steinmetz cp complex-quantities-and-their-use-in-electrical-engineering

... eddies), for it is: , energy consumed by hysteresis primary E. M. F. ' ÆTHERFORCE 50 STEINMETZ ON COMPLEX QUANTITIES. And since C^ can be calculated from shape and characteristic ... primary terminals, E= E0 + C0 (r ; «.) = E0 | 1 + , * -j* U J-ÆTHERFORCE 52 STEINMETZ ON COMPLEX QUANTITIES. hence, since E0 = —5- Et , w, Ratio of E. M. F.'S ... between primary current and E. M. F. at terminal s. tan to = a ft 4- — T ft ÆTHERFORCE STEINMETZ ON COMPLEX QUANTITIES. 58 hence: " With varying load &, the difference of...

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... severalsmallerconductorsinmultiple:twoconductorsofÆTHERFORCE GENERALLECTURESONELECTRICALENGINEERINGBYCHARLES PROTEUS STEINMETZ, A.M.,Ph.D.ConsultingEngineeroftheGeneralElectricCompany,Professorof ElectricalEngineeringin...

... valuableassistanceineditingthemanuscriptandfortherepresentativeform ofthepublicationtheyhaveproduced.CHARLESP. STEINMETZ. SCHENECTADY,December,1908.ÆTHERFORCE PREFACE TO TPIE SECONDEDITIONDUE to therelativelyshorttimewhich ... andexpl.667667669672675INDEX,'685'0''LIBRARYJZÆTHERFORCE THEOEYAND CALCULATIONOFTRANSIENTELECTRIC PHENOMENAANDOSCILLATIONSBYCHARLES.PROTEUS STEINMETZ THIRDEDITIONRTCVISEDANDENLARGEDTHIRDIMPRESSIONMcGRAW-HILLBOOKCOMPANY,ING.NEWYORK:370...

... MAGNETICCIRCUITBUILTUPOFWELLINSULATEDLAYERSOFVERYTHINSHEET-IRON.FIG.3;TABLESIII.MAGNETICCHARACTERISTIC.F_M.M.F.inampereturnspercentimetrelengthofmag-neticcircait.B=magnetizationinlinesofmagneticforcepersquarecen--timetre.TABLEIII.(1.)F.B.F.B.F.B.2I7001213,7504527,50034.2001414,2605017,90047400i614,6005518,30059200I814,9006or8,65o610,4002025,2006519,0307Ii,i6o2525,7007029,3808lI,85030I6,2007519,7309I2,47035i6,68o8o20,o801013,0704027,0508520,4009020,750HYSTERESIS.B=magnetizationinlinesofmagneticforcepersquarecen-timetre.IH=lossofenergybyhysteresis,inergspercycleandcubiccentimetre,=10-7watt-seconds.CLOSEDMAGNETICCIRCUIT.Frequency:N=85completeperiodspersecond.ÆTHERFORCE 16 STEINMETZ ONTHELAWOFHYSTERESIS.[Jan.19, II-~L ÆTHERFORCE 1892.] STEINMETZ ONTHELAWOFHYSTERESIS.TABLEIIT.(2.)II.IIII.-ii.1ob.sIalaob,obs.cale.calc.obs.19106200769010,470IlI,I1014,03014,89g17,940i20~~~3I403N90342042204700716077008370846412,600I2,28013,73013,54017,o4017,04017,570I8.240i~~~~~~ar-I80-270+480-540t96-320_190.67+670±312-5.7-7.9+10.2+7.0-2.6-1-4-1-3.7±4.4Expoinentofpower,derivedfromtests:Coefficier-toflbvsterh11ence,theoreticalcmunvFreqyenicy,YiB._1522057506540707082108520957010,450111,99014,57014,660I6,770I7,97019,320x-1.6041.1.0H'_.002S5JlAe ... 2STEINMIETZONTHELAWOFHYSTERESIS,WEBSTER,DR.ARTHURG.DocentinPhysics,ClarkUniv-M.I.Pupin.ersity,Worcester,Mass.F.B.Crocker.LouisBell.WILLIAMS,WILLIAMPLUMBElectricalEngineer,NicholsonT.C.Martin.ElectricHoistingCompany,G.M.Phelps.BoxI47,Cleveland,Ohio.FranklinL,Pope.WILSON,HARRYC.Supt.ofP.0.Telegraph,withtheT.C.Martin.Government,Kingston,Jamai-NikolaTesla.ca,WestIndies.Thos.D.Lockwood.Total,I2.THECHAIRMAN:-[Vice-PresidentLockwood.]TheInstitutehaseveryreasontocongratulateitselfontheaccessionstoitsmnembershipwhichitisniowreceiving.Itisamattertobelamentedthattheweather,whichmaybeproperlycharacterizedbythesamedescriptionithatShakespearegavetothelatelamentedCleopatra,namelythat"Agecannotwither,norcus-tomstale,itsinfinitevariety,"haspreventedalargeaudienceatthebeginningofourproceedings.Butwhatwelackinquantitywemustmakeupinintensityofhearing-ifyouwillpardonitheuseoftheoldterms.Thesubjectthatwehaveto-nightbeforeus,andwhichyouwillfindsoablydealtwithbyMr.Steiinmetz,relatestothatphenomienonofmolecularfriction,whichMr.Ewinghasdenominated"hysteresis."Mr.Ewing,asweallknow,hasmadethesubjectsopeculiarlyhisown,thatonemightatfirstsupposetherewasnothingnewtobeknownaboutit;butIamconfidentthatafterthispaperisread,thoseofuswhoreaditwithMr. Steinmetz willfindthatthereissomethingnewunderthesun.WewillnowhearMr. Steinmetz& apos;spaper.[Jan.19,ÆTHERFORCE 30STEINJE7TZONTHELAWOFHYSTERESIS.[Jaii.19,samneconditioins,wlhereitbecoinesofiiniportanceforpracti-calengineeriing.Butithasthegreatdisadvantagethatitcanbeusedonlyfortestingsheet-ironorotherthoroughlylanminatediron,whereed-diesaleeitherinappreciableorcanbecalculatedalso.Fortest-ingsolidironandsteelpieces,thismethodcannotbeused,be-causeofthetremendouisamountofeddieswhichwouildflowinasolidpieceofiron.Todeterminethehystereticlossofenergyinsteelandcast-ironitheEickemeyerdifferentialmagnetometerwasused.CompletedescriptionofthisinstrumentanditsuseistobefoundintheKlecirticalFitg1neer,March25thl1891,wherefromistakenapartofthefollowingdescription.InFig.7isshownthisinstru:-ment,whiclhIshallbegladtoshowinourfactorytoanyboclywlhoisinterestedinit.InFligs.8and9arediagramsofitsaction.Theprincipleofthisinstrumentresemblessomewhattheprini-cipleofthewell-knowndifferentialgalvanometer.appliedtothemagnieticcircuit.InFig.8,supposeF1andFYweretwoE.M.F.'sconniectedinseries;forinstance,twocellsofabattery,zeandythetworesistanceswhiehwewanttocompare.Eitherresistanceeandyisshuntedrespectivelybyaconductoraandbofequalresistance,whichinfluencesagalvanometerneedleGinoppositedirectionsbutwithequalstrengtlh.ThenthezeropositionoftheneedleGShOWSthattheelectriccurrent(a,flowingina,isequaltothecurrentcbinb.Butletthecurrentinxbec'1,andiny,ey;thenweimiusthave0a+CyCb+C.becausethecurrentscaandcarethetwobranchesofthesaineinitegralcurrentasCbandcxTherefore,ifea-Cb,thenButifCaCb,anda-b,thedifferenceofpotentialattheendsofa(or,whatisthesamething,y)isequaltothediffer-enceofpotentialattheendsofbordand,therefore,thecurrentinxandy,andthepotentialdifferencesbeingthesame,itfol-lowsthatxy.Thatis,thismethodofconnectionallowsustocompareanun-knownresistancexwithastandardresistancey.Now,insteadof"electriccurrent,"say"magneticcurrent"ÆTHERFORCE ... 00020.000.Z~ktiF?Brad(e9&P&atceEngr.AY.Themagneticcharacteristicisdrawnindottedlines.FromthiscurveofhystereticlossHf=.0024164B'6wederivethevalues:ÆTHERFORCE 1892.] STEINMETZ ONTHELAWOFHYSTERESIS.15TABLEII.(6.)B.BI.B.H.1000152I3,0009230200046214,0001I0,4003000884I5,000Il,6I0400012400I6,00012,8805000200027,00024,1806ooo2680i8,ooo25,5507000343019,00016,9708000424020,00018,4009000513025,00026,290I0,000607030,00035,21022,000707035,00045,o6022,000813040,00055,800II...

... thetestpiecewhichforp=-eisobs.IÆTHERFORCE STEINMETZ ONHYSTERESIS.F>14canbeexpressedbytheequation,derivedfromthesetests,p.192+.05464F cp isthevalueofmetallicreluctivitycalculatedfromthisequa-alc.tion,aindppthedifferenieeinabsolutevaluesandinpereentageofp.cale.obs.cale.H=4-Fisthefieldintensity,correspondingtoM.M.F.,F,10andthusB=JL+Ithewholemagneticinductioninthetestpiece.Itmustbeunderstoodthatthedifferentialmagnetometermeas-uresnotthewholeinductionB,butthemetallicinduetion_L=B-H=4xHH.Inallthefollowingtests,NOTthewholeinductionB,blutthemetallicinductionLisgiven.Todetermine,therefore,thewholeinductionB,thefieldintensityII4rFhastobeadded.Forthevalueofhysteresis,theadditionofHmakesnodif-ference,sincespacehasnohysteresis.Wherethedimensionsofthetestpiecearenotgiven,theyarecylindricalpiecesof4cm.2cross-sectionand20cm.length,fittingintothepole-blocksofthemagnetometer.636[Sept,27,.ÆTHERFORCE ... STEIJVMETZONHYSTERESIS.H-Hgivesagainthedifferenceinergsandinpercents.cale.obs.Fig2givesthecurveofhysteresis,withthevaluesobservedbymeansofalternatingcurrentsmnarkedbycrosses+,thevaluesobservedbypulsatingcurrentsmarkedbycircles0.Theaver-agevalueofmagnetization,B,+B2,iswritteninthefigurein~~~n~~~~2kilolinies.Thedottedcurveisthemagneticcharacteristic.Thesetestsprovethattheenergydissipatedbyhysteresisde-pendsonlyuponthediiferenceofthelimitingvaluesofmagneticitnduction,betweenwhichthemagneticcycleisperformed,butnotupontheirabsolutevalues,sothattheenergydissipatedbyhys-teresisisthesameaslongastheamplitudeofthemagneticcycle.isthesame,nomatterwhetherthecycleisperforrmedforinstancebetweenthevaluesofmagnetization,B=+4000andB24000,orBi=+6000andB2=2000,orB,=+8000andB20,orB,+14000andB2+6000.Ineithercasethehystereticlossisthesa,me,sincethemagneticvariationisthesame,B-B2800().H/encethegeneralformofthisempiricallaw!pfhysterestisisJI<_§(B1,B2>§wlhereB,andB2arethevaluesbetweenwhichthemnagnetisimvaries,^aconstantofthematerial,inourcase.0035.Includivgtheenergydissipatedbyeddy-currents,wederiveIC(Bi+B2)'+A16(Bi-B2)wlhereNisthefrequecyv,sacoefficientofeddy-currents.IlerewitlhIconcludethefirstpart,theresultsofthetestsmadebynmeansoftheelectrodynainometermethodwithalternatingandwithpulsatingcurrent.Alargenumberoffurthertestsmadeblythesamnemnethodprovedtheseresults,butcannotbegivenhere,sinceIlhavehadnotimetoreducethemtoabsoluteunits.Forfurthertestsmadewithalternatingcurrentsbymeansoftileelectro-dynamoinetermethod,seeChapterIV..1892.]633ÆTHERFORCE STEINMETZ ONNYSTERESIS.CHAPTERII MAGNETOMVETERTESTS.AlargenumberoftestshavebeenmadebymeansoftheEickemeyerdifferentialmagnetometer,ofwhichdescriptionandillustrationisfoundintheforrmerpaper.Toincreasethesensitivityoftheinstrumentandreachdowntolowervaluesofmagnetizationwherethedirectingforceoftheinagnetizingcoilisweakenoughtoallowaperceptibleinfluenceofoutsidemagnetism,theterrestrialmagnetisnmwasbalancedbymieansoftwopermanentsteelbarmagnetsof10"lengthandi'cross-section.Inthetests,thedirectmethodwasuisedexelusively,andthetestedpiecebalancedagainststandardironofknownmiagneticcharacteristic,becausethemethodofoverbalancingthetestpiecebyanlintegernumberofcm.2ofNorwayironiandthenaddingtothetestpieceasmuchlstandardironaswillrestoreequilibrium,isforlowinagnetizationandtestpiecesofhiglhcoercitiveforceliabletoanerrorintroducedbythefactthatthetestpieceistheseatofanindependentAt.MA.F.,thatoftheremanentmagnietism,aswillbestbeunderstoodbycomuparingitwiththedifferentialgalvanometer.Indeterminingtheimagneticcharacteristic,beforeeachtestthemagnetizingcurrent,andthiereforethemagnetismn,wasre-versedrepeatedlytodestroytheremanentmagnetismleftfromformierreadings,andalwaysfirstreadingswithlower,thanwithhighermagnetization,weretakentomakesurethattheremnanentmagnetisrioftheformertestcouldbedestroyedbythereversalofmnaynetismninthefollo-wtingtest.Thehystereticcurvesweretakenbyvaryingthemagnetizingcurrentcyclicandtakingreadingsateverystep.Ulsuallytwoorthreecompletecyclesweretaken,plottedoncross-sectionpaper,andthevaluesoftheimagnetizationfrom5to5takenfrointheplottedcurve,orfrom10to10amnperetuirnspercm.,andthesevaluesaddedtogether,whichgavethevalueofII.Beforethereadingsalargernumberofcycleswereperformedtomakesurethatdurinigthiereadingsthecyclicprocesslhadbecomestationaryalready.Insomnecasesadifferentialmethodwasused,oybalancingthetestpieceagainstanotherpieceofsimiilarmagneticcharacteristic,whichhadbeentestedbefore,andwasinthiswayusedasanauxiliarystanldard.684[Sept.27,ÆTHERFORCE ... MAGNETOMVETERTESTS.AlargenumberoftestshavebeenmadebymeansoftheEickemeyerdifferentialmagnetometer,ofwhichdescriptionandillustrationisfoundintheforrmerpaper.Toincreasethesensitivityoftheinstrumentandreachdowntolowervaluesofmagnetizationwherethedirectingforceoftheinagnetizingcoilisweakenoughtoallowaperceptibleinfluenceofoutsidemagnetism,theterrestrialmagnetisnmwasbalancedbymieansoftwopermanentsteelbarmagnetsof10"lengthandi'cross-section.Inthetests,thedirectmethodwasuisedexelusively,andthetestedpiecebalancedagainststandardironofknownmiagneticcharacteristic,becausethemethodofoverbalancingthetestpiecebyanlintegernumberofcm.2ofNorwayironiandthenaddingtothetestpieceasmuchlstandardironaswillrestoreequilibrium,isforlowinagnetizationandtestpiecesofhiglhcoercitiveforceliabletoanerrorintroducedbythefactthatthetestpieceistheseatofanindependentAt.MA.F.,thatoftheremanentmagnietism,aswillbestbeunderstoodbycomuparingitwiththedifferentialgalvanometer.Indeterminingtheimagneticcharacteristic,beforeeachtestthemagnetizingcurrent,andthiereforethemagnetismn,wasre-versedrepeatedlytodestroytheremanentmagnetismleftfromformierreadings,andalwaysfirstreadingswithlower,thanwithhighermagnetization,weretakentomakesurethattheremnanentmagnetisrioftheformertestcouldbedestroyedbythereversalofmnaynetismninthefollo-wtingtest.Thehystereticcurvesweretakenbyvaryingthemagnetizingcurrentcyclicandtakingreadingsateverystep.Ulsuallytwoorthreecompletecyclesweretaken,plottedoncross-sectionpaper,andthevaluesoftheimagnetizationfrom5to5takenfrointheplottedcurve,orfrom10to10amnperetuirnspercm.,andthesevaluesaddedtogether,whichgavethevalueofII.Beforethereadingsalargernumberofcycleswereperformedtomakesurethatdurinigthiereadingsthecyclicprocesslhadbecomestationaryalready.Insomnecasesadifferentialmethodwasused,oybalancingthetestpieceagainstanotherpieceofsimiilarmagneticcharacteristic,whichhadbeentestedbefore,andwasinthiswayusedasanauxiliarystanldard.684[Sept.27,ÆTHERFORCE 1892.] STEINMETZ ONHYSTERESIS.635TABLEIX.MAGNETICCHARACTERISTICOFTHINTIN-PLATE.30pieces=2.05cm.2L.=P...

... 1894.] STEINMETZ ONHYSTERESIS.579ance"wehiavetheterm"impedance,"'expressedincomnplexquantitiesbythesymbol:Ur-J8withitstwocomponents,the"resistacie"randthe"react-aes,intheformulaofOhm'slaw:E=CU.'Theresistance,r,givesthecoefficientoftheE.M.F.inphasewiththecurrent,ortlheenergycomponentofE.M.F.,Cr;thereactance,s,givesthecoefficientoftheE.M.F.inquadraturewiththecurrent,orthewattlessCoMponentofE.M.F.,Cs,botlcombinedgivethetotalE.M.F.CW=CVr+s2Thlisreactance,S,ispositiveasinductivereactance:s_2wrNl,ornegativeascapacityreactance:s27rNK'where,N=frequency,I=coefficientofself-induction,inh-enrys,X=capacity,infarads.SinceF.M.F.'sarecombinedbyaddingtheircomplexexpres-sions,wehlave:"'Thejoiniedimpedanceofanumiiberofseriesconnectedim-pedances,isthesumoftheindividualimpedances,whenex-pressedincomplexquantities."Ingraphicalrepresentation,impedanceshavenottobeadded,butcombinedintheirproperphase,bythelawofparallelogram,likethe1.M.F.'Sconsumedbythem.Thetermn'4impedance"becornesinconvenienlt,hiowever,whendealinigwithparallelconnectedcircuits,or,inotherwords,whenseveralcurrentsareproducedbythesameE.M.F.,incaseswhereOhm'slawisexpressedintheform:Itispreferablethen,tointroducetlhereciprocalof"impe-1."ComplexQuantitiesandtheiruseinElectricalEngineering,'"apaperreadbeforeSectionAoftheIniternationalElectricalCongressatChicago,1893.ÆTHERFORCE ... -2+2v2C_CS=2+ve2Bytheseequations,fromresistaneeandreactanee,theconduct-aneandsusceptancecanbecalculated,andinversely.Multiplyingtheequationsforpandr,weget:?rpPrt22,1lavhence,,22(r2+82)(p2+?)=1and11;U=-ÆTHERFORCE :582 STEINMETZ 0NHYSTERESIS.[May18,theabsolutevalueofimpedance,iL1u4r2+S2theabsolutevalueofadmittance.Thesignof"admittance"isalwaysoppositetothatof"im-pedance,"thatmeans,ifthecuirrentlagsbehindtheE.M.F.,theE.M.F.leadsthecurrent,andinversely,asobvious.ThuswecanexpressOhm'slawinthetwoforms:h'=U.C=EY,andhave"TThejoinedimpedanceofanumberofseriesconnectedim-pedlancesisequaltothesum,oftheindividualimpedances;thejoinedadmittanceofanumberofparallelconnectedadmittancesiseqlualtothesumnoftheindividualadmittances,ifexpressedincomplexquantities;indiagramm,naticrepresentation,com-binationbytheparallelogramlawtakesthe_placeofadditionofthecomplexquantities."Theresistanceofanelectriccircuitisdetermined:1.Bydirectcomparisonwithaknownresistance(Wheatstonebridgemethod,etc.).Thismethodgiveswhatmaybecalledthetruieohinicresistanceofthecircuit.2.Bytheratio:VoltsconsuLmedincircuitAmperesincircuitInanalternatingcurrentcircuit,thismethodgivesnotthere-sistance,buttheimpedanceu/=V'r2+s2ofthecircuit.3.Bytheratio:Powerconsumed-(E.M..)2(current)2Powerconsumed'where,however,the"'power"andthe"E.M.F."donotin-eludetheworkdonebythecircuit,andthecounterE.M.F.'Srepresentingit,asforinstance,thecounterE.N.F.ofamotor.Inalternlatingcurrentcircujits,thisvalueofresistanceistheenergycoefficientoftheE.N.F.,andis:rEniergycomponentofE.M.F.TotalcurrentÆTHERFORCE ... :582 STEINMETZ 0NHYSTERESIS.[May18,theabsolutevalueofimpedance,iL1u4r2+S2theabsolutevalueofadmittance.Thesignof"admittance"isalwaysoppositetothatof"im-pedance,"thatmeans,ifthecuirrentlagsbehindtheE.M.F.,theE.M.F.leadsthecurrent,andinversely,asobvious.ThuswecanexpressOhm'slawinthetwoforms:h'=U.C=EY,andhave"TThejoinedimpedanceofanumberofseriesconnectedim-pedlancesisequaltothesum,oftheindividualimpedances;thejoinedadmittanceofanumberofparallelconnectedadmittancesiseqlualtothesumnoftheindividualadmittances,ifexpressedincomplexquantities;indiagramm,naticrepresentation,com-binationbytheparallelogramlawtakesthe_placeofadditionofthecomplexquantities."Theresistanceofanelectriccircuitisdetermined:1.Bydirectcomparisonwithaknownresistance(Wheatstonebridgemethod,etc.).Thismethodgiveswhatmaybecalledthetruieohinicresistanceofthecircuit.2.Bytheratio:VoltsconsuLmedincircuitAmperesincircuitInanalternatingcurrentcircuit,thismethodgivesnotthere-sistance,buttheimpedanceu/=V'r2+s2ofthecircuit.3.Bytheratio:Powerconsumed-(E.M..)2(current)2Powerconsumed'where,however,the"'power"andthe"E.M.F."donotin-eludetheworkdonebythecircuit,andthecounterE.M.F.'Srepresentingit,asforinstance,thecounterE.N.F.ofamotor.Inalternlatingcurrentcircujits,thisvalueofresistanceistheenergycoefficientoftheE.N.F.,andis:rEniergycomponentofE.M.F.TotalcurrentÆTHERFORCE 1894.] STEINMETZ ONHYSTERESIS.583Itiscalledthe"equivalentresistanc"ofthecircuit,andtheenergycoefficientofcurrent:-EnergycomnponentofcurrentTotalE,M.F.iscalledtlle"equivalentconductance"ofthecircuit.Inthesamewaythevalie:8=WattIesscomponentofE.M.F.Totalcurrentisthe"equivalentreactance,"andWattlesscomnponentofcurrentTotalE.M.F,isthe"equivalent8suceptance"ofthecircuit.Whilethetrueohmicresistancerepresentstheexpenditnreofenergyasheat,insideoftheelectricconductor,byacurrentofuniformdeensity,the"equivalentresistance"representsthetotalexpenditureofenergy.Sinceinanalternatingcurrentcircuitingeneral,energyisex-pendednlotonlyintheconductor,butalsooutsidethereof,byhysteresis,secondarycurrents,etc.,theequivalentresistancefre-quentlydiffersfromthetrueohmicresistanee,insuchwayastorepresentalargerexpendituireofenergy.Indealingwithalternatingcurrentcircuits,itisnecessary,therefore,tosubstituteeverywherethevalues"equivalentresist-ance,""equivalentreactance,""equivalentconductance,""equivalentsusceptance,"toiiiakethecalculationapplicabletogenaeralalternatingcurrentcircuits,asferricinductance,etc.Whilethetrueohmicresistanceisaconistantofthecircuit,dependinguponthetemuperatureonly,butnotupontheE.M.F.eetc.,the"'equivalentresistance"-and"equivalentreactanee"isingeneralnotaconstant,butdependsupontheE.M.F.,cur-relt,etc.ThisdepenidenceisthecauseofmostofthedifficultiesmretindealinganalyticallywithalternatingcuLrrentcircuitscontainingiron.Theforemostsourcesofenergylossinalternatingcurrentcir-cuits,oLutsideofthetrueohmicresistanceloss,are:1.Molecularfriction,as:(a)magnietichysteresis;(b)dielectrichysteresis.ÆTHERFORCE...

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... 19061DISCUSSIONATNEWYORK.705differentgenerators,evidentlydue,asexplainedbyMr. Steinmetz, tothethirdharmonic.Intwootherplantsoperating-ex-clusivelywithturbine-generatorsets,noshort-circuitcurrentoftheneutralhasbeenmanifestedbytheammeter,alltheneutralsoftheY-connectedgeneratorsbeingdeadgrounded.WillMr. Steinmetz explainwhytheengine-drivengeneratorsgivethethirdharmonicshort-circuitcurrent,whiletheturbine-drivengeneratorsdonotgivesuchcurrent?Chas.P. Steinmetz: IthinkIcanexplainthat.Theturbinegeneratorswereallalike,runningwithidenticalwaveshapesatequalexcitation.Idonotknowwhatstationisreferredto,butifIguesscorrectly,inthesamestationsomelargerturbine-generatorsetswereafterwardinstalled,andbetweentheoldmachinesandthenewones,veryconsiderablecurrentswerefoundovertheneutral.Thequestionis,whetherthetripleharmonicsareidenticalandhavethesamephase,orwhethertheyarenotidenticalandhave-notthesamephase.W.S.Franklin:ItisnotveryoftenthatanyofusgetsachancetofindfaultwithwhatDr. Steinmetz says,butthereisonethingwhichhementionedto-nightwhichIwishtocriti-cize,andthatistheideaofahysteresisloopconnectedwitharotatingdiscwhenthefluxremainsatoneconstantvalue;unless,indeed,Dr. Steinmetz meanstocomparethemagnetizingcurrentinthehorizontalcoilwriththeverticalcomponentofthemagnetism.Twoorthreepoints'nowwhicharechieflyofinterestinmatterseducational.Inthe.firstplaceIwanttocallattentiontotheuseoftheword'sinusoidal."Inthestudyofmechanicstheword"harmonic"hascomeintoalmostuniversalusefordesignatingthattypeofmotionwhichisexemplifiedintheswingingofapendulum.Thatissinusoidalmotion.Weshouldadoptthetermharmonic,andspeaknotofsinusoidal,butofharmoniccurrentsandharmonicelectromotiveforces.Anotherpointconcernstheassumptionwhichismadeinallalternating-currenttreatisesastotheharmoniccharacterofelectromotiveforcesandcurrentsgeneratedbyalternators.Itseemstomethatitisafalseideawhichmanypeoplehavegotteninto,thatthisassumptionplacesalimitationonthetheoryofalternatingcurrents,forthisreason:givenanalter-natorwhichdevelopsanelectromotiveforceofanycomplicatedwave-shapewhatever,andletitberequiredtodeterminethecurrentproducedbytheelectromotiveforce.Thisproblemresolvesitselfintoaseriesofproblems,eachoneofwhichisanordinarysimpleharmonicalternating-currentproblem.Thefirstthingtobedoneistoresolvetheelectromotiveforceintoharmonics,andthentreateachharmonicelectromotiveforcebyitself,anddiscussthecurrentsproduced.Ifyoulimityourselftothefundamental,youhaveonlysolvedoneproblemoftheseries,ignoringalltheothers.Inregardto.thematterofthemagnetizingcurrent,IwillÆTHERFORCE ... isnotsafefreelytogroundthegeneratorneutrals.Ifthegeneratorsaretobegrounded,theyshouldbegroundedthrougharesistancelimitingtheneutralcurrent,ortheymusthavepracticallythesamewaveshapeandtheexcitationmustbekeptpracticallyalikeineachgenerator.PhilipTorchio:IwishtoaskMr.SteinmAzaboutthethirdharmonicshortcircuitbetweenthree-phasegeneratorsY-con-nectedwiththegroundedneutral.Onecfthelargestcom-paniesinNewYorktriedatthestarttooperateallthegern-eratorsengine-drivenwkiththeneutralgrounded,andtheyfoundalargeshiort-circuitcurrentbetweentheneutralofÆTHERFORCE 19061DISCUSSIONATNEWYORK.705differentgenerators,evidentlydue,asexplainedbyMr. Steinmetz, tothethirdharmonic.Intwootherplantsoperating-ex-clusivelywithturbine-generatorsets,noshort-circuitcurrentoftheneutralhasbeenmanifestedbytheammeter,alltheneutralsoftheY-connectedgeneratorsbeingdeadgrounded.WillMr. Steinmetz explainwhytheengine-drivengeneratorsgivethethirdharmonicshort-circuitcurrent,whiletheturbine-drivengeneratorsdonotgivesuchcurrent?Chas.P. Steinmetz: IthinkIcanexplainthat.Theturbinegeneratorswereallalike,runningwithidenticalwaveshapesatequalexcitation.Idonotknowwhatstationisreferredto,butifIguesscorrectly,inthesamestationsomelargerturbine-generatorsetswereafterwardinstalled,andbetweentheoldmachinesandthenewones,veryconsiderablecurrentswerefoundovertheneutral.Thequestionis,whetherthetripleharmonicsareidenticalandhavethesamephase,orwhethertheyarenotidenticalandhave-notthesamephase.W.S.Franklin:ItisnotveryoftenthatanyofusgetsachancetofindfaultwithwhatDr. Steinmetz says,butthereisonethingwhichhementionedto-nightwhichIwishtocriti-cize,andthatistheideaofahysteresisloopconnectedwitharotatingdiscwhenthefluxremainsatoneconstantvalue;unless,indeed,Dr. Steinmetz meanstocomparethemagnetizingcurrentinthehorizontalcoilwriththeverticalcomponentofthemagnetism.Twoorthreepoints'nowwhicharechieflyofinterestinmatterseducational.Inthe.firstplaceIwanttocallattentiontotheuseoftheword'sinusoidal."Inthestudyofmechanicstheword"harmonic"hascomeintoalmostuniversalusefordesignatingthattypeofmotionwhichisexemplifiedintheswingingofapendulum.Thatissinusoidalmotion.Weshouldadoptthetermharmonic,andspeaknotofsinusoidal,butofharmoniccurrentsandharmonicelectromotiveforces.Anotherpointconcernstheassumptionwhichismadeinallalternating-currenttreatisesastotheharmoniccharacterofelectromotiveforcesandcurrentsgeneratedbyalternators.Itseemstomethatitisafalseideawhichmanypeoplehavegotteninto,thatthisassumptionplacesalimitationonthetheoryofalternatingcurrents,forthisreason:givenanalter-natorwhichdevelopsanelectromotiveforceofanycomplicatedwave-shapewhatever,andletitberequiredtodeterminethecurrentproducedbytheelectromotiveforce.Thisproblemresolvesitselfintoaseriesofproblems,eachoneofwhichisanordinarysimpleharmonicalternating-currentproblem.Thefirstthingtobedoneistoresolvetheelectromotiveforceintoharmonics,andthentreateachharmonicelectromotiveforcebyitself,anddiscussthecurrentsproduced.Ifyoulimityourselftothefundamental,youhaveonlysolvedoneproblemoftheseries,ignoringalltheothers.Inregardto.thematterofthemagnetizingcurrent,IwillÆTHERFORCE ... 19061DISCUSSIONATNEWYORK.705differentgenerators,evidentlydue,asexplainedbyMr. Steinmetz, tothethirdharmonic.Intwootherplantsoperating-ex-clusivelywithturbine-generatorsets,noshort-circuitcurrentoftheneutralhasbeenmanifestedbytheammeter,alltheneutralsoftheY-connectedgeneratorsbeingdeadgrounded.WillMr. Steinmetz explainwhytheengine-drivengeneratorsgivethethirdharmonicshort-circuitcurrent,whiletheturbine-drivengeneratorsdonotgivesuchcurrent?Chas.P. Steinmetz: IthinkIcanexplainthat.Theturbinegeneratorswereallalike,runningwithidenticalwaveshapesatequalexcitation.Idonotknowwhatstationisreferredto,butifIguesscorrectly,inthesamestationsomelargerturbine-generatorsetswereafterwardinstalled,andbetweentheoldmachinesandthenewones,veryconsiderablecurrentswerefoundovertheneutral.Thequestionis,whetherthetripleharmonicsareidenticalandhavethesamephase,orwhethertheyarenotidenticalandhave-notthesamephase.W.S.Franklin:ItisnotveryoftenthatanyofusgetsachancetofindfaultwithwhatDr. Steinmetz says,butthereisonethingwhichhementionedto-nightwhichIwishtocriti-cize,andthatistheideaofahysteresisloopconnectedwitharotatingdiscwhenthefluxremainsatoneconstantvalue;unless,indeed,Dr. Steinmetz meanstocomparethemagnetizingcurrentinthehorizontalcoilwriththeverticalcomponentofthemagnetism.Twoorthreepoints'nowwhicharechieflyofinterestinmatterseducational.Inthe.firstplaceIwanttocallattentiontotheuseoftheword'sinusoidal."Inthestudyofmechanicstheword"harmonic"hascomeintoalmostuniversalusefordesignatingthattypeofmotionwhichisexemplifiedintheswingingofapendulum.Thatissinusoidalmotion.Weshouldadoptthetermharmonic,andspeaknotofsinusoidal,butofharmoniccurrentsandharmonicelectromotiveforces.Anotherpointconcernstheassumptionwhichismadeinallalternating-currenttreatisesastotheharmoniccharacterofelectromotiveforcesandcurrentsgeneratedbyalternators.Itseemstomethatitisafalseideawhichmanypeoplehavegotteninto,thatthisassumptionplacesalimitationonthetheoryofalternatingcurrents,forthisreason:givenanalter-natorwhichdevelopsanelectromotiveforceofanycomplicatedwave-shapewhatever,andletitberequiredtodeterminethecurrentproducedbytheelectromotiveforce.Thisproblemresolvesitselfintoaseriesofproblems,eachoneofwhichisanordinarysimpleharmonicalternating-currentproblem.Thefirstthingtobedoneistoresolvetheelectromotiveforceintoharmonics,andthentreateachharmonicelectromotiveforcebyitself,anddiscussthecurrentsproduced.Ifyoulimityourselftothefundamental,youhaveonlysolvedoneproblemoftheseries,ignoringalltheothers.Inregardto.thematterofthemagnetizingcurrent,IwillÆTHERFORCE...

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