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About This Presentation
encve,mcededdwe
Slide Content
SUBJECT:-POWER
SYSTEMS-I
Code:-EEC 401
Departmental Core Subject
Academic Session:-2023-24
Semester:-B.Tech4
th
, EE
Chapter-Insulated Cables
Faculty Name:-Aniruddha Bhattacharya
SYSTEMS-I
Code:-EEC 401
Departmental Core Subject
Academic Session:-2023-24
Semester:-B.Tech4
th
, EE
Chapter-Insulated Cables
Faculty Name:-Aniruddha Bhattacharya
Disclaimer
Thestudymaterials/presentationsaresolelymeantforacademicpurposesandtheycanbereused,
reproduced,modified,anddistributedbyothersforacademicpurposesonlywithproperacknowledgements.
2
Thestudymaterials/presentationsaresolelymeantforacademicpurposesandtheycanbereused,
reproduced,modified,anddistributedbyothersforacademicpurposesonlywithproperacknowledgements.
2
Reference
1.S.Y.King,N.A.Halfter,“UndergroundPowerCables”,Hongkong
UniversityPress,1977.
3
1.S.Y.King,N.A.Halfter,“UndergroundPowerCables”,Hongkong
UniversityPress,1977.
3
Insulated Cables
Syllabus:-TypesofL.V.Cablesfordistributionsystems:conductormaterials,importanttypesofinsulating
materials,highvoltagecables,Stressesdeveloped,economicalstressandgradingofdielectricmaterials,
screenedandpressurecables,mechanismofcablebreakdownchargingCurrent,powerfactorandlossesin
cables,determinationofcurrentRatingofcables.
After reading this chapter, the students should be able to:
Understand the need for underground cables.
Provide constructional features and grading of cables.
Calculate the dielectric stress, capacitance for single and three-core cables.
Provide the thermal characteristics and testing of cables.
materials,highvoltagecables,Stressesdeveloped,economicalstressandgradingofdielectricmaterials,
screenedandpressurecables,mechanismofcablebreakdownchargingCurrent,powerfactorandlossesin
cables,determinationofcurrentRatingofcables.
After reading this chapter, the students should be able to:
Understand the need for underground cables.
Provide constructional features and grading of cables.
Calculate the dielectric stress, capacitance for single and three-core cables.
Provide the thermal characteristics and testing of cables.
Introduction:-
•AnInsulatedcableessentiallyconsistsofoneormoreconductorscoveredwithsuitable
insulationandsurroundedbyaprotectingcover.
•Theundergroundcableshaveseveraladvantagessuchas:
lessliabletodamagethroughstormsorlightning,
lowmaintenancecost,
lesschancesoffaults,
smallervoltagedropandbettergeneralappearance.
•However,theirmajordrawbackisthattheyhavegreaterinstallationcostandintroduceinsulationproblemsathigh
voltagescomparedwiththeequivalentoverheadsystem.
•Undergroundcablesareemployedwhereitisimpracticabletouseoverheadlines.Suchlocationsmaybethickly
populatedareaswheremunicipalauthoritiesprohibitoverheadlinesforreasonsofsafety,oraroundplantsand
substationsorwheremaintenanceconditionsdonotpermittheuseofoverheadconstruction.
•Thechiefuseofundergroundcablesformanyyearshasbeenfordistributionofelectricpowerincongestedurban
areasatcomparativelylowormoderatevoltages.
•However,recentimprovementsinthedesignandmanufacturehaveledtothedevelopmentofcablessuitableforuse
athighvoltages.
•Thishasmadeitpossibletoemployundergroundcablesfortransmissionofelectricpowerforshortormoderate
distances.
•AnInsulatedcableessentiallyconsistsofoneormoreconductorscoveredwithsuitable
insulationandsurroundedbyaprotectingcover.
•Theundergroundcableshaveseveraladvantagessuchas:
lessliabletodamagethroughstormsorlightning,
lowmaintenancecost,
lesschancesoffaults,
smallervoltagedropandbettergeneralappearance.
•However,theirmajordrawbackisthattheyhavegreaterinstallationcostandintroduceinsulationproblemsathigh
voltagescomparedwiththeequivalentoverheadsystem.
•Undergroundcablesareemployedwhereitisimpracticabletouseoverheadlines.Suchlocationsmaybethickly
populatedareaswheremunicipalauthoritiesprohibitoverheadlinesforreasonsofsafety,oraroundplantsand
substationsorwheremaintenanceconditionsdonotpermittheuseofoverheadconstruction.
•Thechiefuseofundergroundcablesformanyyearshasbeenfordistributionofelectricpowerincongestedurban
areasatcomparativelylowormoderatevoltages.
•However,recentimprovementsinthedesignandmanufacturehaveledtothedevelopmentofcablessuitableforuse
athighvoltages.
•Thishasmadeitpossibletoemployundergroundcablesfortransmissionofelectricpowerforshortormoderate
distances.
Basic Properties:-
•Althoughseveraltypesofcablesareavailable,thetypeofcabletobeusedwilldependupontheworkingvoltageand
servicerequirements.Ingeneral,acablemustfulfilthefollowingnecessaryrequirements:
•Theconductorusedincablesshouldbetinnedstrandedcopperoraluminiumofhighconductivity.
•Strandingisdonesothatconductormaybecomeflexibleandcarrymorecurrent.
•Theconductorsizeshouldbesuchthatthecablecarriesthedesiredloadcurrentwithoutoverheatingandcausesvoltage
dropwithinpermissiblelimits.
•Thecablemusthaveproperthicknessofinsulationinordertogivehighdegreeofsafetyandreliabilityatthevoltagefor
whichitisdesigned.
•Thecablemustbeprovidedwithsuitablemechanicalprotectionsothatitmaywithstandtheroughuseinlayingit.
•Thematerialsusedinthemanufactureofcablesshouldbesuchthatthereiscompletechemicalandphysicalstability
throughout.
•Althoughseveraltypesofcablesareavailable,thetypeofcabletobeusedwilldependupontheworkingvoltageand
servicerequirements.Ingeneral,acablemustfulfilthefollowingnecessaryrequirements:
•Theconductorusedincablesshouldbetinnedstrandedcopperoraluminiumofhighconductivity.
•Strandingisdonesothatconductormaybecomeflexibleandcarrymorecurrent.
•Theconductorsizeshouldbesuchthatthecablecarriesthedesiredloadcurrentwithoutoverheatingandcausesvoltage
dropwithinpermissiblelimits.
•Thecablemusthaveproperthicknessofinsulationinordertogivehighdegreeofsafetyandreliabilityatthevoltagefor
whichitisdesigned.
•Thecablemustbeprovidedwithsuitablemechanicalprotectionsothatitmaywithstandtheroughuseinlayingit.
•Thematerialsusedinthemanufactureofcablesshouldbesuchthatthereiscompletechemicalandphysicalstability
throughout.
Construction:-
•Figure1showsthegeneralconstructionofa3-conductorcable.Thevariouspartsare:
•CoresorConductors:Acablemayhaveoneormorethanonecore(conductor)dependinguponthetypeofserviceforwhichitisintended.For
instance,the3-conductorcableshowninFigure1isusedfor3-phaseservice.Theconductorsaremadeoftinnedcopperoraluminiumandare
usuallystrandedinordertoprovideflexibilitytothecable.
•Insulation:Eachcoreorconductorisprovidedwithasuitablethicknessofinsulation,thethicknessoflayerdependinguponthevoltagetobe
withstoodbythecable.Thecommonlyusedmaterialsforinsulationareimpregnatedpaper,varnishedcambricorrubbermineralcompound.
•Metallicsheath:Inordertoprotectthecable frommoisture,gasesorotherdamagingliquids(acidsoralkalies)inthesoiland
atmosphere,ametallicsheathofleadoraluminumisprovidedovertheinsulationasshowninFigure1.
•Bedding:Overthemetallicsheathisappliedalayerofbeddingwhichconsistsofafibrousmateriallikejuteorhessiantape.Thepurposeofbedding
istoprotectthemetallicsheathagainstcorrosionandfrommechanicalinjuryduetoarmouring.
•Armouring.Overthebedding,armouringisprovidedwhichconsistsofoneortwolayersofgalvanisedsteelwireorsteeltape.Itspurposeisto
protectthecablefrommechanicalinjurywhilelayingitandduringthecourseofhandling.Armouringmaynotbedoneinthecaseofsomecables.
•Serving.Inordertoprotectarmouringfromatmosphericconditions,alayeroffibrousmaterial(likejute)similartobeddingisprovidedoverthe
armouring.Thisisknownasserving.Itmaynotbeoutofplacetomentionherethatbedding,armouringandservingareonlyappliedtothecables
fortheprotectionofconductorinsulationandtoprotectthemetallicsheathfrommechanicalinjury.
Figure 1
•Figure1showsthegeneralconstructionofa3-conductorcable.Thevariouspartsare:
•CoresorConductors:Acablemayhaveoneormorethanonecore(conductor)dependinguponthetypeofserviceforwhichitisintended.For
instance,the3-conductorcableshowninFigure1isusedfor3-phaseservice.Theconductorsaremadeoftinnedcopperoraluminiumandare
usuallystrandedinordertoprovideflexibilitytothecable.
•Insulation:Eachcoreorconductorisprovidedwithasuitablethicknessofinsulation,thethicknessoflayerdependinguponthevoltagetobe
withstoodbythecable.Thecommonlyusedmaterialsforinsulationareimpregnatedpaper,varnishedcambricorrubbermineralcompound.
•Metallicsheath:Inordertoprotectthecable frommoisture,gasesorotherdamagingliquids(acidsoralkalies)inthesoiland
atmosphere,ametallicsheathofleadoraluminumisprovidedovertheinsulationasshowninFigure1.
•Bedding:Overthemetallicsheathisappliedalayerofbeddingwhichconsistsofafibrousmateriallikejuteorhessiantape.Thepurposeofbedding
istoprotectthemetallicsheathagainstcorrosionandfrommechanicalinjuryduetoarmouring.
•Armouring.Overthebedding,armouringisprovidedwhichconsistsofoneortwolayersofgalvanisedsteelwireorsteeltape.Itspurposeisto
protectthecablefrommechanicalinjurywhilelayingitandduringthecourseofhandling.Armouringmaynotbedoneinthecaseofsomecables.
•Serving.Inordertoprotectarmouringfromatmosphericconditions,alayeroffibrousmaterial(likejute)similartobeddingisprovidedoverthe
armouring.Thisisknownasserving.Itmaynotbeoutofplacetomentionherethatbedding,armouringandservingareonlyappliedtothecables
fortheprotectionofconductorinsulationandtoprotectthemetallicsheathfrommechanicalinjury.
Figure 1
Basic Properties of Insulating Materials for Cables:-
•Ingeneral,theinsulatingmaterialsusedincablesshouldhavethefollowingproperties:
Highinsulationresistancetoavoidleakagecurrent.
Highdielectricstrengthtoavoidelectricalbreakdownofthecable.
Highmechanicalstrengthtowithstandthemechanicalhandlingofcables.
Non-hygroscopici.e.,itshouldnotabsorbmoisturefromairorsoil.
Non-inflammable.
Lowcostsoastomaketheundergroundsystemaviableproposition.
Unaffectedbyacidsandalkaliestoavoidanychemicalaction.
•Noneoftheinsulatingmaterialpossessesalltheabovementionedproperties.
•Therefore,thetypeofinsulatingmaterialtobeuseddependsuponthepurposeforwhichthecableisrequiredand
thequalityofinsulationtobeaimedat.
•Theprincipalinsulatingmaterialsusedincablesare:
•Rubber.
Rubbermaybeobtainedfrommilkysapoftropicaltreesoritmaybeproducedfromoilproducts.
Ithasrelativepermittivityvaryingbetween2and3,dielectricstrengthisabout30kV/mmandresistivityof
insulationis10
17
Ωcm.
Itsuffersfromsomemajordrawbacksviz.,readilyabsorbsmoisture,maximumsafetemperatureislow(about
38ºC),softandliabletodamageduetoroughhandlingandageswhenexposedtolight.
•Ingeneral,theinsulatingmaterialsusedincablesshouldhavethefollowingproperties:
Highinsulationresistancetoavoidleakagecurrent.
Highdielectricstrengthtoavoidelectricalbreakdownofthecable.
Highmechanicalstrengthtowithstandthemechanicalhandlingofcables.
Non-hygroscopici.e.,itshouldnotabsorbmoisturefromairorsoil.
Non-inflammable.
Lowcostsoastomaketheundergroundsystemaviableproposition.
Unaffectedbyacidsandalkaliestoavoidanychemicalaction.
•Noneoftheinsulatingmaterialpossessesalltheabovementionedproperties.
•Therefore,thetypeofinsulatingmaterialtobeuseddependsuponthepurposeforwhichthecableisrequiredand
thequalityofinsulationtobeaimedat.
•Theprincipalinsulatingmaterialsusedincablesare:
•Rubber.
Rubbermaybeobtainedfrommilkysapoftropicaltreesoritmaybeproducedfromoilproducts.
Ithasrelativepermittivityvaryingbetween2and3,dielectricstrengthisabout30kV/mmandresistivityof
insulationis10
17
Ωcm.
Itsuffersfromsomemajordrawbacksviz.,readilyabsorbsmoisture,maximumsafetemperatureislow(about
38ºC),softandliabletodamageduetoroughhandlingandageswhenexposedtolight.
Basic Properties of Insulating Materials for Cables:-
•VulcanisedIndiaRubber(V.I.R.).
Itispreparedbymixingpurerubberwithmineralmattersuchaszincoxide,redleadetc.,and3to5%ofsulphur.
Thecompoundsoformedisrolledintothinsheetsandcutintostrips.
Therubbercompoundisthenappliedtotheconductorandisheatedtoatemperatureofabout150ºC.Thewhole
processiscalledvulcanisation.
VulcanisedIndiarubberhasgreatermechanicalstrength,durabilityandwearresistantpropertythanpurerubber.
Itsmaindrawbackisthatsulphurreactsveryquicklywithcopperandforthisreason,cablesusingVIRinsulation
havetinnedcopperconductor.
•Impregnatedpaper.
Itconsistsofchemicallypulpedpapermadefromwoodchippingsandimpregnatedwithsomecompoundsuchas
paraffinicornapthenicmaterial.
Ithastheadvantagesoflowcost,lowcapacitance,highdielectricstrengthandhighinsulationresistance.
Theonlydisadvantageisthatpaperishygroscopicandevenifitisimpregnatedwithsuitablecompound,it
absorbsmoistureandthuslowerstheinsulationresistanceofthecable.
Thepaperinsulatedcablesarealwaysprovidedwithsomeprotectivecoveringandareneverleftunsealed.
Ifitisrequiredtobeleftunused,itsendsaretemporarilycoveredwithwaxortar.
Theyareusedwherethecableroutehasafewjoints.
•VulcanisedIndiaRubber(V.I.R.).
Itispreparedbymixingpurerubberwithmineralmattersuchaszincoxide,redleadetc.,and3to5%ofsulphur.
Thecompoundsoformedisrolledintothinsheetsandcutintostrips.
Therubbercompoundisthenappliedtotheconductorandisheatedtoatemperatureofabout150ºC.Thewhole
processiscalledvulcanisation.
VulcanisedIndiarubberhasgreatermechanicalstrength,durabilityandwearresistantpropertythanpurerubber.
Itsmaindrawbackisthatsulphurreactsveryquicklywithcopperandforthisreason,cablesusingVIRinsulation
havetinnedcopperconductor.
•Impregnatedpaper.
Itconsistsofchemicallypulpedpapermadefromwoodchippingsandimpregnatedwithsomecompoundsuchas
paraffinicornapthenicmaterial.
Ithastheadvantagesoflowcost,lowcapacitance,highdielectricstrengthandhighinsulationresistance.
Theonlydisadvantageisthatpaperishygroscopicandevenifitisimpregnatedwithsuitablecompound,it
absorbsmoistureandthuslowerstheinsulationresistanceofthecable.
Thepaperinsulatedcablesarealwaysprovidedwithsomeprotectivecoveringandareneverleftunsealed.
Ifitisrequiredtobeleftunused,itsendsaretemporarilycoveredwithwaxortar.
Theyareusedwherethecableroutehasafewjoints.
Basic Properties of Insulating Materials for Cables:-
•Varnishedcambric.
Itisacottonclothimpregnatedandcoatedwithvarnish.
Thecambricislappedontotheconductorintheformofatapeanditssurfacesarecoatedwithpetroleumjelly
compoundtoallowfortheslidingofoneturnoveranotherasthecableisbent.
Asthevarnishedcambricishygroscopic,therefore,suchcablesarealwaysprovidedwithmetallicsheath.Itsdielectric
strengthisabout4kV/mmandpermittivityis2.5to3.8.
•Polyvinylchloride(PVC).
Thisinsulatingmaterialisasyntheticcompound.Itisobtainedfromthepolymerisationofacetyleneandisintheformof
whitepowder.
Forobtainingthismaterialasacableinsulation,itiscompoundedwithcertainmaterialsknownasplasticizerswhichare
liquidswithhighboilingpoint.
Polyvinylchloridehashighinsulationresistance,gooddielectricstrengthandmechanicaltoughnessoverawiderangeof
temperatures.
Itisinerttooxygenandalmostinerttomanyalkaliesandacids.
Therefore,thistypeofinsulationispreferredover VIRinextremeenvironmentalconditions
suchasincementfactoryorchemicalfactory.
Themechanicalproperties(i.e.,elasticityetc.)ofPVCarenotsogood.•XLPEcable
Itstandsforcrosslinkedpolyethylenecable.Itisahydronictubingmanufacturedfrompolyethyleneplastic.XLPE
featuresa3Dmolecularbondstructureandshapememorycharacteristics.
XLPEinsulationperformsatbothhighandlowtemperatures.Duetoitsstructure,XLPEisextremelyresistantto
abrasionandotherwearandtear.Italsoboastsresistancetohighvoltageelectricity,chemicals,andother
hazardousmaterials.Cross-linkedpolyethyleneinsulationisalsoamoreaffordableoption.
•Varnishedcambric.
Itisacottonclothimpregnatedandcoatedwithvarnish.
Thecambricislappedontotheconductorintheformofatapeanditssurfacesarecoatedwithpetroleumjelly
compoundtoallowfortheslidingofoneturnoveranotherasthecableisbent.
Asthevarnishedcambricishygroscopic,therefore,suchcablesarealwaysprovidedwithmetallicsheath.Itsdielectric
strengthisabout4kV/mmandpermittivityis2.5to3.8.
•Polyvinylchloride(PVC).
Thisinsulatingmaterialisasyntheticcompound.Itisobtainedfromthepolymerisationofacetyleneandisintheformof
whitepowder.
Forobtainingthismaterialasacableinsulation,itiscompoundedwithcertainmaterialsknownasplasticizerswhichare
liquidswithhighboilingpoint.
Polyvinylchloridehashighinsulationresistance,gooddielectricstrengthandmechanicaltoughnessoverawiderangeof
temperatures.
Itisinerttooxygenandalmostinerttomanyalkaliesandacids.
Therefore,thistypeofinsulationispreferredover VIRinextremeenvironmentalconditions
suchasincementfactoryorchemicalfactory.
Themechanicalproperties(i.e.,elasticityetc.)ofPVCarenotsogood.•XLPEcable
Itstandsforcrosslinkedpolyethylenecable.Itisahydronictubingmanufacturedfrompolyethyleneplastic.XLPE
featuresa3Dmolecularbondstructureandshapememorycharacteristics.
XLPEinsulationperformsatbothhighandlowtemperatures.Duetoitsstructure,XLPEisextremelyresistantto
abrasionandotherwearandtear.Italsoboastsresistancetohighvoltageelectricity,chemicals,andother
hazardousmaterials.Cross-linkedpolyethyleneinsulationisalsoamoreaffordableoption.
Classification of Cables
:-
•Cablesforundergroundservicemaybeclassifiedintwowaysaccordingto( i)thetypeofinsulating
materialusedintheirmanufacture(ii)thevoltageforwhichtheyaremanufactured.However,thelattermethodof
classificationisgenerallypreferred,accordingtowhichcablescanbedividedintothefollowinggroups:
(i)Low-tension(L.T.)cables—upto1000V
(ii)High-tension(H.T.)cables—upto11kV
(iii)Super-tension(S.T.)cables—from22kVto33kV
(iv)Extrahigh-tension(E.H.T.)cables—from33kVto66kV
(v)Extrasupervoltagecables—beyond132kV
•Acablemayhaveoneormorethanonecoredependinguponthetypeofserviceforwhichitisintended.Itmaybe( i)
single-core(ii)two-core(iii)three-core(iv)four-coreetc.Fora3-phaseservice,either3-single-corecablesorthree-core
cablecanbeuseddependingupontheoperatingvoltageandloaddemand.
Figure 2
•Figure2showstheconstructionaldetailsofasingle-corelowtensioncable.
•Thecablehasordinaryconstructionbecausethestressesdevelopedinthecableforlow
voltagesaregenerallysmall.
•Itconsistsofonecircularcoreoftinnedstrandedcopper(oraluminium)insulatedby
layersofimpregnatedpaper.
•Theinsulationissurroundedbyaleadsheathwhichpreventstheentryofmoistureinto
theinnerparts.Inordertoprotecttheleadsheathfromcorrosion,anoverallservingof
compoundedfibrousmaterial(juteetc.)isprovided.
•Single-corecablesarenotusuallyarmouredinordertoavoidexcessivesheathlosses.
:-
•Cablesforundergroundservicemaybeclassifiedintwowaysaccordingto( i)thetypeofinsulating
materialusedintheirmanufacture(ii)thevoltageforwhichtheyaremanufactured.However,thelattermethodof
classificationisgenerallypreferred,accordingtowhichcablescanbedividedintothefollowinggroups:
(i)Low-tension(L.T.)cables—upto1000V
(ii)High-tension(H.T.)cables—upto11kV
(iii)Super-tension(S.T.)cables—from22kVto33kV
(iv)Extrahigh-tension(E.H.T.)cables—from33kVto66kV
(v)Extrasupervoltagecables—beyond132kV
•Acablemayhaveoneormorethanonecoredependinguponthetypeofserviceforwhichitisintended.Itmaybe( i)
single-core(ii)two-core(iii)three-core(iv)four-coreetc.Fora3-phaseservice,either3-single-corecablesorthree-core
cablecanbeuseddependingupontheoperatingvoltageandloaddemand.
Figure 2
•Figure2showstheconstructionaldetailsofasingle-corelowtensioncable.
•Thecablehasordinaryconstructionbecausethestressesdevelopedinthecableforlow
voltagesaregenerallysmall.
•Itconsistsofonecircularcoreoftinnedstrandedcopper(oraluminium)insulatedby
layersofimpregnatedpaper.
•Theinsulationissurroundedbyaleadsheathwhichpreventstheentryofmoistureinto
theinnerparts.Inordertoprotecttheleadsheathfromcorrosion,anoverallservingof
compoundedfibrousmaterial(juteetc.)isprovided.
•Single-corecablesarenotusuallyarmouredinordertoavoidexcessivesheathlosses.
Classification of 3-Phase Cables:-
•Forthepurpose,ofsending3phasepowereitherthree-corecableorthreesinglecorecablesmaybeused.
•Forvoltagesupto66kV,3-corecable(i.e.,multi-coreconstruction)ispreferredduetoeconomicreasons.
•However,forvoltagesbeyond66kV,3-core-cablesbecometoolargeand,therefore,single-corecablesareused.
•Thefollowingtypesofcablesaregenerallyusedfor3-phaseservice:
Beltedcables—upto11kV
Screenedcables—from22kVto66kV
Pressurecables—beyond66kV.
•Anotherlayerofimpregnatedpapertape,calledpaperbeltiswoundroundthegroupedinsulatedcores.
•Thegapbetweentheinsulatedcoresisfilledwithfibrousinsulatingmaterial(juteetc.)soastogivecircularcross-sectionto
thecable.
•Thecoresaregenerallystrandedandmaybeofnoncircularshapetomakebetteruseofavailablespace.
•Thebeltiscoveredwithleadsheathtoprotectthecableagainstingressofmoistureandmechanicalinjury.
•Theleadsheathmaybecoveredwithoneormorelayersofarmouringwithanouterserving(notshowninthefigure).
Figure 3
•Beltedcables.Thesecablesareusedforvoltagesupto11kVbutinextraordinary
cases,theirusemaybeextendedupto22kV.Figure3showstheconstructionaldetails
ofa3-corebeltedcable.Thecoresareinsulatedfromeachotherbylayersof
impregnatedpaper.
•Forthepurpose,ofsending3phasepowereitherthree-corecableorthreesinglecorecablesmaybeused.
•Forvoltagesupto66kV,3-corecable(i.e.,multi-coreconstruction)ispreferredduetoeconomicreasons.
•However,forvoltagesbeyond66kV,3-core-cablesbecometoolargeand,therefore,single-corecablesareused.
•Thefollowingtypesofcablesaregenerallyusedfor3-phaseservice:
Beltedcables—upto11kV
Screenedcables—from22kVto66kV
Pressurecables—beyond66kV.
•Anotherlayerofimpregnatedpapertape,calledpaperbeltiswoundroundthegroupedinsulatedcores.
•Thegapbetweentheinsulatedcoresisfilledwithfibrousinsulatingmaterial(juteetc.)soastogivecircularcross-sectionto
thecable.
•Thecoresaregenerallystrandedandmaybeofnoncircularshapetomakebetteruseofavailablespace.
•Thebeltiscoveredwithleadsheathtoprotectthecableagainstingressofmoistureandmechanicalinjury.
•Theleadsheathmaybecoveredwithoneormorelayersofarmouringwithanouterserving(notshowninthefigure).
Figure 3
•Beltedcables.Thesecablesareusedforvoltagesupto11kVbutinextraordinary
cases,theirusemaybeextendedupto22kV.Figure3showstheconstructionaldetails
ofa3-corebeltedcable.Thecoresareinsulatedfromeachotherbylayersof
impregnatedpaper.
Classification of 3-Phase Cables:-
•Thebeltedtypeconstructionissuitableonlyforlowandmediumvoltagesastheelectrostaticstressesdevelopedinthe
cablesforthesevoltagesaremoreorlessradiali.e.,acrosstheinsulation.
•However,forhighvoltages(beyond22kV),thetangentialstressesalsobecomeimportant.Thesestressesactalongthelayers
ofpaperinsulation.
•Astheinsulationresistanceofpaperisquitesmallalongthelayers,therefore,tangentialstressessetupleakagecurrentalong
thelayersofpaperinsulation.
•Theleakagecurrentcauseslocalheating,resultingintheriskofbreakdownofinsulationatanymoment.
•Inordertoovercomethisdifficulty,screenedcablesareusedwhereleakagecurrentsareconductedtoearththroughmetallic
screens.
•Screenedcables.Thesecablesaremeantforuseupto33kV,butinparticularcasestheirusemaybeextendedtooperating
voltagesupto66kV.TwoprincipaltypesofscreenedcablesareH-typecablesandS.L.typecables.
•(i)H-typecables.ThistypeofcablewasfirstdesignedbyH.Hochstadterandhencethename.
Figure4showstheconstructionaldetailsofatypical3-core,H-typecable.
Figure 4
•Eachcoreisinsulatedbylayersofimpregnatedpaper.
•Theinsulationoneachcoreiscoveredwithametallicscreenwhichusually
consistsofaperforatedaluminiumfoil.
•Thecoresarelaidinsuchawaythatmetallicscreensmakecontactwithone
another.
•Anadditionalconductingbelt(copperwovenfabrictape)iswrappedroundthe
threecores.Thecablehasnoinsulatingbeltbutleadsheath,bedding,armouring
andservingfollowasusual.
•Thebeltedtypeconstructionissuitableonlyforlowandmediumvoltagesastheelectrostaticstressesdevelopedinthe
cablesforthesevoltagesaremoreorlessradiali.e.,acrosstheinsulation.
•However,forhighvoltages(beyond22kV),thetangentialstressesalsobecomeimportant.Thesestressesactalongthelayers
ofpaperinsulation.
•Astheinsulationresistanceofpaperisquitesmallalongthelayers,therefore,tangentialstressessetupleakagecurrentalong
thelayersofpaperinsulation.
•Theleakagecurrentcauseslocalheating,resultingintheriskofbreakdownofinsulationatanymoment.
•Inordertoovercomethisdifficulty,screenedcablesareusedwhereleakagecurrentsareconductedtoearththroughmetallic
screens.
•Screenedcables.Thesecablesaremeantforuseupto33kV,butinparticularcasestheirusemaybeextendedtooperating
voltagesupto66kV.TwoprincipaltypesofscreenedcablesareH-typecablesandS.L.typecables.
•(i)H-typecables.ThistypeofcablewasfirstdesignedbyH.Hochstadterandhencethename.
Figure4showstheconstructionaldetailsofatypical3-core,H-typecable.
Figure 4
•Eachcoreisinsulatedbylayersofimpregnatedpaper.
•Theinsulationoneachcoreiscoveredwithametallicscreenwhichusually
consistsofaperforatedaluminiumfoil.
•Thecoresarelaidinsuchawaythatmetallicscreensmakecontactwithone
another.
•Anadditionalconductingbelt(copperwovenfabrictape)iswrappedroundthe
threecores.Thecablehasnoinsulatingbeltbutleadsheath,bedding,armouring
andservingfollowasusual.
Classification of 3-Phase Cables:-
•It is easy to see that each core screen is in electrical contact with the conducting belt and the lead sheath.
•As all the four screens (3 core screens and one conducting belt) and the lead sheath are at earth potential, therefore, the
electrical stresses are purely radial and consequently dielectric losses are reduced.
•Two principal advantages are claimed for H-type cables.
•Firstly, the perforations in the metallic screens assist in the complete impregnation of the cable with the compound and thus
the possibility of air pockets or voids (vacuous spaces) in the dielectric is eliminated. The voids if present tend to reduce the
breakdown strength of the cable and may cause considerable damage to the paper insulation.
•Secondly, the metallic screens increase the heat dissipating power of the cable.
•(ii) S.L. type cables: Figure 5 shows the constructional details of a 3-core S.L. (separate lead) type cable. It is basically H-type
cable but the screen round each core insulation is covered by its own lead sheath.
•There is no overall lead sheath but only armouringand serving are provided. The S.L. type cables have two main advantages
over H-type cables.
Figure 5
•Firstly,theseparatesheathsminimisethepossibilityofcore-to-corebreakdown.
•Secondly,bendingofcablesbecomeseasyduetotheeliminationofoveralllead
sheath.
•However,thedisadvantageisthatthethreeleadsheathsofS.L.cablearemuch
thinnerthanthesinglesheathofH-cableand,therefore,callforgreatercarein
manufacture.
•It is easy to see that each core screen is in electrical contact with the conducting belt and the lead sheath.
•As all the four screens (3 core screens and one conducting belt) and the lead sheath are at earth potential, therefore, the
electrical stresses are purely radial and consequently dielectric losses are reduced.
•Two principal advantages are claimed for H-type cables.
•Firstly, the perforations in the metallic screens assist in the complete impregnation of the cable with the compound and thus
the possibility of air pockets or voids (vacuous spaces) in the dielectric is eliminated. The voids if present tend to reduce the
breakdown strength of the cable and may cause considerable damage to the paper insulation.
•Secondly, the metallic screens increase the heat dissipating power of the cable.
•(ii) S.L. type cables: Figure 5 shows the constructional details of a 3-core S.L. (separate lead) type cable. It is basically H-type
cable but the screen round each core insulation is covered by its own lead sheath.
•There is no overall lead sheath but only armouringand serving are provided. The S.L. type cables have two main advantages
over H-type cables.
Figure 5
•Firstly,theseparatesheathsminimisethepossibilityofcore-to-corebreakdown.
•Secondly,bendingofcablesbecomeseasyduetotheeliminationofoveralllead
sheath.
•However,thedisadvantageisthatthethreeleadsheathsofS.L.cablearemuch
thinnerthanthesinglesheathofH-cableand,therefore,callforgreatercarein
manufacture.
Limitations of solid type cables:-
Allthecablesmentionedearlier,arereferredtoassolidtypecablesbecausesolidinsulationisusedandnogasor
oilcirculatesinthecablesheath.Thevoltagelimitforsolidtypecablesis66kVduetothefollowingreasons:
Asasolidcablecarriestheload,itsconductortemperatureincreasesandthecablecompound(i.e.,insulatingcompound
overpaper)expands.Thisactionstretchestheleadsheathandmaydamageit.
Whentheloadonthecabledecreases,theconductorcoolsandapartialvacuumisformedwithinthecablesheath.Ifthe
pinholesarepresentintheleadsheath,moistairmaybedrawnintothecable.Themoisturereducesthedielectric
strengthofinsulationandmayeventuallycausethebreakdownofthecable.
Inpractice,voidsarealwayspresentintheinsulationofacable.Moderntechniquesofmanufacturinghaveresultedin
voidfreecables.However,underoperatingconditions,thevoidsareformedasaresultofthedifferentialexpansionand
contractionofthesheathandimpregnatedcompound.Thebreakdownstrengthofvoidsisconsiderablylessthanthatof
theinsulation.Ifthevoidissmallenough,theelectrostaticstressacrossitmaycauseitsbreakdown.Thevoidsnearestto
theconductorarethefirsttobreakdown,thechemicalandthermaleffectsofionisationcausingpermanentdamageto
thepaperinsulation.
Allthecablesmentionedearlier,arereferredtoassolidtypecablesbecausesolidinsulationisusedandnogasor
oilcirculatesinthecablesheath.Thevoltagelimitforsolidtypecablesis66kVduetothefollowingreasons:
Asasolidcablecarriestheload,itsconductortemperatureincreasesandthecablecompound(i.e.,insulatingcompound
overpaper)expands.Thisactionstretchestheleadsheathandmaydamageit.
Whentheloadonthecabledecreases,theconductorcoolsandapartialvacuumisformedwithinthecablesheath.Ifthe
pinholesarepresentintheleadsheath,moistairmaybedrawnintothecable.Themoisturereducesthedielectric
strengthofinsulationandmayeventuallycausethebreakdownofthecable.
Inpractice,voidsarealwayspresentintheinsulationofacable.Moderntechniquesofmanufacturinghaveresultedin
voidfreecables.However,underoperatingconditions,thevoidsareformedasaresultofthedifferentialexpansionand
contractionofthesheathandimpregnatedcompound.Thebreakdownstrengthofvoidsisconsiderablylessthanthatof
theinsulation.Ifthevoidissmallenough,theelectrostaticstressacrossitmaycauseitsbreakdown.Thevoidsnearestto
theconductorarethefirsttobreakdown,thechemicalandthermaleffectsofionisationcausingpermanentdamageto
thepaperinsulation.
Classification of 3-Phase Cables:-
•Pressurecables:Whentheoperatingvoltagesaregreaterthan66kV,pressurecablesareused.Insuchcables,voidsare
eliminatedbyincreasingthepressureofcompoundandforthisreasontheyarecalledpressurecables.
•Twotypesofpressurecablesvizoil-filledcablesandgaspressurecablesarecommonlyused.
•Oil-filledcables:-
Insuchtypesofcables,channelsorductsareprovidedinthecableforoil
circulation.Theoilunderpressure(itisthesameoilusedforimpregnation)iskeptconstantlysuppliedtothechannelby
meansofexternalreservoirsplacedatsuitabledistances(say500m)alongtherouteofthecable.
Oilunderpressurecompressesthelayersofpaperinsulationandisforcedintoanyvoidsthatmayhaveformedbetween
thelayers.
Duetotheeliminationofvoids,oil-filledcablescanbeusedforhighervoltages,therangebeingfrom66kVupto230kV.
Oil-filledcablesareofthreetypesviz.,single-coreconductorchannel,single-coresheathchannelandthree-corefiller-
spacechannels.
Figure 6
Figure6showstheconstructionaldetailsofasingle-coreconductorchannel,oil
filledcable.Theoilchannelisformedatthecentrebystrandingtheconductorwire
aroundahollowcylindricalsteelspiraltape.Theoilunderpressureissuppliedto
thechannelbymeansofexternalreservoir.Asthechannelismadeofspiralsteel
tape,itallowstheoiltopercolatebetweencopperstrandstothewrapped
insulation.Theoilpressurecompressesthelayersofpaperinsulationandprevents
thepossibilityofvoidformation.
•Pressurecables:Whentheoperatingvoltagesaregreaterthan66kV,pressurecablesareused.Insuchcables,voidsare
eliminatedbyincreasingthepressureofcompoundandforthisreasontheyarecalledpressurecables.
•Twotypesofpressurecablesvizoil-filledcablesandgaspressurecablesarecommonlyused.
•Oil-filledcables:-
Insuchtypesofcables,channelsorductsareprovidedinthecableforoil
circulation.Theoilunderpressure(itisthesameoilusedforimpregnation)iskeptconstantlysuppliedtothechannelby
meansofexternalreservoirsplacedatsuitabledistances(say500m)alongtherouteofthecable.
Oilunderpressurecompressesthelayersofpaperinsulationandisforcedintoanyvoidsthatmayhaveformedbetween
thelayers.
Duetotheeliminationofvoids,oil-filledcablescanbeusedforhighervoltages,therangebeingfrom66kVupto230kV.
Oil-filledcablesareofthreetypesviz.,single-coreconductorchannel,single-coresheathchannelandthree-corefiller-
spacechannels.
Figure 6
Figure6showstheconstructionaldetailsofasingle-coreconductorchannel,oil
filledcable.Theoilchannelisformedatthecentrebystrandingtheconductorwire
aroundahollowcylindricalsteelspiraltape.Theoilunderpressureissuppliedto
thechannelbymeansofexternalreservoir.Asthechannelismadeofspiralsteel
tape,itallowstheoiltopercolatebetweencopperstrandstothewrapped
insulation.Theoilpressurecompressesthelayersofpaperinsulationandprevents
thepossibilityofvoidformation.
Classification of 3-Phase Cables:-
Thesystemissodesignedthatwhentheoilgetsexpandedduetoincreaseincabletemperature,theextraoilcollectsinthe
reservoir.However,whenthecabletemperaturefallsduringlightloadconditions,theoilfromthereservoirflowstothe
channel.
Thedisadvantageofthistypeofcableisthatthechannelisatthemiddleofthecableandisatfullvoltagew.r.t.earth,sothat
averycomplicatedsystemofjointsisnecessary.
Figure 7
Figure7showstheconstructionaldetailsofasinglecoresheathchanneloil-filled
cable.Inthistypeofcable,theconductorissolidsimilartothatofsolidcableandis
paperinsulated.However,oilductsareprovidedinthemetallicsheathasshown.
Inthe3-coreoil-fillercableshowninFigure8,theoilductsarelocatedinthefiller
spaces.
Thesechannelsarecomposedofperforatedmetal-ribbontubingandareatearth
potential.
Theoil-filledcableshavethreeprincipaladvantages.
Firstly,formationofvoidsandionizationareavoided.
Secondly,allowabletemperaturerangeanddielectricstrengthareincreased.
Thirdly,ifthereisleakage,thedefectintheleadsheathisatonceindicated
andthepossibilityofearthfaultsisdecreased.
However,theirmajordisadvantagesarethehighinitialcostandcomplicatedsystem
oflaying.
Figure 8
Thesystemissodesignedthatwhentheoilgetsexpandedduetoincreaseincabletemperature,theextraoilcollectsinthe
reservoir.However,whenthecabletemperaturefallsduringlightloadconditions,theoilfromthereservoirflowstothe
channel.
Thedisadvantageofthistypeofcableisthatthechannelisatthemiddleofthecableandisatfullvoltagew.r.t.earth,sothat
averycomplicatedsystemofjointsisnecessary.
Figure 7
Figure7showstheconstructionaldetailsofasinglecoresheathchanneloil-filled
cable.Inthistypeofcable,theconductorissolidsimilartothatofsolidcableandis
paperinsulated.However,oilductsareprovidedinthemetallicsheathasshown.
Inthe3-coreoil-fillercableshowninFigure8,theoilductsarelocatedinthefiller
spaces.
Thesechannelsarecomposedofperforatedmetal-ribbontubingandareatearth
potential.
Theoil-filledcableshavethreeprincipaladvantages.
Firstly,formationofvoidsandionizationareavoided.
Secondly,allowabletemperaturerangeanddielectricstrengthareincreased.
Thirdly,ifthereisleakage,thedefectintheleadsheathisatonceindicated
andthepossibilityofearthfaultsisdecreased.
However,theirmajordisadvantagesarethehighinitialcostandcomplicatedsystem
oflaying.
Figure 8
Classification of 3-Phase Cables:-
•Gaspressurecables:-
•Thevoltagerequiredtosetupionisationinsideavoidincreasesasthepressureisincreased.Therefore,ifordinarycableis
subjectedtoasufficientlyhighpressure,theionisationcanbealtogethereliminated.
•Atthesametime,theincreasedpressureproducesradialcompressionwhichtendstocloseanyvoids.Thisistheunderlying
principleofgaspressurecables.
•Figure9showsthesectionofexternalpressurecable.Theconstructionofthecableissimilartothatofanordinarysolidtype
exceptthatitisoftriangularshapeandthicknessofleadsheathis75%thatofsolidcable.
•Thetriangularsectionreducestheweightandgiveslowthermalresistancebutthemainreasonfortriangularshapeisthat
theleadsheathactsasapressuremembrane.Thesheathisprotectedbyathinmetaltape.
•Thecableislaidinagas-tightsteelpipe.Thepipeisfilledwithdrynitrogengasat12to15atmospheres.Thegaspressure
producesradialcompressionandclosesthevoidsthatmayhaveformedbetweenthelayersofpaperinsulation.
•Suchcablescancarrymoreloadcurrentandoperateathighervoltagesthananormalcable.
•Moreover,maintenancecostissmallandthenitrogengashelpsinquenchinganyflame.
•However,ithasthedisadvantagethattheoverallcostisveryhigh.
Figure 9
•Gaspressurecables:-
•Thevoltagerequiredtosetupionisationinsideavoidincreasesasthepressureisincreased.Therefore,ifordinarycableis
subjectedtoasufficientlyhighpressure,theionisationcanbealtogethereliminated.
•Atthesametime,theincreasedpressureproducesradialcompressionwhichtendstocloseanyvoids.Thisistheunderlying
principleofgaspressurecables.
•Figure9showsthesectionofexternalpressurecable.Theconstructionofthecableissimilartothatofanordinarysolidtype
exceptthatitisoftriangularshapeandthicknessofleadsheathis75%thatofsolidcable.
•Thetriangularsectionreducestheweightandgiveslowthermalresistancebutthemainreasonfortriangularshapeisthat
theleadsheathactsasapressuremembrane.Thesheathisprotectedbyathinmetaltape.
•Thecableislaidinagas-tightsteelpipe.Thepipeisfilledwithdrynitrogengasat12to15atmospheres.Thegaspressure
producesradialcompressionandclosesthevoidsthatmayhaveformedbetweenthelayersofpaperinsulation.
•Suchcablescancarrymoreloadcurrentandoperateathighervoltagesthananormalcable.
•Moreover,maintenancecostissmallandthenitrogengashelpsinquenchinganyflame.
•However,ithasthedisadvantagethattheoverallcostisveryhigh.
Figure 9
Underground Cable Laying:-
•Therearethreemainmethodsoflayingundergroundcablesviz.,directlaying,draw-insystem
andthesolidsystem.
•Directlaying:-Thismethodoflayingundergroundcablesissimpleandcheapandismuch
favouredinmodernpractice.Inthismethod,atrenchisdug.Thetrenchiscoveredwithalayer
offinesandandthecableislaidoverthissandbed.Thesandpreventstheentryofmoisture
fromthegroundandthusprotectsthecablefromdecay.Afterthecablehasbeenlaidinthe
trench,itiscoveredwithanotherlayerofsand.Thetrenchisthencoveredwithbricksandother
materialsinordertoprotectthecablefrommechanicalinjury.
•Draw-insystem:-Inthismethod,conduitorductofglazedstoneorcastironorconcretearelaid
inthegroundwithmanholesatsuitablepositionsalongthecableroute.Thecablesarethen
pulledintopositionfrommanholes.Thecablestobelaidinthiswayneednotbearmouredbut
mustbeprovidedwithservingofhessianandjuteinordertoprotectthemwhenbeingpulled
intotheducts.
•Solidsystem:-Inthismethodoflaying,thecableislaidinopenpipesortroughsdugoutin
earthalongthecableroute.Thetroughingisofcastiron,stoneware,asphaltortreatedwood.
Afterthecableislaidinposition,thetroughingisfilledwithabituminousorasphaltic
compoundandcoveredover.Cableslaidinthismannerareusuallyplainleadcoveredbecause
troughingaffordsgoodmechanicalprotection.
Figure 10
Figure 11
•Therearethreemainmethodsoflayingundergroundcablesviz.,directlaying,draw-insystem
andthesolidsystem.
•Directlaying:-Thismethodoflayingundergroundcablesissimpleandcheapandismuch
favouredinmodernpractice.Inthismethod,atrenchisdug.Thetrenchiscoveredwithalayer
offinesandandthecableislaidoverthissandbed.Thesandpreventstheentryofmoisture
fromthegroundandthusprotectsthecablefromdecay.Afterthecablehasbeenlaidinthe
trench,itiscoveredwithanotherlayerofsand.Thetrenchisthencoveredwithbricksandother
materialsinordertoprotectthecablefrommechanicalinjury.
•Draw-insystem:-Inthismethod,conduitorductofglazedstoneorcastironorconcretearelaid
inthegroundwithmanholesatsuitablepositionsalongthecableroute.Thecablesarethen
pulledintopositionfrommanholes.Thecablestobelaidinthiswayneednotbearmouredbut
mustbeprovidedwithservingofhessianandjuteinordertoprotectthemwhenbeingpulled
intotheducts.
•Solidsystem:-Inthismethodoflaying,thecableislaidinopenpipesortroughsdugoutin
earthalongthecableroute.Thetroughingisofcastiron,stoneware,asphaltortreatedwood.
Afterthecableislaidinposition,thetroughingisfilledwithabituminousorasphaltic
compoundandcoveredover.Cableslaidinthismannerareusuallyplainleadcoveredbecause
troughingaffordsgoodmechanicalprotection.
Figure 10
Figure 11
Insulation Resistance of a Single-Core Cable:-
•Thecableconductorisprovidedwithasuitablethicknessofinsulatingmaterialinordertopreventleakagecurrent.Thepath
forleakagecurrentisradialthroughtheinsulation.
•Theoppositionofferedbyinsulationtoleakagecurrentisknownasinsulationresistanceofthecable.Forsatisfactory
operation,theinsulationresistanceofthecableshouldbeveryhigh.
•Considerasingle-corecableofconductorradius??????
1
andinternalsheathradius??????
2
asshowninFigure12.
•Let??????bethelengthofthecableandρbetheresistivityoftheinsulation.
•Consideraverysmalllayerofinsulationofthickness????????????ataradius??????.Thelengththroughwhichleakagecurrenttendstoflow
is????????????andtheareaofX-sectionofferedtothisflowis2??????????????????.
•So,Insulationresistanceofconsideredlayer=??????
??
6??
•Insulationresistanceofthewholecableis
??????=∫??????
??
6??
=
?6
?5
6?
∫
??
?
?6
?5
??????=
6?
????????????
?
6
?
5
•Thisshowsthatinsulationresistanceofacableisinverselyproportionaltoitslength.Inotherwords,ifthecablelength
increases,itsinsulationresistancedecreasesandvice-versa.
Figure 12
•Thecableconductorisprovidedwithasuitablethicknessofinsulatingmaterialinordertopreventleakagecurrent.Thepath
forleakagecurrentisradialthroughtheinsulation.
•Theoppositionofferedbyinsulationtoleakagecurrentisknownasinsulationresistanceofthecable.Forsatisfactory
operation,theinsulationresistanceofthecableshouldbeveryhigh.
•Considerasingle-corecableofconductorradius??????
1
andinternalsheathradius??????
2
asshowninFigure12.
•Let??????bethelengthofthecableandρbetheresistivityoftheinsulation.
•Consideraverysmalllayerofinsulationofthickness????????????ataradius??????.Thelengththroughwhichleakagecurrenttendstoflow
is????????????andtheareaofX-sectionofferedtothisflowis2??????????????????.
•So,Insulationresistanceofconsideredlayer=??????
??
6??
•Insulationresistanceofthewholecableis
??????=∫??????
??
6??
=
?6
?5
6?
∫
??
?
?6
?5
??????=
6?
????????????
?
6
?
5
•Thisshowsthatinsulationresistanceofacableisinverselyproportionaltoitslength.Inotherwords,ifthecablelength
increases,itsinsulationresistancedecreasesandvice-versa.
Figure 12
Capacitance of a Single-Core Cable:-
•Asingle-corecablecanbeconsideredtobeequivalenttotwolongco-axialcylinders.
•Theconductor(orcore)ofthecableistheinnercylinderwhiletheoutercylinderisrepresentedbyleadsheathwhichisat
earthpotential.
•ConsiderasinglecorecablewithconductordiameterdandinnersheathdiameterD(Figurein13).Letthechargepermetre
axiallengthofthecablebeQcoulombsandεbethepermittivityoftheinsulationmaterialbetweencoreandleadsheath.
Obviously?????? = ??????
0
??????
??????
where,??????
??????
istherelativepermittivityoftheinsulation.
•Consideracylinderofradius??????metresandaxiallength1metre.Thesurfaceareaofthiscylinderis= 2????????????×1=2???????????? m
2
.
ElectricfluxdensityatanypointPontheconsideredcylinderis??????
??????
=
?
6
??????/??????
2
•ElectricintensityatpointP,??????
??????
=
?
?
=
?
6?
4
?
volts/m
•TheworkdoneinmovingaunitpositivechargefrompointPthroughadistance????????????inthedirectionofelectricfieldis??????
??????
????????????.
•Hence,theworkdoneinmovingaunitpositivechargefromconductortosheath,whichisthepotentialdifferenceVbetween
conductorandsheath,isgivenby:
•??????=∫??????
??????
????????????
?/6
?/6
=∫
?
6?
4
?
????????????=
?
6
4
?
????????????
?
?
?/6
?/6
•Capacitanceofthecableis
??????=
?
?
=
?
?
.
,
?
??
?
?
??????/??????
=
6
4
?
??
?
?
=
6×<.<98×54
7-.
?
??
?
?
F/m
•Ifthecablehasalengthof?????? meters,thecapacitanceofthecableis
??????=
6?×<.<98×54
7-.
?
??
?
?
F/m
Figure 13
•Asingle-corecablecanbeconsideredtobeequivalenttotwolongco-axialcylinders.
•Theconductor(orcore)ofthecableistheinnercylinderwhiletheoutercylinderisrepresentedbyleadsheathwhichisat
earthpotential.
•ConsiderasinglecorecablewithconductordiameterdandinnersheathdiameterD(Figurein13).Letthechargepermetre
axiallengthofthecablebeQcoulombsandεbethepermittivityoftheinsulationmaterialbetweencoreandleadsheath.
Obviously?????? = ??????
0
??????
??????
where,??????
??????
istherelativepermittivityoftheinsulation.
•Consideracylinderofradius??????metresandaxiallength1metre.Thesurfaceareaofthiscylinderis= 2????????????×1=2???????????? m
2
.
ElectricfluxdensityatanypointPontheconsideredcylinderis??????
??????
=
?
6
??????/??????
2
•ElectricintensityatpointP,??????
??????
=
?
?
=
?
6?
4
?
volts/m
•TheworkdoneinmovingaunitpositivechargefrompointPthroughadistance????????????inthedirectionofelectricfieldis??????
??????
????????????.
•Hence,theworkdoneinmovingaunitpositivechargefromconductortosheath,whichisthepotentialdifferenceVbetween
conductorandsheath,isgivenby:
•??????=∫??????
??????
????????????
?/6
?/6
=∫
?
6?
4
?
????????????=
?
6
4
?
????????????
?
?
?/6
?/6
•Capacitanceofthecableis
??????=
?
?
=
?
?
.
,
?
??
?
?
??????/??????
=
6
4
?
??
?
?
=
6×<.<98×54
7-.
?
??
?
?
F/m
•Ifthecablehasalengthof?????? meters,thecapacitanceofthecableis
??????=
6?×<.<98×54
7-.
?
??
?
?
F/m
Figure 13
Dielectric Stress in a Single-Core Cable:-
•Underoperatingconditions,theinsulationofacableissubjectedtoelectrostaticforces.Thisisknownasdielectricstress.The
dielectricstressatanypointinacableisinfactthepotentialgradient(orelectricintensity)atthatpoint.
•Considerasinglecorecablewithcorediameter??????andinternalsheathdiameter??????.Theelectricintensityatapoint??????metres
fromthecentreofthecableis??????
??????
=
?
6?
4
?
??????????????????????????????/??????
•Bydefinition,electricintensityisequaltopotentialgradient.Therefore,potentialgradient??????atapoint??????metresfromthe
centreofcableisg=??????
??????
=
?
6?
4
?
??????????????????????????????/??????
•Asderivedearlier,thepotentialgradientbetweenconductorandthesheathis
??????=
?
6
4
?
????????????
?
?
??????????????????????????????
Or,??????=
6
4
?
??
?
?
??????
•Substitutingthevalueof??????intheexpressionof??????,weget
??????=
?
???
?
?
??????????????????????????????/??????
•Itisclearthatpotentialgradientvariesinverselyasthedistance??????.Therefore,potentialgradientwillbemaximumwhen?????? is
minimumi.e.,when?????? = ??????/2oratthesurfaceoftheconductor.Ontheotherhand,potentialgradientwillbeminimumat
?????? = ??????/2oratsheathsurface.
•Hence,maximumpotentialgradientis??????
??????????????????
=
6?
?×??
?
?
??????/??????
•Minimumpotentialgradientis??????
??????????????????
=
6?
?×??
?
?
??????/??????
Figure 14
•Underoperatingconditions,theinsulationofacableissubjectedtoelectrostaticforces.Thisisknownasdielectricstress.The
dielectricstressatanypointinacableisinfactthepotentialgradient(orelectricintensity)atthatpoint.
•Considerasinglecorecablewithcorediameter??????andinternalsheathdiameter??????.Theelectricintensityatapoint??????metres
fromthecentreofthecableis??????
??????
=
?
6?
4
?
??????????????????????????????/??????
•Bydefinition,electricintensityisequaltopotentialgradient.Therefore,potentialgradient??????atapoint??????metresfromthe
centreofcableisg=??????
??????
=
?
6?
4
?
??????????????????????????????/??????
•Asderivedearlier,thepotentialgradientbetweenconductorandthesheathis
??????=
?
6
4
?
????????????
?
?
??????????????????????????????
Or,??????=
6
4
?
??
?
?
??????
•Substitutingthevalueof??????intheexpressionof??????,weget
??????=
?
???
?
?
??????????????????????????????/??????
•Itisclearthatpotentialgradientvariesinverselyasthedistance??????.Therefore,potentialgradientwillbemaximumwhen?????? is
minimumi.e.,when?????? = ??????/2oratthesurfaceoftheconductor.Ontheotherhand,potentialgradientwillbeminimumat
?????? = ??????/2oratsheathsurface.
•Hence,maximumpotentialgradientis??????
??????????????????
=
6?
?×??
?
?
??????/??????
•Minimumpotentialgradientis??????
??????????????????
=
6?
?×??
?
?
??????/??????
Figure 14
Most Economical Conductor Size in a Cable:-
•Ithasalreadybeenshownthatmaximumstressinacableoccursatthesurfaceoftheconductor.Forsafeworkingofthecable,dielectric
strengthoftheinsulationshouldbemorethanthemaximumstress.
•Rewritingtheexpressionformaximumstress,weget,??????
??????????????????
=
6?
?×??
?
?
??????/??????
•Thevaluesofworkingvoltage??????andinternalsheathdiameter??????havetobekeptfixedatcertainvaluesduetodesignconsiderations.This
leavesconductordiameter??????tobetheonlyvariable.Forgivenvaluesof??????and??????,themosteconomicalconductordiameterwillbeonefor
which??????
??????????????????
hasaminimumvalue.Thevalueof??????
??????????????????
willbeminimumwhen??????ln (??????/??????)ismaximumi.e.
??
jl (?/?)
??
=0
Or,ln
?
?
+??????.
?
?
.
??
?
6
=0
Or,ln
?
?
=1
Or,
?
?
=??????=2.718
•Mosteconomicalconductordiameteris??????=
?
6.;5<
and
thevalueof??????
??????????????????
underthisconditionis??????
??????????????????
=
6?
?
Volts/m.
•Forlowandmediumvoltagecables,thevalueofconductordiameterarrivedatbythismethod(i.e.,?????? = 2??????/??????
??????????????????
)isoftentoosmall
fromthepointofviewofcurrentdensity.
•Therefore,theconductordiameterofsuchcablesisdeterminedfromtheconsiderationofsafecurrentdensity.
•Forhighvoltagecables,designsbasedonthistheorygiveaveryhighvalueof??????,toolargefromthepointofviewofcurrentcarrying
capacityanditis,therefore,advantageoustoincreasetheconductordiametertothisvalue.Therearethreewaysofdoingthis
withoutusingexcessivecopper:
(i) Using aluminiuminstead of copper because for the same current, diameter of aluminiumwill be more than that of
copper.
(ii) Using copper wires stranded round a central core of hemp.
(iii) Using a central lead tube instead of hemp.
•Ithasalreadybeenshownthatmaximumstressinacableoccursatthesurfaceoftheconductor.Forsafeworkingofthecable,dielectric
strengthoftheinsulationshouldbemorethanthemaximumstress.
•Rewritingtheexpressionformaximumstress,weget,??????
??????????????????
=
6?
?×??
?
?
??????/??????
•Thevaluesofworkingvoltage??????andinternalsheathdiameter??????havetobekeptfixedatcertainvaluesduetodesignconsiderations.This
leavesconductordiameter??????tobetheonlyvariable.Forgivenvaluesof??????and??????,themosteconomicalconductordiameterwillbeonefor
which??????
??????????????????
hasaminimumvalue.Thevalueof??????
??????????????????
willbeminimumwhen??????ln (??????/??????)ismaximumi.e.
??
jl (?/?)
??
=0
Or,ln
?
?
+??????.
?
?
.
??
?
6
=0
Or,ln
?
?
=1
Or,
?
?
=??????=2.718
•Mosteconomicalconductordiameteris??????=
?
6.;5<
and
thevalueof??????
??????????????????
underthisconditionis??????
??????????????????
=
6?
?
Volts/m.
•Forlowandmediumvoltagecables,thevalueofconductordiameterarrivedatbythismethod(i.e.,?????? = 2??????/??????
??????????????????
)isoftentoosmall
fromthepointofviewofcurrentdensity.
•Therefore,theconductordiameterofsuchcablesisdeterminedfromtheconsiderationofsafecurrentdensity.
•Forhighvoltagecables,designsbasedonthistheorygiveaveryhighvalueof??????,toolargefromthepointofviewofcurrentcarrying
capacityanditis,therefore,advantageoustoincreasetheconductordiametertothisvalue.Therearethreewaysofdoingthis
withoutusingexcessivecopper:
(i) Using aluminiuminstead of copper because for the same current, diameter of aluminiumwill be more than that of
copper.
(ii) Using copper wires stranded round a central core of hemp.
(iii) Using a central lead tube instead of hemp.
Grading of Cables:-
•Theprocessofachievinguniformelectrostaticstressinthedielectricofcablesisknownasgradingofcables.
•Ithasalreadybeenshownthatelectrostaticstressinasinglecorecablehasamaximumvalue(??????
??????????????????
)attheconductorsurface
andgoesondecreasingaswemovetowardsthesheath.
•Themaximumvoltagethatcanbesafelyappliedtoacabledependsupon ??????
??????????????????
i.e.,electrostaticstressatthe
conductorsurface.Forsafeworkingofacablehavinghomogeneousdielectric,thestrengthofdi
electricmustbemore
than??????
??????????????????
.
•Ifadielectricofhighstrengthisusedforacable,itisusefulonlyneartheconductorwherestressismaximum.
Butaswemoveawayfromtheconductor,theelectrostaticstressdecreases,sothedielectricwillbe
unnecessarilyoverstrong.
•Theunequalstressdistributioninacableisundesirablefortworeasons.Firstly,insulationofgreaterthicknessis
requiredwhichincreasesthecablesize.
•Secondly,itmayleadtothebreakdownofinsulation.Inordertoovercomeabovedisadvantages,itisnecessary
tohaveauniformstressdistributionincables.
•Thiscanbeachievedbydistributingthestressinsuchawaythatitsvalueisincreasedintheouterlayersof
dielectric.Thisisknownasgradingofcables.Thefollowingarethetwomainmethodsofgradingofcables:
(i)Capacitancegrading(ii)Intersheathgrading
•Theprocessofachievinguniformelectrostaticstressinthedielectricofcablesisknownasgradingofcables.
•Ithasalreadybeenshownthatelectrostaticstressinasinglecorecablehasamaximumvalue(??????
??????????????????
)attheconductorsurface
andgoesondecreasingaswemovetowardsthesheath.
•Themaximumvoltagethatcanbesafelyappliedtoacabledependsupon ??????
??????????????????
i.e.,electrostaticstressatthe
conductorsurface.Forsafeworkingofacablehavinghomogeneousdielectric,thestrengthofdi
electricmustbemore
than??????
??????????????????
.
•Ifadielectricofhighstrengthisusedforacable,itisusefulonlyneartheconductorwherestressismaximum.
Butaswemoveawayfromtheconductor,theelectrostaticstressdecreases,sothedielectricwillbe
unnecessarilyoverstrong.
•Theunequalstressdistributioninacableisundesirablefortworeasons.Firstly,insulationofgreaterthicknessis
requiredwhichincreasesthecablesize.
•Secondly,itmayleadtothebreakdownofinsulation.Inordertoovercomeabovedisadvantages,itisnecessary
tohaveauniformstressdistributionincables.
•Thiscanbeachievedbydistributingthestressinsuchawaythatitsvalueisincreasedintheouterlayersof
dielectric.Thisisknownasgradingofcables.Thefollowingarethetwomainmethodsofgradingofcables:
(i)Capacitancegrading(ii)Intersheathgrading
Capacitance Grading
•Incapacitancegrading,thehomogeneousdielectricisreplacedbyacompositedielectric.
•Thecompositedielectricconsistsofvariouslayersofdifferentdielectricsinsuchamannerthat
relativepermittivity??????
??????
ofanylayerisinverselyproportionaltoitsdistancefromthecentre.
•Undersuchconditions,thevalueofpotentialgradientatanypointinthedielectricisconstantand
isindependentofitsdistancefromthecentre.
•Inotherwords,thedielectricstressinthecableissameeverywhereandthegradingisidealone.
•However,idealgradingrequirestheuseofaninfinitenumberofdielectricswhichisanimpossible
task.
•Inpractice,twoorthreedielectricsareusedinthedecreasingorderofpermittivity;thedielectric
ofhighestpermittivitybeingusednearthecore.
•ThecapacitancegradingcanbeexplainedbyreferringtoFigure15.Therearethreedielectricsof
outerdiameter??????
1
,??????
2
and??????andofrelativepermittivity??????
1
,??????
2
and??????
3
respectively.
•Ifthepermittivityaresuchthat??????
1
> ??????
2
> ??????
3
andthethreedielectricsareworkedatthesame
maximumstress,then,
1
??????
1
??????
=
1
??????
2
??????
1
=
1
??????
3
??????
2
Or,??????
1
??????=??????
2
??????
1
=??????
3
??????
2
•Potentialdifferenceacrosstheinnerlayeris
??????
1
=???????????????????
?
5
/6
?/6
=?
??????
2????????????
0
??????
1
??????
????????????
?
5
/6
?/6
=
??????
2????????????
0
??????
1
ln
??????
1
??????
=
??????
??????????????????
2
??????ln
??????
1
??????
Figure 15
•Incapacitancegrading,thehomogeneousdielectricisreplacedbyacompositedielectric.
•Thecompositedielectricconsistsofvariouslayersofdifferentdielectricsinsuchamannerthat
relativepermittivity??????
??????
ofanylayerisinverselyproportionaltoitsdistancefromthecentre.
•Undersuchconditions,thevalueofpotentialgradientatanypointinthedielectricisconstantand
isindependentofitsdistancefromthecentre.
•Inotherwords,thedielectricstressinthecableissameeverywhereandthegradingisidealone.
•However,idealgradingrequirestheuseofaninfinitenumberofdielectricswhichisanimpossible
task.
•Inpractice,twoorthreedielectricsareusedinthedecreasingorderofpermittivity;thedielectric
ofhighestpermittivitybeingusednearthecore.
•ThecapacitancegradingcanbeexplainedbyreferringtoFigure15.Therearethreedielectricsof
outerdiameter??????
1
,??????
2
and??????andofrelativepermittivity??????
1
,??????
2
and??????
3
respectively.
•Ifthepermittivityaresuchthat??????
1
> ??????
2
> ??????
3
andthethreedielectricsareworkedatthesame
maximumstress,then,
1
??????
1
??????
=
1
??????
2
??????
1
=
1
??????
3
??????
2
Or,??????
1
??????=??????
2
??????
1
=??????
3
??????
2
•Potentialdifferenceacrosstheinnerlayeris
??????
1
=???????????????????
?
5
/6
?/6
=?
??????
2????????????
0
??????
1
??????
????????????
?
5
/6
?/6
=
??????
2????????????
0
??????
1
ln
??????
1
??????
=
??????
??????????????????
2
??????ln
??????
1
??????
Figure 15
Capacitance Grading
•Similarly,potentialacrosssecondlayer(??????
2
)andthirdlayer(??????
3
)isgivenby:
??????
2
=
?
???
6
??????
1
ln(
?
6
?
5
);??????
3
=
?
???
6
??????
2
ln(
?
?
6
)
•Totalpotentialdifferencebetweencoreandearthedsheathis
??????=
?
???
6
??????ln
?
5
?
+??????
1
ln
?
6
?
5
+??????
2
ln(
?
?
6
)
•Ifthecablehadhomogeneousdielectric,then,forthesamevaluesof??????,??????and??????
??????????????????
,thepermissiblepotentialdifference
betweencoreandearthedsheathwouldhavebeen
??????
?
=
??????
??????????????????
2
??????ln(
??????
??????
)
•Obviously,?????? > ??????′ i.e.,forgivendimensionsofthecable,agradedcablecanbeworkedata
greaterpotentialthannon-gradedcable.
•Alternatively,forthesamesafepotential,thesizeofgradedcablewillbelessthanthatofnon-gradedcable.
•Thefollowingpointsmaybenoted:
(i)Asthepermissiblevaluesof??????
??????????????????
arepeakvalues,therefore,allthevoltagesinaboveexpressionsshouldbetakenas
peakvaluesandnotther.m.s.values.
(ii)Ifthemaximumstressinthethreedielectricsisnotthesame,then,
??????=
??????
????????????????????????
??????
??????ln
??????
1
??????
+
??????
????????????????????????
??????
??????
1
ln
??????
2
??????
1
+
??????
????????????????????????
??????
??????
2
ln
??????
??????
2
•Theprincipaldisadvantageofthismethodisthatthereareafewhighgradedielectricsofreasonablecostwhose
permittivitiesvaryovertherequiredrange.
•Similarly,potentialacrosssecondlayer(??????
2
)andthirdlayer(??????
3
)isgivenby:
??????
2
=
?
???
6
??????
1
ln(
?
6
?
5
);??????
3
=
?
???
6
??????
2
ln(
?
?
6
)
•Totalpotentialdifferencebetweencoreandearthedsheathis
??????=
?
???
6
??????ln
?
5
?
+??????
1
ln
?
6
?
5
+??????
2
ln(
?
?
6
)
•Ifthecablehadhomogeneousdielectric,then,forthesamevaluesof??????,??????and??????
??????????????????
,thepermissiblepotentialdifference
betweencoreandearthedsheathwouldhavebeen
??????
?
=
??????
??????????????????
2
??????ln(
??????
??????
)
•Obviously,?????? > ??????′ i.e.,forgivendimensionsofthecable,agradedcablecanbeworkedata
greaterpotentialthannon-gradedcable.
•Alternatively,forthesamesafepotential,thesizeofgradedcablewillbelessthanthatofnon-gradedcable.
•Thefollowingpointsmaybenoted:
(i)Asthepermissiblevaluesof??????
??????????????????
arepeakvalues,therefore,allthevoltagesinaboveexpressionsshouldbetakenas
peakvaluesandnotther.m.s.values.
(ii)Ifthemaximumstressinthethreedielectricsisnotthesame,then,
??????=
??????
????????????????????????
??????
??????ln
??????
1
??????
+
??????
????????????????????????
??????
??????
1
ln
??????
2
??????
1
+
??????
????????????????????????
??????
??????
2
ln
??????
??????
2
•Theprincipaldisadvantageofthismethodisthatthereareafewhighgradedielectricsofreasonablecostwhose
permittivitiesvaryovertherequiredrange.
IntersheathGrading
•Inthismethodofcablegrading,ahomogeneousdielectricisused,butitisdividedintovariouslayersby
placingmetallicintersheathsbetweenthecoreandleadsheath.
•Theintersheathsareheldatsuitablepotentialswhichareinbetweenthecorepotentialandearth
potential.Thisarrangementimprovesvoltagedistributioninthedielectricofthecableandconsequently
moreuniformpotentialgradientisobtained.
•Consideracableofcorediameter??????andouterleadsheathofdiameter ??????.Supposethattwo
intersheathsofdiameters??????
1
and??????
2
areinsertedintothehomogeneousdielectricandmaintainedat
somefixedpotentials.
•Let??????
1
,??????
2
?????????????????? ??????
3
respectivelybethevoltagebetweencoreandintersheath1,betweenintersheath1
and2andbetweenintersheath2andouterleadsheath.
•Asthereisadefinitepotentialdifferencebetweentheinnerandouterlayersofeachintersheath,
therefore,eachsheathcanbetreatedlikeahomogeneoussinglecorecable.Asprovedalready,
Maximumstressbetweencoreandintersheath1is
??????
1??????????????????
=
??????
1
??????
2
ln (
??????
1
??????
)
??????
2??????????????????
=
??????
2
??????
1
2
ln (
??????
2
??????
1
)
??????
3??????????????????
=
??????
3
??????
2
2
ln (
??????
??????
2
)
Figure 15
•Inthismethodofcablegrading,ahomogeneousdielectricisused,butitisdividedintovariouslayersby
placingmetallicintersheathsbetweenthecoreandleadsheath.
•Theintersheathsareheldatsuitablepotentialswhichareinbetweenthecorepotentialandearth
potential.Thisarrangementimprovesvoltagedistributioninthedielectricofthecableandconsequently
moreuniformpotentialgradientisobtained.
•Consideracableofcorediameter??????andouterleadsheathofdiameter ??????.Supposethattwo
intersheathsofdiameters??????
1
and??????
2
areinsertedintothehomogeneousdielectricandmaintainedat
somefixedpotentials.
•Let??????
1
,??????
2
?????????????????? ??????
3
respectivelybethevoltagebetweencoreandintersheath1,betweenintersheath1
and2andbetweenintersheath2andouterleadsheath.
•Asthereisadefinitepotentialdifferencebetweentheinnerandouterlayersofeachintersheath,
therefore,eachsheathcanbetreatedlikeahomogeneoussinglecorecable.Asprovedalready,
Maximumstressbetweencoreandintersheath1is
??????
1??????????????????
=
??????
1
??????
2
ln (
??????
1
??????
)
??????
2??????????????????
=
??????
2
??????
1
2
ln (
??????
2
??????
1
)
??????
3??????????????????
=
??????
3
??????
2
2
ln (
??????
??????
2
)
Figure 15
IntersheathGrading
•Sincethedielectricishomogeneous,themaximumstressineachlayeristhesamei.e.,
•Asthecablebehaveslikethreecapacitorsinseries,therefore,allthepotentialsareinphasei.e.Voltagebetweenconductor
andearthedleadsheathis?????? = ??????
1
+ ??????
2
+ ??????
3
•Intersheathgradinghasthreeprincipaldisadvantages.
Firstly,therearecomplicationsinfixingthesheathpotentials.
Secondly,theintersheathsarelikelytobedamagedduringtransportationandinstallationwhichmightresultinlocal
concentrationsofpotentialgradient.
Thirdly,thereareconsiderablelossesintheintersheathsduetochargingcurrents.
•Forthesereasons,intersheathgradingisrarelyused.
•Sincethedielectricishomogeneous,themaximumstressineachlayeristhesamei.e.,
•Asthecablebehaveslikethreecapacitorsinseries,therefore,allthepotentialsareinphasei.e.Voltagebetweenconductor
andearthedleadsheathis?????? = ??????
1
+ ??????
2
+ ??????
3
•Intersheathgradinghasthreeprincipaldisadvantages.
Firstly,therearecomplicationsinfixingthesheathpotentials.
Secondly,theintersheathsarelikelytobedamagedduringtransportationandinstallationwhichmightresultinlocal
concentrationsofpotentialgradient.
Thirdly,thereareconsiderablelossesintheintersheathsduetochargingcurrents.
•Forthesereasons,intersheathgradingisrarelyused.
Capacitance of 3-Core Cables
•Thecapacitanceofacablesystemismuchmoreimportantthanthatofoverheadlinebecauseincables(i)conductors
arenearertoeachotherandtotheearthedsheath(ii)theyareseparatedbyadielectricofpermittivitymuchgreater
thanthatofair.
•Figure16showsasystemofcapacitancesina3-corebeltedcableusedfor3-phasesystem.Sincepotentialdifference
existsbetweenpairsofconductorsandbetweeneachconductorandthesheath,electrostaticfieldsaresetupinthe
cableasshowninFig.16(i).
•Theseelectrostaticfieldsgiverisetocore-corecapacitances??????
??????
andconductor-earthcapacitances??????
??????
asshowninFigure
16(ii).
•Thethree??????
??????
aredeltaconnectedwhereasthethree??????
??????
arestarconnected,thesheathformingthestarpointasshown
inFigure16(iii).
•Theylayofabeltedcablemakesitreasonabletoassumeequalityofeach??????
??????
andeach??????
??????
.Thethreedeltaconnected
capacitances??????
??????
asshowninFigure17(i)canbeconvertedintoequivalentstarconnectedcapacitancesasshowninFig.
17(ii).ItcanbeeasilyshownthatequivalentstarcapacitanceC
eq
isequaltothreetimesthedeltacapacitanceC
c
i.e.C
eq
=3C
c
.
Figure 16 Figure 17
•Thecapacitanceofacablesystemismuchmoreimportantthanthatofoverheadlinebecauseincables(i)conductors
arenearertoeachotherandtotheearthedsheath(ii)theyareseparatedbyadielectricofpermittivitymuchgreater
thanthatofair.
•Figure16showsasystemofcapacitancesina3-corebeltedcableusedfor3-phasesystem.Sincepotentialdifference
existsbetweenpairsofconductorsandbetweeneachconductorandthesheath,electrostaticfieldsaresetupinthe
cableasshowninFig.16(i).
•Theseelectrostaticfieldsgiverisetocore-corecapacitances??????
??????
andconductor-earthcapacitances??????
??????
asshowninFigure
16(ii).
•Thethree??????
??????
aredeltaconnectedwhereasthethree??????
??????
arestarconnected,thesheathformingthestarpointasshown
inFigure16(iii).
•Theylayofabeltedcablemakesitreasonabletoassumeequalityofeach??????
??????
andeach??????
??????
.Thethreedeltaconnected
capacitances??????
??????
asshowninFigure17(i)canbeconvertedintoequivalentstarconnectedcapacitancesasshowninFig.
17(ii).ItcanbeeasilyshownthatequivalentstarcapacitanceC
eq
isequaltothreetimesthedeltacapacitanceC
c
i.e.C
eq
=3C
c
.
Figure 16 Figure 17
Capacitance of 3-Core Cables
Figure 18
•Figure 16 (iii) reduces to the equivalent circuit shown in Figure 17 (i). Therefore, the whole cable is equivalent to three
star-connected capacitors each of capacitance ??????
??????
= ??????
??????
+ ??????
????????????
= ??????
??????
+ 3????????????
•If ??????
??????ℎ
is the phase voltage, then charging current ??????
??????
is given by:
??????
??????
=??????
??????ℎ
/ ???????????????????????????????????????????????????????????? ?????????????????????????????????????????????????????? ?????????????????? ??????ℎ?????????????????? = 2??????????????????
??????ℎ
??????
??????
= 2??????????????????
??????ℎ
(??????
??????
+ 3????????????)
Figure 18
•Figure 16 (iii) reduces to the equivalent circuit shown in Figure 17 (i). Therefore, the whole cable is equivalent to three
star-connected capacitors each of capacitance ??????
??????
= ??????
??????
+ ??????
????????????
= ??????
??????
+ 3????????????
•If ??????
??????ℎ
is the phase voltage, then charging current ??????
??????
is given by:
??????
??????
=??????
??????ℎ
/ ???????????????????????????????????????????????????????????? ?????????????????????????????????????????????????????? ?????????????????? ??????ℎ?????????????????? = 2??????????????????
??????ℎ
??????
??????
= 2??????????????????
??????ℎ
(??????
??????
+ 3????????????)
Measurements of and
•Althoughcore-corecapacitance??????
??????
andcore-earthcapacitance??????
??????
canbeobtainedfromtheempiricalformulasfor
beltedcables,theirvaluescanalsobedeterminedbymeasurements.
•Forthispurpose,thefollowingtwomeasurementsarerequired:
(i)Inthefirstmeasurement,thethreecoresarebunchedtogether(i.e.commoned)andthecapacitanceis
measuredbetweenthebunchedcoresandthesheath.Thebunchingeliminatesallthethreecapacitors??????
??????
,leavingthe
threecapacitors??????
??????
inparallel.Therefore,if??????
1
isthemeasuredcapacitance,thistestyields:??????
1
=3????????????or??????
??????
=??????
1
/3.
Knowingthevalueof??????
1
,thevalueof??????
??????
canbedetermined.
(ii)Inthesecondmeasurement,twocoresarebunchedwiththesheathandcapacitanceismeasured
betweenthemandthethirdcore.Thistestyields2????????????+????????????.If??????
2
isthemeasuredcapacitance,then,??????
2
=2????????????+????????????.As
thevalueof??????
??????
isknownfromfirsttestand??????
2
isfoundexperimentally,therefore,valueof??????
??????
canbedetermined.
•Itmaybenotedherethatifvalueof??????
??????
(= ??????
??????
+ 3????????????) isdesired,itcanbefounddirectlybyanothertest.Inthis
test,thecapacitancebetweentwocoresorlinesismeasuredwiththethirdcorefreeorconnectedtothesheath.
Thiseliminatesoneofthecapacitors??????
??????
sothatif??????
3
isthemeasuredcapacitance,then,
??????
3
=????????????+
??????
??????
2
+
??????
??????
2
=
1
2
????????????+3????????????=
1
2
??????
??????
•Althoughcore-corecapacitance??????
??????
andcore-earthcapacitance??????
??????
canbeobtainedfromtheempiricalformulasfor
beltedcables,theirvaluescanalsobedeterminedbymeasurements.
•Forthispurpose,thefollowingtwomeasurementsarerequired:
(i)Inthefirstmeasurement,thethreecoresarebunchedtogether(i.e.commoned)andthecapacitanceis
measuredbetweenthebunchedcoresandthesheath.Thebunchingeliminatesallthethreecapacitors??????
??????
,leavingthe
threecapacitors??????
??????
inparallel.Therefore,if??????
1
isthemeasuredcapacitance,thistestyields:??????
1
=3????????????or??????
??????
=??????
1
/3.
Knowingthevalueof??????
1
,thevalueof??????
??????
canbedetermined.
(ii)Inthesecondmeasurement,twocoresarebunchedwiththesheathandcapacitanceismeasured
betweenthemandthethirdcore.Thistestyields2????????????+????????????.If??????
2
isthemeasuredcapacitance,then,??????
2
=2????????????+????????????.As
thevalueof??????
??????
isknownfromfirsttestand??????
2
isfoundexperimentally,therefore,valueof??????
??????
canbedetermined.
•Itmaybenotedherethatifvalueof??????
??????
(= ??????
??????
+ 3????????????) isdesired,itcanbefounddirectlybyanothertest.Inthis
test,thecapacitancebetweentwocoresorlinesismeasuredwiththethirdcorefreeorconnectedtothesheath.
Thiseliminatesoneofthecapacitors??????
??????
sothatif??????
3
isthemeasuredcapacitance,then,
??????
3
=????????????+
??????
??????
2
+
??????
??????
2
=
1
2
????????????+3????????????=
1
2
??????
??????
Thecapacitancesperkilometreofa3-phasecableare0·63µFbetweenthethreecoresbunchedtogether
andthesheathand0·37µFbetweenonecoreandtheothertwoconnectedtothesheath.Calculatethe
chargingcurrenttakenbyeightkilometresofthiscablewhenconnectedtoa3-phase,50Hz,6600V
supply.
andthesheathand0·37µFbetweenonecoreandtheothertwoconnectedtothesheath.Calculatethe
chargingcurrenttakenbyeightkilometresofthiscablewhenconnectedtoa3-phase,50Hz,6600V
supply.
Types of Cable Faults
•Cablesaregenerallylaiddirectlyinthegroundorinductsintheundergrounddistributionsystem.Forthisreason,there
arelittlechancesoffaultsinundergroundcables.However,ifafaultdoesoccur,itisdifficulttolocateandrepairthe
faultbecauseconductorsarenotvisible.Nevertheless,thefollowingarethefaultsmostlikelytooccurinunderground
cables:
(i)Open-circuitfault
(ii)Short-circuitfault
(iii)Earthfault.
(i)Open-circuitfault:-Whenthereisabreakintheconductorofacable,itiscalledopencircuitfault.Theopen-circuitfault
canbecheckedbyamegger.Forthispurpose,thethreeconductorsofthe3-corecableatthefarendareshortedand
earthed.Thenresistancebetweeneachconductorandearthismeasuredbyamegger.Themeggerwillindicatezero
resistanceinthecircuitoftheconductorthatisnotbroken.However,iftheconductorisbroken,themeggerwillindicate
infiniteresistanceinitscircuit.
(ii)Short-circuitfault:-Whentwoconductorsofamulti-corecablecomeinelectricalcontactwitheachotherdueto
insulationfailure,itiscalledashort-circuitfault.Again,wecanseekthehelpofameggertocheckthisfault.Forthis
purpose,thetwoterminalsofthemeggerareconnectedtoanytwoconductors.Ifthemeggergiveszeroreading,it
indicatesshortcircuitfaultbetweentheseconductors.Thesamestepisrepeatedforotherconductorstakingtwoatatime.
(iii)Earthfault:-Whentheconductorofacablecomesincontactwithearth,itiscalledearthfaultorgroundfault.To
identifythisfault,oneterminalofthemeggerisconnectedtotheconductorandtheotherterminalconnectedtoearth.If
themeggerindicateszeroreading,itmeanstheconductorisearthed.Thesameprocedureisrepeatedforotherconductors
ofthecable.
•Cablesaregenerallylaiddirectlyinthegroundorinductsintheundergrounddistributionsystem.Forthisreason,there
arelittlechancesoffaultsinundergroundcables.However,ifafaultdoesoccur,itisdifficulttolocateandrepairthe
faultbecauseconductorsarenotvisible.Nevertheless,thefollowingarethefaultsmostlikelytooccurinunderground
cables:
(i)Open-circuitfault
(ii)Short-circuitfault
(iii)Earthfault.
(i)Open-circuitfault:-Whenthereisabreakintheconductorofacable,itiscalledopencircuitfault.Theopen-circuitfault
canbecheckedbyamegger.Forthispurpose,thethreeconductorsofthe3-corecableatthefarendareshortedand
earthed.Thenresistancebetweeneachconductorandearthismeasuredbyamegger.Themeggerwillindicatezero
resistanceinthecircuitoftheconductorthatisnotbroken.However,iftheconductorisbroken,themeggerwillindicate
infiniteresistanceinitscircuit.
(ii)Short-circuitfault:-Whentwoconductorsofamulti-corecablecomeinelectricalcontactwitheachotherdueto
insulationfailure,itiscalledashort-circuitfault.Again,wecanseekthehelpofameggertocheckthisfault.Forthis
purpose,thetwoterminalsofthemeggerareconnectedtoanytwoconductors.Ifthemeggergiveszeroreading,it
indicatesshortcircuitfaultbetweentheseconductors.Thesamestepisrepeatedforotherconductorstakingtwoatatime.
(iii)Earthfault:-Whentheconductorofacablecomesincontactwithearth,itiscalledearthfaultorgroundfault.To
identifythisfault,oneterminalofthemeggerisconnectedtotheconductorandtheotherterminalconnectedtoearth.If
themeggerindicateszeroreading,itmeanstheconductorisearthed.Thesameprocedureisrepeatedforotherconductors
ofthecable.
Permissible Current Loading
•Thesafecurrent-carryingcapacityofanundergroundcableisdeterminedbythemaximumpermissibletemperature
rise.Thecauseoftemperatureriseisthelossesthatoccurinacablewhichappearasheat.Theselossesare:
(i)Copperlossesintheconductors
(ii)Hysteresislossesinthedielectric
(iii)Eddycurrentlossesinthesheath
•Thesafeworkingconductortemperatureis65ºCforarmouredcablesand50ºCforlead-sheathedcableslaidinducts.
•Themaximumsteadytemperatureconditionsprevailwhentheheatgeneratedinthecableisequaltotheheat
dissipated.
•Theheatdissipationoftheconductorlossesisbyconductionthroughtheinsulationtothesheathfromwhichthetotal
losses(includingdielectricandsheathlosses)maybeconductedtotheearth.
•Therefore,inordertofindpermissiblecurrentloading,thethermalresistivitiesoftheinsulation,theprotectivecovering
andthesoilmustbeknown.
•Thesafecurrent-carryingcapacityofanundergroundcableisdeterminedbythemaximumpermissibletemperature
rise.Thecauseoftemperatureriseisthelossesthatoccurinacablewhichappearasheat.Theselossesare:
(i)Copperlossesintheconductors
(ii)Hysteresislossesinthedielectric
(iii)Eddycurrentlossesinthesheath
•Thesafeworkingconductortemperatureis65ºCforarmouredcablesand50ºCforlead-sheathedcableslaidinducts.
•Themaximumsteadytemperatureconditionsprevailwhentheheatgeneratedinthecableisequaltotheheat
dissipated.
•Theheatdissipationoftheconductorlossesisbyconductionthroughtheinsulationtothesheathfromwhichthetotal
losses(includingdielectricandsheathlosses)maybeconductedtotheearth.
•Therefore,inordertofindpermissiblecurrentloading,thethermalresistivitiesoftheinsulation,theprotectivecovering
andthesoilmustbeknown.
Permissible Current Loading
•Whenconsideringheatdissipationinundergroundcables,thevariousthermalresistancesprovidingaheatdissipation
pathareinseries.Therefore,theyadduplikeelectricalresistancesinseries.
•Consideracablelaidinsoil.
•Let??????=permissiblecurrentperconductor
•??????=numberofconductors
•??????=electricalresistancepermetrelengthoftheconductorattheworkingtemperature
•??????=totalthermalresistance(i.e.sumofthermalresistancesofdielectricandsoil)permetrelength
•??????=temperaturedifference(rise)betweentheconductorandthesoil
•Neglectingthedielectricandsheathlosses,wehave,
?????????????????????????????? ???????????????????????????????????????????????????????????? = ????????????
2
??????
?????????????????????????????? ???????????????????????????????????????????????????????????? = ?????????????????????????????????????????????????????????????????? ????????????????????????/??????ℎ?????????????????????????????? ????????????????????????????????????????????????????????????
or,????????????
2
??????=
?
?
??????=
???????????
6
????????????
?
5
?
??????ℎ?????????????????????????????? ??????ℎ?????? ?????????????????? ??????????????????????????????
or,??????=
?
???
Itshouldbenotedthatwhencablesarelaidinproximitytoeachother,thepermissiblecurrentisreducedfurtheron
accountofmutualheating.
•Whenconsideringheatdissipationinundergroundcables,thevariousthermalresistancesprovidingaheatdissipation
pathareinseries.Therefore,theyadduplikeelectricalresistancesinseries.
•Consideracablelaidinsoil.
•Let??????=permissiblecurrentperconductor
•??????=numberofconductors
•??????=electricalresistancepermetrelengthoftheconductorattheworkingtemperature
•??????=totalthermalresistance(i.e.sumofthermalresistancesofdielectricandsoil)permetrelength
•??????=temperaturedifference(rise)betweentheconductorandthesoil
•Neglectingthedielectricandsheathlosses,wehave,
?????????????????????????????? ???????????????????????????????????????????????????????????? = ????????????
2
??????
?????????????????????????????? ???????????????????????????????????????????????????????????? = ?????????????????????????????????????????????????????????????????? ????????????????????????/??????ℎ?????????????????????????????? ????????????????????????????????????????????????????????????
or,????????????
2
??????=
?
?
??????=
???????????
6
????????????
?
5
?
??????ℎ?????????????????????????????? ??????ℎ?????? ?????????????????? ??????????????????????????????
or,??????=
?
???
Itshouldbenotedthatwhencablesarelaidinproximitytoeachother,thepermissiblecurrentisreducedfurtheron
accountofmutualheating.
Dielectric Loss
•Dielectrics(insulatingmaterialsforexample)whensubjectedtoavaryingelectricfield,willhavesomeenergyloss.
•Thevaryingelectricfieldcausessmallrealignmentofweaklybondedmolecules,whichleadtotheproductionofheat.
•Theamountoflossincreasesasthevoltagelevelisincreased.Forlowvoltagecables,thelossisusuallyinsignificantand
isgenerallyignored.
•Forhighervoltagecables,thelossandheatgeneratedcanbecomeimportantandneedstobetakenintoconsideration.
•Dielectriclossismeasuredusingwhatisknownasthelosstangentortandelta(tan ??????).
•Insimpleterms,tandeltaisthetangentoftheanglebetweenthealternatingfieldvectorandthelosscomponentofthe
material.Thehigherthevalueoftan ??????thegreaterthedielectriclosswillbe.
•Giventhetanδandcapacitanceofthecable,thedielectriclossiseasilycalculated:
????????????????????????=??????????????????
2
????????????????????????
•Dielectrics(insulatingmaterialsforexample)whensubjectedtoavaryingelectricfield,willhavesomeenergyloss.
•Thevaryingelectricfieldcausessmallrealignmentofweaklybondedmolecules,whichleadtotheproductionofheat.
•Theamountoflossincreasesasthevoltagelevelisincreased.Forlowvoltagecables,thelossisusuallyinsignificantand
isgenerallyignored.
•Forhighervoltagecables,thelossandheatgeneratedcanbecomeimportantandneedstobetakenintoconsideration.
•Dielectriclossismeasuredusingwhatisknownasthelosstangentortandelta(tan ??????).
•Insimpleterms,tandeltaisthetangentoftheanglebetweenthealternatingfieldvectorandthelosscomponentofthe
material.Thehigherthevalueoftan ??????thegreaterthedielectriclosswillbe.
•Giventhetanδandcapacitanceofthecable,thedielectriclossiseasilycalculated:
????????????????????????=??????????????????
2
????????????????????????
An11kV,50Hz,singlephasecable2.5kmlong,hasadiameterof20mmandinternalsheathradiusof
15mm.Ifthedielectrichasarelativepermittivityof2.4,determine(i)capacitance(ii)chargingcurrent
(iii)totalchargingkVAR.
15mm.Ifthedielectrichasarelativepermittivityof2.4,determine(i)capacitance(ii)chargingcurrent
(iii)totalchargingkVAR.
Asinglecorecableforuseon11kV,50Hzsystemhasconductorareaof0·645
cm
2
andinternaldiameterofsheathis2·18cm.Thepermittivityofthedielectricusedinthecableis
3·5.Find(i)themaximumelectrostaticstressinthecable(ii)minimumelectrostaticstressinthe
cable(iii)capacitanceofthecableperkmlength(iv)chargingcurrent.
cm
2
andinternaldiameterofsheathis2·18cm.Thepermittivityofthedielectricusedinthecableis
3·5.Find(i)themaximumelectrostaticstressinthecable(ii)minimumelectrostaticstressinthe
cable(iii)capacitanceofthecableperkmlength(iv)chargingcurrent.
Findthemosteconomicalsizeofasingle-corecableworkingona132kV,3-
phasesystem,ifadielectricstressof60kV/cmcanbeallowed.
phasesystem,ifadielectricstressof60kV/cmcanbeallowed.
Asingle-core66kVcablehasaconductordiameterof2cmandasheathofinsidediameter5·3cm.The
cablehasaninnerlayerof1cmthickofrubberofdielectricconstant4·5andtherestimpregnatedpaper
ofdielectricconstant3·6.Findthemaximumstressintherubberandinthepaper.
cablehasaninnerlayerof1cmthickofrubberofdielectricconstant4·5andtherestimpregnatedpaper
ofdielectricconstant3·6.Findthemaximumstressintherubberandinthepaper.
Asingle-corecableworkingon66kVon3-phasesystemhasaconductordiameterof2cmandasheath
ofinsidediameter5·3cm.Iftwointersheathsareused,findthebestpositions,maximumstressandthe
voltageontheintersheaths.
ofinsidediameter5·3cm.Iftwointersheathsareused,findthebestpositions,maximumstressandthe
voltageontheintersheaths.
Determinetheinsulationresistanceofasingle-corecableoflength3kmandhavingconductor
radius12·5mm,insulationthickness10mmandspecificresistanceofinsulationof5×10
12
Ωm.
radius12·5mm,insulationthickness10mmandspecificresistanceofinsulationof5×10
12
Ωm.
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