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EE491/492 Design Document
Superconducting
Generators for Wind
Turbine
Abrahem Al‐afandi
Hamad Almutawa
Majed Ataishi
Rehman Shahzad‐491
Nikhil Purma‐491
2
Table of Contents
1‐Design Description………………………………………………….……………………………… 3
1.1 Project Definition………………………………………………..………………………………...………. 3
1.2 Project goals and Deliverables………………………………………………………………………. .3
2‐ System Level Design………………………………………………………………………………..3
2.1 System Requirements………………………………………………………………………………………3
2.2 Functional Decomposition……………………………………………………………………………….4
2.3 PMSG vs. HTs……………………………………………………………………………….……….4
3‐ Detailed Design & attributes…………………………………………………………………..6
3.1 Implementation & Optimization challenges……………………………………….….………..6
3.2 Different Topologies within HTS……………………………………………..……………….………7
3.3 Different topologies within PMSG……………………………………………………….…….…..11
4‐ Suggested Designs…………………………………………………………………………………15
4.1 Design 1 (PMSG)…………………………………………………………………………………….……….15
4.2 Design 2 (HTS)………………………………………………………………………………………………...16
5‐ Performance Evaluation…………………………………………………………………………16
6‐ Cooling Systems………………………………………………………………………….………….18
6.1 PMSG Cooling System……………………………………………………………………………………..18
6.2 HTS Cooling System………………………………………………………………………….………………19
7‐ Cost Analysis…………………………………………………………………………………………..20
7.1 Assumptions………………………………………………………………………………………….…………20
7.2 Cost Model……………………………………………………………………………………………..……….20
7.3 Results & Evaluation……………………………………………………………………………….…..…..21
8‐ Design Approach & System Level diagram………………………………………..…….23
8.1 Design Approach………………………………………………………………………………………...…..23
8.2 System Level Diagram………………………………………………………………………….……..……24
References………………………………………………………………………………………….….…..25
Appendix A……………………………………………………………………………………….……..….28
Appendix B………………………………………………………………………………………...……….29
Appendix C…………………………………………………………………………………………….……31
3
1. DesignDescription
1.1 projectdefinition
Inthisdesignproject,wewillexaminesuperconductinggeneratordesignsforhighcapacityland‐basedthree‐bladehorizontal‐axiswindturbines(HAWT).Theworkwillovercomethreemainbarrierswithinwind‐turbinedesign.Theprimaryfocuswillbeongearless,direct‐driveconfigurationsutilizingpowerelectronicinterfacesratedatfullturbinecapacitywithhigh‐temperaturesuperconducting(HTS)orpermanentmagnet(PM)generators.
1.2 ProjectGoalsandDeliverables Suggested5MWturbineusingpermanentmagnetgenerator. Suggested10MWturbineusinghightemperatureSuperconductorgenerator.
Eachsuggesteddesignhas:
Tobecost‐effective. Highenergyyield. Lowweightandvolume. Suitablecoolingsystem. TobeefficientwithminimizedAClossesandfluxleakage. VolumeandB‐fieldshouldbebalanced,sincepowerisproportionaltoarea,
lengthandB‐field.
2. SystemLevelDesign
2.1 SystemRequirements Gearless,Direct‐Drivewindturbineconfiguration. Outputpoweristobeintherangeof5MW‐10MW. Thesizeofthegeneratormustbetransportedwithoutdifficulty. Systemiscapableofwithstandingthetorqueduringnormaloperationas
wellasshort‐circuitfaultssituation.[2] Mustwithstandanywindspeed. Coolingsystemmustbereliableandself‐maintained.
4
2.2 FunctionalDecomposition
SynchronousGenerator:Inasynchronousgenerator,aDCcurrentisapplied
totherotorwindingproducingarotormagneticfield.Therotoristhenturnedbyexternalmeans(propellerofthewindturbine)producingarotatingmagneticfield,whichinducesa3‐phasevoltagewithinthestatorwinding(Copper).Fieldwindingsarethewindingsproducingthemainmagneticfield,whicharerotorwindings.Armaturewindingsarethewindingswherethemainvoltageisinduced,whicharestatorwindings[9].
Coolingsystem:ThecoolingsystemisrequiredtocooldowntheHTSwires,whichoperateat20Ktemperaturetomaintainastablecryogenic(Verylowtemperature)environment.Thishelpsinminimizinglosses,whichisaresultoftheheatcomingoutofwiresbecauseoftheresistivity.
Converters:Convertershelpthewindturbinegeneratorwithgridintegration.
Asthewindturbineoperatesatvariablespeedsthefrequencyofthegeneratorisdifferentthanthefrequencyofthegrid.Thisiswhypowerconvertersareneeded.Theyalsohelptostabilizethevoltageofthegenerator.
2.3 PMSGVs.HTS
Figure1: PMSG Block Diagram [4]
5
Figure2: HTS Block Diagram [5]
System Description:
The propeller takes in the kinetic energy of the wind, which rotates the shaft. The shaft is connected to the rotor, which rotates it. The DC exciter will energize the field windings on the rotor, which will create magnetic field. The rotating rotor will create a change in magnetic field, which will induce voltage on the stator windings. The stator is connected to the converters that are connected to the grid. Schematically, the difference between HTS and PMSG is that HTS is using an external DC exciter to energize the field windings, while in PMSG; permanent magnets provide the excitation instead of field windings.
5MW PMSG & 10MW HTS:
Permanent magnet synchronous generators (PMSG) have been announced by Siemens Power Generation and GE Energy for the Megawatt class [15]. They are characterized as having large air gaps. However, the increase of output power requires a reduction in cost of energy.PMSG are feasible up to 5MW, because a 10MW PM generators are above 300 tons (Figure 3) and their diameter are larger than 10 m [2]. Therefore, heavy weight and large diameter always translate to high cost, which limits PMSG from commercialization for the 10 MW level.
Figure 3: HTS Block Diagram [20]
6
On the other hand, HTS generators are new and strong candidates for 10 MW level. They are well known for their low weight, small size, and high efficiency (Figure 4).
Figure 4: HTS Block Diagram [20]
American Superconductor (AMSC) has designed a 10 MW SC direct-drive generator with weight of about 160 tons [2]. When referring to weight, volume and the overall drive train cost, HTS generator concept is superior. A study conducted by the National Renewable Energy Laboratory (NREL) [25] shows That PMDD generator is the heaviest (Figure 5), the AMSC HTSDD generator is second heaviest, and the geared turbines generator is the lightest. The roughly 50% reduction in mass between the PMDD and AMSC HTSDD generators at 10 MW is one of the core advantages of HTS generators.
Figure 5: HTS Block Diagram [25]
3. DetailedDesign&attributes
3.1 Implementation&OptimizationChallenges
Nospecificsoftwaretosimulatefindings,sinceHTSandPMSGarenowtonext
generationtechnologies.
Optimizationtokeepcostandvolumewithinreasonablelimits.
7
Thereneedtobeabalanceamongelectrical,magnetic,thermal,mechanical,and
economicfactorsforawell‐designedgenerator[2].Thesefactorsarealways
conflictingwitheachother,nomatterwhatkindofmethodsdesignersuseto
optimize,thekeysarelowcost.highreliabilityandavailability.Highcostalways
preventsgeneratorsfromcommercialization.
Ingeneral,thebesttopologyofDDgeneratorshasthemaximumoutput,minimum
expensesandhighestreliability.
3.2 DifferenttopologieswithinHTS
3.2.1 FullySuperconductingVs.PartiallySuperconducting[2]
Table[1]:FullySCvs.PartiallySC
PartiallySuperconducting
ismoresuitable,unless
thereisabreakthroughin
reducingAClossesinfully
SC.
Figure 6: Partially Superconducting [2]
8
3.2.2 RadialVs.AxialFlux[2]
Table[2]:Axialfluxvs.Radialflux
Radialfluxtopologyismorepromisingand
mostwidelyusedforMWpowerratings.
Figure 7: Radial Flux generator [2]
3.2.3 RotatingFieldVs.Rotatingarmature[2]
Type Advantages Disadvantages
RotatingField 1. Many ongoing projects areusingRF.Ex.AMSC.
2. Makesarmaturedesigneasier3. Permits current density &
magneticfluxdensity.4. Easier to make armature
reinforcementforhightorques.5. Stator’scoolingsystemiseasier
tobuild.
1.Rotatingcryogeniccooling
Tech.mustbeadvanced.
Rotatingarmature 1.Eliminatestheneedofrotatingseal.
2.WithstationaryLTScoils,costis
reduced.
3.Stationaryfieldisdesirable,because
coolingsystemiswithSCcoils.
1.Requirescooling&
electricalcircuitsto
accommodatevibrationdue
torotation.
9
Figure 8: Stationary Armature Vs. Rotating Armature [2]
3.2.4 Statorwithair‐gapVs.Statorwithironteethwinding[2]
Table[4]:airgapstatorvs.ironteethstator
Ingeneral,HTSgeneratorsoperatedunderhighlymagneticallysaturatedconditions
withironcoretopologyhavebetterperformances.Whentakingintoaccounttheprice
trendofHTSwire.However,air‐core,air‐rotor,andair‐gapwindingisapromising
futuredesign.
Figure 9: Air-gap teeth vs. iron-teeth [2]
10
3.2.5 Air‐corevs.Iron‐corevs.TypesofIron‐core[2]
Table[4]ironCoreTypes
Figure 10: HTS generator [8]
11
3.3 DifferenttopologieswithinPMSG
3.3.1 DesignDecisionsDescription
Air‐gapOrientation:
Theairgapisnecessaryasameansformechanicallyseparatingthe
rotorfromthestator.Itformsasurfacebetweentherotorandthe
stator.Thevectornormaltotheairgapsurfacecaneitherberadially
orientedoraxiallyoriented.Inthefirstcase,thevectoris
perpendiculartotheaxisofrotation,whereinthesecondcase,the
vectorisparalleltotheaxisofrotation.[16]Thisisillustratedin
figure11.
Figure 11: Air gap orientation [16]
StatorCoreorientation:Thestatorcorecarriesfluxaroundthestatorwindinginordertocreateanelectromotiveforceinthatwinding.Thefluxcanbetransportedinadirectionparalleltothedirectionofmotionormainlyperpendiculartothedirectionofmotion.Inthefirstcase,themachineissaidtobelongitudinalandinthesecondcase,themachineissaidtobetransverse.[16]
12
Figure 12: Stator Core Orientation [16]
PMorientationwithrespecttoairgap: ThePMsaremountedontotherotoriron.ThePMmagnetizationhasadirection,whichcaneitherbeparallelorperpendiculartoavectornormaltothesurfaceoftheairgap[16],asillustratedinfigure13.
Figure 13: PM orientation [16]
CopperHousing: Thestatorlaminationscanbemadeeitherwithorwithoutteeth.Inthetoothedstator,theteethareusedtocarrythemagneticfluxandtomaintainthestatorconductorsinplace.Inthetoothlessstator,thestatorconductorsareplacedintheairgapandthemagneticfluxmustthencrossamuchthickerspaceofnon‐magneticmedium,whichwillleadtothickermagnetsor/andlowerno‐loadfluxdensity.[16]
Figure 14: Slotted vs. Slotless [16]
13
Cogging Torque:
CoggingtorqueisaninherentcharacteristicofPMgeneratorsandiscaused
bythegeometryofthegenerator.Itaffectsself‐startabilityandproduces
noiseandmechanicalvibration.Thus,minimizingCoggingtorqueis
importantinimprovingtheoperationofwindturbines.[17]
3.3.2 MajorDesignDecisions[10],[11]
Themaindesigndecisionsarelistedintable5.
Table[5]:MajorDesignDecisions
3.3.3 PromisingDesignsofPMSG[10],[11]
ListedarethefourdesignsofthePMSGbasedonthedecisionsmadefrom
table5.
14
Table[6]:PromisingPMdesigns
3.3.4 LimitingFactorstoConsider[10],[11]
Limitingfactorsencounteredarelistedin
Table[7]:LimitingFactors
15
4. SuggestedDesigns
4.1 Design1(PMSG)
5‐MWPMSGwindGenerator
Outofthefourdesignconfigurationlistedintable6,theinnerrotor,andouter
rotorRF‐L‐SM‐ICispromisingandwidelyused.Eg.ABB.
Table[8]:SuggestedDesign1
Figure 15: Inner rotor vs. Outer rotor
16
4.2 Design2(HTS)
10MWSCDDWindGenerator:
PartiallySCwithHTSfieldwindingontherotor.
Stationaryarmaturewindings.
Radialfluxmachine.
Iron‐coredrotorwithironteethstatorwinding.
Figure[16]:AMSC
5. PerformanceEvaluation
ThecriteriausedinmostresearchpaperstofindasuitablePMSGdesignwastolook
atCost/Torque(CT)andTorquedensityorTorque/mass(TM)ratios.
ThedesignwithlowCTrationandahighTMrationwasisconsideredafeasible
design.
Figure17,and18showsthatsuggesteddesign1(PMSG)maynothaveagood
torquedensity,butithasthebestCTratiowhichisthereasonitswidely
commercialized.
17
Figure[17]:Torquedensitycomparison[18]
TheabovepictureshowsthatRFPMhasarelativelylowTorquedensity.However
figure18showsthatRFPMhasthelowestCost/Torqueration.
Figure[18]:Cost/TorqueComparison[18]
• Additionally,Figures17,18confirmthataxialmachinesarenotsuitedforMW
powerratings,sincetheouterradiusbecomeslarger,andthemechanicaldynamic
balancemustbetakenintoconsideration.Moreover,aspowerratingsgethigher
costgetslowerforradialmachines.
18
6. CoolingSystems
6.1 PMSGCoolingsystem
Liquidcoolingisanewtechnologyforwindturbinesanditsimpactonreliability
mustbeevaluated.Paper[19]presentsareliabilityanalysisforaliquid‐cooled8
MWDD‐PMSGcoupledwithprimaryandsecondaryliquidcoolantsystems.
Reliabilityhasbeencalculatedanalyticallyandassessedbasedonthefollowing
reliabilitymetrics:MTBF,MDT,MTTF,failureintensity,andavailability.
Paperconcludesthatthecoolingsystemwasbrokenoutintotwosubsystems:
thegeneratorwithitsprimaryliquidcoolingloopandthesecondarysidecooling
system.Bothaliquid‐to‐liquidandliquid‐to‐airsecondarysidecoolingsolutions
wereanalyzed.
Note:EconomicAnalysiswasnotperformedforthiscoolingtopologyas
mentionedby[19].
Figure[19]showsthegeneratorandcoolingsystembasedonliquid‐to‐liquid
heatexchanger,Figure[20]showsliquidtoairheatexchanger.
Figure[19],[20]:Liquid‐to‐liquid&Liquid‐to‐air[19]
19
6.2 HTSCoolingsystem[20]
TheHTSneedsanoperationtemperatureofabout30‐40K.
CoolingisdonebyexpansionofcompressedHelium.
Compressorscanbesomewhereoutsidetheturbine.
Acouplingbetweennon‐rotationalpartandrotationalpart(rotor)isneeded.
Figure[21]showsthesuggestedcoolingsystemforHTScoilsby[20].
Figure[21]:HTScoolingSystem[20]
20
7. Costanalysis
Thispartwillmainlycovertheassumption,methodofevaluation,&resultsofthewindturbinecostanalysis.TheFirststepwasstatingseveralassumptionsandcheckediftheseassumptionswererealistic.Afterthat,acostmodelwasneededtogetthecostofenergyofourdesigns.Comingupwithcostmodelisfairlycomplextask,thusanexistingmodelwaschosen[21]thathavebeenbuiltbytheNationalRenewableEnergyLab(NREL).Usingthismodelsomeresultswereobtainedandthenevaluatedbasedonresearchstudiesthatusedthismodelandsomeexistingmodel.
7.1 Assumptions
Inordertogettheresults,it’sessentialtochoosethehubheight,rotordiameter,
andtheratedpowerforourdesigns.Table9containsthevalueschosenforthe
twodesigns‐PMSG&HTS‐basedondesigndecisionsfromthepreviouspartsof
thedocument.
Variables PMSG HTS
Rated Power 5MW 10MW
Hub height 120m 140m
Rotor Diameter 120m 160m
Table9
7.2 CostModel
ThecostmodelthathasbeenusedinthisdocumentwasdevelopedbyNREL[21].Thepurposeofthemodelistogettheinstalledcapitalcost(ICC)andtheannualoperatingexpenses(AOE).ThevaluesforAOEandICCcanbeobtainedusingtable2[24].Thenextstepwastolookattheannualenergyproduction[21]:
AEP CF ∗ P ∗ 8760hours
CFreferstothecapacityfactor.Thecapacityfactorvariesforlocationtoanotherdependingontheaveragewindspeed.AtypicalCFforin‐landwindfarmsisfrom30%‐40%.
21
Table10[24]
TheCOEcancalculatedforeachdesign[24]:
TheFCRisaround12%accordingto[21],[22]and[23].Table11
Itshouldbenotedthatthismodelisvalidforpowerrangefrom0.75‐5MW&rotordiameterof80‐120m.It’salsovalidforextrapolationforpowerupto10MWandrotordiameterof200m[22].
7.3 Results&Evaluation
Table12showstheresultsfortheproposeddesignsusingExcel.Thefilecanbe
modifiedtothedesiredhubheight,rotordiameter,andratedpowerandit
generatethevaluesneededtocomputeCOE.
COE Cost of energy
FCR Fix charge rate
ICC Installed Capital cost
AOE Annual operating expenses
AEP Annual energy production
22
Table12
TheuncertaintyrangefortheAEPandtheCOEwascalculatedbasedonthedifferentcapacityfactorsthatcanbeobtainedfromdifferentlocation.Table13showstheuncertaintyrangefortheproposeddesigns.
Table13
Inordertoevaluatethedesigns,aquickcomparisonwithanexistingwindturbinesofthesamecategory.Table6showsaquickcomparisonbetweentheproposed5MWgeneratorandGamesa4.5MWgenerator[27].Itcanbeseenthattheresultsobtainedforthe5MWgeneratorisveryclosetotheexistinggenerator.
Generator 5 MW 10 MW
AEP 13140 MWh 26280 MWh
ICC (total) 5583.62k $ 25510.96k $
AOE 145.4k $ 290.6k $
COE 0.061 $/KWh 0.13 $/KWh
Generator 5MW 10MW
AEP ~2% ~5%
COE ~5% ~9%
23
8. DesignApproach&SystemLeveldiagram
8.1 DesignApproach
24
8.2 SystemLeveldiagram
25
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10. Chan,T;Lai,L,"AnAxial‐FluxPermanent‐MagnetSynchronousGeneratorforaDirect‐CoupledWind‐TurbineSystem".IEEETransactionsonEnergyConversion,VOL.22,NO.1.March2007.
11. Cao,J;Yang,X,"DesignandMagneticFieldAnalysisofaDual‐RotorPermanent‐MagnetSynchronousWindGenerator",SouthChinaUniversityofTechnology/CollegeofElectricPower,China.
12. Hae‐JinSung,Gyeong‐HunKim,KwangminKim,MinwonPark,In‐‐‐KeunYu,Jong‐YulKim,"Designandcomparativeanalysisof10MWclasssuperconductingwindpowergeneratorsaccordingtodifferenttypesofsuperconductingwires,"PhysicaC:Superconductivity,Volume494,15November2013,Pages255‐261,ISSN0921‐4534.
13. Mihai,A.M.;Benelghali,S.;Livadaru,L.;Simion,Al.;Outbib,R.2012XXthInternationalConferenceonElectricalMachines,Sept.2012,pp.267‐273IEEE
14. Eriksson,Sandra;Bernhoff,Hans2012XXthInternationalConferenceonElectricalMachines,Sept.2012,pp.1419‐1423IEEE
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15. Okedu,Kenneth,E.“WindTurbineDrivenbyPermanentMagnetSynchronousGenerator”,ThePacificJournalofScienceandTechnology,volume12,No.2.Nov.2011.
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18. Dubois,M.R.;Polinder,H.;Ferreira,J.A.,“Comparisonofgeneratortopologiesfordirect‐drivewindturbines”,Lab.OfElectricalPowerProcessingMekelweg4,KamerLB03.6602628CDDelft,TheNetherland.
19. Polikarpova,Maria;Semken,Scott;Pyrhönen,Juha,“ReliabilityAnalysisofaDirect‐LiquidCoolingSystemofDirectDrivePermanentMagnetSynchronousGenerator”,LappeenrantaUniversityofTechnology.
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27. ] H. Polinder, Frank F. A. vander Piji, Ger‐Jan de vilder and Peter J. Tavner, “Comparison of direct‐drive and geared generator concepts for wind turbines”, in 2005 IEEE International Conference on Electric Machines and Drives, May. 2005, pp. 543‐550.
28. A. B. Abrahamsen, N. Mijatovic, E. Seiler, M. P. Sorensen, M. Koch, P. B. Norgard, N. F. Pedersen, C. Traeholt, N. H. Andersen, and J.Ostergard, “Practical Design of a 10 MW Superconducting Wind Power Generator Considering Weight Issue” IEEE Trans. Appl. Supercond., vol. 23, no. 3, 2013.
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31. H. Polinder, Frank F. A. vander Piji, Ger-Jan de vilder and Peter J. Tavner, “Comparison of direct-drive and geared generator concepts for wind turbines”, in 2005 IEEE International Conference on Electric Machines and Drives, May. 2005, pp. 543-550.
32. A. B. Abrahamsen, N. Mijatovic, E. Seiler, M. P. Sorensen, M. Koch, P. B. Norgard, N. F. Pedersen, C. Traeholt, N. H. Andersen, and J.Ostergard, “Practical Design of a 10 MW Superconducting Wind Power Generator Considering Weight Issue” IEEE Trans. Appl. Supercond., vol. 23, no. 3, 2013.
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28
AppendixA
1. PropertiesofdifferentSCwires[12]
2. TypicalMaterialsusedin10MWHTS[12]
3. Comparativeadvantageofeachmaterial[12]
29
AppendixB
MaterialselectionforPermanentmagnet:
Thematerialselectionshouldbebasedonthedifferentdesiredqualities.Forinstance,reducecost,weigh,volume,heatriseandincreaseoutput.ThesequalitiesdependsonthePMmaterialswith:
Advantages&disadvantages:
Ferritemagnet
TheferritemagnethaslowremanentfluxdensitycomparedtoNdFeBandSmCo,whichreducestheefficiencyofmagneticenergy.Also,inordertoproducethesameoutputpowerasNdFeBorSmCo,wewillneedtoincreasetheweightofthePMmaterialinthegeneratordesign.ThismeansthattheFerritemagnetdesignwillhaveahigherweightcomparedtoNdFeBdesign.However,itisthecheapestmaterialbetweenthemandsomedesignsconsiderusingitduetothehighperformance/priceratio,whichgivesitaneconomicadvantage.[13],[14].
Neodymiumironboron(NdFeB)
ThisPMmaterialbyfaristhebestbetweentheelementsinthegroupintermsofperformance.Themagneticenergyis+300kJ/ 3,whichis10timesbetterthantheferritemagnetandabout30%betterthanSmComagnet.TheNeodymiumis5timesmoreprevalentthanthesamarium,whichmightreducetheproductioncostofthefinalproduct.
30
ButitshouldbenotedthattheNeodymiumpriceisnotstablebecausethemainproducerofitisChinaanditscontrolsthepricesofit.TheNdFeBgeneratordesignwillrequireacoolingsystembecauseoftheLowoperationtemperature(115Celsius).
SamariumCobalt(SmCo)
TheSmCosharessimilarcharacteristicsasNdFeB,butperformancewisetheNdFeBisbetter.OneoftheDrawbacksoftheSmCoPMisthefragilityofit.It’sverybrittlecomparedtotheothersPMinthegroups.However,thepriceofSmCoPMisstablecomparedtoNdFeB,whichmakesiteconomicallypreferable.Also,SmCohasbettercorrosionresistancethantheNdFeBPM.
31
AppendixC
PMSG active Materials
In order to calculate the total cost of active materials (copper, iron, and neodymium) for PMSG, the
following needed to be found:
1) Weight of active materials:
The weight of active materials has a dramatic relation to the rated power. The relationship
between active materials and rated power is almost linear [30] (page 101). This would indicate
that the percentage of active materials in the generators would be the same regardless of the
rated power.
Figure 25
Figure 26
32
The plan was to find the weight of Neodymium, which is obtainable using the following relations [30]
page (64):
An estimation for the mass of copper and iron needed for 5MW generator was made based on
comparing the percentage of active materials in two different designs, which have different
specifications.
1) The magnet weight and rated power graph (figure1) was extrapolated with the assumption of
its linearity. Here are the percentages of active materials that we found:
Figure 27
33
2) The values given for a direct‐drive permanent magnet generator [31] was used to find the
percentages of the active materials in the generator:
The percentage of copper was noticed be the same in both designs. The range of iron mass percentage
is from 41.8% to 75.1% and the range of Neodymium mass percentage is from 7.05% to 40.4%.
Generally, the price of Neodymium is higher than the price of iron. Therefore, the design of the second
generator, which include higher amount of iron and lower amount of Neodymium was used in our cost
analysis. The total weight of the generator was obtained from the value of magnet weight:
Total weight = 28.65 ton
The values given for a direct‐drive permanent magnet generator [31] was used to find the percentage of
the active materials in the generator.
2) Cost of active materials: After finding the weight of active materials, it is possible to find the cost for each type of
materials using the price that we used in the previous semester.
Here is a table that includes our cost analysis for 5 PMSG generator:
34
HTS active materials cost
For a partially 10 MW superconducting generator, there are 6 parts which consist active materials [32]:
Component Type of material
Rotor body nonmagnetic material
Vacuum shield nonmagnetic material
Stator teeth nonmagnetic material
Stator coil copper
Rotor coil YBCO
Magnetic shield laminated silicon
The total weight of the active materials is 71 ton. The total is distributed among the five parts of the
superconducting generator in the following way:
Nonmagnetic material
Iron was our choice as the nonmagnetic material since our design was iron‐cored. 38 ton of iron
is needed in our design. The price of iron in dollar‐per‐kg ($5/kg) that was already used for
PMSG cost analysis was also used to find the total cost of copper in the HTSG cost analysis.
($5/kg)*38ton = $172365
Copper
The price of copper in dollar‐per‐kg ($7/kg) that was already used for PMSG cost analysis was
also used to find the total cost of copper in the HTSG cost analysis.
($7/kg)* 4 ton = $25401
YBCO
The rated filed current from our design specifications was used to since YBCO wires are used in
the design. This number is multiplies by the length of HTS wires that also found in our design
specifications.
Component Weight
Rotor body 10 tons
Vacuum shield 12 tons
Stator teeth 16 tons
Rotor coil 2 tons
Magnetic shield 16 tons
Stator coil 4 tons
35
Kiloamp‐meters = rated field current*length of HTS wire
= 0.1kA*920000m=92000kAm
Total cost of YBCO = cost of YBCO per kiloamp‐meter*kiloamp‐meters
($10/kAm)*92000kAm = $920000
Laminated silicon:
The price of silicon ($0.995/LB) that was found in metalprices.com was used to find the total
cost of silicon [33].
Total cost of laminated silicon = ($0.995/LB)*16 ton = $ 318400
Total cost of the active materials = $1436166
Here is a table that includes our cost analysis for 10 HTSG generator: