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Transients in Large HV Cable Networks: Modeling and calculations Ametani,Xue,OhnoandKhalilnezhad Volume212 BatteryStateEstimation:MethodsandModelsS.Wang Volume905 PowerSystemProtection,4VolumesTheElectricityTrainingAssociation(Editor) Synchronous Reluctance Machines Analysis, optimization and applications Nicola Bianchi, Cristian Babetto and Giacomo Bacco TheInstitutionofEngineeringandTechnology PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom TheInstitutionofEngineeringandTechnologyisregisteredasaCharityinEngland&Wales (no.211014)andScotland(no.SC038698). ©TheInstitutionofEngineeringandTechnology2022 Firstpublished2021 ThispublicationiscopyrightundertheBerneConventionandtheUniversalCopyright Convention.Allrightsreserved.Apartfromanyfairdealingforthepurposesofresearch orprivatestudy,orcriticismorreview,aspermittedundertheCopyright,Designsand PatentsAct1988,thispublicationmaybereproduced,storedortransmitted,inany formorbyanymeans,onlywiththepriorpermissioninwritingofthepublishers,orin thecaseofreprographicreproductioninaccordancewiththetermsoflicencesissued bytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethose termsshouldbesenttothepublisherattheundermentionedaddress: TheInstitutionofEngineeringandTechnology MichaelFaradayHouse SixHillsWay,Stevenage Herts,SG12AY,UnitedKingdom www.theiet.org Whiletheauthorsandpublisherbelievethattheinformationandguidancegiveninthis workarecorrect,allpartiesmustrelyupontheirownskillandjudgementwhenmaking useofthem.Neithertheauthorsnorpublisherassumesanyliabilitytoanyoneforany lossordamagecausedbyanyerrororomissioninthework,whethersuchanerroror omissionistheresultofnegligenceoranyothercause.Anyandallsuchliability isdisclaimed. Themoralrightsoftheauthorstobeidentifiedasauthorsofthisworkhavebeen assertedbytheminaccordancewiththeCopyright,DesignsandPatentsAct1988. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisproductisavailablefromtheBritishLibrary ISBN978-1-83953-263-4(hardback) ISBN978-1-83953-264-1(PDF) TypesetinIndiabyMPSLimited PrintedintheUKbyCPIGroup(UK)Ltd,Croydon Contents Abouttheauthors xv Listofacronyms xvii Listofsymbols xix 1 Introduction 1 1.1 Abriefhistory 2 1.2 Drawbacksinusingrare-earthPMs 2 1.3 IncreasinginterestinSynchronousReluctancemachines 4 2 Magneticmaterials 7 2.1 Ferromagneticmaterials 9 2.2 Permanentmagnets 11 2.2.1 B–H Loopandmagnetizationcharacteristic 12 2.2.2 Temperatureeffects 13 2.2.3 Simplemagneticcircuits 14 2.2.4 FiniteelementsimulationsofPM 16 2.3 Bondedmagnets 17 2.4 BMspreparation 18 2.4.1 Compressionmolding 18 2.4.2 Injectionmolding 18 2.5 BMsmagnetizationandcharacterization 19 2.5.1 Magnetization 19 2.5.2 Magneticcharacterization 20 2.6 Lossesinmagneticmaterials 20 2.6.1 Hysteresislosses 21 2.6.2 Eddycurrentlosses 22 2.6.3 Measuringtheironlosses 22 3 Synchronousreluctancemotorgeometrydrawing 27 3.1 Fluidflux-barrierrotorgeometry 27 3.1.1 Flowpastacylinder 28 3.1.2 Conformalmapping 29 3.1.3 Computationofflux-barrierbasepoints 29 3.1.4 Outerbasepoints 31 3.1.5 Flux-barriersidelinepoints 33 3.1.6 Examples 33 viii Synchronousreluctancemachines 3.2 Segmentedflux-barrierrotor 34 3.2.1 Flux-barrieredgesidentification 34 3.2.2 Flux-barrierendfillet 36 3.2.3 Radialribs 37 3.2.4 MiddlePMslot 37 3.2.5 Flux-barrieredgesfillet 38 3.2.6 Automaticsegmentedflux-barrierdrawingalgorithm 39 3.2.7 Examples 40 3.3 Flux-barriersandironchannelsdesign 40 3.3.1 Magneticinsulationratiok 41 air 3.3.2 Ironchannelwidthsdesign 42 3.3.3 Flux-barrierthicknessesdesign 43 3.3.4 Flux-barrierinnerandoutermiddleradii 44 3.3.5 Automaticdrawingalgorithm 45 4 Reluctance network model of high-speed synchronous reluctance machines 47 4.1 Improvedreluctancenetwork 48 4.1.1 Statorandairgapmagneticnetwork 48 4.1.2 Rotormagneticnetwork 49 4.2 Finiteelementanalysisresults 50 4.3 Resultscomparison 51 4.3.1 Simplifiedreluctancenetworkresults 51 4.3.2 Improvedreluctancenetworkresults 51 4.4 Discussion 53 5 Nonlinearanalyticalmodelforsynchronousreluctancemachines 55 5.1 Developmentoftheanalyticalmodel 55 5.2 Analyticalmodel 59 5.3 Rotormagneticpotentialscomputation 60 5.3.1 Reluctanceofthefluxbarriers 62 5.3.2 Reluctanceofpartialair-gap 62 5.3.3 mmfgeneratorexpression 62 5.3.4 Air-gapfluxdensity 63 5.3.5 Torquederivation 64 5.3.6 Toothfluxdensity 65 5.3.7 Statoryokefluxdensity 65 5.3.8 Rotorfluxes 66 5.4 Radialironribscomputation 68 5.4.1 Simplifiedmethod 68 5.4.2 Accuratemethod 69 5.5 Computationofthesleevethickness 70 5.6 AnalyticalmodeloftheSYRmotor 71 5.6.1 d-Axisinductancecomputation 71 5.6.2 q-Axisinductancecomputation 72 5.6.3 Torqueandpowerequations 75 Contents ix 5.7 Analyticalmodelwithsaturation 76 5.7.1 Rotorchannelandislandsmagneticvoltagedrop 77 5.7.2 Statorteethandyokemagneticvoltagedrops 78 5.7.3 Totalmagneticvoltagedropandsaturationfactor 80 5.8 Torquemaps 80 5.9 Discussion 83 6 Designcriteriaofflux-barriersinsynchronousreluctancemachines 85 6.1 Thesimplifiedanalyticalmodel 85 6.1.1 Applicationofanonlinearmodel 86 6.1.2 Simplificationofthemodel 86 6.2 Oneflux-barrierrotor 87 6.2.1 Practicalresults 90 6.2.2 FEvalidation 91 6.3 Twoflux-barrierrotor 93 6.3.1 Practicalresults 94 6.3.2 FEvalidation 94 6.4 Threeflux-barriersrotor 97 6.4.1 FEvalidation 98 6.5 Designofasymmetricflux-barriersinSyRM 99 6.5.1 Determinationofsolutionsgettingminimumtorque harmonic 99 6.5.2 Combinationofminimasolutions 101 6.5.3 Combinationsforoneflux-barrierrotorandvalidation 102 6.6 Rotorwithtwoflux-barriersperpole 103 6.6.1 Validations 105 6.7 Experimentalmeasurements 106 6.8 Discussion 108 7 StructuralanalysiswithGetDP 109 7.1 BriefpresentationofGetDP 109 7.2 Mathematicalformulationforstructuralanalysis 109 7.2.1 Basicequations 111 7.3 Cantileverbeamwithsingleloadattheend 112 7.3.1 Analyticalsolution 112 7.3.2 GetDPsolution 113 7.3.3 Results 117 7.4 Cantileverbeamwithdistributedload 117 7.4.1 Analyticalsolution 118 7.4.2 GetDPsolution 118 7.5 Rotatinghollowdisk 119 7.5.1 Analyticalsolution 120 7.5.2 GetDPsolution 121 7.6 RotatingSyRrotorgeometry 125 7.6.1 Modelgeometry 126 7.6.2 Results 126