandwillresultintheminimumamountofthepowersystembeingdisconnected.Operationoftheback-up protection will be, of necessity, slower and willresultinagreaterproportionoftheprimarysystembeing lost.Theextentandtypeofback-upprotectionappliedwillnaturallyberelatedtothefailurerisksandrelativeeconomicimportanceofthesystem.Fordistributionsystems where fault clearance times are not critical, timedelayedremoteback-upprotectionmaybeadequate.For EHV systems, where system stability is at risk unlessafaultisclearedquickly,multipleprimaryprotectionsystems,operatinginparallelandpossiblyofdifferenttypes (e.g. distance and unit protection), will be used toensurefastandreliabletripping.Back-upovercurrentprotection may then optionally be applied to ensure thattwoseparateprotectionsystemsareavailableduringmaintenance of one of the primary protection systems.Back-upprotectionsystemsshould,ideally,becompletelyseparatefromtheprimarysystems.Forexample a circuit protected by a current differential relaymayalsohavetimegradedovercurrentandearthfaultrelaysaddedtoprovidecircuitbreakertrippingintheevent of failure of the main primary unit protection.Tomaintain complete separation and thus integrity, currenttransformers, voltage transformers, relays, circuit breakertripcoilsandd.c.supplieswouldbeduplicated.Thisidealisrarelyattainedinpractice.Thefollowingcompromises are typical:a. separatecurrenttransformers(coresandsecondarywindings only) are provided.This involves little extracostoraccommodationcomparedwiththeuseof 2 Fundamentals ofProtection PracticeFigure 2.8:Typical power/time relationshipfor various fault typesTimeLoad powerPhase-earthPhase-phaseThree-phasePhase-phase-earthN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d ecommoncurrenttransformersthatwouldhavetobelarger because of the combined burden.This practiceisbecominglesscommonwhendigitalornumericalrelaysareused,becauseoftheextremelylowinputburden of these relay typesb. voltagetransformersarenotduplicatedbecauseofcost and space considerations.Each protection relaysupplyisseparatelyprotected(fuseorMCB)andcontinuouslysupervisedtoensuresecurityoftheVToutput.An alarm is given on failure of the supply and,where appropriate, prevent an unwanted operation ofthe protectionc. tripsuppliestothetwoprotectionsshouldbeseparatelyprotected(fuseorMCB).Duplicationoftripping batteries and of circuit breaker tripping coilsmay be provided.Trip circuits should be continuouslysupervisedd. it is desirable that the main and back-up protections (orduplicate main protections) should operate on differentprinciples,sothatunusualeventsthatmaycausefailure of the one will be less likely to affect the otherDigitalandnumericalrelaysmayincorporatesuitableback-upprotectionfunctions(e.g.adistancerelaymayalsoincorporatetime-delayedovercurrentprotectionelements as well).A reduction in the hardware required toprovide back-up protection is obtained, but at the risk thatacommonrelayelementfailure(e.g.thepowersupply)will result in simultaneous loss of both main and back-upprotection.Theacceptabilityofthissituationmustbeevaluated on a case-by-case basis.2. 10RELAYOUTPUTDEVI CESIn order to perform their intended function, relays must befittedwithsomemeansofprovidingthevariousoutputsignalsrequired.Contactsofvarioustypesusuallyfulfilthis function.2.10.1 Contact SystemsRelaysmaybefittedwithavarietyofcontactsystemsforprovidingelectricaloutputsfortrippingandremoteindicationpurposes.Themostcommontypesencountered are as follows:a. Self-resetThe contacts remain in the operated condition onlywhile the controlling quantity is applied, returningto their original condition when it is removedb. Hand or electrical resetThesecontactsremainintheoperatedconditionafter the controlling quantity is removed.They canbereseteitherbyhandorbyanauxiliaryelectromagnetic elementThe majority of protection relay elements have self-resetcontact systems, which, if so desired, can be modified toprovidehandresetoutputcontactsbytheuseofauxiliary elements.Hand or electrically reset relays areused when it is necessary to maintain a signal or lockoutcondition.Contactsareshownondiagramsinthepositioncorrespondingtotheun-operatedorde-energised condition, regardless of the continuous serviceconditionoftheequipment.Forexample,anundervoltagerelay,whichiscontinuallyenergisedinnormalcircumstances,wouldstillbeshowninthede-energised condition.A 'make' contact is one that closes when the relay picksup, whereas a 'break' contact is one that is closed whenthe relay is de-energised and opens when the relay picksup.Examplesoftheseconventionsandvariationsareshown in Figure 2.9.Aprotectionrelayisusuallyrequiredtotripacircuitbreaker,thetrippingmechanismofwhichmaybeasolenoidwithaplungeractingdirectlyonthemechanismlatchoranelectricallyoperatedvalve.Thepower required by the trip coil of the circuit breaker mayrangefromupto50wattsforasmall'distribution'circuitbreaker,to3000wattsforalarge,extra-high-voltage circuit breaker.Therelaymaythereforeenergisethetrippingcoildirectly, or, according to the coil rating and the numberofcircuitstobeenergised,maydosothroughtheagency of another multi-contact auxiliary relay.The basic trip circuit is simple, being made up of a hand-tripcontrolswitchandthecontactsoftheprotectionrelays in parallel to energise the trip coil from a battery,throughanormallyopenauxiliaryswitchoperatedbythecircuitbreaker.Thisauxiliaryswitchisneededtoopenthetripcircuitwhenthecircuitbreakeropenssince the protection relay contacts will usually be quiteincapableofperformingtheinterruptingduty.Theauxiliaryswitchwillbeadjustedtocloseasearlyaspossibleintheclosingstroke,tomaketheprotectioneffective in case the breaker is being closed on to a fault. 2 Fundamentals ofProtection Practice 1 2 Figure 2.9:Contact typesSelf resetFigure 2.9: Contact typesHand reset`make' contacts(normally open)`break' contacts(normally open)Time delay onpick upTime delay ondrop-offN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 3 Wheremultipleoutputcontacts,orcontactswithappreciablecurrent-carryingcapacityarerequired,interposing, contactor type elements will normally be used.In general, static and microprocessor relays have discretemeasuringandtrippingcircuits,ormodules.Thefunctioning of the measuring modules is independent ofoperationofthetrippingmodules.Sucharelayisequivalent to a sensitive electromechanical relay with atrippingcontactor,sothatthenumberorratingofoutputs has no more significance than the fact that theyhave been provided.Forlargerswitchgearinstallationsthetrippingpowerrequirement of each circuit breaker is considerable, andfurther, two or more breakers may have to be tripped byoneprotectionsystem.Theremayalsoberemotesignallingrequirements,interlockingwithotherfunctions(forexampleauto-reclosingarrangements),andothercontrolfunctionstobeperformed.Thesevariousoperationsmaythenbecarriedoutbymulti-contacttrippingrelays,whichareenergisedbytheprotectionrelaysandprovidethenecessarynumberofadequately rated output contacts.2.10.2 Operation IndicatorsProtectionsystemsareinvariablyprovidedwithindicatingdevices,called'flags',or'targets',asaguidefor operations personnel.Not every relay will have one,asindicatorsarearrangedtooperateonlyifatripoperationisinitiated.Indicators,withveryfewexceptions,arebi-stabledevices,andmaybeeithermechanical or electrical.A mechanical indicator consistsof a small shutter that is released by the protection relaymovement to expose the indicator pattern.Electricalindicatorsmaybesimpleattractedarmatureelements,whereoperationofthearmaturereleasesashuttertoexposeanindicatorasabove,orindicatorlights (usually light emitting diodes).For the latter, somekindofmemorycircuitisprovidedtoensurethattheindicator remains lit after the initiating event has passed.Withtheadventofdigitalandnumericalrelays,theoperationindicatorhasalmostbecomeredundant.Relays will be provided with one or two simple indicatorsthat indicate that the relay is powered up and whetheranoperationhasoccurred.Theremainderoftheinformationpreviouslypresentedviaindicatorsisavailablebyinterrogatingtherelaylocallyviaaman-machineinterface(e.g.akeypadandliquidcrystaldisplay screen), or remotely via a communication system.2. 11TRI PPI NGCI RCUI TSTherearethreemaincircuitsinuseforcircuitbreakertripping:a. series sealingb. shunt reinforcingc. shunt reinforcement with sealingThese are illustrated in Figure 2.10.Forelectromechanicalrelays,electricallyoperatedindicators, actuated after the main contacts have closed,avoidimposinganadditionalfrictionloadonthemeasuringelement,whichwouldbeaserioushandicapforcertaintypes.Caremustbetakenwithdirectlyoperatedindicatorstolineuptheiroperationwiththeclosureofthemaincontacts.Theindicatormusthaveoperatedbythetimethecontactsmake,butmustnothave done so more than marginally earlier.This is to stopindication occurring when the tripping operation has notbeen completed.Withmoderndigitalandnumericalrelays,theuseofvariousalternativemethodsofprovidingtripcircuitfunctionsislargelyobsolete.Auxiliaryminiaturecontactorsareprovidedwithintherelaytoprovideoutputcontactfunctionsandtheoperationofthesecontactorsisindependentofthemeasuringsystem,asmentionedpreviously.Themakingcurrentoftherelayoutputcontactsandtheneedtoavoidthesecontactsbreakingthetripcoilcurrentlargelydictatescircuitbreakertripcoilarrangements.Commentsonthevariousmeansofprovidingtrippingarrangementsare,however,includedbelowasahistoricalreferenceapplicable to earlier electromechanical relay designs. 2 Fundamentals ofProtection PracticeFigure 2.10:Typical relay tripping circuits(a) Series sealingFigure 2.10: Typical relay tripping circuitsPRTCPRTCPRTC52a(b) Shunt reinforcing52a(c) Shunt reinforcing with series sealing52aN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e2.11.1 Series sealingThecoiloftheseriescontactorcarriesthetripcurrentinitiated by the protection relay, and the contactor closesacontactinparallelwiththeprotectionrelaycontact.This closure relieves the protection relay contact of furtherduty and keeps the tripping circuit securely closed, even ifchatter occurs at the main contact.The total tripping timeisnotaffected,andtheindicatordoesnotoperateuntilcurrent is actually flowing through the trip coil.The main disadvantage of this method is that such serieselementsmusthavetheircoilsmatchedwiththetripcircuit with which they are associated.Thecoilofthesecontactsmustbeoflowimpedance,with about 5% of the trip supply voltage being droppedacross them.Whenusedinassociationwithhigh-speedtriprelays,whichusuallyinterrupttheirowncoilcurrent,theauxiliaryelementsmustbefastenoughtooperateandrelease the flag before their coil current is cut off.Thismayposeaproblemindesignifavariablenumberofauxiliaryelements(fordifferentphasesandsoon)maybe required to operate in parallel to energise a commontripping relay.2.11.2 Shunt reinforcingHerethesensitivecontactsarearrangedtotripthecircuitbreakerandsimultaneouslytoenergisetheauxiliary unit, which then reinforces the contact that isenergising the trip coil.Two contacts are required on the protection relay, sinceitisnotpermissibletoenergisethetripcoilandthereinforcing contactor in parallel.If this were done, andmorethanoneprotectionrelaywereconnectedtotripthe same circuit breaker, all the auxiliary relays would beenergisedinparallelforeachrelayoperationandtheindication would be confused.The duplicate main contacts are frequently provided as athree-pointarrangementtoreducethenumberofcontact fingers.2.11.3 Shunt reinforcement with sealingThis is a development of the shunt reinforcing circuit tomakeitapplicabletosituationswherethereisapossibility of contact bounce for any reason.Usingtheshuntreinforcingsystemunderthesecircumstances would result in chattering on the auxiliaryunit,andthepossibleburningoutofthecontacts,notonlyofthesensitiveelementbutalsooftheauxiliaryunit.Thechatteringwouldendonlywhenthecircuitbreaker had finally tripped.The effect of contact bounceiscounteredbymeansofafurthercontactontheauxiliary unit connected as a retaining contact.This means that provision must be made for releasing thesealingcircuitwhentrippingiscomplete;thisisadisadvantage,becauseitissometimesinconvenienttofind a suitable contact to use for this purpose.2. 12TRI PCI RCUI TSUPERVI SI ONThetripcircuitincludestheprotectionrelayandothercomponents, such as fuses, links, relay contacts, auxiliaryswitchcontacts,etc.,andinsomecasesthroughaconsiderable amount of circuit wiring with intermediateterminalboards.Theseinterconnections,coupledwiththe importance of the circuit, result in a requirement inmany cases to monitor the integrity of the circuit.Thisisknownastripcircuitsupervision.Thesimplestarrangementcontainsahealthytriplamp,asshowninFigure 2.11(a).Theresistanceinserieswiththelamppreventsthebreaker being tripped by an internal short circuit causedbyfailureofthelamp.Thisprovidessupervisionwhilethecircuitbreakerisclosed;asimpleextensiongivespre-closing supervision.Figure2.11(b)showshow,theadditionofanormallyclosed auxiliary switch and a resistance unit can providesupervision while the breaker is both open and closed. 2 Fundamentals ofProtection Practice 1 4 Figure 2.11:Trip circuit supervision circuits.PRTC52aPRTCPRTC52a52b(c) Supervision with circuit breaker open or closed with remote alarm (scheme H7)52aAAlarm52a52bTCCircuit breakerTripTrip(d) Implementation of H5 scheme in numerical relay(a) Supervision while circuit breaker is closed (scheme H4)(b) Supervision while circuit breaker is open or closed (scheme H5)CBN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 5 Ineithercase,theadditionofanormallyopenpush-buttoncontactinserieswiththelampwillmakethesupervision indication available only when required.Schemes using a lamp to indicate continuity are suitableforlocallycontrolledinstallations,butwhencontrolisexercisedfromadistanceitisnecessarytousearelaysystem.Figure 2.11(c) illustrates such a scheme, which isapplicable wherever a remote signal is required.With the circuit healthy, either or both of relays A and Bare operated and energise relay C.Both A and B mustreset to allow C to drop-off.Relays A, B and C are timedelayedtopreventspuriousalarmsduringtrippingorclosing operations.The resistors are mounted separatelyfrom the relays and their values are chosen such that ifanyonecomponentisinadvertentlyshort-circuited,tripping will not take place.The alarm supply should be independent of the trippingsupplysothatindicationwillbeobtainedincaseoffailure of the tripping supply.The above schemes are commonly known as the H4, H5and H7 schemes, arising from the diagram references oftheUtilityspecificationinwhichtheyoriginallyappeared.Figure2.11(d)showsimplementationofschemeH5usingthefacilitiesofamodernnumericalrelay.Remoteindicationisachievedthroughuseofprogrammablelogicandadditionalauxiliaryoutputsavailable in the protection relay. 2 Fundamentals ofProtection PracticeIntroduction 3.1Vector algebra 3.2Manipulation of complex quantities 3.3Circuit quantities and conventions 3.4Impedance notation 3.5Basic circuit laws, 3.6theorems and network reductionReferences 3.7 3 F u n d a m e n t a l T h e o r yN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 7 3. 1I NTRODUCTI ONTheProtectionEngineerisconcernedwithlimitingtheeffectsofdisturbancesinapowersystem.Thesedisturbances,ifallowedtopersist,maydamageplantandinterruptthesupplyofelectricenergy.Theyaredescribedasfaults(shortandopencircuits)orpowerswings,andresultfromnaturalhazards(forinstancelightning), plant failure or human error.To facilitate rapid removal of a disturbance from a powersystem,thesystemisdividedinto'protectionzones'.Relaysmonitorthesystemquantities(current,voltage)appearing in these zones; if a fault occurs inside a zone,the relays operate to isolate the zone from the remainderof the power system.Theoperatingcharacteristicofarelaydependsontheenergizing quantities fed to it such as current or voltage,or various combinations of these two quantities, and onthe manner in which the relay is designed to respond tothisinformation.Forexample,adirectionalrelaycharacteristic would be obtained by designing the relayto compare the phase angle between voltage and currentattherelayingpoint.Animpedance-measuringcharacteristic, on the other hand, would be obtained bydesigningtherelaytodividevoltagebycurrent.Manyothermorecomplexrelaycharacteristicsmaybeobtainedbysupplyingvariouscombinationsofcurrentand voltage to the relay.Relays may also be designed torespondtoothersystemquantitiessuchasfrequency,power, etc.In order to apply protection relays, it is usually necessaryto know the limiting values of current and voltage, andtheirrelativephasedisplacementattherelaylocation,for various types of short circuit and their position in thesystem.This normally requires some system analysis forfaults occurring at various points in the system.The main components that make up a power system aregeneratingsources,transmissionanddistributionnetworks, and loads. Many transmission and distributioncircuits radiate from key points in the system and thesecircuitsarecontrolledbycircuitbreakers.Forthepurposeofanalysis,thepowersystemistreatedasanetworkofcircuitelementscontainedinbranchesradiatingfromnodestoformclosedloopsormeshes.Thesystemvariablesarecurrentandvoltage,andin 3 Fundamental Theor yN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e3Fundamental Theory 1 8 steady state analysis, they are regarded as time varyingquantitiesatasingleandconstantfrequency.Thenetworkparametersareimpedanceandadmittance;these are assumed to be linear, bilateral (independent ofcurrent direction) and constant for a constant frequency.3. 2VECTORALGEBRAAvectorrepresentsaquantityinbothmagnitudeanddirection.InFigure3.1thevectorOPhasamagnitude|Z| at an angle with the reference axis OX.Figure 3.1It may be resolved into two components at right anglestoeachother,inthiscasex andy.Themagnitudeorscalar value of vector Z is known as the modulus |Z|, andtheangleistheargument,andiswrittenasarg.Z. Theconventionalmethodofexpressingavector Zistowrite simply |Z|.Thisformcompletelyspecifiesavectorforgraphicalrepresentation or conversion into other forms.Forvectorstobeuseful,theymustbeexpressedalgebraically. In Figure 3.1, the vectorZ is the resultantofvectoriallyaddingitscomponentsx andy;algebraically this vector may be written as:Z = x + jy Equation 3.1wheretheoperatorj indicatesthatthecomponent y isperpendiculartocomponentx.Inelectricalnomenclature, the axis OC is the 'real' or 'in-phase' axis,andtheverticalaxisOYiscalledthe'imaginary'or'quadrature'axis.Theoperatorj rotatesavectoranti-clockwise through 90.If a vector is made to rotate anti-clockwisethrough180,thentheoperatorj hasperformeditsfunctiontwice,andsincethevectorhasreversed its sense, then:j x j or j2= -1whencej = -1Therepresentationofavectorquantityalgebraicallyinterms of its rectangular co-ordinates is called a 'complexquantity'.Therefore, x + jy is a complex quantity and isthe rectangular form of the vector |Z| where:Equation 3.2From Equations 3.1 and 3.2:Z = |Z| (cos + jsin) Equation 3.3andsincecos andsinmaybeexpressedinexponential form by the identities:it follows thatZ may also be written as:Z =|Z| ejEquation 3.4Therefore,avectorquantitymayalsoberepresentedtrigonometrically and exponentially.3. 3MANI PULATI ONOFCOMPLEXQUANTI TI ESComplexquantitiesmayberepresentedinanyofthefour co-ordinate systems given below:a. Polar Z b. Rectangular x + jyc. Trigonometric |Z| (cos + jsin)d. Exponential |Z| ejThe modulus |Z| and the argument are together knownas'polarco-ordinates',andx andy aredescribedas'cartesianco-ordinates'.Conversionbetweenco-ordinatesystemsiseasilyachieved.Astheoperatorjobeys the ordinary laws of algebra, complex quantities inrectangularformcanbemanipulatedalgebraically,ascan be seen by the following:Z1+Z2= (x1+x2) + j(y1+y2) Equation 3.5Z1-Z2= (x1-x2) + j(y1-y2) Equation 3.6(see Figure 3.2)cos =e ej j2sin =e ejj j2Z x yyxx Zy Z= +( )===,2 21tancossinFigure 3.1:Vector OP Figure 3.1:Vector OP0YXP|Z|yxqN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 9 3Fundamental TheoryEquation 3.73.3.1 Complex variablesSome complex quantities are variable with, for example,time;whenmanipulatingsuchvariablesindifferentialequationsitisexpedienttowritethecomplexquantityin exponential form.Whendealingwithsuchfunctionsitisimportanttoappreciate that the quantity contains real and imaginarycomponents.Ifitisrequiredtoinvestigateonlyonecomponentofthecomplexvariable,separationintocomponents must be carried out after the mathematicaloperation has taken place.Example:Determinetherateofchangeoftherealcomponent of a vector |Z|wt with time.|Z|wt = |Z| (coswt + jsinwt)= |Z| ejwtThe real component of the vector is |Z|coswt.Differentiating |Z| e jwtwith respect to time:= jw|Z| (coswt + jsinwt)Separating into real and imaginary components:Thus,therateofchangeoftherealcomponentofavector |Z|wt is:-|Z| w sinwtddtZe Z w wt jw wtjwt( )= +( )sin cosddt Ze jw Zejwt jwt=Z Z Z ZZZZZ1 2 1 2 1 212121 2= += , 3.3.2 Complex NumbersAcomplexnumbermaybedefinedasaconstantthatrepresentstherealandimaginarycomponentsofaphysicalquantity.Theimpedanceparameterofanelectriccircuitisacomplexnumberhavingrealandimaginary components, which are described as resistanceand reactance respectively.Confusionoftenarisesbetweenvectorsandcomplexnumbers.Avector,aspreviouslydefined,maybeacomplex number.In this context, it is simply a physicalquantityofconstantmagnitudeactinginaconstantdirection.Acomplexnumber,which,beingaphysicalquantityrelatingstimulusandresponseinagivenoperation,isknownasa'complexoperator'.Inthiscontext, it is distinguished from a vector by the fact thatit has no direction of its own.Because complex numbers assume a passive role in anycalculation,theformtakenbythevariablesintheproblem determines the method of representing them.3.3.3 Mathematical OperatorsMathematicaloperatorsarecomplexnumbersthatareusedtomoveavectorthroughagivenanglewithoutchanging the magnitude or character of the vector.Anoperator is not a physical quantity; it is dimensionless.Thesymbolj,whichhasbeencompoundedwithquadraturecomponentsofcomplexquantities,isanoperator that rotates a quantity anti-clockwise through90.Anotherusefuloperatorisonewhichmovesavectoranti-clockwisethrough120,commonlyrepresented by the symbol a.Operators are distinguished by one further feature; theyaretherootsofunity.UsingDeMoivre'stheorem,thenth root of unity is given by solving the expression:11/n= (cos2m + jsin2m)1/nwhere m is any integer. Hence:where m has values 1, 2, 3, ... (n-1)From the above expression j is found to be the 4th rootand a the 3rd root of unity, as they have four and threedistinct values respectively.Table 3.1 gives some usefulfunctions of the a operator.12 21/cos sinnmnjmn= + Figure 3.2:Addition of vectorsFigure 3.2:Addition of vectors0YXy1y2x2x1|Z1||Z2|N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e1=1+ j0 = ej01+ a + a2 = 0Table 3.1: Properties of the a operator3. 4CI RCUI TQUANTI TI ESANDCONVENTI ONSCircuitanalysismaybedescribedasthestudyoftheresponseofacircuittoanimposedcondition,forexample a short circuit.The circuit variables are currentandvoltage.Conventionally,currentflowresultsfromtheapplicationofadrivingvoltage,butthereiscompletedualitybetweenthevariablesandeithermaybe regarded as the cause of the other.When a circuit exists, there is an interchange of energy;a circuit may be described as being made up of 'sources'and 'sinks' for energy.The parts of a circuit are describedaselements;a'source'mayberegardedasan'active'element and a 'sink' as a 'passive' element.Some circuitelementsaredissipative,thatis,theyarecontinuoussinksforenergy,forexampleresistance.Othercircuitelementsmaybealternatelysourcesandsinks,forexample capacitance and inductance.The elements of acircuit are connected together to form a network havingnodes(terminalsorjunctions)andbranches(seriesgroups of elements) that form closed loops (meshes).In steady state a.c. circuit theory, the ability of a circuittoacceptacurrentflowresultingfromagivendrivingvoltageiscalledtheimpedanceofthecircuit.Sincecurrent and voltage are duals the impedance parametermust also have a dual, called admittance.3.4.1 Circuit VariablesAs current and voltage are sinusoidal functions of time,varyingatasingleandconstantfrequency,theyareregardedasrotatingvectorsandcanbedrawnasplanvectors (that is, vectors defined by two co-ordinates) ona vector diagram.ja a=23a a j =231 32 = a j a1 32 = a j aa j ej2431232= =a j ej= + =123223Forexample,theinstantaneousvalue,e,ofavoltagevarying sinusoidally with time is:e=Emsin(wt+) Equation 3.8where:Emis the maximum amplitude of the waveform;=2f, the angular velocity, is the argument defining the amplitude of thevoltage at a time t=0At t=0, the actual value of the voltage is Emsin.So ifEmisregardedasthemodulusofavector,whoseargument is , then Emsin is the imaginary componentof the vector |Em|.Figure 3.3 illustrates this quantityas a vector and as a sinusoidal function of time.Figure 3.3The current resulting from applying a voltage to a circuitdepends upon the circuit impedance.If the voltage is asinusoidalfunctionatagivenfrequencyandtheimpedanceisconstantthecurrentwillalsovaryharmonically at the same frequency, so it can be shownon the same vector diagram as the voltage vector, and isgiven by the equationEquation 3.9where:Equation 3.10FromEquations3.9and3.10itcanbeseenthattheangular displacement between the current and voltagevectorsandthecurrentmagnitude|Im|=|Em|/|Z| isdependent upon the impedanceZ .In complex form theimpedancemaybewrittenZ=R+jX.The'realcomponent',R,isthecircuitresistance,andtheZ R XX LCXR= +=

_,

=,2 211 taniEZwtm= + ( )sin 3Fundamental Theory 2 0 Figure 3.3:Representationof a sinusoidal functionFigure 3.3:Representation of a sinusoidal functionYX' X 0Y'et = 0t|Em|EmN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 2 1 'imaginary component', X, is the circuit reactance.Whenthe circuit reactance is inductive (that is, wL>1/wC), thecurrent'lags'thevoltagebyanangle ,andwhenitiscapacitive (that is, 1/wC>wL) it 'leads' the voltage by anangle .When drawing vector diagrams, one vector is chosen asthe'referencevector'andallothervectorsaredrawnrelativetothereferencevectorintermsofmagnitudeandangle.Thecircuitimpedance|Z|isacomplexoperatorandisdistinguishedfromavectoronlybythefactthatithasnodirectionofitsown.Afurtherconventionisthatsinusoidallyvaryingquantitiesaredescribed by their 'effective' or 'root mean square' (r.m.s.)values;theseareusuallywrittenusingtherelevantsymbol without a suffix.Thus:Equation 3.11The 'root mean square' value is that value which has thesame heating effect as a direct current quantity of thatvalueinthesamecircuit,andthisdefinitionappliestonon-sinusoidal as well as sinusoidal quantities.3.4.2 Sign ConventionsIndescribingtheelectricalstateofacircuit,itisoftennecessarytorefertothe'potentialdifference'existingbetween two points in the circuit.Since wherever sucha potential difference exists, current will flow and energywilleitherbetransferredorabsorbed,itisobviouslynecessary to define a potential difference in more exactterms.For this reason, the terms voltage rise and voltagedrop are used to define more accurately the nature of thepotential difference.Voltageriseisariseinpotentialmeasuredinthedirection of current flow between two points in a circuit.Voltagedropistheconverse.Acircuitelementwithavoltage rise across it acts as a source of energy.A circuitelementwithavoltagedropacrossitactsasasinkofenergy.Voltagesourcesareusuallyactivecircuitelements,whilesinksareusuallypassivecircuitelements.The positive direction of energy flow is fromsources to sinks.Kirchhoff'sfirstlawstatesthatthesumofthedrivingvoltages must equal the sum of the passive voltages in aclosedloop.Thisisillustratedbythefundamentalequation of an electric circuit:Equation 3.12where the terms on the left hand side of the equation arevoltagedropsacrossthecircuitelements.ExpressediniRLdidt Cidt e + + =1I IE Emm==,22steady state terms Equation 3.12 may be written:Equation 3.13and this is known as the equated-voltage equation [3.1].Itistheequationmostusuallyadoptedinelectricalnetworkcalculations,sinceitequatesthedrivingvoltages,whichareknown,tothepassivevoltages,which are functions of the currents to be calculated.Indescribingcircuitsanddrawingvectordiagrams,forformal analysis or calculations, it is necessary to adopt anotation which defines the positive direction of assumedcurrentflow,andestablishesthedirectioninwhichpositivevoltagedropsandvoltagerisesact.Twomethods are available; one, the double suffix method, isused for symbolic analysis, the other, the single suffix ordiagrammaticmethod,isusedfornumericalcalculations.Inthedoublesuffixmethodthepositivedirectionofcurrent flow is assumed to be from node a to node b andthecurrentisdesignatedIab.Withthediagrammaticmethod, an arrow indicates the direction of current flow.Thevoltagerisesarepositivewhenactinginthedirection of current flow.It can be seen from Figure 3.4thatE1andEanarepositivevoltagerisesandE2andEbnarenegativevoltagerises.Inthediagrammaticmethod their direction of action is simply indicated by anarrow, whereas in the double suffix method,EanandEbnindicate that there is a potential rise in directions na and nb.Figure 3.4 Methods or representing a circuitE I Z =3Fundamental Theory(a) DiagrammaticFigure 3.4: Circuit representation methods(b) Double suffixa bnabIZ3Z2Z1E1ZanZabEanZbnEbnE2E1-E2=(Z1+Z2+Z3)IEan-Ebn=(Zan+Zab+Zbn)IabIFigure 3.4 Methods of representing a circuitN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eVoltagedropsarealsopositivewhenactinginthedirectionofcurrentflow.FromFigure3.4(a)itcanbeseen that (Z1+Z2+Z3)I is the total voltage drop in theloop in the direction of current flow, and must equate tothe total voltage rise E1-E2.In Figure 3.4(b), the voltagedropbetweennodesa andb designated Vabindicatesthat point b is at a lower potential than a, and is positivewhencurrentflowsfroma tob.Conversely Vbaisanegative voltage drop.Symbolically:Vab= Van- VbnVba= Vbn- VanEquation 3.14where n is a common reference point.3.4.3 PowerTheproductofthepotentialdifferenceacrossandthecurrent through a branch of a circuit is a measure of therate at which energy is exchanged between that branchandtheremainderofthecircuit.Ifthepotentialdifferenceisapositivevoltagedrop,thebranchispassive and absorbs energy.Conversely, if the potentialdifference is a positive voltage rise, the branch is activeand supplies energy.Therateatwhichenergyisexchangedisknownaspower,andbyconvention,thepowerispositivewhenenergyisbeingabsorbedandnegativewhenbeingsupplied.With a.c. circuits the power alternates, so, toobtain a rate at which energy is supplied or absorbed, itisnecessarytotaketheaveragepoweroveronewholecycle.If e=Emsin(wt+) and i=Imsin(wt+-), then the powerequation is:p=ei=P[1-cos2(wt+)]+Qsin2(wt+)Equation 3.15where:P=|E||I|cos andQ=|E||I|sinFromEquation3.15itcanbeseenthatthequantityPvaries from 0 to 2P and quantity Q varies from -Q to +Qinonecycle,andthatthewaveformisoftwicetheperiodic frequency of the current voltage waveform.The average value of the power exchanged in one cycleis a constant, equal to quantity P, and as this quantity isthe product of the voltage and the component of currentwhichis'inphase'withthevoltageitisknownasthe'real' or 'active' power.The average value of quantity Q is zero when taken overa cycle, suggesting that energy is stored in one half-cycleandreturnedtothecircuitintheremaininghalf-cycle.Q istheproductofvoltageandthequadratureab an bnba bn anV V VV V V= = ,component of current, and is known as 'reactive power'.AsP andQ areconstantswhichspecifythepowerexchangeinagivencircuit,andareproductsofthecurrentandvoltagevectors,thenifS isthevectorproduct EI it follows that withE as the reference vectorand as the angle betweenE andI :S = P + jQ Equation 3.16The quantityS is described as the 'apparent power', andisthetermusedinestablishingtheratingofacircuit.S has units of VA.3.4.4 Single-Phase and Polyphase SystemsA system is single or polyphase depending upon whetherthe sources feeding it are single or polyphase.A sourceis single or polyphase according to whether there are oneorseveraldrivingvoltagesassociatedwithit.Forexample,athree-phasesourceisasourcecontainingthreealternatingdrivingvoltagesthatareassumedtoreachamaximuminphaseorder,A,B,C.Eachphasedriving voltage is associated with a phase branch of thesystem network as shown in Figure 3.5(a).Ifapolyphasesystemhasbalancedvoltages,thatis,equal in magnitude and reaching a maximum at equallydisplacedtimeintervals,andthephasebranchimpedances are identical, it is called a 'balanced' system.Itwillbecome'unbalanced'ifanyoftheaboveconditionsarenotsatisfied.Calculationsusingabalancedpolyphasesystemaresimplified,asitisonlynecessary to solve for a single phase, the solution for theremaining phases being obtained by symmetry.The power system is normally operated as a three-phase,balanced, system.For this reason the phase voltages areequalinmagnitudeandcanberepresentedbythreevectors spaced 120 or 2/3 radians apart, as shown inFigure 3.5(b).3Fundamental Theory 2 2 Figure 3.5:Three-phase systems(a) Three-phase systemFigure 3.5:Three-phase systemsB C B' C'NN'EanEcn EbnA' APhase branchesDirection of rotation(b) Balanced system of vectors120120120EaEc=aEaEb=a2EaN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 2 3 Sincethevoltagesaresymmetrical,theymaybeexpressed in terms of one, that is:Ea= EaEb= a2EaEc= aEaEquation 3.17where a is the vector operator ej2/3. Further, if the phasebranch impedances are identical in a balanced system, itfollows that the resulting currents are also balanced.3.5 IMPEDANCE NOTATIONItcanbeseenbyinspectionofanypowersystemdiagram that:a. several voltage levels exist in a systemb. itiscommonpracticetorefertoplantMVAinterms of per unit or percentage valuesc. transmission line and cable constants are given inohms/kmBeforeanysystemcalculationscantakeplace,thesystem parameters must be referred to 'base quantities'andrepresentedasaunifiedsystemofimpedancesineither ohmic, percentage, or per unit values.Thebasequantitiesarepowerandvoltage.Normally,they are given in terms of the three-phase power in MVAand the line voltage in kV.The base impedance resultingfrom the above base quantities is:ohms Equation 3.18and,providedthesystemisbalanced,thebaseimpedancemaybecalculatedusingeithersingle-phaseor three-phase quantities.The per unit or percentage value of any impedance in thesystem is the ratio of actual to base impedance values.Hence:Equation 3.19where MVAb= base MVAkVb= base kVSimple transposition of the above formulae will refer theohmic value of impedance to the per unit or percentagevalues and base quantities.Having chosen base quantities of suitable magnitude allZ p u Z ohmsMVAkVZ Z p ubb. .% . .( )=( )( )( )=( ),2100ZkVMVAb=( )2a ab ac aE EE EE Eaa===,2systemimpedancesmaybeconvertedtothosebasequantities by using the equations given below:Equation 3.20where suffix b1 denotes the value to the original baseand b2 denotes the value to new baseThechoiceofimpedancenotationdependsuponthecomplexity of the system, plant impedance notation andthe nature of the system calculations envisaged.Ifthesystemisrelativelysimpleandcontainsmainlytransmissionlinedata,giveninohms,thentheohmicmethodcanbeadoptedwithadvantage.However,theperunitmethodofimpedancenotationisthemostcommon for general system studies since:1. impedances are the same referred to either side ofatransformeriftheratioofbasevoltagesonthetwosidesofatransformerisequaltothetransformer turns ratio2. confusion caused by the introduction of powers of100 in percentage calculations is avoided3. byasuitablechoiceofbases,themagnitudesofthe data and results are kept within a predictablerange, and hence errors in data and computationsare easier to spotMostpowersystemstudiesarecarriedoutusingsoftwareinperunitquantities.Irrespectiveofthemethodofcalculation,thechoiceofbasevoltage,andunifyingsystemimpedancestothisbase,shouldbeapproachedwithcaution,asshowninthefollowingexample.Z ZMVAMVAZ ZkVkVb bbbb bbb2 1212 1122= =

_,

,3Fundamental TheoryFigure 3.6:Selection of base voltagesFigure 3.6:Selection of base voltages11.8kV 11.8/141kV132kVOverhead line132/11kVDistribution11kVWrong selection of base voltage11.8kV 132kV 11kVRight selection11.8kV 141kV x 11=11.7kV141132N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eFrom Figure 3.6 it can be seen that the base voltages inthethreecircuitsarerelatedbytheturnsratiosoftheinterveningtransformers.Careisrequiredasthenominaltransformationratiosofthetransformersquotedmaybedifferentfromtheturnsratios-e.g.a110/33kV(nominal)transformermayhaveaturnsratioof 110/34.5kV.Therefore, the rule for hand calculationsis:'toreferanimpedanceinohmsfromonecircuittoanothermultiplythegivenimpedancebythesquareoftheturnsratio(opencircuitvoltageratio)oftheintervening transformer'.Wherepowersystemsimulationsoftwareisused,thesoftwarenormallyhascalculationroutinesbuiltintoadjusttransformerparameterstotakeaccountofdifferences between the nominal primary and secondaryvoltages and turns ratios.In this case, the choice of basevoltages may be more conveniently made as the nominalvoltagesofeachsectionofthepowersystem.Thisapproachavoidsconfusionwhenperunitorpercentvaluesareusedincalculationsintranslatingthefinalresults into volts, amps, etc.For example, in Figure 3.7, generators G1and G2have asub-transientreactanceof26%on66.6MVAratingat11kV,andtransformersT1andT2avoltageratioof11/145kVandanimpedanceof12.5%on75MVA.Choosing100MVAasbaseMVAand132kVasbasevoltage,findthepercentageimpedancestonewbasequantities.a. Generator reactances to new bases are:b. Transformer reactances to new bases are:NOTE:The base voltages of the generator and circuitsare11kVand145kVrespectively,thatis,theturnsratioofthetransformer.Thecorrespondingperunitvalues can be found by dividing by 100, and the ohmicvalue can be found by using Equation 3.19.Figure 3.712 51007514513220 122. .% ( )( )=2610066 6111320 2722 ( )( )=.. %3. 6BASI CCI RCUI TLAWS,THEOREMSANDNETWORKREDUCTI ONMostpracticalpowersystemproblemsaresolvedbyusing steady state analytical methods.The assumptionsmadearethatthecircuitparametersarelinearandbilateralandconstantforconstantfrequencycircuitvariables.Insomeproblems,describedasinitialvalueproblems,itisnecessarytostudythebehaviourofacircuitinthetransientstate.Suchproblemscanbesolvedusingoperationalmethods.Again,inotherproblems,whichfortunatelyarefewinnumber,theassumptionoflinear,bilateralcircuitparametersisnolonger valid.These problems are solved using advancedmathematicaltechniquesthatarebeyondthescopeofthis book.3.6.1 Circuit LawsInlinear,bilateralcircuits,threebasicnetworklawsapply,regardlessofthestateofthecircuit,atanyparticularinstantoftime.Theselawsarethebranch,junction and mesh laws, due to Ohm and Kirchhoff, andare stated below, using steady state a.c. nomenclature.3.6.1.1 Branch lawThecurrentI inagivenbranchofimpedanceZ isproportionaltothepotentialdifferenceV appearingacross the branch, that is,V =IZ .3.6.1.2 Junction lawThealgebraicsumofallcurrentsenteringanyjunction(or node) in a network is zero, that is:3.6.1.3 Mesh lawThealgebraicsumofallthedrivingvoltagesinanyclosedpath(ormesh)inanetworkisequaltothealgebraic sum of all the passive voltages (products of theimpedancesandthecurrents)inthecomponentsbranches, that is:Alternatively,thetotalchangeinpotentialaroundaclosed loop is zero.3.6.2 Circuit TheoremsFrom the above network laws, many theorems have beenderivedfortherationalisationofnetworks,eithertoreachaquick,simple,solutiontoaproblemortorepresent a complicated circuit by an equivalent.Thesetheoremsaredividedintotwoclasses:thoseconcernedwiththegeneralpropertiesofnetworksandthoseE ZI = I =03Fundamental Theory 2 4 Figure 3.7:Section of a power systemFigure 3.7:Section of a power systemG1T1T2G2132kVoverheadlinesN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 2 5 concerned with network reduction.Ofthemanytheoremsthatexist,thethreemostimportantaregiven.Theseare:theSuperpositionTheorem,Thvenin'sTheoremandKennelly'sStar/DeltaTheorem.3.6.2.1 Superposition Theorem(general network theorem)Theresultantcurrentthatflowsinanybranchofanetworkduetothesimultaneousactionofseveraldrivingvoltagesisequaltothealgebraicsumofthecomponentcurrentsduetoeachdrivingvoltageactingalone with the remainder short-circuited.3.6.2.2 Thvenin's Theorem(active network reduction theorem)Anyactivenetworkthatmaybeviewedfromtwoterminalscanbereplacedbyasingledrivingvoltageactinginserieswithasingleimpedance.Thedrivingvoltageistheopen-circuitvoltagebetweenthetwoterminalsandtheimpedanceistheimpedanceofthenetworkviewedfromtheterminalswithallsourcesshort-circuited.3.6.2.3Kennelly's Star/Delta Theorem(passive network reduction theorem)Any three-terminal network can be replaced by a delta orstarimpedanceequivalentwithoutdisturbingtheexternal network.The formulae relating the replacementofadeltanetworkbytheequivalentstarnetworkisasfollows (Figure 3.8):Zco = Z13Z23 / (Z12 +Z13 +Z23)and so on.Figure 3.8: Star/Delta network reductionThe impedance of a delta network corresponding to andreplacing any star network is:Z12= Zao+Zbo+Zao ZboZcoand so on.3.6.3 Network ReductionThe aim of network reduction is to reduce a system to asimpleequivalentwhileretainingtheidentityofthatpart of the system to be studied.Forexample,considerthesystemshowninFigure3.9.ThenetworkhastwosourcesEandE,alineAOBshunted by an impedance, which may be regarded as thereduction of a further network connected between A andB, and a load connected between O and N.The object ofthe reduction is to study the effect of opening a breakerat A or B during normal system operations, or of a faultat A or B.Thus the identity of nodes A and B must beretainedtogetherwiththesources,butthebranchONcan be eliminated, simplifying the study.Proceeding, A,B, N, forms a star branch and can therefore be convertedto an equivalent delta.Figure 3.9= 51 ohms=30.6 ohms= 1.2 ohms (since ZNO>>> ZAOZBO)Figure 3.10Z Z ZZ ZZAN AO BOAO BONO= + += + +0 45 18 850 45 18 850 75. .. ..Z Z ZZ ZZBN BO NOBO NOAO= + += + +0 75 18 850 75 18 850 45. .. ..Z Z ZZ ZZAN AO NOAO NOBO= + +3Fundamental TheoryFigure 3.8:Star-Delta network transformationFigure 3.8:Star-Delta network transformationcZaoZboZ12Z23Z13Oa b 1 23(a) Star network (b) Delta networkZcoFigure 3.9:Typical power system networkFigure 3.9:Typical power system networkE' E''N0A B1.60.75 0.4518.852.550.4N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eThe network is now reduced as shown in Figure 3.10.By applying Thvenin's theorem to the active loops, thesecan be replaced by a single driving voltage in series withan impedance as shown in Figure 3.11.Figure 3.11The network shown in Figure 3.9 is now reduced to thatshown in Figure 3.12 with the nodes A and B retainingtheiridentity.Further,theloadimpedancehasbeencompletely eliminated.ThenetworkshowninFigure3.12maynowbeusedtostudysystemdisturbances,forexamplepowerswingswith and without faults.Figure 3.12Most reduction problems follow the same pattern as theexampleabove.Therulestoapplyinpracticalnetworkreduction are:a. decideonthenatureofthedisturbanceordisturbances to be studiedb. decideontheinformationrequired,forexamplethe branch currents in the network for a fault at aparticular locationc. reduceallpassivesectionsofthenetworknotdirectlyinvolvedwiththesectionunderexaminationd. reduceallactivemeshestoasimpleequivalent,thatis,toasimplesourceinserieswithasingleimpedanceWiththewidespreadavailabilityofcomputer-basedpower system simulation software, it is now usual to usesuch software on a routine basis for network calculationswithoutsignificantnetworkreductiontakingplace.However, the network reduction techniques given abovearestillvalid,astherewillbeoccasionswheresuchsoftwareisnotimmediatelyavailableandahandcalculation must be carried out.In certain circuits, for example parallel lines on the sametowers,thereismutualcouplingbetweenbranches.Correctcircuitreductionmusttakeaccountofthiscoupling.Figure 3.13Three cases are of interest.These are:a. two branches connected together at their nodesb. two branches connected together at one node onlyc. two branches that remain unconnected3Fundamental Theory 2 6 Figure 3.10:Reduction usingstar/delta transformE'A51 30.60.42.51.2 1.6NBE''Figure 3.12:Reduction of typicalpower system networkFigure 3.12:Reduction of typical power system networkNA B1.22.51.550.97E'0.390.99E''Figure 3.11:Reduction of active meshes: Thvenin's TheoremFigure 3.11:Reduction of active meshes: Thvenin's TheoremE'AN(a) Reduction of left active meshNA(b) Reduction of right active meshE''NB BNE''3130.630.6310.4 x 30.652.61.6 x 51E'52.651511.60.4Figure 3.13:Reduction of two brancheswith mutual couplingFigure 3.13:Reduction of two branches with mutual coupling(a) Actual circuitIP QP Q(b) Equivalent when ZaaZbb(c) Equivalent when Zaa=ZbbP Q21Z= (Zaa+Zbb)ZaaZbbZ=ZaaZbb-Z2abZaa+Zbb-2ZabZabIaIbIIN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 2 7 Considering each case in turn:a. considerthecircuitshowninFigure3.13(a).Theapplication of a voltage V between the terminals Pand Q gives:V = IaZaa + IbZabV = IaZab + IbZbbwhere Iaand Ibare the currents in branches a andb,respectivelyandI =Ia+ Ib,thetotalcurrententering at terminal P and leaving at terminal Q.Solving for Iaand Ib:from whichandsothattheequivalentimpedanceoftheoriginalcircuit is: Equation 3.21(Figure 3.13(b)), and, if the branch impedances areequal, the usual case, then:Equation 3.22(Figure 3.13(c)).b. consider the circuit in Figure 3.14(a).Z Z Zaa ab= +( )12ZVIZ Z ZZ Z Zaa bb abaa bb ab= =+ 22I I IVZ Z ZZ Z Za baa bb abaa bb ab= + =+ ( )22IZ Z VZ Z Zbaa abaa bb ab=( )2IZ Z VZ Z Zabb abaa bb ab=( )2Theassumptionismadethatanequivalentstarnetworkcanreplacethenetworkshown.Frominspection with one terminal isolated in turn and avoltage V impressed across the remaining terminalsit can be seen that:Za+Zc=ZaaZb+Zc=ZbbZa+Zb=Zaa+Zbb-2ZabSolving these equations gives:Equation 3.23-see Figure 3.14(b).c. consider the four-terminal network given in Figure3.15(a),inwhichthebranches11'and22'areelectrically separate except for a mutual link.Theequations defining the network are:V1=Z11I1+Z12I2V2=Z21I1+Z22I2I1=Y11V1+Y12V2I2=Y21V1+Y22V2whereZ12=Z21andY12=Y21,ifthenetworkisassumedtobereciprocal.Further,bysolvingtheabove equations it can be shown that:Equation 3.24Therearethreeindependentcoefficients,namelyZ12,Z11,Z22,sotheoriginalcircuitmaybereplacedbyanequivalentmeshcontainingfourexternalterminals,eachterminalbeingconnectedto the other three by branch impedances as shownin Figure 3.15(b).Y ZY ZY ZZZ Z11 2222 1112 1211 22 122==== ,Z Z ZZ Z ZZ Za aa abb bb abc ab= = =,3Fundamental TheoryFigure 3.14:Reduction of mutually-coupled brancheswith a common terminalACB(b) Equivalent circuitBCAFigure 3.14: Reduction of mutually-coupled branches with a common terminal(a) Actual circuitZaaZbbZabZa=Zaa-ZabZb=Zbb-ZabZc=ZabFigure 3.15 :Equivalent circuits forfour terminal network with mutual coupling(a) Actual circuit212'1'2'1'2'1'(b) Equivalent circuit(d) Equivalent circuit211 1C 2(c) Equivalent with allnodes commonedZ11Z11Z12Z22Z11Z11Z12Z12Z12-Z12-Z12Z22Z12Z12Z12Z12Z12Z21N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d edefining the equivalent mesh in Figure 3.15(b), andinserting radial branches having impedances equaltoZ11andZ22interminals1 and2,resultsinFigure 3.15(d).3. 7REFERENCES3.1 PowerSystemAnalysis. J.R.MortlockandM. W. Humphrey Davies.Chapman & Hall.3.2 Equivalent Circuits I. Frank M. Starr, Proc. A.I.E.E.Vol. 51. 1932, pp. 287-298.3Fundamental Theory 2 8 Figure 3.15:Equivalent circuits forfour terminal network with mutual couplingFigure 3.15:Equivalent circuits for four terminal network with mutual coupling(a) Actual circuit212'1'2'1'2'1'(b) Equivalent circuit(d) Equivalent circuit211 1C 2(c) Equivalent with allnodes commonedexcept 1Z11Z11Z12Z22Z11Z11Z12Z12Z12-Z12-Z12Z22Z12Z12Z12Z12Z12Z21In order to evaluate the branches of the equivalentmesh let all points of entry of the actual circuit becommoned except node 1 of circuit 1, as shown inFigure 3.15(c).Then all impressed voltages exceptV1will be zero and:I1 = Y11V1I2 = Y12V1If the same conditions are applied to the equivalentmesh, then:I1 = V1Z11I2 = -V1/Z12 = -V1/Z12These relations follow from the fact that the branchconnectingnodes1 and1' carriescurrentI1andthe branches connecting nodes 1 and 2' and 1 and2 carry current I2.This must be true since branchesbetweenpairsofcommonednodescancarrynocurrent.Byconsideringeachnodeinturnwiththeremaindercommoned,thefollowingrelationshipsare found:Z11 = 1/Y11Z22 = 1/Y22Z12= -1/Y12Z12 = Z1 2= -Z21 = -Z12 Hence:Z11= Z11Z22-Z212_______________Z22Z22= Z11Z22-Z212_______________Z11Z12= Z11Z22-Z212_______________Z12Equation 3.25AsimilarbutequallyrigorousequivalentcircuitisshowninFigure3.15(d).Thiscircuit[3.2]followsfrom the fact that the self-impedance of any circuitisindependentofallothercircuits.Therefore,itneed not appear in any of the mutual branches if itislumpedasaradialbranchattheterminals.Soputting Z11and Z22equal to zero in Equation 3.25,ZZZ ZZZZZ ZZZZZ ZZ1111 22 122222211 22 122111211 22 12212''===,Introduction 4.1Three phase fault calculations 4.2Symmetrical component analysis 4.3of a three-phase networkEquations and network connections 4.4for various types of faultsCurrent and voltage distribution 4.5in a system due to a faultEffect of system earthing 4.6on zero sequence quantitiesReferences4.7 4 F a u l t C a l c u l a t i o n sN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 3 1 4. 1I NTRODUCTI ONApowersystemisnormallytreatedasabalancedsymmetrical three-phase network.When a fault occurs,the symmetry is normally upset, resulting in unbalancedcurrents and voltages appearing in the network.The onlyexceptionisthethree-phasefault,which,becauseitinvolves all three phases equally at the same location, isdescribed as a symmetrical fault.By using symmetricalcomponentanalysisandreplacingthenormalsystemsources by a source at the fault location, it is possible toanalyse these fault conditions.For the correct application of protection equipment, it isessentialtoknowthefaultcurrentdistributionthroughoutthesystemandthevoltagesindifferentparts of the system due to the fault.Further, boundaryvalues of current at any relaying point must be known ifthefaultistobeclearedwithdiscrimination.Theinformationnormallyrequiredforeachkindoffaultateach relaying point is:i. maximum fault currentii. minimum fault currentiii. maximum through fault currentToobtaintheaboveinformation,thelimitsofstablegenerationandpossibleoperatingconditions,includingthe method of system earthing, must be known.Faultsare always assumed to be through zero fault impedance.4. 2THREE-PHASEFAULTCALCULATI ONSThree-phase faults are unique in that they are balanced,thatis,symmetricalinthethreephases,andcanbecalculatedfromthesingle-phaseimpedancediagramand the operating conditions existing prior to the fault.A fault condition is a sudden abnormal alteration to thenormalcircuitarrangement.Thecircuitquantities,currentandvoltage,willalter,andthecircuitwillpassthroughatransientstatetoasteadystate.Inthetransient state, the initial magnitude of the fault currentwill depend upon the point on the voltage wave at whichthefaultoccurs.Thedecayofthetransientcondition,untilitmergesintosteadystate,isafunctionoftheparameters of the circuit elements.The transient currentmayberegardedasad.c.exponentialcurrent 4 Faul t Cal c ul at i onsN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e4Fault Calculations 3 2 superimposedonthesymmetricalsteadystatefaultcurrent.Ina.c.machines,owingtoarmaturereaction,the machine reactances pass through 'sub transient' and'transient'stagesbeforereachingtheirsteadystatesynchronous values.For this reason, the resultant faultcurrent during the transient period, from fault inceptionto steady state also depends on the location of the faultin the network relative to that of the rotating plant.In a system containing many voltage sources, or havinga complex network arrangement, it is tedious to use thenormalsystemvoltagesourcestoevaluatethefaultcurrentinthefaultybranchortocalculatethefaultcurrentdistributioninthesystem.Amorepracticalmethod [4.1] is to replace the system voltages by a singledriving voltage at the fault point.This driving voltage isthevoltageexistingatthefaultpointbeforethefaultoccurs.Consider the circuit given in Figure 4.1 where the drivingvoltages are E and E, the impedances on either side offaultpointF are Z1and Z1,andthecurrentthroughpoint F before the fault occurs is I .Figure 4.1:The voltageV at F before fault inception is:V = E - IZ = E +IZAfter the fault the voltageV is zero.Hence, the changein voltage is -V.Because of the fault, the change in thecurrent flowing into the network from F is:and, since no current was flowing into the network fromF priortothefault,thefaultcurrentflowingfromthenetwork into the fault is:Byapplyingtheprincipleofsuperposition,theloadcurrents circulating in the system prior to the fault mayI fI VZ ZZ Z= =+( )1 11 1' ' '' ' 'IVZVZ ZZ Z= = +( )11 11 1' ' '' ' 'be added to the currents circulating in the system due tothe fault, to give the total current in any branch of thesystem at the time of fault inception.However, in mostproblems, the load current is small in comparison to thefault current and is usually ignored.Inapracticalpowersystem,thesystemregulationissuch that the load voltage at any point in the system iswithin 10% of the declared open-circuit voltage at thatpoint.For this reason, it is usual to regard the pre-faultvoltageatthefaultasbeingtheopen-circuitvoltage,andthisassumptionisalsomadeinanumberofthestandards dealing with fault level calculations.Foranexampleofpracticalthree-phasefaultcalculations, consider a fault at A in Figure 3.9.With thenetwork reduced as shown in Figure 4.2, the load voltageat A before the fault occurs is:Figure 4.2:V = 0.97E - 1.55IForpracticalworkingconditions,E1.55I and E 1.207I .HenceE E V. Replacingthedrivingvoltages Eand EbytheloadvoltageVbetween A and N modifies the circuit as shownin Figure 4.3(a).The node A is the junction of three branches.In practice,thenodewouldbeabusbar,andthebranchesarefeedersradiatingfromthebusviacircuitbreakers,asshown in Figure 4.3(b).There are two possible locationsforafaultatA;thebusbarsideofthebreakersortheline side of the breakers.In this example, it is assumedthat the fault is at X, and it is required to calculate thecurrent flowing from the bus to X.ThenetworkviewedfromAN hasadrivingpointimpedance |Z1| = 0.68 ohms.The current in the fault is.VZ1V E I = +++ 0 991 2 2 52 5 1 20 39 .. .. ..' 'Figure 4.1:Network with fault at FNFZ '1Z''1IVE' E''Figure 4.2:Reduction of typicalpower system networkN1.55 A B2.5 1.2 0.39 0.99E ''0.97E 'N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 3 3 4Fault CalculationsLetthiscurrentbe1.0perunit.Itisnownecessarytofind the fault current distribution in the various branchesof the network and in particular the current flowing fromA to X on the assumption that a relay at X is to detectthefaultcondition.Theequivalentimpedancesviewedfrom either side of the fault are shown in Figure 4.4(a).Figure 4.3Figure 4.4The currents from Figure 4.4(a) are as follows:From the right: From the left:There is a parallel branch to the right of A1 212 760 437... = p.u.1 552 760 563... = p.u.Therefore, current in 2.5 ohm branchand the current in 1.2 ohm branchTotal current entering X from the left, that is, from A toX,is0.437+0.183=0.62p.u.andfromB toX is0.38p.u. TheequivalentnetworkasviewedfromtherelayisasshowninFigure4.4(b).Theimpedancesoneither side are:0.68/0.62 = 1.1 ohmsand0.68/0.38 = 1.79 ohmsThecircuitofFigure4.4(b)hasbeenincludedbecausethe Protection Engineer is interested in these equivalentparameterswhenapplyingcertaintypesofprotectionrelay.4. 3SYMMETRI CALCOMPONENTANALYSI S OFATHREE-PHASENETWORKThe Protection Engineer is interested in a wider variety offaults than just a three-phase fault.The most commonfaultisasingle-phasetoearthfault,which,inLVsystems, can produce a higher fault current than a three-phase fault.Similarly, because protection is expected tooperatecorrectlyforalltypesoffault,itmaybenecessarytoconsiderthefaultcurrentsduetomanydifferenttypesoffault.Sincethethree-phasefaultisuniqueinbeingabalancedfault,amethodofanalysisthat is applicable to unbalanced faults is required.It canbeshown[4.2]that,byapplyingthe'PrincipleofSuperposition',anygeneralthree-phasesystemofvectorsmaybereplacedbythreesetsofbalanced(symmetrical)vectors;twosetsarethree-phasebuthaving opposite phase rotation and one set is co-phasal.These vector sets are described as the positive, negativeand zero sequence sets respectively.The equations between phase and sequence voltages aregiven below:Equation 4.1E E E EE a E aE EE aE a E Eabc= + += + += + +1 2 021 2 0122 0==2 5 0 5633 70 38. ... p.u.==1 2 0 5633 70 183. ... p.u.Figure 4.3:Network with fault at node ANAVBAX(b) Typical physical arrangement of node A with a fault shown at X(a) Three - phase fault diagram for a fault at node ABusbarCircuit breaker1.551.22.50.39Figure 4.4:Impedances viewed from faultNVANVX1.55 1.211.79 1.1(a) Impedance viewed from node A(b) Equivalent impedances viewed from node XN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eEquation 4.2where all quantities are referred to the reference phaseA.Asimilarsetofequationscanbewrittenforphaseandsequencecurrents.Figure4.5illustratestheresolution of a system of unbalanced vectors.Figure 4.5Whenafaultoccursinapowersystem,thephaseimpedances are no longer identical (except in the case ofthree-phasefaults)andtheresultingcurrentsandvoltages are unbalanced, the point of greatest unbalancebeing at the fault point.It has been shown in Chapter 3thatthefaultmaybestudiedbyshort-circuitingallnormal driving voltages in the system and replacing thefaultconnectionbyasourcewhosedrivingvoltageisequal to the pre-fault voltage at the fault point.Hence,the system impedances remain symmetrical, viewed fromthe fault, and the fault point may now be regarded as thepointofinjectionofunbalancedvoltagesandcurrentsinto the system.Thisisamostimportantapproachindefiningthefaultconditionssinceitallowsthesystemtoberepresentedbysequencenetworks[4.3]usingthemethodofsymmetrical components.4.3.1 Positive Sequence NetworkDuringnormalbalancedsystemconditions,onlypositivesequencecurrentsandvoltagescanexistinthesystem,and therefore the normal system impedance network is apositive sequence network.When a fault occurs in a power system, the current in theE E aE a EE E a E aEE E E Ea b ca b ca b c12220131313= + +( )= + +( )= + +( )faultbranchchangesfrom0 to I andthepositivesequence voltage across the branch changes from V toV1;replacing the fault branch by a source equal to the changein voltage and short-circuiting all normal driving voltagesinthesystemresultsinacurrentI flowingintothesystem, and:Equation 4.3where Z1isthepositivesequenceimpedanceofthesystemviewedfromthefault.Asbeforethefaultnocurrentwasflowingfromthefaultintothesystem,itfollowsthat I1,thefaultcurrentflowingfromthesystem into the fault must equal - I .Therefore:V1=V -I1Z1Equation 4.4istherelationshipbetweenpositivesequencecurrentsand voltages in the fault branch during a fault.InFigure4.6,whichrepresentsasimplesystem,thevoltagedrops I1Z1and I1Z1areequalto( V - V1)where the currents I1and I1enter the fault from theleftandrightrespectivelyandimpedancesZ1andZ1are the total system impedances viewed from either sideof the fault branch.The voltage V is equal to the open-circuit voltage in the system, and it has been shown thatV E E(seeSection3.7).Sothepositivesequencevoltages in the system due to the fault are greatest at thesource, as shown in the gradient diagram, Figure 4.6(b).Figure 4.64.3.2 Negative Sequence NetworkIfonlypositivesequencequantitiesappearinapowersystem under normal conditions, then negative sequencequantities can only exist during an unbalanced fault.IfnonegativesequencequantitiesarepresentintheIV VZ= ) ( 114Fault Calculations 3 4 Figure 4.6:Fault at F:Positive sequence diagrams(a) System diagramNFXNXFN'(b) Gradient diagramZS1Z'1Z'1Z'1Z''1I '1I '1I '1I1V1V1V'1+I '1Z'1VI ''1E' E''Figure 4.5:Resolution of a systemof unbalanced vectorsa2E2a2E1aE1aE2EoEoEoE1E2EaEbEcN e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 3 5 fault branch prior to the fault, then, when a fault occurs,the change in voltage is V2, and the resulting current I2flowing from the network into the fault is:Equation 4.5Theimpedancesinthenegativesequencenetworkaregenerallythesameasthoseinthepositivesequencenetwork.Inmachines Z1 Z2,butthedifferenceisgenerally ignored, particularly in large networks.The negative sequence diagrams, shown in Figure 4.7, aresimilartothepositivesequencediagrams,withtwoimportantdifferences;nodrivingvoltagesexistbeforethefaultandthenegativesequencevoltage V2isgreatest at the fault point.Figure 4.74.3.3 Zero Sequence NetworkThezerosequencecurrentandvoltagerelationshipsduringafaultconditionarethesameasthoseinthenegative sequence network.Hence:V0= -I0Z0Equation 4.6Also,thezerosequencediagramisthatofFigure4.7,substituting I0for I2, and so on.The currents and voltages in the zero sequence networkareco-phasal,thatis,allthesamephase.Forzerosequencecurrentstoflowinasystemtheremustbeareturn connection through either a neutral conductor orthegeneralmassofearth.Notemustbetakenofthisfact when determining zero sequence equivalent circuits.Further,ingeneral Z1 Z0andthevalueof Z0 variesaccording to the type of plant, the winding arrangementand the method of earthing.IVZ222= 4.4 EQUATIONS AND NETWORK CONNECTIONS FOR VARIOUS TYPES OF FAULTSThe most important types of faults are as follows:a. single-phase to earthb. phase to phasec. phase-phase-earthd. three-phase (with or without earth)Theabovefaultsaredescribedassingleshuntfaultsbecausetheyoccuratonelocationandinvolveaconnection between one phase and another or to earth.Inaddition,theProtectionEngineeroftenstudiestwoother types of fault:e. single-phase open circuitf. cross-country faultBydeterminingthecurrentsandvoltagesatthefaultpoint, it is possible to define the fault and connect thesequencenetworkstorepresentthefaultcondition.From the initial equations and the network diagram, thenatureofthefaultcurrentsandvoltagesindifferentbranches of the system can be determined.For shunt faults of zero impedance, and neglecting loadcurrent, the equations defining each fault (using phase-neutral values) can be written down as follows:a. Single-phase-earth (A-E)Equation 4.7b. Phase-phase (B-C)Equation 4.8c. Phase-phase-earth (B-C-E)Equation 4.9d. Three-phase (A-B-C or A-B-C-E)Equation 4.10It should be noted from the above that for any type offaulttherearethreeequationsthatdefinethefaultconditions.I I IV VV Va b ca bb c+ + ===0IVVabc===000II IV Vab cb c== =0IIVbca===0004Fault CalculationsFigure 4.7:Fault at F:Negative sequence diagram(a) Negative sequence networkNFXFXN(b) Gradient diagramZS1 Z'1Z'1Z''1I '2I2V2V2V2+ I '2Z'1I ''2N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d eWhen there is a fault impedance, this must be taken intoaccount when writing down the equations.For example,with a single-phase-earth fault through fault impedanceZf, Equations 4.7 are re-written:Equation 4.11Figure 4.84.4.1 Single-phase-earth Fault (A-E)Consider a fault defined by Equations 4.7 and by Figure4.8(a).ConvertingEquations4.7intosequencequantities by using Equations 4.1 and 4.2, then: Equation 4.12V1= - ( V2+ V0) Equation 4.13Substitutingfor V1, V2and V0inEquation4.13fromEquations 4.4, 4.5 and 4.6:V -I1 Z1 = I2 Z2 + I0 Z0 but, from Equation 4.12, I1=I2=I0, therefore:V =I1(Z1 +Z2 +Z3) Equation 4.14TheconstraintsimposedbyEquations4.12and4.14indicatethattheequivalentcircuitforthefaultisobtained by connecting the sequence networks in series,as shown in Figure 4.8(b).4.4.2 Phase-phase Fault (B-C)From Equation 4.8 and using Equations 4.1 and 4.2:I1= -I2Equation 4.15I0= 0V1= V2Equation 4.16From network Equations 4.4 and 4.5, Equation 4.16 canbe re-written:V -I1 Z1 = I2 Z2 + I0 Z0 I I I Io a 1 213= = =IIV I Zbca a f===00V -I1 Z1 = I2 Z2 and substitut