factor and the capacity load rating to Efﬁciency of superconducting transmission lines: An analysis withrespect Electric Power Systems Research

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ElectricPowerSystemsResearch141(2016)381–391

ContentslistsavailableatScienceDirect

Electric Power Systems Research

jou rn al h om e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / e p s r

Efﬁciency of superconducting transmission lines: An analysis with respect to the load factor and capacity rating

Heiko Thomas

^a^,∗

, Adela Marian

^a

, Alexander Chervyakov

^a

, Stefan Stückrad

^a

, Carlo Rubbia

^a^,^b

aInstituteforAdvancedSustainabilityStudiese.V.(IASS),Potsdam,Germany

bEuropeanOrganizationforNuclearResearch(CERN),Geneva,Switzerland

a r t i c l e i n f o

Articlehistory:

Received3February2015

Receivedinrevisedform5February2016 Accepted5July2016

Availableonline6September2016

Keywords:

Transmissionline Efﬁciency Superconducting Loadfactor Sustainablegrid HVDC

a b s t r a c t

Superconductingtransmissionlines(SCTL)areaninnovativeoptionforthefutureelectricitygridandin particularforhigh-capacityHVDCpowertransmission.Thepromiseofsuperconductingelectriclineslies principallyintheirsmallsize,withpotentialadvantagesintermsofefficiency,environmentalimpactand publicacceptance.Furthermore,contrarytostandardconductors,SCTLdonothaveanyresistivelosses, thereforetheonlyremainingpowerlossisduetothecoolingsystemthatisneededtokeepthesupercon- ductoratitscryogenicoperatingtemperature.InordertoobtainarealisticvaluefortheSCTLefficiency, boththeactualloadfactorandthecapacityratinghavetobetakenintoaccount.Thispaperanalyzesthe transmissionefficiencycharacteristicsfortwolong-distanceSCTLdesignsdevelopedattheIASSandat EPRIasafunctionoftheloadfactorforcapacitiesupto10GW,andincomparisonwithestablishedtrans- missiontechnologies.ThefocusofthisstudyistheplannedexpansionoftheHVDCtransmissionsystem inGermany,whichisaimedatachievingthecurrentCO2reductiongoalsbyintegratinganincreasedshare ofintermittentrenewableenergy(RE)intothegrid.Theresultscanbereadilyextendedtootherscenarios andcanprovidecomplementaryinformationfordecisionprocessesdirectedatplanningasustainable futuregrid.

1. Introduction

Asustainableelectricenergysupplyisoneofthemajortasks in the near future, especially in the context of increasing the renewable energy share to reduce greenhouse gas emissions and to meet the steadily growing global energy demand. Any innovativetechnologythat canimprovetheefﬁciencyof future electricgridswillbeawelcomeandmuchneededadditiontothe establishedtransmission-anddistributionlineoptions.Supercon- ducting transmissionlines(SCTL) havea numberof advantages comparedtostandardtechnologies,inparticularforhighcapacity HVDCpowertransmission.Besidestheirsmallsize,thepotentialfor animprovedtransmissionefﬁciencyisoneofthekeyadvantages.

AdditionalbeneﬁtsofSCTLarerelatedtotheeasieracceptanceby thepublic(smallcorridorwidth,underground,noelectricﬁelds) [1]andpossiblyeconomicadvantages[2].Duetotheabsenceof electricalresistance,theonlyremaininglossforDCapplicationsis theconstantamountofpowerperunitlengthcausedbythecooling

∗Correspondingauthor.

E-mailaddress:heiko.thomas.ut@gmail.com(H.Thomas).

systemthatisneededtokeepthesuperconductoratitscryogenic operatingtemperature.Therealefficiencyofanytransmissionline, beitastandardtechnologyoraSCTL,dependsstronglyontheload factorthatinturndependsontheoverallscenariotheTLisembed- dedinandtheboundaryconditionsthereof.Theactualshareof renewablesintheelectricitymixhasahugeimpactontheload factor,asforinstancewindisanintrinsicallyintermittentenergy sourcecomparedtohydropowerwhereelectricenergyisgener- atedusingawaterreservoirandthepoweroutputcanbecontrolled toacertaindegree.Thecomplexityoftheelectricgridinwhichthe HVDChighcapacityTLisembeddedplaysasignificantroletooas itbecomesmore challengingtooptimizethepowerflowforan overallminimizationofenergylossesbetweennumerouscenters ofenergygenerationanddemandinameshedgridincludingthe ACgrid.

Theaimofthispaperistogiveamoredetailedinsightintothe efﬁciencyofsuperconducting transmissionlinesina realworld applicationwithrespecttotheloadfactorinasustainablefuture electric transmission grid that integrates high shares of RE. A high-efﬁciency transmissionline translates intolow equivalent greenhousegasemissions,whichisoneofthemainreasonsfor switchingtoREgenerationinorderachievethe2^◦Cgoal.

http://dx.doi.org/10.1016/j.epsr.2016.07.007

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Inthefollowing,GermanyanditsplannedHVDCtransmission systemarechosenasthecasestudyforinvestigatingtheefﬁciency ofsuperconductinglines.Thisshouldbemerelyseenasaconve- nientexampledue totheexisting availabilityof concreteplans anddetailedinformation[3,4].Conclusionscanbeadaptedtoother regionsorprojectswithsimilarloadfactorandcapacityratings.

TheplannedHVDCtransmission corridorsfor theyear2025 aredisplayedinFig.1forscenarioBofthemostrecentGerman GridDevelopmentPlan(GDP2025draftbytheFederalNetwork Agency[3]).ThetimehorizonsfortheGDPsare10and20years.

Therequiredlevelofpowerlinerouteexpansionwascalculated tobe3200kmforHVDCcorridorstotalingatransmissioncapac- ityof10GW.ThisdoesnotincludetheGermanshareinthethree DCinterconnectorsbetweenGermanyandBelgium,Denmarkand Norway.OfparticularinterestforthispaperarecorridorAinthe farwest(andherethenorthernpartA1)andcorridorC(alsocalled SüdlinkinGermany).

2. TheloadfactorinthecontextofREintegration

Assumingagridthatintegratesahighshareofrenewableenergy generationsforafuturesustainableenergysupplyitwillbehard toachievea100%loadfactorbecause:

1.Thevariationoftheenergydemandovertheyearandduringthe day.

2.TheintermittentnatureofRE–withanRESoftheenergymixin Germanyofalready25%(2014)and80%by2050[5,6].

3.Generalconsiderationstendtomatchthecapacityoftransmis- sionlinestothehighestpossibleoutputofREsources.

Thesefactorsleadtoalimitationandreductionoftheaverage loadoftransmissionlinesandinparticularofHVDChighcapacity transmissionlineswhichareconsideredinthispaper.

In contrast to SCTL, standard conductors have an electrical resistanceandpowerlossesshowaquadraticdependenceonthe transportcurrentfordirectcurrent(DC)applicationsPLoss∼I².Load factorsoflessthan100%ofthemaximumtransmissionlinecapacity thereforeresultinlowerrelativeelectriclossesandhigherefficien- ciesforstandardconductorsbutinlowerefficienciesforSCTLdue tothefixedenergyconsumptionofthecryogenicsystem.

Asimulation oftheloadfactors oftheplannedNorth-South HVDCTLinGermanywasdonebytheCenterforEnergyGrazas partofastudyontherequiredGermangridextensioncommis- sionedbytheFederalNetworkAgency[4].Theaverageloadfactors wereinvestigatedforvariousplannedHVDCtransmissioncorridors inGermanybasedontheGDPfrom2012.Thesimulationassumes theforecastedinstalled REandconventional generationcapaci- tiesaccordingtoscenarioBoftheGDP2012.Thesecapacitiesare listedinTable1fortheyears2024and2034takenfromtheGDP (20142nd)andtheyear2022usedby[4](basedontheGDP2012 whichhasbeenupdatedwithnowslightlydifferentnumbers).The studyincludedtheforecastedpowergeneration(mix)ofadjacent countriesandcrossborderelectricenergyexchange.

Theaverageloadfactorsarefoundtobebetween54%(corridor Cwith4GWcapacityasofGDP2012)and86%(corridorA1with 2GWcapacity)fortheyear2022andtobebetween21%(corridor Cwith9.2GWcapacity)and91%(corridorA1with6GWcapacity) fortheyear2032.TheseresultsstemfromthecalculationB.NEP4K assumingallcorridorsA,B,CandDtobeinplace.Pleasenotethat theGDP20142ndupgradedthecapacityforcorridorCto6GW in2024.AnimproperconnectiontotheACgridatthesouthern endofHVDCcorridorCispartlyresponsibleforthelowaverage loadfactor of that corridor. In any case, there are huge differ- encesintheaverageloadfactorwhencomparingallcorridors.The efﬁciencyofa hypotheticalsuperconductingTLwouldtherefore

Table1

NetgenerationcapacitiesinGermanyaccordingtothebaselinescenarioBin2022 (usedforTUGrazsimulations),2024and2034.

NetcapacityinGW B-2022 B-2024 B-2034

Conventional

Nuclear 0.0 0.0 0.0

Browncoal 18.6 15.4 11.3

Hardcoal 25.1 25.8 18.4

Naturalgas 31.3 28.2 37.5

Oil 2.9 1.8 1.1

Storage(incl.pumpstorage) 9.0 10.0 10.7

Others 2.3 3.7 2.7

Sum(conventional) 89.2 84.9 81.7

Renewables

Hydro 4.7 4.7 5.0

Windonshore 47.5 55.0 72.0

Windoffshore 13.0 12.7 25.3

Photovoltaics 54.0 56.0 59.5

Biomass 8.4 8.7 9.2

Otherrenewables 2.2 1.5 2.3

SumRE 129.8 138.6 173.3

Sumtotalgeneration 219.0 223.5 255.0

varytremendouslydependingonthecorridor,aswouldtheefﬁ- ciencyofstandardconductors.PleasenotethatcorridorCactually consistofsub-corridorsthathavedifferentstartandendpoints wheretheyconnecttotheACgridbutarelocatedingeograph- icalproximity.DC-ACconverterandentrypointswillbelocated closetoshutdownnuclearpowerplantstotakeadvantageofexist- ingACgridinfrastructure.PleasealsonotethatbulkenergyHVDC transmissionlines have beenrealized sofarmainly bymaking point-to-pointconnectionsandusingLine-Commutated-Converter (LCC)technologythatdoesnotallowtobuildameshedDC-grid duetotheirblackstartinability.TheplannedHVDCcorridorsin GermanyareincontrastbasedonVoltage-Source-Converter(VSC) technologythatismoreﬂexibleandallowstobuildanHVDC-grid, similartotheexistingACgrid,forinstancetoconnectseveralwind farmstoonetransmissionlineortosimplymakea3-foldDCinter- connection.

3. Methodsforcalculation

3.1. Long-distancesuperconductingtransmissionlinebasedon MgB2developedatIASS

Results shown are based on a bi-polar long-distance SCTL developed at the Institute for Advanced Sustainability Studies in Potsdam/Germany (IASS) which is based on the affordable superconducting material magnesium diboride (MgB₂) [7]. The underlyingideawastoconnectremoteplacesofrenewableenergy generationbyahighlyefﬁcienttransmissiontechnology.AnMgB2

basedSCTLcanhavemuchlowercoststhanSCTLprojectsbasedon high-temperaturesuperconductors(HTS)primarilyduetolower productioncostsandcanthereforefacilitateanacceleratedadop- tionofthispromisingtechnology.ThisMgB₂SCTLwasdesigned tohaveacapacityratingof10GWatavoltageandcurrentrating of±125kVand40kAwithcoolingstationslocatedevery300km.

Itcaneitherbecooledbyliquidhydrogenorgaseousheliumplus liquidnitrogen.Thisvoltageislowerthanthatofstate-of-the-art HVDCcablesbasedonstandardconductors(525kV).Reducingthe voltagelevelcanleadtolowercostandsimpleroperationofrele- vantgridequipment.Superconductorshavehighcurrentdensities, meaningtheyhavetheabilitytotransferahighcurrentpercross sectionoftheconductor.Thisallowsforloweroperatingvoltages leadingtoasimpliﬁeddesignwithasmallerouterdiameter,thus reducingtheheatinﬂux.WithinacooperationofCERNandthe

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H.Thomasetal./ElectricPowerSystemsResearch141(2016)381–391 383

Fig.1.PlannedHVDCcorridors–griddevelopmentplanGermanyscenarioB12025[1].DC1andDC2displaytheformercorridorA,DC3andDC4displaytheformercorridor CasuseduntilGDP2024.

Source:NEP2025,Stand:February2016,www.netzentwicklungsplan.debasedonmap“DeutschesHöchstspannungsnetz”fromVDE.

IASS,asuperconductingprototypecablebasedonMgB₂wassuc- cessfullytestedin2014withadirectcurrentratingof20kA.The totaldiameterofthecablesetupandthecryogenicenvelopewas only16cm.Thepromiseofthistechnologystimulatedintereston thepartof variousindustrialand transmissionsystemoperator (TSO)partnersandledtotheformationofaEuropeanconsortiumof industry,researchcentersandTSOswiththegoaltodesignandtest ahigh-voltage(200–320kV)prototypeMgB₂cabletovalidateits operationunderrealgridconditions(BESTPATHSprojectaspartof the7thEuropeanFrameworkProgram).Thisvoltagelevelreﬂects thevoltageofstate-of-the-artstandardundergroundcables,inpar- ticularthe±320kVHVDCXLPEcables.

Uptonowhigh-temperaturesuperconductorshavebeenthe preferredchoicefortransmissionpurposesmainlyduetothefact

thatliquidnitrogen(LN₂)canbeusedforcooling.HandlingLN₂is mucheasierthanliquidhelium(forlowtemperatureSC)orliquid hydrogen(forMgB2)andallowssigniﬁcantenergysavingsdueto itshigheroperatingtemperatureandthereforehigherefﬁciencyof theunderlyingthermodynamiccycle(Carnot).Inthispaper,weuse a5GWHTStransmissiondesigndevelopedattheElectricPower ResearchInstituteintheUS[8]whencomparisonsarecalledfor.

AdetailedtechnicaldescriptionofSCTLingeneralandtheMgB₂ SCTLinparticularispublishedelsewhere[7,8].Howeveritismean- ingfultogiveabrieftechnicalinsightforgeneralunderstanding.

Firstly,asuperconductorhasnoresistivelossesinDCapplications (inAC applications,SCexhibit losseswhich very much depend on the design and geometry of the cable/conductor), and sec- ondly,ithasanextremelyhighcurrentdensityresultinginafairly

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Fig.2.Simpliﬁedenergyconsumptionandefﬁciencyschemeofasuperconducting (SC)transmissionlinecooledbyliquidhydrogen(LH2).

smallsuperconductorsizecomparedtotheouterdiameterofthe complete(cryogenic)system.Doublingthenominalcurrentofa SCTLwillthusnotleadtoadoublingoftheouterdiameter.The heatinfluxandthereforetheelectricpowerconsumptiontokeep thecryogenatits operatingtemperature isproportional tothe outerdiameterofthecoolingsystemandmainlydeterminedbythe necessaryhydraulicdiametersthatfulfillthemassflowandheat transportrequirements.Besidestheoperatingtemperaturethedis- tancebetweencoolingstationsandthetypeofcryogenalsoplay amajorrolehere.Loweroperatingtemperaturesleadtoalower efficiencyoftheunderlyingthermodynamiccycle(Carnot)ofthe refrigerationsystemwithsubsequenthigherelectricpowerlosses forcooling,assketchedinFig.2.

Theoperatingtemperatureformagnesiumdiboride(MgB₂)is 15–20K.Thismaterialwasonlyrecentlydiscoveredtobesuper- conductingin 2001[9]but is verypromising due toitssimple manufacturingprocess and low costs compared to HTS. Ultra- highvoltagescanleadtoanincreasedouterdiameterlargerthan requiredby thehydraulicdiameters of thecoolant transferring tubesduetothenecessaryelectricinsulationofthecable.Butonly forextremevoltage/currentcombinationscanthenecessaryelec- tricinsulationhaveasubstantialinﬂuenceontheouterdiameter.

SCTLcanthereforehaveextremelyhighpowerefficienciesandare anincrediblyinterestingchoiceforamoreefficientandsustainable grid,especiallyforlong-distanceandhighcapacitytransmissionof renewableenergyfromremotesourcesorhighcapacitytransmis- sionindenselypopulatedareas.Thoughthispaperonlydiscusses HVDCapplications,itisworthmentioningthatSCTLcanalsobe operatedinACmode.However,electriclosseswillthenoccurin thesuperconductorcausedbytheoscillatingelectro-magneticfield thatgreatlydependsonthedesignofthecable.

3.2. ElectriclossesofSCTLinDCmodeareindependentoftheir capacityrating

Oneofthecentralassumptionsinthispaperisthatthecool- ingpowerlossesofSCTLareconstantandindependentfromthe capacity.Formedium-andlong-distancepowertransmissionand voltageratingsof20–150kV,theouterdiameterandthereforethe electricpowerconsumptionaretoacertainextentindependent ofthecapacity.ThisaspectdistinguishesSCTLfromstandardcon- ductortransmission lines.Theseexperienceresistivelosses and multipletransmissionsystemshavetobecombinedtoreachthe desiredcapacity.Thisincludescablesthathavetobeaddedtomake upforadecreasedampacityduetoatemperatureincreaseofthe conductortriggeredforinstancebyhigherlocalsoiltemperatures.

Toverifythepriorassumption,calculationsfor4differentcombi- nationsofvoltageandcurrentvalueswerecarriedout(constant voltageof30kVand125kVrespectively,andconstantcurrentof 40kAand100kArespectively).Theaimistoﬁndtheresultingouter diameteroftheMgB2basedSCTLwhichthenisproportionaltothe

Fig.3.Schemeusedforthecalculationoftheouterdiameteroftheinnertube holdingthesuperconductingcable.Forsimplicity,itisassumedthatthetwosuper- conductingpolesoftheMgB2SCTLdesignactlikeonecablewithequalcrosssection.

ThehatchedareaistheenclosedﬂuidareaA.

heatinﬂuxandthepowerlossesduetocooling.Parametersarethe superconductingcablecrosssectionwhichisproportionaltothe currentratingandthewidthofthenecessaryelectricinsulation layer.Thereferenceisthebi-polarMgB₂SCTLdesigndevelopedat IASStotransfer10GWofpower[7].Thebreakdownvoltageper lengthofcryogensisapprox.1000kV/cminDCmode[10]andthe coolantmaybeusedforelectricinsulation,whatisassumedhere.

ThehydraulicdiameterdHisthesameforeverycapacity–outer diameterpairtoensureconsistentﬂuiddynamicproperties.Itcan becalculatedbymultiplyingtheenclosedﬂuidareaAwith4and dividingbythewettedouterperimeterC=C₁+C₂(Fig.3)leading to

dH=4A

C = (d²_out−2d²_cable) (dout+√

2dcable)=dout−√

2dcable (1)

and

dout=dH+√

2dcable (2)

Becausethesuperconducting cablediameterbasedonMgB₂ (withoutelectricinsulationbutwithcopperforthermalstabiliza- tion)isonly2–3cmfor40kAampacity(with2cablesinbi-polar operation)andthedesignvalueforthemostinnertubediameteris 17cm,itisevidentthattheouterdiameterdoesnotchangesigniﬁ- cantlyfordifferentcapacitiesforconstantvoltages.Inthiscase,the constantvoltagescenarioat125kVresultsinthesamediameteras theconstantcurrentscenarioat40kA.

Alltube diameters carrying cryogenic fluidswere chosento allowforproperhydrodynamiccharacteristicslikehighenough massflowabletocarrytheheatinflux,alowpressuredropand smalltemperatureincreasebetweencoolingstations.Theneces- saryelectricinsulationcaninprinciplebeprovidedbythecryogen forbothconstantcurrentscenariosbecausetheinnertubediame- terislargeenoughthatthenecessarydistanceforproperelectric insulationisfulfilled.Thisisavisionaryconceptthatwouldrequire theconductortobeexactlycenteredintheinnercryogenictube.

Theouterdiameteristhereforeconstantfortheassumed40kAand 100kAconstantcurrentscenarios.Evenconsideringstandardelec- tricinsulationusingpaper(soakedwiththecryogen)andassuming avoltagebreakdownsafetyfactorof20leadingto2×1cmadded diameterperextra50kV(1cm/MVvoltagebreakdowndistance) resultsonlyinasmallincreaseofheatinﬂuxduetothelargerouter diameter.

AsseeninFig.4,theconstantvoltagescenariosshowaslight positive slope because the diameter of the inner tube has to increasewithincreasingcapacity,i.e.increasingcurrentandthere- foreincreasingsuperconductingcablediameter.Ifthediameterof theinnertubechanges,alldiametersoftheoutertubeswillsubse- quentlyincrease.Theslopeisverymoderatebecausethecurrent densityofsuperconductorsisextremelyhigh.Thisismirroredinto thesmallchangeoftheouterdiameter.Consequentlyaconstant totalouterdiameterandheatinﬂuxareassumedinthispaperfor allconsiderationsbecausetheemphasisisputonmedium-and

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Fig.4.TotalouterdiameterandheatinfluxinarbitraryunitsaredisplayedfordifferentfixedvoltageandcurrentratingsdependentoncapacityforanMgB2SCTLdesign cooledbyliquidhydrogendevelopedatIASS.Afixedvoltagemeansthatthecurrentratingischosentomeetthecapacityratinghencethesmallincreaseofthediameter withcapacity.Thehydraulicdiametersarethesameforeveryexample.

long-distanceTLs.Theouterdiameteris32cmfortheMgB₂based SCTLcooledbyLH2forinstance,duetohydrodynamicandthermo- dynamicboundaryconditionslikeheattransferandpressuredrop alongtheline.Becausetheheatinﬂuxisassumedtobeconstant, thepowerlossescausedbycoolingareassumedtobeconstanttoo.

3.3. Powerlossesofstandardtransmissionoptions

Thetechnologyofchoiceforfuturegridapplicationsdepends onthespecificproject.Besidesinvestmentandoperatingcosts,the transmissionefficiency,publicacceptanceissuesandtheenviron- mentalimpactaremostrelevant.Inthisregard,SCTLarecompeting withstandardtechnologieslike±320kVHVDCXLPEunderground cablesand±500/800kVHVDCoverheadlines(OHL)asthoseare thesolutionpreferredbyTSOsforhighcapacitylong-andmedium distancetransferofelectricenergyuptonow.Efficiencynumbers forthesetechnologiesweresuppliedbyABB/Switzerlandandby theFrenchElectricityTransmissionNetwork(RTE).Thementioned cableshavelossesof6.5%per1000kmatfullload[11]andadou- blebi-polarsystemof±500kVHVDCOHLexperienceslossesof 3.35%/1000kmiftransferring4GW[12].Fordifferentcapacities, theelectriclossesofstandardTLoptions,especiallyforOHL,can changeabruptlybecauseeachsystemhasafixedcapacityrating.

Dependingonthechosencapacity,asystemcanbeatitstrans- missionlimitwithsubsequentmaximumlossesiftheloadreaches maximumcapacity,oritcanhavelowerlossesifthemaximum loadissmallerthanthecapacityrating.Forinstance,two±500kV OHLsystemsthatareabletotransferamaximumof6GWtotal powerhavemuchlowerresistivelossesifonly4GWneedtobe transferred.However,thesecondOHLnecessaryfortransporting thelastGWcomeswithextracostsandright-of-waywidth.

3.4. Converterlosses

Theelectriclossesofconvertersarenotincludedintheefﬁciency calculationsbecausethecapacityratingisthesameforeverytrans- missionoption.VSCconvertersarebuiltusingIGBTmoduleswith currentratingsof400–900Aandoutputvoltagesofapproximately 2kV,muchbelowtherequiredgridvoltage.Acertainnumberof moduleshavetobestackedandwiredtomatchthegridvoltageand capacity[13].Thenumberofthesemoduleswillthereforebethe

sameforallHVDCtransmissionlineoptionsandthusthelossesare assumedtobethesame(∼1%oftheconvertedpowerformodular multilevelVSC).

3.5. Calculationofloadfactordependentefﬁciency

TheefﬁciencyεofSCTLinDCmodeiscalculatedbydividing thepowerlossesP_Loss–whichareonlycausedbycooling–bythe powertransferredP_Trans,i.e.bythecapacity ratingCRtimesthe loadfactorLF:

ε= PLoss

PTrans = PLoss

CR·LF (3)

Asmentionedearlieritwasassumedthatthepowerlossesof SCTLareindependentfromthecapacityratingandthatnoextra lossesoccurinadditiontocoolinglossesbecausethesuperconduct- ingcableisoperatedinDCmode.Thiswasveriﬁedbycalculations basedontheIASSlong-distanceSCTLdesign.

3.6. Impactoftheenvironmentontheefﬁciency

The soiltemperature influencestheelectric lossesof buried standard conductorsas wellasthe electriclosses for coolinga superconductingtransmissionline.Whereasforstandardconduc- torsinDCapplicationsthisisdescribedbythelineartemperature coefficient˛(3.9×10⁻³forCuat20^◦C)andanaccordingincreasein resistanceRandpowerlossesP=I²Rwithincreasedtemperature oftheconductorR=R20^◦C(1+˛(T−20^◦C)),thesituationismore complicatedforSCTL.Highlyreflectivethinlayersandstacksofalu- minizedMylarfoilseparatedbyfiberglassorpolyesterareinserted inthevacuumtofurtherreducetheheatinfluxbythedominant radiationlossesaccordingtotheStefan-Boltzmannlaw.Thetotal heatinfluxqenteringacryogenicsystemcanbedescribedbyan empiricalformula[14,15]

q(n)= (T₂²−T₁²)a

2n +(T₂⁴−T₁⁴)b

n , [W/m²] (4)

with a=4.025×10⁻⁴W/m²K² and b=2.349×10⁻⁹W/m²K⁴ 60 layersofMylarandcryogentemperaturesofT=20K(LH₂)respec- tively65K(LN₂)wereassumedfortheefﬁciencycalculationsdone fortheMgB2 transmissionlines.A(soil)temperatureincreaseof

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10Kfrom300Kto310Kwouldthereforeleadtoan11%increase inheatinfluxforeitherLH2orLN2,causingincreasedpowerlosses duetocooling.Anincreaseinsoiltemperatureleadstoalimited maximumoperatingcurrent topreventathermal runaway and overheatingoftheconductor,asdescribedbytheNeher–McGrath formula[16].Themaximumampacityisgreatlyinfluencedbythe soilmoisturethatismuchsmallerinhotclimatesandalsodirectly affectedbytheheatthatisproducedduetotheresistiveunder- groundcableconductor.Forhotterclimatestheresultisaneedfor anincreasednumberofstandardcableswithawiderseparation thattranslates intoincreasedcapital costsand wider transmis- sioncorridors.Also,thetotalampacityislimitedbytheweakest point along the line, i.e. the lowest local ampacity due to, for instance,otherlocalheatsources.Asanexample,thenumberof cablesisdoubledandthetrenchwidthtripledfora5GWcapac- ityHVDCundergroundtransmissionlinelocatedinNorthAfrica, ascomparedtotheNorthofFrance[11].Thisisnotthecasefor superconductingTLsandconstitutesoneoftheirintrinsicadvan- tages.Especiallyinhotclimateswherethesunirradianceishigh andsolarpowerinstallationsaremostefficientcanSCTLbeuti- lizedforelectric powertransmission(forinstanceinSouthwest US,Mexico,ArabianPeninsula,mostpartsofAfrica,Andesplateau, Australia,India).

4. Results

4.1. Theimpactofloadfactorandcapacityratingonthe efﬁciencyofSCTL

Theelectriclossesandtheefﬁcienciesofsuperconductingand standardtransmissionlineoptionswillbediscussedfordifferent scenarios,capacitiesandloadfactors.First,aTLwith4GWcapac- ityand810kmlengthisassumedbasedontheparametersofthe Südlink/HVDCcorridorCofthegridextensionplaninGermany.

Second,aTLwith10GWcapacityand3000kmlengthisassumed simulatingalong-distanceTL.Third,thecapacityandloaddepend- entefﬁcienciesaregivenfortwoSCTLoptionsbasedonHTScooled byliquidnitrogenandMgB₂cooledbyliquidhydrogenforcapaci- tiesupto10GW.TheMgB₂basedSCTLoptionusingliquidnitrogen plusgaseous heliumascoolants hasvery similarelectriclosses as theHTS option due to employing thesame coolant for the outermosttubeandresultsarethereforenotdisplayed.Theelec- triclossesforMgB2basedsuperconductingtransmissionlinesare 29.7MWand9.5MWforalengthof810km(Table2),usingliq- uidhydrogenorgaseoushelium+liquidnitrogenascryogen.These valuesstemfromthelong-distanceSCTLdesigndevelopedatIASS.

Theelectriclossforthehightemperaturesuperconductor(HTS) transmissionlineis7.3MWfor810km(Table2)and wastaken fromadesigndevelopedattheElectricPowerResearchInstitute (EPRI)withanoperatingvoltageof±100kV[8].Fora4GWcapac- ityTL,theelectricpowerlossesof±500kVHVDCOHLand±320kV HVDCXLPEcablesaremuchhigherat100%loadcomparedtoall superconductingoptions(Table2,Fig.5).Powerlossesofstandard cablesarefor instance31× higherthanfor anHTSbasedSCTL.

Whenoperatedat50%load,thelossesofstandardoverheadlines arealreadylowerthan thelossesof hydrogencooledMgB2 TLs andare smallerthan everyconsideredSCTLoption at25%load for4GWcapacity.AsaconsequenceSCTLareespeciallysuitedfor highcapacityTLswithhighaverageloadfactorssuchascorridor A1oftheGermangriddevelopmentplan,andarenotsoappropri- atefromanenergeticefﬁciencypointofviewforTLswithalow averageloadfactorlikecorridorC(year 2032).Baseloadtrans- missionwithaconstantenergytransferathighloadfactorsseems tobeoneofthemostreasonableapplicationsforSCTL.TheHVDC transmissioncorridorA1inGermanycanbetakenasanexample,

especiallyifoneconsidersthelikelypublicacceptanceadvantage ofSCTLcomparedtostandardtransmissionlinetechnologiesinthe denselypopulatedstateofNorth-Rhine-Westphalia.SCTLwould reallyexcelinefﬁciencyforlong-distancetransmissionoversev- eral1000km ofbulkelectric energyontheorder of10GW,for instancegeneratedbyhydroorgeothermalpowerplants.Long- distancetransmissionlineswithcapacitiesupto6GWbasedon standardtechnologiesareforinstancealreadyoperatinginChina andSouthAmerica.Fig.5graphicallydisplaystheelectrictransmis- sionlossesversusloadassumingthelengthandcapacityratingof theSüdlinkHVDCcorridorinGermany,whichare810kmand4GW respectivelyfortheyear2022.Thiscorridorisenvisionedtohavea capacityof10GWin2034(50HertzTransmissionGmbH,Amprion GmbH,TenneTTSOGmbH,TransnetBWGmbH,2014).Thisvalue islowerthancalculatedinthegriddevelopmentplanpreparedin 2013thatmentions12GWforcorridorCfortheyear2032.

Thetransmissionlinelossespertransferredenergyunitwould thenbelowerforSCTLbecausethelossesarefixed.Thisstillholds trueifoneassumestwoseparate5GWSCTLtofulfill(n−1)require- ments.HTSbasedSCTLusingonlyliquidnitrogenascoolanthave muchlowerlossesthananyotheroptiondownto29%load,where standard±500kVOHLbecomemoreefficient.Pleaseremember thatthiswascalculatedfor2OHLsystemstransferring4GWtotal power,hencetherelativelylow electriclossesfortheOHL.The MgB2basedSCTLreachparityat32%(LN2+GHe)and37%(LH2).

ForthespeciﬁccaseofcorridorCin2022withasimulatedload of54%(EnergieZentrumGraz,2012)theliquidhydrogencooled MgB2SCTLhassimilarlossesasthestandard±500kVHVDCOHL andhalfthelossesofstandard±320kVcables.Thelossesasafunc- tionofcapacityandloadaredisplayedinFig.6foraliquidhydrogen cooledMgB2basedSCTLandinFig.7foraliquidnitrogencooled HTSbasedSCTL.

Itisevidentthatsuperconductingtransmissionlineshavean efficiency disadvantage at low loads and small capacities. The relativelossfunctionis:Loss[%]=C/(load×capacity)withCrep- resenting the fixedcooling losses (36.7MWfor LH₂/MgB₂ and 9MWforLN2/HTS).Therededgeofthecontourplotsmarksthe 6%loss/1000km line,thatseparatestheload–capacitycombina- tionswithanon-acceptableefficiency(non-colored).Thelimitwas takenfromthelossesof±320kV standardcables at100% load.

Evenconsideringthesizeadvantageandapotentialincreaseofthe publicacceptance,SCTLshouldnotbeconsideredasanoptionfor thoseload–capacitycombinationsduetounacceptablyhighelec- tricpowerlosses.Theblacklineinthecontourplotsshowswhen thelossesofstandard±320kVcablesequalthetotalelectricpower lossesofaliquidhydrogencooledMgB₂basedSCTL(Fig.6)anda liquidnitrogencooledHTSbasedSCTL(Fig.7).Fromanenergetic efficiencypointofview,SCTLshouldbepreferredabovethatblack linebecauseanincreasedloadfactormeansincreasedlossesfor standardcables(±320kV)butnotforSCTL.Forcomparison,theTLs forcorridorsA1andCoftheGermanHVDCgridwiththeircorre- spondingcapacityratingandsimulatedloadfactorintheyear2032 aremarkedinthecontourplots.WhereascorridorA1favorsboth superconductingtransmissionlinesoverstandard±320kVHVDC cablestogainahigherefficiency,thereisnoclearwinnerforcorri- dorCduetoitsconsiderablylowloadfactorof21%.Theminimum capacitiestohaveelectriclossesnothigherthan6%/1000km,aloss numberthatstemsfromstandardundergroundcablesandshould notbeexceededduetosustainabilityandefficiencyreasons,are listedinTable3.

Thesenumbersarebasedonthelong-andmediumdistance designs developed at IASS for MgB₂ withrefrigeration stations locatedevery300kmandatEPRIforHTSwithrefrigerationsta- tionslocatedevery20km.Powerlossesduetocoolingwillchange forotherseparationdistancesduetochangingouterdiametersand alsoduetochangedefﬁcienciesofcoolingmachineswithdifferent

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Fig.5.RelativeelectriclossesofHVDCtransmissionlineoptionsfor4GWand810kmnotincludingconverterlosses(CorridorC/Südlink).

Fig.6.ThecoloredcontourplotshowsthepercentileelectricpowerlossesforaspeciﬁcloadandcapacityofaLH2cooledsuperconductingtransmissionline(MgB2).The blacklinedisplaysequaltotallossescomparedtostandard±320kVXLPEcables–itmarksthe38MWloss/1000kmline.Abovethatline,thesuperconductingcable(LH2)has lowertotallossescomparedto±320kVXLPETLs.(Forinterpretationofthereferencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

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Table2

Electriclossesoftransmissionlineoptionsfor4GWand810km.

Electricallosses[load]–4GW,810km MgB2LH2 MgB2GHe+LN2 HTScable ±500kVHVDCOHL ±320kVHVDCcable Load:100%

Powerlosses[MW] 29.7 9.5 7.3 92.6 223.4

Powerlosses[%]ofload 0.72 0.23 0.18 2.23 5.24

Load:50%

Powerlosses[MW] 29.7 9.5 7.3 23.2 55.9

Load:25%

Powerlosses[MW] 29.7 9.5 7.3 5.8 14.0

Fig.7. ThecoloredcontourplotshowsthepercentilelossesforaspeciﬁcloadandcapacityofaLN2cooledsuperconductingtransmissionline(HTS).(Forinterpretationof thereferencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

powerratings.Theabove-mentionedminimumcapacitieswould thereforehavebeentobereevaluated.Arealisticloadfactorof50%

leadstominimumcapacitiesof1.2GWfortheLH₂cooledSCTLand 300MWforLN2cooledSCTL.Belowthesecapacities,areasonably

efﬁcientoperationofSCTLisnotpossibleforthedesignsdiscussed here.Tohaveelectriclossesequaltothoseofstandardcablesthe capacitieshave tobeevenhigherwith550MW(EPRI LN₂)and 2.2GW(IASSLH2)ata50%loadfactor.

Table3

MinimumcapacityratingsforSCTLoptionsfordifferentloadfactorstohavemaximumlossesof6%/1000kmandtoequallossesof±320kVHVDCstandardcables.

100%loadfactor,max.6%losses 50%loadfactor,max.6%losses 50%loadfactor,max.±320kVcablelosses

LH2MgB2SCTL 610MW 1220MW 2200MW

LN2HTSSCTL 150MW 300MW 550MW

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Table4

PowerlossesandefﬁciencyofHVDCoptionsandassociatedcostsassuminga810kmlongtransmissionlinewithanetcapacityof4GWand50%load(corridorC2022/Südlink).

AC-DCconverterlossesandcostsarenotincluded.

Electricallossesandassociatedcosts MgB2LH2 MgB2GHe+LN2 HTScable ±500kVHVDCOHL ±320kVHVDCcable

Powerlosses[MW] 29.7 9.5 7.3 23.4 56.6

Transmissionlineloss[MWh/y] 261,063 83,066 64,079 206,114 497,457

Totallosses(losses/input)[%] 1.46 0.47 0.36 1.13 2.66

%ofelectricitydemandinGER(555TWh/y) 0.047 0.015 0.012 0.037 0.090

Transmissionlosscosts@82$/MWh[M$/y] 21 7 5 17 41

Presentvalue40y.period[M$] 322 102 79 254 614

Table5

PowerlossesandefﬁciencyofHVDCoptionsandassociatedcostsassuminga3000kmlongtransmissionlinewithanetcapacityof10GWand100%load.AC-DCconverter lossesandcostsarenotincluded.

Electricallossesandassociatedcosts MgB2LH2 MgB2GHe+LN2 HTScable ±500kVHVDCOHL ±320kVHVDCcable

Powerlosses[MW] 110.0 35.0 27.0 939.3 2470.3

Transmissionlineloss[MWh/y] 966,900 307,650 237,330 8,256,477 21,713,526

Totallosses(losses/input)[%] 1.08 0.35 0.27 8.39 19.72

%ofelectricitydemandinGER(555TWh/y) 0.174 0.055 0.043 1.488 3.912

Transmissionlosscosts@82$/MWh[M$/y] 79 25 19 677 1781

Presentvalue40y.period[M$] 1193 380 293 10,187 26,790

4.2. Overallenergeticandmonetaryimpact

Therelevancewithrespecttothetotalelectricenergyconsump- tioninGermanyaswellasthemonetaryimpactofelectriclossesare listedinTable4forthediscussedcorridorCoftheGermangridwith 4GWcapacityassuminga50%loadfactorandinTable5forahypo- thetical10GWtransmissionlineat100%loadfactorasdeveloped attheInstituteofAdvancedSustainabilityStudiesinPotsdam.All SCTLhaveanefﬁciencyadvantagecomparedtostandard±320kV HVDCcablesevenata50%loadfactorwithtotalenergylossesof13%

forliquidnitrogencooledSCTLto52%forliquidhydrogencooled SCTL.TheresultsalsoshowthatSCTLwith4GWcapacityata50%

loadfactorarecompetitiveintermsofefﬁciencywithHVDCOHLs, notonlycomparedto±500kVbutalsocomparedto±800kVHVDC OHLwhichhavebeenemployedinChinaforbulkelectricenergy transmission.Theamountofelectriclossescomparedtotheelec- tricitydemandinGermanyispracticallyinsigniﬁcantforalloptions forasingleTLat50%loadfactor.However,consideringthatthetotal installedHVDCNorth-SouthcapacityinGermanyin2032isonthe orderof25GWandtheaverageloadfactormaybehigher,asolu- tionusingonlystandardHVDCcablescouldleadtoelectriclosses reaching1%oftheelectricenergydemandinGermany.

The costsassociated with theelectric losses over a 40 year lifetimeare614M$forstandard cablesand 79(HTS)to322M$

(MgB₂ LH₂)for SCTL (Tables 4and 5).Converterlosses arenot included.Capitalcostsfora4GW,810kmlengthTLhavebeenesti- matedtobe1.4B$(±125kVMgB2 LH2),2.6B$(±125kVMgB2

He+LN₂),5 B$(±100kVHTS),1.6B$(±500kVHVDCOHL)and 4.2B$(±320kVHVDCXLPEcable)[1,2].Itisnotsurprisingthat thelossesofstandardtransmissionlinesandespecially±320kV XLPEcablesarequiteenormousat100%loadandfora3000km longTL.ATLwiththoseparametersreachesaremarkable4%ofthe annualelectricitydemandofGermany.Pleasenotethatinorderto deliveranetpowerof10GW,theinputpowerhastobehigherto makeupforthelossesoccurringalongthelengthof3000km,which alsomeansanincreaseofthenominalAC-DCconvertercapacityat theentrypointwithsubsequenthigherconverterlossesandcosts.

Presentvaluelosscostsfora40-yearlifetimeadduptoabout66%

ofthecapitalcostfora3000kmlength,10GWcapacityTLbasedon

±320kVXLPEcables(45B$withoutconvertercost)[1,2].Costswill alsoincreasebecausethecapacityoftheTLitselfhastobehigher.

ThisisnotdirectlyrelevantforSCTLastheconductingmaterialhas noelectriclossesitselfinDCoperationandatsuchhighcapacity

ratings,thelossesduetocoolingarealmostnegligibleiftapped straightfromtheTL.

4.3. ImpactonCO₂emissions

The EUCommission’s CO₂ emission reduction targetsare to achieveacutby40%untiltheyear2030basedonthepolicyframe- work for climateand energy. Germany’s goal is toreduce CO2

emissionsby80%until2050.VeryrecentlytheUSannouncedthe goaltocutemissionsby26–28%until2025andChinatoachieve astopandpeakofemissionsuntil2030.Nomatterwhetherthis canbeachievedornot,itisclearthatasubstantialfractionofelec- tricenergywillstillbegeneratedworldwideusingfossilenergy sourcesalsointheyear2050.Globally,thereisasubstantialpoten- tialfornewhigh-capacity long-distancetransmissionlines.The powerlossesoftransmissionlinescanbelinkedtoCO₂emissions becauselossesofelectricalenergyneedtobecompensatedbyan increaseofthegeneratedelectricenergyunlessoneassumesthat ahypotheticalSCTLwouldtransfer100%ofREwithanexcessof REavailableforcooling.Therenewableenergyshare(RES)ofthe electricitymixinGermanywas23%attheendof2012.Theaverage emissionofCO₂pergeneratedkWhwas563gin2010[17].TheCO₂ emissionsofsuperconductingtransmissionlinesarecomparedto standardoverheadandundergroundtransmissionlinesinTable6 fortheexampleofcorridorCoftheGermangriddevelopmentplan (Südlink)assumingaloadfactorof50%.

Forinstancewouldstandardcablesexperiencelossesequivalent to6.5%oftheCO2emittedbyatypicalsteam-cyclecoalpowerplant (4300GWh/year).Consistentwiththeelectriclosses,theemissions arelowestforliquidnitrogencooledSCTL(0.8–1.1%coalpower plantCO2emissionequivalent).Theefﬁciencydrasticallychanges infavoroftheSCTLswithincreasingcapacityandloadfactordue totheﬁxedamountofenergyneededforcoolingSCTL.Asanexam- ple,theCO2emissionsfora3000kmlongtransmissionlinewitha 10GWnet-capacityat100%loadarelistedinTable7.

Theemissionsassociatedwiththeelectriclossesforstandard cableswouldbeequivalenttoalmost3coalpowerplants!HVDC overheadlineswouldalsoberesponsiblefortheemissionof30× theamountofCO₂nitrogencooledSCTLindirectlyemit.TheGer- manelectricgrid(AC)experiencestotalelectriclossesof5–6%for transmissionandvoltageconversionwhenbringingelectricenergy fromsourcetoload.Thelowvoltagelevelisresponsibleforthe largestfractionoftheselosses,followedbythemedium-voltage

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Table6

CO2emissionsassociatedwithpowerlossesoftransmissionlines(4GW,810kmlength)assumingtheRESof2012inGermany–load:50%.

CO2equivalentemissionoflosses MgB2LH2 MgB2GHe+LN2 HTScable ±500kVHVDCOHL ±320kVHVDCcable Electricitymix2012(563g/kWh)

Peryear[t] 146,717 46,683 36,012 115,836 279,571

For40years[t] 5,868,696 1,867,312 1,440,498 4,633,439 11,182,826

CoalpowerplantCO2equivalentemission[%] 3.4 1.1 0.8 2.7 6.5

Table7

CO2emissionsassociatedwithpowerlossesoftransmissionlines(10GW,3000kmlength)–load:100%.

CO2equivalentemissionoflosses MgB2LH2 MgB2GHe+LN2 HTScable ±500kVHVDCOHL ±320kVHVDCcable Electricitymix2012(563g/kWh)

Peryear[t] 543,398 172,899 133,379 4,640,140 12,203,002

For40years[t] 21,735,912 6,915,972 5,335,178 185,605,613 488,120,066

CoalpowerplantCO2equivalentemission[%] 12.6 4.0 3.1 107.9 283.8

distributiongridandthehigh/ultra-highvoltagetransmissiongrid.

Thatisprimarilyrelatedtothetotallength.Thecapacityoflowvolt- agetransmissionlinesmaybetoolowforSCTLtobemoreefﬁcient thanstandardtechnologies,buttheuseofSCTLcanofferadvan- tagestolocaldistributiongridsintermsofefﬁciency.Considering thelengthofplannedHVDCcorridorsinGermanyandelsewhere, theuseofSCTLcanleadtoreducedCO2emissionsfortheseappli- cations.Ultimately,onecanthinkofacombinedtransmissionand distributiongridcompletelyutilizingSCTLatonlyonevoltagelevel allthewayfromgeneration(10–30kVturbine/generatoroutput voltage)tothedistributioncenters.Thusonewouldgetridofup- and-downtransformerstationsandsaveassociatedelectriclosses (0.3–1.1%,municipalutilitiesMunichandBerlin).

4.4. UsingSCTLtostoreexcessRE

Asmentioned in thebeginning,simply connectingintermit- tentrenewableenergysourcesathighefficienciesusingSCTLwill requireasophisticatedenergymanagementsystemtoachievea highaverageloadfactor.Inthisrespect,thecryogenicsystemof SCTLscouldstoreexcessenergyduringtimesofhighREgenera- tionbycoolingthecryogentolowertemperaturesandwarm-up toregularoperatingtemperaturesattimesoflowloadwithnouse ofelectricenergy.Ascoolingatcryogenictemperaturesisrequired anywayforoperation,theefficiencyofthistypeofstoragewouldbe relativelyhighinthisspecificcase.Thepowerandcapacitywould besmallthough–like7–30MWforthedescribed800kmlongSCTL aswouldbethestoragecapacity(afewMWhperKelvinforLH₂@ 17K/17bar)–pleasecomparewithTable2–howevermuchless inpureurbanshortlengthapplicationsdue tothesmallernec- essarydiameterandlowercryogenmass.TheshortlengthLong IslandPowerAuthority(LIPA)SCTLbasedonHTScoolingsystem hasapowerof6kW@70Kincomparison.Thispossiblestoragein thecryogenicsystemisinlinewiththephysicalcharacteristicsof asuperconductortoexhibitaclearlyincreasedcurrentdensityat lowertemperatures,whichtranslatesintoahighercapacityofthe SCTL.ExcessiveREcouldalsobestoredashydrogeninSCTLasa coolantbymeansofelectrolysisandliquefactionandtransferred thisway.Theliquefactionprocesshoweverisveryinefficientand themassflowofthecryogenlow.

5. Summary

Theefﬁciencyadvantageofsuperconductingtransmissionlines isoftenhighlightedinrelevantdebates.However,theelectriclosses ofSCTLarepersenotlowerthanforstandardtransmissiontech- nologiesandacarefulevaluationofeverytransmissionlinecasehas tobemade.Asabasicrule,thehigherthecapacityandthehigher theaverageloadfactor,thehighertheefﬁciencyforSCTL.Thefull

energyefﬁciencyadvantagesofSCTLcanbebestexploitedifthis technologyisusedtoconnectpowerplantswithaconstantenergy outputwithconstantloadcenters,inordertoobtainahighloadfac- tororsimplytoprovidetheminimumbaseload.Fromanenergy efﬁciencypointofview,connectingremotegeothermalandhydro powerplantswithcapacitiesofseveralGWoreventensofGWmay beoneofthetopapplicationsforSCTLinthefutureelectricitygrid duetotheirhighcapacityfactors(70%forgeothermaland50%for hydro[18])aslongasothermoreintermittentREsourceslikewind andsolararenotbackedbyadequatestoragecapacity.Energystor- agecouldalsoberealizedbyreducingtheoperatingtemperature throughanincreaseoftherefrigerationpowerattimesofhighload, andviceversabylettingthecryogenwarmupattimesoflowload.

Inthemeantime,SCTLwillbeutilizedonmuchsmallerscalein localandregionalgridsnotforanefficiencyadvantagebutforpub- licacceptanceandreducedspacerequirementreasons.Standard technologiescanhave equalor evenhigher efficienciesfor low averageloadfactors.Recently,“standard”HVDCXLPEcableswere developedwithvoltageratingsof±525kVcomparedtotheformer limitof±325kVandhencecorrespondinglowerelectriclosses(or highercapacities).Inthisrespect,SCTLcanhaveatechnological edgeastheycouldbeoperatedatsignificantlylowervoltageswith thesamecapacity.AnexampleistheAmpacityprojectinEssen byRWEthatrecentlyannouncedthefailure-freeoperationsince startofoperationinearly2014.Finally,SCTLhavethepotential toreduceCO2emissions,butinordertoobtainarealisticnumber fortheefficiencyofSCTL,thecharacteristicsoftheadjacentgrid, especiallytheloadfactor,havetobeincluded.

Acknowledgements

ThisworkwasfundedbytheGermanFederalMinistryofEduca- tionandResearch(BMBF)andthestateofBrandenburg/Germany.

Appendix. Acronymsandnomenclature

AC alternatingcurrent cm centimeter DC directcurrent GHe gaseoushelium GW gigawatt GWh gigawatthours

HTS hightemperaturesuperconductors HV highvoltage

HVDC highvoltagedirectcurrent IGBT insulatedgatebi-polartransistor

K Kelvin

kA kiloampere

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H.Thomasetal./ElectricPowerSystemsResearch141(2016)381–391 391 km kilometer

kV kilovolt kWh kilowatthours

LCC linecommutatedconverter LH2 liquidhydrogen

LN₂ liquidnitrogen

LTS lowtemperaturesuperconductors

m meter

MgB₂ magnesium-di-boride MLI multilayerinsulation

MW megawatt

OHL overheadline q heatinﬂux RE renewableenergy RES renewableenergyshare ROW right-of-way

SC superconductors

SCTL superconductingtransmissionline T temperature

TL transmissionline

TSO transmissionsystemoperator VSC voltagesourceconverter

W watt

XLPE crosslinkedpolyethylene References

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