transient behaviour of induction motors in island
TRANSCRIPT
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Transientbehaviourofinductionmotorsinislandconditionsduetointerruptionsin
theship’selectricalpowersupply
Bachelor’sdissertation
FacultatdeNàuticadeBarcelonaUniversitatPolitècnicadeCatalunya
Student:HarmanpreetSinghRattan
Director:
Dr.PauCasalsTorrens
Bachelor’sdegreeinMarineTechnologies
Barcelona,19thofOctoberof2017
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Summary
Thefocuspresentdissertationwasaproblemthatoccursinindustrialinstallationsandships.
Thesaidinstallationsexperienceovervoltageincaseofpowercut.Thisproblemisaresultof
installingcapacitivecompensationparalleltomotors.Thisdissertationstudiedthisproblem
withtwodifferentelectricmotorswidelyusedinbiginstallations.
The motors were tested in laboratory in different operational conditions; with different
connections (D and WYE), with different loads and without load and with and without
capacitivecompensation.Thecapacitorbank,sourceofcapacitivecompensation,wasalso
connectedinDandWYEduringthetests.
Theovervoltagewasobservedwithcapacitivecompensationonlywhenthecapacitorbank
wasconnectedinDandthemotorswereconnectedinWYE.Themechanicalloadontheshaft
hasdeterminedthepeakvalueofthetransientvoltageandthedurationofthewaveform.
The laboratory testing circuits, inwhich the overvoltagewas observed,were recreated in
Matlabtovalidatetheresultsobtainedinreal-world.Thesimulationresultswereverysimilar
totheirreal-worldcounterpartsin3ofthe4cases.
In conclusion, theovervoltagehasmanifestedwhen thevoltage receivedby thecapacitor
bankwassuperiorthanthemotor’s.Theloadhasalsoplayedanimportantroleindetermining
thepeakvalueoftransientofwaveform.
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Tableofcontents1 Introduction................................................................................................................8
2 Mathematicalmodel.................................................................................................102.1 Physicalaspects............................................................................................................10
2.1.1 Workingprincipleofamotor..........................................................................................11
2.2 Equivalentcircuit..........................................................................................................112.2.1 Approximantequivalentcircuits......................................................................................13
2.3 Characterizationofinductionmotor.............................................................................142.3.1 Blockedrotortest............................................................................................................16
2.3.2 No-loadtest.....................................................................................................................17
3 LaboratoryTesting....................................................................................................243.1 Testinginstallation........................................................................................................25
3.1.1 Electriccircuit..................................................................................................................30
3.2 Formula-basedanalysis.................................................................................................343.2.1 Dynamicanalysis.............................................................................................................35
4 Test’sresults.............................................................................................................364.1 Results’analysis............................................................................................................46
5 Matlabsimulation....................................................................................................475.1 Simulationresults.........................................................................................................51
5.1.1 Simulationresults’analysis..............................................................................................53
6 Conclusion................................................................................................................56
7 Bibliography.............................................................................................................57
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TableoffiguresFigure1:Motor'sparts............................................................................................................10
Figure2:Exactequivalentcircuit............................................................................................12
Figure3:Exactequivalentcircuitwithloadresistance...........................................................13
Figure4:Approximantequivalentcircuitwithoutload..........................................................14
Figure5:Approximantequivalentcircuitwithload................................................................14
Figure6:Squirrelcageinductionmotor..................................................................................15
Figure7:Woundrotorinductionmotor..................................................................................15
Figure8:(Right)Dconnectionand(Left)WYEconnection.....................................................15
Figure9:Testingcircuit(Source:Máquinaseléctricas:PauCasalsTorrens[1]).....................16
Figure10:TheVo^2-Pographofmotorno.1.........................................................................18
Figure11:TheVo^2-Pographofmotorno.2.........................................................................19
Figure12:Simulationofexactequivalentcircuitinno-loadcondition(motorno.1)............21
Figure13:Simulationofexactequivalentcircuitinblockedrotorcondition(motorno.1)...21
Figure14:Simulationofexactequivalentcircuitinno-loadcondition(motorno.2)............21
Figure15:Simulationofexactequivalentcircuitinblockedrotorcondition(motorno.2)...22
Figure16:Powertriangle........................................................................................................24
Figure17:Thecontactor.........................................................................................................26
Figure18:Thecapacitorbank.................................................................................................26
Figure19:Thetachometer(Onfarright),themechanicalbrake(Onfarleft)andtheammeter
(Behindthetachometer).................................................................................................26
Figure20:Theanalyser...........................................................................................................27
Figure21:DatawatchPro'smainwindow...............................................................................27
Figure22:Theanalysermountedintheprotectivecase........................................................28
Figure23:Connectiondiagramoftheanalyser......................................................................28
Figure24:Circuitimplementationoftheanalyser..................................................................29
Figure25:TheOscilloscope.....................................................................................................29
Figure26:ThemotorconnectedinD......................................................................................30
Figure27:ThemotorconnectedinWYE.................................................................................30
Figure28:MotorandcapacitorconnectedinWYE.................................................................30
Figure29:MotorconnectedinWYEandcapacitorbankinD.................................................30
Figure30:MotorconnectedinDandcapacitorbankinWYE.................................................31
Figure31:MotorandcapacitorconnectedinD.....................................................................31
Figure32:Phase-neutralconnectionofthecapacitorandthemotor....................................31
Figure33:AsynchronousMachine(SIunits)...........................................................................47
Figure34:Asynchronousmachine'sparameterswindow.......................................................48
Figure35:Three-phaseprogrammablevoltagesource..........................................................49
Figure36:Three-phaseload....................................................................................................49
Figure37:Three-phasebreaker..............................................................................................49
Figure38:Three-phaseV-Imeasurement...............................................................................50
Figure39:Voltagemeasurement............................................................................................50
Figure40:Scope......................................................................................................................50
Figure41:Step........................................................................................................................50
Figure42:Gain........................................................................................................................50
Figure43:Ground...................................................................................................................51
Figure44:Powergui................................................................................................................51
Figure45:Simulationcircuit....................................................................................................51
Figure46:Testno.5-Simulationresult..................................................................................52
Figure47:Testno.5-Labtestresult......................................................................................52
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Figure48:Testno.7-Simulationresult..................................................................................52
Figure49:Testno.7-Labtestresult.......................................................................................52
Figure50:Testno.30-Simulationresult................................................................................52
Figure51:Testno.30-Labtestresult....................................................................................52
Figure52:Testno.32-Simulationresult................................................................................53
Figure53:Testno.32-Labtestresult....................................................................................53
Figure54:Testno.34-Simulationresult................................................................................53
Figure55:Testno.34-Labtestresult....................................................................................53
Figure56:Transientthree-phasevoltagewaveform..............................................................54
Figure57:Transientwaveformofthethree-phasecurrent....................................................55
Figure58:TransientwaveformoftheRMS.............................................................................55
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TableoftablesTable1:Ratedvaluesofmotors..............................................................................................14
Table2:No-loadtestresults...................................................................................................18
Table3:Mechanicallossesofmotors.....................................................................................19
Table4:No-loadandblockedrotortests'results...................................................................20
Table5:Motors'parameters...................................................................................................20
Table6:Simulatedno-loadandblockedrotortest.................................................................23
Table7:Simulatedvalueofimpedances.................................................................................23
Table8:Differenttestconditions............................................................................................33
Table9:Tableofequivalentimpedances................................................................................34
Table10:Tableofresultsoflaboratorytests..........................................................................45
Table11:Relationbetweenpowerandinertia(Source:Máquinaseléctricas.JesúsFraileMora
[2])...................................................................................................................................48
Table12:Valuesofmutualinductionandinertiaofsimulatedmotors..................................48
Table13:Simulation’swaveforms..........................................................................................53
Table14:Comparisonofsimulationresultsandtestresults..................................................54
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1 IntroductionThe inventionof alternative currentmotor revolutionized theworld. It is efficient and
requiresminimalmaintenance.Nowadays,thesemotorscanbespottedatanyindustry.
Themainreasonofthatisitsscalability.Theycanbeasbigasorassmallasitstaskrequires
ittobe.Anotherreasonforitspopularityisitsversatility.Bymakingsmallmodifications
initsdesign,theoptimaloperationalpointcanbechanged.Inotherwords,itisrelatively
easytotweakitsoptimalpower,speedandtorqueoutput.
Themostwell-known and popularmotor in industrial environment is the three-phase
inductionmotor. The principal behind the inductionmotor, also known as alternative
currentmotor, functioning isthesameasthegeneratorofthealternativecurrent, i.e.,
electromagneticinduction.Sincetheworkingprincipleofthesetwomachinesistheone
and same, theoretically, the inductionmotor canoperateas thegenerator and supply
currenttodevicesconnectedonsamenetwork.Anditdoesthat,foraverylittleduration,
everytimethepowersupplyisshutdown.
Innormaloperationalconditionsthisphenomenon isnotharmful.Becausethecurrent
that the motor produces can be considered non-existent compared to what is being
suppliedtootherequipmentbythenetwork.Theproblembeginswhenthereisapower
cutandthemotor’soperationisinterrupted.Nowthecurrentthatisbeingproducedby
themotor is reaching to the other electrical devices that are connected on the same
networkorgridasthemotor.
Themagnitudeandfrequencyofthecurrentandvoltageareanythingbutnominal.The
electronicequipmentthatishighlysensibletosmallvariationsofthecurrentareinagreat
danger under these circumstances. Theworst case scenario is when themotors have
capacitivecompensationbecauseitcanproduceovervoltage.
Theovervoltagederivedfromcapacitivecompensationcancorruptthedata,damagethe
internalcomponentsorevencauseburninthewholeequipment.Thisphenomenontakes
placeonshipsandinindustrialinstallations.That’swhythroughoutthisdissertationthere
willbenodistinctionbetweenshipandindustrialnetwork.
Sotheobjectiveof thisdissertation is toanalysethis transientbehaviourof themotor
whenthereisapowercutandithascapacitivecompensation.Differentstepstoachieve
thatgoalarelistedbelow:
Ø The transientbehaviourwill be studiedon twodifferent typesmotors that are
widelyusedintheindustry.
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Ø Itwillbestudiedindifferentoperationalconditionsforeachmotor.
Ø Itwillbestudiedthathowtheloadconnectedtothemotorcanaffectthecurrent
producedbyitandhowtheabsenceofloadcontributestothisphenomenon.
Ø Itwillbestudiedwhilethecapacitorbankisconnectedparalleltothemotor.
Later on, the results gathered during the lab experiments will be compared with the
simulated results onMatlab. The outcomes from the real-world experimentation and
computersimulationshouldbeverysimilarifnotthesame.
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2 Mathematicalmodel2.1 Physicalaspects
Before looking intoamodel that representsanelectricmotor it ispertinent todiscuss
aboutdifferentpartsofmotorandhowtheyinteractwitheachother.That’swhythispart
isdedicatedtothemainpartsofthemotorandtheirfunction.
Athreephaseinductionmotor,oranyelectricmotorforthatmatter,consistsoftwomajor
parts:astatorandarotor.Therotorisnotattachedtothestatorinanyway;thereisa
smallseparationdistancebetweenthetwoknownasairgap.Therotarymovementisthe
resultofinteractionofmagneticfieldscreatedbythewindingsoftherotorandstator.
Thestatorconsistsofframe,coreandwinding.Thestatorframeisanenclosureandthe
outermost part of the induction motor. It houses the junction box where cables are
connected that provide electric current to themotor. It acts as a protection fromany
external damage that might occur. It provides mechanical strength to the internal
components.
Thestatorcore’smainpurposeistoserveashousingforthestatorwindings.Themagnetic
fluxflowsthroughthecoreandtoreducetheeddycurrentsthecoreismadelaminated.
Ithasvariousequidistantperipheralslotsparalleltoitscentralaxis.
Therotoristhepartoftheinductionmotorthatisresponsiblefortherotarymovement.
Ithasashaftthatconnectstothemechanicalloadandinthemiddleislocatedalaminated
structureofcylindricalformthathousesslotsforthewinding.Thiswindingcanbeoftwo
type:
i. Conventionalthreephasewindingmadeofcopperwire
ii. Squirrelcagewinding.
Figure1:Motor'sparts
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Thesquirrelcagewindingconsistsofaluminiumorcopperbarsthatareinsertedinthe
slotspreviouslymentioned.Attheextremesofthecylinderthesebarsareweldedtothe
ringsmadeof samematerialas thebars.Thisway the ringsand thebars formaclose
circuit.
Theinductionmotorsarenameddependingontheirrotorconfiguration.Theoneswith
squirrel cage windings are known as squirrel cage induction motor. The ones with
conventionalwindingsareknownaswoundmotors.Thelatterisalsoknownasslipring
motorsdue to the fact that ithasslip ringsmountedon its shaft thatareused toadd
resistancetotherotor.Bydoingthis,thetorque-speedcurvaturecanbechangedtoobtain
desiredstartingtorque.
2.1.1 Workingprincipleofamotor
The current enters through the junction box in the stator windings. When it starts
circulating through the stator windings it creates a rotary magnetic field. Due to
electromagnetism,thismagneticfieldinducescurrentinrotorwindings,i.e.,theelectrons
intherotorwindingsstartmovinginaparticulardirection.
Thecurrentthatnowcirculatesthroughtherotorwindingsalsocreatesarotarymagnetic
field.Thetworotarymagneticfieldsinteractwitheachother.Theresultofthisinteraction
istherotatorymotionoftherotor.
2.2 Equivalentcircuit
In order to analyse and study machine’s behaviour it is necessary to represent its
functionalityinacomprehensiveway.Thisrepresentationmustenglobeeverykeyaspect
ofthemachine;every importantcomponentmustbeincludedintherepresentation. It
hastobesufficienttounderstandthathowthemachineworks,whatareitsparameters
andhowtheseparametersinterconnectwitheachothertomakethemachinefunctional.
Ininductionmotors,thisrepresentationisachievedbySteinmetzequivalentcircuit.This
equivalent circuit features all the essential components required for the analysis of
inductionmotors.That’swhy,itisfeaturedinalmosteverybookthattalksaboutinduction
motors.
Althoughtheinductionmotorisathree-phasemachine,theequivalentcircuitisasingle-
phase representation for the sake of simplicity. For that reason, when using this
representation onemust procure to use phase voltage since the connection is phase-
neutral.
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Thecircuitthatisshownbelowisknownasexactequivalentcircuit.Obviously,theactual
motorcomponentsarenotconnectedinthismanner.However,itdoesgiveanideathat
howthesepiecesinteractanddependoneachother.Themainpurposeofthiscircuitis
todeterminethathowmuchcurrentpassesthrougheachwindingwhichwillultimately
beusedtocalculatethepoweroutput.
Where:
Re=Statorresistance(W)Xe=Statorleakagereactance(W)Rr’/s=Rotorresistancereferredtostator(W)Xr’=Rotorleakagereactancereferredtostator(W)Rm=Corelosesresistance(W)Xm=Magnetizingreactance(W)
Thecurrent thatenters through stator (I1) isdivided into twocurrents,one that flows
through rotor (I2’) and another one that flows through magnetizing branch (I0). The
amount of current that passes through the two fractions depends directly on the
rotationalspeedandtorqueoutput.Thesetwoparametersdecidethevalueofslip(s)that
isillustratedinthecircuit.So,therotorresistancedependsonthespeedandthetorque
outputofthemotor.
Themagnetizingbranch isnotaphysical componentof the inductionmotor.Rather it
representstheimpedancethatisimposedbythecoreofthestator.Thecurrentthatflows
throughthisbranch is theoneresponsible forcreatingtherotatingmagnetic fieldthat
inducescurrentintherotor.
I1 I2
I0
Figure2:Exactequivalentcircuit
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Figure3:Exactequivalentcircuitwithloadresistance
Inordertomakethecalculationseasiertherotorresistanceisdividedintotwoelements.
Rr’+Rr’('()))=Rr’+Rr’('
)− 1)=Rr’/s (2.1)
Rr’('()))=Resistancethatrepresentsmechanicalloadontheinductionmotor.
With this distinction it is very easy to calculate thedevelopedpowerby themotor as
illustratedintheformulabelow.
Pi=3*(I2’)2*[Rr’('()))] (2.2)
Bysubtractingthemechanical lossesofthemotorfromthedevelopedpowerthetotal
outputpowerisobtained.
PO=Pi-Pm (2.3)
Thedifferencebetweentwocurrents,I0andI2’,valueisratherbigindifferentoperational
states. Therefore, an approximate equivalent circuit is used inwhich either current is
considerednegligibledependingonoperationalstate.
Therearetwomainstatesunderwhichaninductionmotorcanoperate,i.e.,underload
ornoload.Thedistinctionbetweenthesetwooperationalstatesisimportantbecausethe
presence or absence of load determines the path that current takes after node of
magnetizingbranch.
2.2.1 Approximantequivalentcircuits
Whenthereisnoloadattherotorasmallfractionofcurrentpassesthroughrotor,enough
to produce sufficient torque to overcome friction and winding losses associated with
rotation.Soitcanbeconsiderednegligible.Underthisconditionthemajorityofcurrentis
usedtoproducereactivepowerthatgeneratesthemagneticfield,i.e.,I1»I0.
I1I2’
I0
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Figure4:Approximantequivalentcircuitwithoutload
TheRminthemagnetizingbranchrepresentstheresistanceofairinairgap.Itisusually
veryhigh.Forthatreason,manytimesitisomittedfromthecircuitsalltogetherbecause
verylittleamountofcurrentpassesthroughthere.Itmakesthecalculationseasier.
Whenthemotorisrotatingsomethingi.e.thereisaloadconnected,itneedstorqueand
consequently power to rotate that load. Under load, the majority of current passes
throughtherotorandthemagnetizingbranch’scurrentcanbeneglected,i.e.,I1»I2’.Thiscurrent isusedtocalculatethepoweroutputofthe inductionmotor.Thismechanical
powerdependshighlyonthevalueofslip.
Figure5:Approximantequivalentcircuitwithload
2.3 Characterizationofinductionmotor
For thepurposeof thisdissertation,parametersof twodifferent inductionmotorsare
determined.One is a squirrel cage inductionmotorandanotherone is awound rotor
motor.Theveryfirststeptowardsthecharacterizationistocollecttheratedvaluesofthe
motor. It iseasilydonebyextracting information from thenameplate that is attached
motorhousing.
Motorno.1 Motorno.2Motortype Squirrelcageinductionmoto Woundrotorinductionmotor
Ratedvoltage 220/380V 220/380V
Ratedcurrent 4.8/2.8A 2.5/1.4A
Nominalpower 1000W 600W
Ratedspeed 1420rpm 1500rpm
Frequency 50Hz 50Hz
Powerfactor - 0.8
Table1:Ratedvaluesofmotors
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Asitcanbeseen,therearetworatedvoltagesandcurrentsforeachmotor.Thatiswhy
becausethreephasemachinesallowtwodifferenttypesofconnection,WYEandD(delta).
Thetypeofconnectiondependsonthenominalvoltageofthenetwork.Ifthevoltageis
thesameasthemotor’s,thentheconnectionmustbeinD.Ifthevoltageis3squareroot
timesthenominalvoltageofmotor,thentheconnectionmustbedoneinWYE.
Theapproachtakenindeterminingthesemotors’parametersisthemosttraditionalone.
Itconsistsofdoingtwotestsonsubjectmotors,namely,no-loadtestandlocked-rotortest,
andmeasuringthefollowingparameter:
Figure6:Squirrelcageinductionmotor
Figure7:Woundrotorinductionmotor
Figure8:(Right)Dconnectionand(Left)WYEconnection
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- Activepower(W)
- Voltage(V)
- Current(A)
- Reactivepower(VAr)
- Apparentpower(VA)
- Powerfactor
Withthisdatacollectedfromthebothtestsabovementionedresistancesandleakages
reactancearecalculated.Variousformulasandassumptionsareemployedintheprocess
ofcalculation.
Bothtestsaredoneataroomtemperatureof24ºC.Beforecommencingthetests,the
stator resistance of both motors is measured with an Ohmmeter. To measure the
parametersabovementioned,followingcircuitisimplemented:
2.3.1 Blockedrotortest.
As the name suggests, during this test the rotor is blocked, i.e., there is no rotatory
movement.Whenthereisnorotationthevalueofslip(s)is1.Oncetherotorissecured,
withthehelpofvariablevoltagesourcesmallvoltageincrementsareapplied.Thevoltage
supplymustbestoppedwhenthecurrentreachesitsratedvalue.Thisreadingisnamed
asIRB.
Apartfromthecurrentfollowingdataiscollected:
VRB:Thevalueofthisvoltageiswellbelowtheratedone.Sincethevoltageissmalland
theresistanceofthemagnetizingbranchisbig,theintensitydoesnotflowthroughthere.
PRB:Itistheelectricpowerconsumedbythemotor.Itrepresentsthecopperlosses,due
toJouleheating,inthestatorandtherotor.
Figure9:Testingcircuit(Source:Máquinaseléctricas:PauCasalsTorrens[1])
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fpRB:Ithasrelativelyhighvalue.
Onceallthedataiscollectedfollowingformulasaretocalculatetheimpedances:
ZRB=>RB?RB (2.4)
ZRB=RRB+jXRB (2.5)
RRB=DRB
E∗?RB^H (2.6)
RRB=Re+Rr’ÞRr’=RRB–Re (2.7)
XRB=Xe+Xr’ (2.8)
ThereisnoeasywaytoobtaintheXeandXr’.Forthemotorslessthan5.5kW,following
relationbetweenreactancesisacceptable[2].
Xe=Xr’=XRB/2 (2.9)
2.3.2 No-loadtest
Asthenamesuggests,thistestisperformedwithoutcouplinganyloadtothemotorshaft.
Andagain, voltage (V0), intensity (I0),power (P0)and fparemeasuredusing the same
equipment.Thesereadingsareusedtoestimatethepowerlossesinthemotor,namely,
mechanical, coreandcopper losses.Thepower (P0) that is consumedby themotor is
dividedasfollowing:
P0=Pm+PH+Pcu (2.10)
Pcu=3*Re*I02 (2.11)
PH:Corelossespertainingtothemagnetizingbranch
Pm:Mechanicallosses
Pcu:Copperlosses
Thistestisperformedwithvariousvoltages.Eachvoltagedeliversdifferentpower.With
differentvaluesofvoltageandpowerV02-P0graphcanbetraced.Withthehelpofthis
graphthevalueofpowercanbedeterminedwhenthevoltageis0.Withthevoltagebeing
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0,corelossesarealso0sincethereisnocurrentflowingthroughthemagnetizingbranch.
Sothatvalueofpowerrepresentsthemechanicallosses.
Motorno.1 Motorno.2V0(V) P0(W) V0(V) P0(W)
101,7 42,4 100 70,2
125 52,1 125 83,05
150 66,7 150 92,45
175,4 76,7 175 100,73
200,4 96,5 200 109,1
219 143,4 230 128
225,2 157,4 - -
Table2:No-loadtestresults
Followingthevalues listed inthetableabove,thevaluesofPmofbothmotorscanbe
determined.Thevariationinvoltagesappliedtobothmotorsisduetothefactthatthe
voltageofthegridisneverconstant.
Figure10:TheVo^2-Pographofmotorno.1
Whentheaxisofabscissasisformedbysquarenumberandtheaxisofordinatesisformed
bynumbersthatarenotsquaredthegraphisrectilinear.That’swhy,inthegraphabove,
atrendlinehasbeenusedtodescribetherelationbetweenP0andV0.Thistrendline
passesclosetotherealpoints.
Thesamestrategyhasbeenemployedinthegraphbelow.Bothtrendlineshavetheir
correspondentequations.Tocalculatethemechanicallosses,thexissubstitutedwith0.
y=0,0027x+6,1611
0
50
100
150
200
0 10000 20000 30000 40000 50000 60000
Po(W)
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Figure11:TheVo^2-Pographofmotorno.2
Motorno.1 Motorno.2Pm(W) 6 61
Table3:Mechanicallossesofmotors
Intheabovetable,theapproximatevalueofmechanicallossesislisted.Becauseofthe
small variationof speed inno-loadand full-loadconditions thePmcanbeconsidered
constantineveryoperationalcondition.Thereisonlyoneparameterlefttodetermine
and that is Xm. To calculate the Xm of magnetizing branch following formulas are
employed:
Z0=>0?0 (2.12)
Z0=R0+jX0 (2.13)
X0=Xe+XmÞXm=X0–Xe (2.14)
Thereadingsobtainedfromthetestperformedonthemotorsaredisplayinthetables
below.
No-loadtest Motorno.1 Motorno.2V0(V) 219 230
I0(A) 2.65 1.926
P0(W) 143.1 128
Q0(VAr) 994.7 756.4
S0(VA) 1005 767
fp 0.14 0.17
y=0,0013x+61,25
0
20
40
60
80
100
120
140
0 10000 20000 30000 40000 50000 60000
Po(W)
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BlockedrotortestVRB(V) 116.8 45.4
IRB(A) 4.81 2.5
PRB(W) 870 146.4
QRB(VAr) 430 131.3
SRB(VA) 960 196.6
fpRB 0.9 0.74
Table4:No-loadandblockedrotortests'results
After applying the formulas mentioned earlier following values of impedances are
obtained:
Motorno.1 Motorno.2Re(measured) 9.5 6.68
ZRB 12.6+j6.1 7.76+j7.05
Z0 6.7+j47.45 11.72+j67.94
Rr’ 3.1/s 1.08/s
Xe=Xr’ j3.05 j3.525
Xm j44.4 J64.42
Ze 9.5+j3.05 6.68+j3.525
Zr’ 3.1/s+j3.05 1.08/s+j3.525
Table5:Motors'parameters
Atfirst,thereseemstobenoproblemwiththevaluesofimpedancesofmotorno.1.But
acloseexaminationshowssomecontradiction in thevalues.Forexample, thecopper
lossesintheno-loadtestare,atminimum:
PCU=3*9.5*2.65^2=200.14W (2.15)
ThisvalueclearlysurpassestheP0obtainedduringthetests.TheP0mustbe,at least,
equaltothecorelosses.Theimpedancecalculatedinno-loadconditionrepresentsthe
sumofresistanceandreactancesofthestatorandthemagnetizingbranch.
Themeasuredresistanceofthestatorandthecalculatedonedonotmatchwitheach
otherinbothcases.Partlytheworkingtemperatureistoblame.Thetemperatureofthe
windingsissubjecttochangewiththetemperature.
Inordertovalidatetheseresultsandobtainthetruevalueofeveryparameter,aMatlab
simulation is employed. This simulation contains an exact equivalent circuit. The
simulatedcircuithasalotofblocksformeasuringthesignals.
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Figure12:Simulationofexactequivalentcircuitinno-loadcondition(motorno.1)
Figure13:Simulationofexactequivalentcircuitinblockedrotorcondition(motorno.1)
Figure14:Simulationofexactequivalentcircuitinno-loadcondition(motorno.2)
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Figure15:Simulationofexactequivalentcircuitinblockedrotorcondition(motorno.2)
The no-load and the blocked rotor test will be simulated in this circuit with the
correspondingvoltages. For theno-load test the slip (s)willbe close to0and for the
blockedrotortestitsvaluewillbe1.Thesourcevoltagewillbesameasmeasuredduring
tests.
Asmentionedbefore,theresistancesareunreliablewiththevaryingtemperature.But
thisisnotthecaseforreactances.That’swhy,thestartingpointofthesesimulationswill
betheRmandleakedreactancesofstatorandrotor.Thesevalueswillremainalmostthe
sameduringthesimulations.
Atstarting,thevalueoftheresistancewillbeclosetotheonemeasured.Fromthere,
smallchangeswillbemadeinthevaluesofresistancesuntilthereadingsarecoherent.
Theconsumedcurrentshouldbeveryclosetoonemeasured.
Afternumeroustriesfollowingvaluesareobtained.Thesimulatedvaluesareveryclose
totheirreal-worldcounterpart.
No-loadtest Motorno.1 Motorno.2 Measured Simulated Measured SimulatedV0(V) 219 219 230 230
I0(A) 2.65 2.62 1.926 1.817
P0(W) 143.1 182.1 128 127.4
Q0(VAr) 994.7 981.5 756.4 712.4
S0(VA) 1005 998.25 767 723.7
fp 0.14 0.18 0.17 0.176
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BlockedrotortestVRB(V) 116.8 116.8 45.4 45.4
IRB(A) 4.81 4.95 2.5 2.55
PRB(W) 870 887.2 146.4 148.5
QRB(VAr) 430 456.4 131.3 134.8
SRB(VA) 960 997.7 196.6 200.56
fpRB 0.9 0.889 0.74 0.74
Table6:Simulatedno-loadandblockedrotortest
Motorno.1 Motorno.2 Calculated Simulated Calculated Simulated
Re 9.5 8.5 6.68 6.2
ZRB 12.6+j6.1 12.6+j6.1 7.76+j7.05 7.76+j7.05
Z0 6.7+j47.45 8.73+j47.68 11.72+j67.94 12.86+j71.94
Rr’ 3.1/s 4.1/s 1.08/s 1.56/s
Xe=Xr’ j3.05 3.05 j3.525 3.525
Xm j44.4 J44.6 J64.42 J69.11
Ze 9.5+j3.05 8.5+j3.05 6.68+j3.525 6.2+j3.525
Zr’ 3.1/s+j3.05 4.1/s+j3.05 1.08/s+j3.525 1.56/s+j3.525
Table7:Simulatedvalueofimpedances
Nowthevaluesareintunewitheachotherwithsmallvariations.Theonlyexceptionis
theRethatdoesnotmatchwithresistanceofZ0.Everythingelse,fitsrightinplace.
These obtained values of impedances will be later used in theMatlab simulation to
validatetheresultsobtainedinthetests.Morespecifically,theymustbeintroducedin
theblockofmotorsothatitcansimulatethemotor’sbehaviour.
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3 LaboratoryTesting
As outlined in the introduction, in this part, the transient behaviour of the motors
willbeobservedwhenthereisapowercut.Asmentionedbefore,thesubjectofthese
testsaretwothree-phaseelectricmotors,namely,squirrelmotorandwoundrotormotor
thatwillbetestedindifferentoperationalconditions.
Thesetestsarecarriedout in laboratoryconditions.Sotherearesomefactorsthatare
verydifferentfromwhatonecanfindinfactories.Forexample,theroomtemperatureis
notexcessivelyhot,therearenoEMI(electromagneticinterference)sourcesnearby,there
isnoabruptvoltagechangesinthenetwork(duetohighenergyconsumptionelements
connectinganddisconnecting)andtherearenoexternalvibrations.
Saidthat,therearefactorsthatcanbecontrolledinthelaboratoryfacility.Thosefactors
aregivenbelow.
1) Theoperationalconditionsofmotorscanvaryfromonedaytoanother,speciallythe
load.Sotosimulatethoseconditionsthetestswillbedonewithdifferentload.Itis
achieved by connecting a mechanical brake with variable resistant torque to the
motor. The torque that applies this brake can be controlled from a dedicated
switchboard.
2) Other than the load that varies, there is also two different type of connections
possible,WYEandD.Mostofthetimes,thenominalvoltageofanygivengridisfixed
since every security element and other elements are installed for one particular
nominalvoltage.So, theconnectionof themotor remains thesameas longas the
motoroperatesinthesamenetwork. Inthelaboratory,thenominalvoltageisaround230V.Sometimes,it’scloseto225V
andothertimesitmayexceeditsnominalvalue,eventhough,itcannotbeconsidered
overvoltage.Thesubjectmotorsoperate,nominally,at220V.Buttheavailablevoltage
canbeconsideredvalidtoperformthetestssinceavariationofupto10%isadmitted.
Nowasdiscussedearlier,itiscrystalclearthattheconnectioninthejunctionboxmust
beinD.However,forthesakeofexperimentation,therewillbesometestingdone
withWYEconnection.Thereasonforthatistoobservethathowtheoutcomevoltage
willbewhenthemotorispoweredwithavoltagelowerthanitsnominal.
3) Whenpeopletalkaboutpowerorelectricpowertheyrefertowatts(W)orkilowatts
(kW) which is the active power. But
there are two other powers that areFigure16:Powertriangle
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consumedbyamachine.Thesearereactivepower(Q)andapparentpower(S)with
unitsVArandVArespectively.Therelationbetweenthreeisshownbelow.
P=V*I*cosj (3.1)Q=V*I*sinj (3.2)S=V*I (3.3)S= (PH + QH) (3.4)
j=Thepowerfactor.
The active power is the responsible for creating the output power. However, the
powerconsumedbythemachineistheapparentpower.Thereactivepower,inthe
caseofmotors,isinductiveanditisusedforcreatingthemagneticfield.Thepower
factor shows the relation between S and P, the smaller the angle smaller is the
differencebetweenbothpowers.
Thebigger is reactivepowerbigger is theapparentpower,eventhough, theactive
power remains the same.Which translates into bigger electric bill. That’swhy the
capacitorbanksareusedtominimizethereactivepower. It isachievedbyinjecting
capacitivereactivepower,whichhasanoppositedirectionthantheinductiveone,into
theinstallation.
Very often, industrial installations have capacitor banks to minimize the reactive
powerconsumption.Since,motorsconsumeinductivereactivepower,thecapacitor
banks lower the overall installation reactive power by contributing the capacitive
reactivepower.ThesecanalsobeconnectedinWYEorDasperdemand.
Consideringalloftheabove,thereareseveralpossiblecombinationsthatwillresultin
different operational conditions. That’s why, tests will be done with different load
conditions, i.e., no load, with mechanical brake coupled with the motor and with
mechanicalbrakeperformingthetorqueof2N.m.intheoppositedirectionofthemotion
ofmotor. Additiontothat,theeffectsofcapacitivecompensationonthevoltagegenerationwillbe
observed.Forthat,testwillbedonewhenthecapacitorsareinWYEconnectionandD
connection.And,asmentionedearlier,therewillbeexperimentationwithbothtypesof
possibleconnections.
3.1 Testinginstallation
Thelaboratorytestsarecarriedoutusingfollowingequipment:
• Themotors
• ElectricCables–Forthesetests,electricwireswithcrosssectionareaof1.5mm2are
employed.Thissectionismorethanenoughbecausethecurrentthatpassesthrough
themissmall.
• A contactor - throughout the tests many power interruptions will be made.
Disconnectingthewiresdirectlyfromswitchboardisveryrisky.Thispracticecanlead
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toseriousinjuriesordeathduetoelectrocution.Toavoidthisdanger,acontactorwill
beemployed.Itisaswitchthatcloseswhenitisconnected24V(DC)current.With
thisamountofcurrentthereisnodangerofelectrocution.
• Acapacitorbank–Itconstitutesofthreecapacitorsof10µF.ThesecanbeconnectedinWYEorDconfiguration.
Figure18:Thecapacitorbank
• Anadjustablemechanicalbrake–Thisdeviceisusedtoproducecounter-torque.
• Atachometer–Thisdevicemeasurestherevolutionsperminute(rpm)ofthemotor.
Itconnectsontheoppositeofthemechanicalbrake.
• Anammeter–Thisdevice isusedtomeasuretheamps(A). Itwillbeconnected in
serieswithoneofthephaseofthemotor. It isverysimpleandreliableelementto
monitorthecurrent.
Figure19:Thetachometer(Onfarright),themechanicalbrake(Onfarleft)andtheammeter(Behindthetachometer)
Figure17:Thecontactor
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Thefigure19representsthetypicalsetupduringthetests.Whenthereisnoneedfor
load,themechanicalbrakeissimplydetachedfromthemotor.Theammeterisalways
connected to one of the phases. The probe of oscilloscope connects in one of the
terminalsofjunctionbox.
• Ananalyser - Thisdevice isused toanalyseanarrayofparametersofdomesticor
industrialgrid.Itcanbeemployedinthree-phaseorsingle-phasenetwork.It isalso
equippedwithportsthatcancontrolrelaysandalarmsifnecessary.Thepowersource
ofthisdeviceisonethephases.
Figure20:Theanalyser
Themeasurementsaredisplayedonasmalldisplaymountedonthedevice.Themost
commononesarevoltageandcurrent.Theanalyserhasmanymorefunctionsandto
takeadvantageofitsfullcapabilitiesitisconnectedtoacomputeroralaptop.
The connection is via Ethernet. The readings andmuchmore is visualized using a
specializedsoftware.Thissoftwareismadebythesamecompanyastheanalyserand
is called Datawatch Pro. Once the software is installed, the analyser is simply
connectedtothecomputerusingRJ45cableandisconfiguredasperinstructions.
Every reading taken by the analyser can be visualized on a computer in a form of
numerical values or graphs in real time. Further to these readings, the device also
measuresthepowerconsumption.Everyreadingandmeasurementisstoredlocally
onthecomputerwhichcanbeconsultedonanylaterdate.
Figure21:DatawatchPro'smainwindow
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Theanalyseralsomeasuresharmonicspresentintheelectriccurrent.Notonlythat,it
separatesthemaccordingtotheirtype.All inall, it isagreatdevicetomonitorthe
parametersandqualityofelectriccurrent.
Figure22:Theanalysermountedintheprotectivecase
Theanalyserismountedinaplasticboxinordertoprotectitfromanyphysicalabuse.
Itisconnectedbetweenthegridandthemachine,inthiscaseamotor.Thewiresfrom
bothsidesareconnectedintheterminalstripadjacenttotheprotectivecase.
Asitcanbeseen,therearefourpointstoconnectthewiresandoneofthemisfor
neutralwire.InsidetheboxtherearethreeRogowskicoilsresponsibleformeasuring
thecurrentofeveryphase.Thedelicatewireconnectionsofthesecoilsareanother
reasontouseaprotectivecase.
Figure23:Connectiondiagramoftheanalyser
In thisparticular case,between theanalyserand themotor there isa contactoras
showninthefigure24.Theanalyserturnsonautomaticallywhenconnectedtothe
network.Beforecommencingwithanyoperation,thebuttonofstartreadingisclicked
onthefirstpage.
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Figure24:Circuitimplementationoftheanalyser
Aftercommencingwithtesting,therewasaveryapparentproblem.Thedevicewas
notregisteringthehighcurrentconsumption,around5timestheratedcurrent,atthe
momentofstarting.Thisphenomenonisverycharacteristicoftheinductionmotors.
Furthermore,itwasnotregisteringorreadinganytransientwaveformofthevoltage
afterpowershutdown.Thevalueofthevoltagedroppedto0afterstoppingthesupply
ofelectricity.Thisconditionwasconsistentineverytestperformedwiththeanalyser.
Afterinspectionofeverysettinginthesoftware,itwasfoundthatitwasreadingor
takingsampleseverysecond(s).Thatwasthesmallestpossiblesampletimeavailable.
That is why, the mentioned phenomena did not appear on screen because they
happenedinamatterofmilliseconds(ms).
For the reasonmentioned above, it is impossible to perceive the transient voltage
usingtheanalyser.Tovisualizeandcapturethetransientwaveformanoscilloscope
willbeused.
• Anoscilloscope–Thisapparatuswillbeusedtoobservethetransientwaveformofthe
voltage.
Figure25:TheOscilloscope
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3.1.1 ElectriccircuitAsithasbeenexplainedbefore,thecapacitorbankandthemotorwillbeconnectedwith
each other electrically in different forms. There are various possible configurations
becausesometimes thecapacitorswillnotbeconnectedandother times theywillbe
connectedintheWYEorDconnection.Allthesixpossiblecombinationsarelistedbelow.
Figure27:ThemotorconnectedinWYE
Figure28:MotorandcapacitorconnectedinWYE
Figure29:MotorconnectedinWYEandcapacitorbankinD
Figure26:ThemotorconnectedinD
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Figure30:MotorconnectedinDandcapacitorbankinWYE
Figure31:MotorandcapacitorconnectedinD
Figure32:Phase-neutralconnectionofthecapacitorandthemotor
All these combinations offer different equivalent impedance that is perceived by the
electricgrid.Thefirststeptowardsfindingtheequivalentimpedancecircuitistoknow
the impedanceofmotorduringeveryoperation. Thereare variouspoints to keep in
mind:
• Therotorresistancevarieswiththeload(Rr’/s).Slipcanbecalculatedbyknowing
thespeedineverycaseandsynchronousspeedofthemotor(ns).
s=b)(bc
b) (3.5)
• When there is no load connected, following the approximant equivalent
circuit,ZeandXmaresummeduptocalculatetheimpedanceofthemotor.
• Whenthereisaloadconnected,followingtheapproximantequivalentcircuit,ZeandZr’aresummeduptocalculatetheimpedanceofthemotor.
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• If the capacitor bank is not connected to the grid, then the equivalentimpedancewillbelongtooneofthecasesmentionedabove.
• IfthecapacitorbankisconnectedinWYE,thenimpedancesofthemotorandthecapacitorbankaresummedasinanyotherparallelRLCcircuit.
Zt=
qr∗qsqrtqs
(3.6)
Ifnot,thentheimpedanceofcapacitorbankinDmustbeconvertedintoitsequivalentimpedanceinWYEusingthefollowingformula.
ZD-Y=qs^HE∗qs
(3.7)
Once the conversion is completed, the equivalent impedance is calculated
accordingtotheformula3.6.
Theimpedancehastwoparts,onerealandoneimaginary.Iftheimaginarypartisbigger
than0thenthecircuitisinductive.Iftheimaginarypartissmallerthan0thenthecircuit
iscapacitive.Theoreticallyspeaking,themorecapacitiveiscircuit,thelargeritsimpact
wouldbeonthetransientvoltage.
Additiontothedifferentcombinationsmentionedabove,themechanicalbrake isalso
connected to themotor in somecases. In total,34 testare carriedoutwithdifferent
combinationsofcapacitorbank,motorandmechanicalbrake.Thesecombinationsare
listedbelowwiththeircorrespondenttestnumber.
Testno. Motor MC CB Brake(N.m)1 1 WYE No No
2 1 WYE No 0
3 1 WYE No 2
4 1 WYE WYE No
5 1 WYE D No
6 1 WYE WYE 0
7 1 WYE D 0
8 1 WYE WYE 2
9 1 WYE D 2
10 1 D WYE No
11 1 D D No
12 1 D WYE 0
13 1 D D 0
14 1 D WYE 2
15 1 D D 2
16 1 D D 4,2
17 2 D No No
18 2 D No 0
19 2 D No 2
20 2 D WYE No
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21 2 D D No
22 2 D WYE 0
23 2 D D 0
24 2 D WYE 2
25 2 D D 2
26 2 WYE No No
27 2 WYE No 0
28 2 WYE No 2
29 2 WYE WYE No
30 2 WYE D No
31 2 WYE WYE 0
32 2 WYE D 0
33 2 WYE WYE 2
34 2 WYE D 2Table8:Differenttestconditions
MC:ItstandsformotorconnectionwhichcanbeinWYEorD.
CB:Itstandsforcapacitorbankwhichcanbeconnectedornottothemotor.Itcanbe
connectedinDorWYE.
Brake:IfitsaysNothenthemechanicalbrakeisnotconnectedtothemotor.Ifthevalue
is0thenitisconnectedtothemotorbutitisnotperforminganycounter-torque.Ifthe
valueisgreaterthan0thenitrepresentsthecounter-torqueitisproducingonthemotor.
Theequivalentimpedancehasbeencalculatedforeverytestdoneinthelaboratory.The
list of these impedances can be found below. For the calculation of these equivalent
impedances,thefactorsabovementionedaretakenintoconsideration.
Testno. Equivalentimpedance1 8,5+47,65i
2 90,5+6,1i
3 22,17+6,1i
4 11,74+55,67i
5 27,43+82,51i
6 86,78-18,93i
7 56,01-44,21i
8 50,19-1,74i
9 44,76-15,68i
10 11,74+55,67i
11 27,43+82,50i
12 116,09-42,68i
13 56,01-44,21i
14 86,78-18,93i
15 44,76-15,68i
16 15,21-29,01i
17 6,2+72,635i
18 45,2+7,05i
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19 21,8+7,05i
20 10,40+93,85i
21 60,25+219,11i
22 46,29+0,49i
23 42,92-12,032i
24 25,89+5,14i
25 26,89+0,78i
26 6,2+72,635i
27 22,91+7,05i
28 12,88+7,05i
29 10,40+93,85i
30 60,25+219,11i
31 15,86+6,43i
32 24,96+1,78i
33 13,45+6,651i
34 13,96+5,81i
Table9:Tableofequivalentimpedances
Theseimpedanceswillbecrosscheckedwiththecasesinwhichovervoltageisproduced.
Thisway,itcanbeprovediftheequivalentimpedancehasanyimpactonthetransient
voltageornot.
3.2 Formula-basedanalysis
Acircuitinwhichacapacitor,aninductorandaresistanceisconnectedtoeachotheris
knownasasecondordersystem.Itisnamedlikethisbecauseithastwoenergystoring
device,i.e.,thecapacitorandtheinductor.ItisalsoknownasRLCcircuit.Essentially,the
RLCcircuit is thesameas thecapacitorandthemotorconnected inparallel inphase-
neutralconfigurationasillustratedinFigure25.
Whenthepoweriscutofffromthiscircuit,itproducestransientvoltageinsimilarfashion
as the inductionmotors.Thisphenomenon isdubbedas transient responseofsecond
ordersystem.This transient responsecanbestudiedwith formulas.Theoretically, the
samemethodcanbeemployedtostudythetransientwaveformproducedbythemotor.
vc(t)=2*úA1ú*e-at*cos(wdt+/A1),t>0 (3.8)
The formula 3.8 describes the waveform produced by the RLC circuit. The negative
exponentensuresthattheendvalueis0.Thespeedwithwhichthisequationequatesto
0dependsonaandt.Thebiggerisathefasteritequatesto0.Theparametersofthis
formulaforaparallelRLCcircuitarethefollowing:
a= xHy (3.9)
w02=
'yz (3.10)
wd= aH + {0H (3.11)
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p1,p2=-a±wdi (3.12)
TheR,LandCare, respectively, resistance, inductanceof inductorandcapacitanceof
capacitor. The value of A1, which is a complex number, is obtained by solving the
followingmatrixoperation.
1 1|1 |2 x
}1}2 =
~ 0t
~�(0t) (3.13)
y(0+)=vc(0
+)=vc(0
-)=V (3.14)
y’(0+)=vc’(0
+)=0 (3.15)
A2iscomplexconjugateofA1.Itmeansthatthemagnitudeofrealpartandimaginary
partofA2issamebutthevalueofcomplexcomponentofA2isoppositeinsign.TheVis
thevoltageofthegridtowhichthecircuitisconnected.
This formula-based analysis can be used to validate the results of real-world tests.
However,inthecaseofinductionmotors,thephenomenonofovervoltageoccursatt=
0.Thisformulaisusefulwhenthetimeisgreaterthan0.AlsotheproductofA1and2is
equal to the voltage suppliedby the grid. So, themaximumvalueobtained from this
formulawillneverexceedthevalueofnetwork’svoltage.
3.2.1 Dynamicanalysis
The next step in formula-based analysis of motor is to analyse its behaviour during
acceleration and deceleration. Since the transient voltage is produced during the
deceleration.Thisanalysiscommenceswiththefollowingformula:
T–Tr=J dωdt (3.16)
Where:
T:Electromagnetictorqueofmotor(Nm)
Tr:Counter-torqueoftheload(Nm)
J:Inertia(kg.m2)
ω:Rotationalspeedofmotor(rad/s)
Aftertheprocessofintegrationofthegivenequation,followingequationisobtained:
τmec=ÇÉ
ÑÖÜá (3.17)
Thisequationgivestheelectro-mechanictimeconstant,alsocalledtau,thatdetermines
thetimethatarotorwithJinertiataketoacceleratetothesynchronousspeed(ω)under
theinfluenceofthemaximumtorque(Tmax)
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4 Test’sresults
Followingeverythingexplainedupuntilnow34testareperformed.Theresultsofthese
tests are catalogued in the tablebelow. Theparametersobtained from the tests are
motor’sspeed,consumedcurrent,peakvalueoftransientwaveformandthedurationof
thesaidwaveform.Theimageoftransientvoltagewaveformproducedineverytestcan
befoundonthefarrightofthetable.
Thetransientwaveformisobservedandanalysedontheoscilloscope.Theparameters
suchaspeakvalueoftransientwaveformanditsdurationaremeasureddirectlyonthe
oscilloscope.
Theapparatusdoesnothavetheabilitytotellifthereisanyovervoltage.However,itis
relativelyeasytovisuallytellthepresenceofanovervoltage.
Thepeakvalueofthetransientwaveformiscomparedwiththepeakvalueofvoltagethat
isbeingsuppliedbythegrid.Ifthevalueoflatterishigherthenthereisnoovervoltage.
Forthesakeofthiscomparison,thepeakvalueofgrid’svoltageisalsolistedinthetable.
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Testno. Motor Vp(V) RPM I(A) Vm(V) t(ms) Overvoltage Transientwaveform
1 1 179,65 1450 0,66 124 482 No
2 1 179,65 1425 1,53 122 334 No
3 1 179,65 1050 3,85 90 158 No
4 1 179,65 1450 0,3 172 940 No
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5 1 179,65 1450 0,63 228 1060 Yes
6 1 179,65 1425 0,5 148 434 No
7 1 179,65 1425 0,7 200 432 Yes
8 1 179,65 1350 1,25 144 216 No
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9 1 179,65 1350 1,35 148 170 No
10 1 311,17 1450 2,6 148 519 No
11 1 311,17 1450 1,7 140 990 No
12 1 311,17 1450 2,5 136 474 No
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13 1 311,17 1425 1,7 140 508 No
14 1 311,17 1425 2,82 176 162 No
15 1 311,17 1350 2,2 134 252 No
16 1 311,17 1400 3,5 94 112 No
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17 2 311,17 1450 2 150 180 No
18 2 311,17 1440 2,2 144 164 No
19 2 311,17 1350 2,5 148 144 No
20 2 311,17 1450 1,65 128 200 No
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21 2 311,17 1450 0,85 164 400 No
22 2 311,17 1440 1,65 180 216 No
23 2 311,17 1440 0,9 156 286 No
24 2 311,17 1375 2,2 168 134 No
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25 2 311,17 1375 1,55 138 190 No
26 2 179,65 1440 0,6 144 300 No
27 2 179,65 1360 0,75 168 150 No
28 2 179,65 1150 1,6 68 138 No
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29 2 179,65 1440 0,3 158 552 No
30 2 179,65 1440 0,7 296 600 Yes
31 2 179,65 1240 1,2 112 175 No
32 2 179,65 1360 0,82 248 434 Yes
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Table10:Tableofresultsoflaboratorytests
Motor:Ittellsthenumberofthemotorbeingtested.Vp:Itisthepeakvalueofvoltage.Itrepresentsthehighestvalueofthesinusoidalwaveformofthevoltage.ItissmallerinWYEconnection.RPM:Itrepresentsthespeedofthemotorineverycase.I:Itrepresentsthecurrentconsumedbythemotor.Vm:Itrepresentsthepeakvalueofthevoltageproducedbythemotoraftershuttingdownthepower.t:Itrepresentsthedurationofthevoltagewaveformproducedbythemotors.Overvoltage:IfitsaysNothenthereisnoovervoltageproduced.IfitsaysYesthentherehasbeenanovervoltage.
33 2 179,65 1150 1,4 132 156 No
34 2 179,65 1120 1,55 208 158 Yes
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4.1 Results’analysis
Theovervoltageisobservedinfivedifferentcases,twoformotor1andthreeformotor2.Ineverycase,thecapacitorbankisconnectedparalleltothemotor.Andineverycase,thecapacitorbankisconnectedinDandthemotorisconnectedinWYE.Inthemotorno.1,theovervoltageisproducedwhenitisnotconnectedtoanyloadanditisconnectedtothemechanicalbrake.Inthelattercase,therewasnocounter-torqueperformedonthemotor.Apartfromtheovervoltage,thecapacitorbankalsocontributesinextendingthetransienttimeregardlessofitstypeofconnection.Even if there is noovervoltage, theVm is greater in the caseswhereCB is connectedcomparedtothoseinwhichthereisnocapacitivecompensation.TheeffectsofCBaremitigatedwhenthemechanicalbrakeisconnectedInthemotorno.2,theovervoltageisproducedinthreedifferentinstances,inno-loadcondition,when it is connected to theMBwithoutanycounter-torqueandwhen it isconnectedtotheMBwiththecounter-torqueof2N.m.WhenthemotorsareconnectedinDconnection,theresultingVmisusuallyhigherwhentheCBisconnectedinWYEconfiguration.AndwhenthemotorsareinWYEconnectiontheVmisalwayshigherwhentheCBisinDconnection.Theloadconnectedtothemotoralwaysmitigatesthetransientvoltage.Bothinitspeakvalueandthetransienttime.Ifthereiscounter-torquetheeffectsofloadareaggravated.Butthereseemstobesomeexceptionsinthistrend.As for equivalent impedance, there seems to be no relation between the value ofimpedanceandthevoltageproduced.Thetestno.7istheonlycapacitivecircuitinwhichtheovervoltageisobserved.Intherestofthecases,thecircuitsareinductive.In conclusion, themotors do produce an overvoltage when they are connected to acapacitorbank.Forthattohappen,theCBmustbeconnectedtothehighervoltagethanthemotor.Evenifthereisnoovervoltage,thecapacitivecompensationleadstohigherVmthanthecaseswithoutanyCBconnected.
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5 Matlabsimulation
As outlined in the introduction, the data collected from tests is validated using thesimulationofthephenomenon.Forthesimulation,Matlabisused.Thecircuitusedinthelaboratorytestingisreproducedinthissoftware.
It has an extensive library of elements to choose from. Every device, machine andapparatususedinthelaboratoryisavailableinMatlabintheformofblocks.Theseblockshave several parameters that one must know in order to make it functional in thedesirableway.Once the blocks have been updated with the correct information, they must beinterconnectedwitheachotherintherightway.Thesimulationwouldnotworkifanyessentialinformationisnotintroduced;itwouldgiveanerror.Thesimulationcircuitsforboththemotorsaresame.Theonlythingsthatchangearetheparameters.Now,followingtheintroduction,thecasesthatpresentovervoltagewillbesimulated. Thewaveforms of voltage of the simulationwill be compared to the onesobtainedduringthetests.Theblocksthatareusedinthesimulationsarelistedbelow.
• Theasynchronousmachine(SIunits):Thisblockrepresentsthethree-phasemotor.It
can be used as squirrel cagemotor or wound rotormotor. It has three inputs toconnectthewires.Italsohasaninputtointroducethecounter-torque(Tm)whichisnotused.Because, if thecounter-torque isestablished, itkeepsrotatingthemotorevenifthereisapowercut.Ithasoneoutputportwhichcanbeconfiguredtoshowavarietyofparameters.Forthesakeofthetesting,therotorspeedisselectedbecausethedataofmotor’sspeedisavailablefromthelaboratorytest.
Asfortheparameters,basicmotorinformationisintroduced,suchasnominalpower,rated voltage and frequency. The motor’s resistances are also introduced in theparameterssection.Sincetherotorresistancereferredtothestator(Rr’/s)dependsonspeeditisadjustedwitheverychangeinthespeed.Anotherthanresistances,leakedreactancesarealsoaddedintheformofinduction(H).Theloadthatisdraggedbythemotoriscontrolledbyfrictionfactor.Actually,the
Figure33:AsynchronousMachine(SIunits)
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frictionfactordirectlyaffectsthespeed,thehigherthefrictionfactorthelowerthespeed.Sincetheloadaffectsthespeed,bycontrollingthespeedtheeffectofloadonthemotorissimulated.
Figure34:Asynchronousmachine'sparameterswindow
Other parameters, such as, mutual induction and inertia cannot be found in thetechnicalspecificationsnorcanbecalculated.AccordingtotheJesúsFraileMorainhisbookMáquinas eléctricas [2], the value of the inertia can be between 0.0015 and0.0035J(kg.m2).Belowisatablecontainingthevaluesofinertiafordifferentpowers.
kW J(kg.m2)0.55 0.00150.75 0.00181.1 0.00251.5 0.0035
Table11:Relationbetweenpowerandinertia(Source:Máquinaseléctricas.JesúsFraileMora[2])
Thevaluespresentedinthetableserveasguidance.Asforthemutualinduction,itisamatteroftrialanderror.So,inordertogetthedesirableresults,manycombinationsofmutualinductionandinertiaaretried.Oncetheresultmatchwith,orcomescloseto,oneoftheresultsobtainedinthetests,thetwoparametersaredetermined.Theselectedvaluesofthesetwoparametersarelistedbelow.
Squirrelcagemotor WoundrotormotorMutualinduction(H) 0.46 0.5Inertia(J(kg.m2)) 0.003 0.003
Table12:Valuesofmutualinductionandinertiaofsimulatedmotors
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Now for simulatingdifferent caseson the samemotor theonly things that requirealterationarethefrictionfactorandtherotorresistance.Therestoftheparametersremainunchanged.TheonlylimitationofthisblockofmotoristhatitispreconfiguredtorunwithWYEconnection.But,thisrestrictiondoesnotaffectthesimulations inanywaybecauseeveryovervoltagecaseintestswaswithmotorinWYEconnection.
• Three-phaseprogrammablevoltagesource:Withoutthisblockthesimulationwouldnotwork.Thetwoparametersthatmustbeaddedtothisblockarelinetolinevoltageandthefrequencythatare220Vand50Hz.
Figure35:Three-phaseprogrammablevoltagesource
• Three-phase load:Thisblockrepresentsthecapacitorbank.Thetypeofconnectionmustbeselected;inthiscase,itisdelta(D)connection.Andthepowerproducedbythecapacitorsmustbeintroduced.
QC=3*(VL^2)*2*p*50*C (4.1)
Byapplyingthisformula,thecapacitivereactivepowerofthecapacitorsiscalculated.SincetheCis10µF,theQCis456.16VAr.
Figure36:Three-phaseload
• Three-phasebreaker:Thisblockisusedtointerruptthepowersupplytothemotor.It
isequivalentof thecontactoremployed inthetesting. Itcutsoff thepowersupplyafter3seconds.
Figure37:Three-phasebreaker
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• Three-phaseV-Imeasurement:Thisblockhasanoutputportsthatshowsthevoltageandcurrentofeverysinglephase.
Figure38:Three-phaseV-Imeasurement
• Voltagereader:Thisblockisusedtomeasurethevoltageofasinglephase.Thereading
ofthisblockisusedforthecomparisonsofthewaveforms.
Figure39:Voltagemeasurement
• Scopes:Theseblocksillustratethemeasurementsoftheblockstheyareconnectedto.
Figure40:Scope
• Step:Thisblockisusedtointroduceaconstantvalueinanyblock.Itisconnectedto
theinputportofthecounter-torque(Tm)withvalue0.IftheTmisleftunconnectedthesimulationwouldnotwork.
Figure41:Step
• Gain:Thisblockisusedtomultiplythesignalwiththeestablishednumber.Theoutput
signalofthemotorgivesthespeedinrad/s.Thestepblockisusedtoconvertrad/sintorpm.
Figure42:Gain
• Ground:Thisblockisusedtogroundanyelectriccircuit.Itisanessentialelementin
powergridsthatcansavelivesinthecaseofshortcircuits.
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Figure43:Ground
• Powergui: Themajority of the abovementioned blocks fall under the category of
SimscapePowerSystemSpecializedTechnologymodels.Whentheblocks fromthiscategoryareused,thepowerguiblockmustbeincludedinthesimulation.
Figure44:Powergui
Thefinalcircuitafterconnectingalltheblockslooksasfollowing.
Figure45:Simulationcircuit
5.1 Simulationresults
Asmentionedearlier,fivedifferentsimulationsareexecuted,twoformotorno.1(squirrelcage motor) and three for motor no.2 (wound rotor motor). In order to do a visualcomparisonbetweenthe results fromtestingandsimulation, themeasurements fromtwoareplaceddownsidebysideinthefollowingtable.Alongsidetwomeasurements,thecorrespondingtestno.canbefound.
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Testno.
Simulationresult Testresult
5
Figure46:Testno.5-Simulationresult
Figure47:Testno.5-Labtestresult
7
Figure48:Testno.7-Simulationresult
Figure49:Testno.7-Labtestresult
30
Figure50:Testno.30-Simulationresult
Figure51:Testno.30-Labtestresult
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32
Figure52:Testno.32-Simulationresult
Figure53:Testno.32-Labtestresult
34
Figure54:Testno.34-Simulationresult
Figure55:Testno.34-Labtestresult
Table13:Simulation’swaveforms
5.1.1 Simulationresults’analysis
Thefirsttworeadings,i.e.,testno.5and7,belongtomotorno.1.Andtheotherthreereadings,i.e.,testsno.30,32and34belongtothemotorno.2.Asitcanbeobserved,thesimulationresultsareveryclosetotheonesoflaboratorytesting.Thecomparisonsofthemeasurementscanbefoundbelow.
Testno. Test Simulation5 Vp(V) 228 227 t(ms) 1060 800 I(A) 0.63 1.27 Vp(V) 200 218 t(ms) 432 500 I(A) 0.7 1.230 Vp(V) 296 295 t(ms) 600 550 I(A) 0.7 1.132 Vp(V) 248 160 t(ms) 500 300 I(A) 0.82 1.4
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34 Vp(V) 208 120 t(ms) 160 130 I(A) 1.55 5.85
Table14:Comparisonofsimulationresultsandtestresults
Thesimulatedtransientvoltageshownintheaboveimagesissingle-phase.Ithasbeenimplementedthiswaytoensureaneasycomparisonbetweentwokindofwaveforms.Thethree-phasewaveformhasappearanceasinfigure56.
Figure56:Transientthree-phasevoltagewaveform
Thefirstthreesimulationsareveryclosetotheirreal-worldcounterpart.Thepeakvalueofthetransientvoltageisverysimilartotheonesobtainedinthetests.Theshapeofthesimulation waveforms has a similar resemblance to ones of the oscilloscope. Withexceptionofthesecondcase,thetimeoftransientwaveformalwaysfallsshort.
Thesecondsimulationhasagreaterpeakvaluethanthereal-worldtesting.Thetransientwaveformtimeisalsolongerinthesimulation.However,thewaveformlooksverymuchlikethewaveformofthetests.
Inthefourthsimulation,thereisnoovervoltagewhereasthereisclearlyanovervoltageinthelaboratorytests.Eveninthetransienttimethereisabigdifferenceof200ms.Eventheformofthewaveformisdifferent. It issafetosaythatthesimulatedwaveformismitigatedineveryaspect.
In the fifth case,during the test, theovervoltage seems tobe the resultof change inoperationalcondition.Manyfactorscontributetothemomentarilyovervoltage.Oneofthesefactorsisanabruptinterruptionoftheelectricityinacriticalmoment.Itissafetosaythatthisovervoltagewasnotproducebythecapacitivecompensation.
Eventhough,thesecondpeakoftransientwaveformhasapproximatelythesamevalueastheoneobservedintests.Itisaround100V.Andthetransientwaveformtimeisalsoclosetoitsreal-worldcounterpart.
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The current consumed in the simulation is always superior than its real-worldcounterpart.Thereisnopatternthatcoulddescribethisaugmentationineverycurrent.Inthecaseno.34,thevalueofsimulatedcurrentisexceptionallyhigher.Thecurrentisalsoaffectedbytheovervoltage.Themagnitudeofcurrentisaugmentedin the same fashion as of voltage, resulting in an overcurrent. The waveform of thistransientcurrentisassameasthewaveformofthetransientvoltage.Thedurationofthewaveformisalsothesameasthevoltage’sduration.For instance, in figure 56, it can be seen the three-phase transient waveformcorrespondenttotestno.7.Theformofthistransientwaveformissameasthetransientvoltagewaveform.
Figure57:Transientwaveformofthethree-phasecurrent
Whensomeonetalksaboutvoltageof220V,heorshereferstotheratedvoltagewhichistheRMSvalueofvoltage.Inthefigure58,theRMSvalueofthetransientvoltagecanbe seen. Before turning the power off the RMS value of voltagewas constant. Afterinterrupting thepowersupply, theRMSvaluestarted tobehave likeawaveform.Thereasonsbehindthispatternareprobablythechangesinthepeakvalueandfrequency.
Figure58:TransientwaveformoftheRMS
Theintensificationandmitigationofthewaveformsinthesimulationinrespecttoreal-world testing can be a product of many unforeseen factors and reasons. The mostimportant thing toemphasizehere is the fact that even simulated circuits experienceovervoltageandunderthesameconditionastherealcircuits.
Havingsaidthat,itcanbeconfirmedthatthemeasurementsobservedinthelaboratorytestsarevalid.
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6 Conclusion
After many hours of laboratory testing and simulation, it is clear that the capacitivecompensation in the motors causes overvoltage under certain conditions. Withoutcapacitivecompensationtherewasnoovervoltageproducedineithermotors.Apartfromtheeffectofload,thevoltagereceivedbythemotorandthecapacitorbankinfluenced greatly on the voltage production. The overvoltage manifested when themotorreceivedvoltagelowerthantheratedvoltageandthecapacitorbankreceivedthevoltagethatishasbeendesignedfor.TheMatlabsoftwarehasallowedthevalidationofthedatacollectedinthelaboratory.Thesimulationresultswereverysimilar to their real-worldcounterparts.Without thispowerfultool itwouldhavebeenverydifficulttoknowifthelabresultswereactuallytrueorjustsomecoincidences.Theobjectivesoutlinedintheintroductionhavebeenmet.Theovervoltageproducedbythemotorwasobservedandhowitcanbeaffectedbytheloadconnectedtothemotor’sshaft.Itwasalsoobservedthathowthevoltagereceivedbymotorandcapacitorbankscanchangethevoltageproduction.Thisdissertationhasservedthepurposeofoutliningaproblemthatexistsintheshipsandindustrialinstallations.Moreworkisneededinthisfieldinordertocollectmoredata.Thenextdissertationinthisfieldshouldalsoexperimentwithmorepowerfulinductionmotors.Thecollecteddatamayhelpthecompaniestocomeupwithasolutiontocounterattackthisphenomenon.
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7 Bibliography
1. Casals Torrens, Pau; Bosch Tous, Ricard. Máquinas eléctricas: Aplicaciones deingenieríaeléctricaainstalacionesnavalesymarinas.Prácticas.1sted.Barcelona:UPC,2005.ISBN84-8301-813-6
2. Fraile Mora, Jesús. Máquinas Eléctricas. 2nd ed. Barcelona: Servicio depublicaciones.ColegiodeIngenierosdeCamino,CanalesyPuertos,1993.ISBN84-7493-143-6
3. Carlson,A.Bruce.Circuitos.1sted.Australia:ThomsonLearning,2001.ISBN970-686-033-9
4. Glendinning, Eric H. English in electrical Engineering and Electronics. 13th ed.Oxford:OxfordUniversityPress,1992.ISBN019437517X
5. Hayt, William H.; Kemmerly, Jack E.; Durbin, Steven M. Engineering CircuitAnalysis.8thed.NewYork:McGraw-Hill,2012.ISBN978-0-07-131706-1
6. Corrales Martín, Juan. Cálculo Industrial de Máquinas Eléctricas: Tomo I.
Barcelona:U.P.B.,1976.ISBN84-600-6752-1
7. Slemon, G.R.; Straughen, A. Electric Machines. 2nd ed. Reading- UK: Addison-WesleyPublishingCompany,1980.ISBN0-201-07730-2