Availableonlineatwww.sciencedirect.com
Journal of Applied Research and Technology
www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology14(2016)87–92
Original
Core saturation effects of geomagnetic induced currents in power transformers
José Ramírez-Ni˜no, Carlos Haro-Hernández, Joaquín Héctor Rodriguez-Rodriguez
∗, Rito Mijarez
InstitutodeInvestigacionesEléctricas,113ReformaAve.,Col.Palmira,62490Cuernavaca,Morelos,Mexico Received20January2015;accepted1March2016
Availableonline5May2016
Abstract
SaturationofthemagneticcoreoftransformersinapowersystemisanimportanteffectthatcanbeattributedtosolarGeomagneticInduced Currents(GICs).Thissaturationcanconducetovoltage-controlproblems,generatingharmoniccurrents,andheatingofthetransformerinternal components,leadingtogasrelayalarm/operationandpossibledamage.ThispaperpresentsananalogphysicalreducedscalemodelofGICsin powertransformers.Theinstrumentationemployedtocarryoutthisstudyconsistsofasingle-phasereducedscaletransformer,acontrollable currentsource,aresistiveloadandadataacquisitionsystem.Theworkestablishesnotonlythatitispossibletomodelthebehaviorofmagnetic variablesandtoextrapolatetheresultstolargefullsizepowertransformers,butalsoprovidesinsightintoGICsgenerationandtheireffectson powertransformers.Obtainedresultsarerelatedtothenon-linearbehaviorofGICsduetoasymmetricsaturationofthemagneticcoreinthepower transformer,wherecomputationalmodelsimulationisnotabletogiveacceptableoutcomes.ResultsarediscussedforseveralGICsmagnitudes, whichincludevoltage,current,harmonicswaveforms,magneticcorepointofoperation,thebehaviorofthestrayflow,instantaneouspowerand coretemperature.
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Keywords:Geomagneticcurrents;Scalemodel;Asymmetricnon-linearbehavior
1. Introduction
GeomagneticInduced Currents(GICs) arecurrents related tocurrentflowintheionospherethatinteractwithpowersys- tems. Thesecurrents are associated withsolar storm activity andproducecurrentsinthepowergridthatflowthroughtrans- mission lines. These currents have a very low-frequency of 0.01–0.001Hz(quasiDC)withaveragemagnitudesof10–15A andpeaksofupto100Afor1–2min(Heindletal.,2011).
Transformerswithstar connections andgrounded neutrals thatarelinkedbylongtransmissionlines,asdepictedinFigure1, aresusceptible toGICsproblemsduetothe inducedcurrents thatflowthroughthetransmissionlineandtheneutralsthatare groundedtoclosethecircuit.
Severalundesirableeffects,producedbyGICsinelectrical powergridsandtransformers, havebeen reported.Moreover,
∗Correspondingauthor.
E-mailaddress:[email protected](J.H.Rodriguez-Rodriguez).
PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.
whentheDCmagneticfluxissuperimposedontheACflux,the magneticcoresinthetransformersareasymmetricallysaturated (Lahtinen &Elovaara, 2002;Takasu, Oshi, Miyawaki,Saito,
&Fujiwara,1994).Thereportedfailuresintransformersdueto GICsaremainlydielectricandnotaresultofoverheating.The effectsofGICsonthegridandthetransformersaresummarized asfollow:effectsontheelectricgrid;ontheonesidewhenthe reactiveloadsinthesystemarechanged,theprotectionsaremis- alignedandtheinternalresonantfrequenciesofthetransformer change.
Thisprocessgeneratesvoltagesurgesthateventuallydegrade theinsulation.Ontheotherside,themagnetizationimpedance decreases,andthemagnetizingcurrentandthelosseswithout loadingincrease.Reactiveloadabsorptioncancauseinstability intheelectricgrid(Berge,Varma,&Marti,2011).Moreover, harmonics arecontributedtothesystem, andevenharmonics aregenerated.
Effectsonthetransformersarerelatedtotherelativepermit- tivity of the magneticcore andthe magnetizationimpedance decreasesignificantly(Bolduc,Gaudreau,&Dutil,2000;Price, 2001).Themagneticcorelossesincreaseduetohysteresis,and
http://dx.doi.org/10.1016/j.jart.2016.04.003
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Transformer 2
Transformer 1
Ground current
Magnetic field
Ionosfer current
Fig.1.SchematicdiagramoftheGICsflowintheelectricalpowergridtrans- missionline.
eddycurrentsandthelossesinthewindingsduetotheJoule effectincrease.Furthermore,the skineffectthat isassociated withharmonicsinthecurrentandinthemagneticfluxincreases.
Heatincreasesinthefittingsandtankduetotheeffectsofeddy currentsthatareassociatedwithincreasingstrayfluxandwith the appearance of even harmonics (Picher, Bolduc, Dutil, &
Pham,1997;Walling&Khan,1991;Zhigangetal.,2010).The firstharmonicvibrationcomponentinthetransformerarisesdue tomagnetostriction.Residualmagnetismoccursinthecoreeven whenGICsarenolongerpresentandtheInrushphenomenon occursuntilthetransienthasdiedaway.
These effects make it difficult to determine transformer design parameters that consider the effects of the GICs and adequatelysupportthem.Thesimulationoftheseoperatingcon- ditionswithareduced-scalefunctionalmodel providesuseful information regarding the non-linear behavior of the trans- former.Inarealpowertransformer,thesetestsareverydifficult to carry out, due to the big magnitudes of the currents and powersinvolved.Thisproblemwasresolvedbyusingapproxi- matenumericalsolutions.However,onlyrealmeasurementsare capableofvalidatingtheseresults.Currently,digitalsimulation toolsdonotaccountfortime-dependentasymmetricsaturation, whichrequiresthedevelopmentofspecificmodelsforeachtype oftransformer(Egorov,2007).Theapproachproposedinthis workconsidersafabricatedsmallreduced-scaletransformer,an experimentalsetupthatpermitsthesimulationofGICsandthe useofinstrumentationformeasuringkeyvariables.
2. Reduced-scalemodelandGICssimulator
The transformermodel is specified andscaled in orderto simulateGICseffectsoverrealtransformers.Thefocusinthis workis tosimulate onlythe core losses, lossesin the wind- ings produced by GICs, which are the dominant sources of heatassociatedwiththecurrentsandmagneticfluxesharmonic content.
Vac Ip
Vp Vs
Is
R
Temperature Bleakage
IDC
Fig.2.MonophasictransformerGICsimulatorblockdiagram.
2.1. Reduced-scaletransformer
To manufacture transformer scaled must consider several design parametersso that their behavior isas closeas possi- bletorealtransformers.Forexample,theoperatingpointofthe magneticcoreisdesiredtobeequaltotherealtransformers.The sectionalareaofthemagneticcoreandwindingsmustbescaled basedonthetransformer’spower.Highvoltagewindingswere notconsideredsinceonlytheeffectsofthecurrentsinthetrans- formerareintended tobeanalyzed.Asinglephaseof athree phasetransformerbankscaledmanufacturedtosimulateinthe GICswasselected.
2.2. StructureoftheGICssimulator
The simulator consists of atransformer withsingle-phase reduced scalewiththreelegs,acontrollablecurrent source,a resistiveloadandtheelectronicinstrumentationdataacquisition systemformeasuringtheprimaryandsecondaryvoltagesand currents,DCcurrentinordertosimulateGICs,thedensitystray magnetic flux outside the magneticcoreand the temperature ofthetransformercorefordifferentoperatingpoints.Figure2 showsasimplifiedschematicdiagramofthesimulator.
Thescaledsingle-phasetransformerwasdesignedtobefeed withavoltageof120Vintheprimaryandthesecondary6.0V andaloadcurrent inthesecondaryof100mA andshell-type construction.Aresistiveloadof50,whichistheratedtrans- formerload,wasconsidered.Theobjectiveofthissimulatoris toevaluatetheeffectofGICswiththetransformeroperatingat itsratedload.
Thereduced-scaletransformerisfeedbyavariacthatallows changing the supply voltagefrom 0 to 120VAC.The source of DCcurrent “IDC”thatsimulatestheGICs, allowsthecur- rentsuppliedtothesecondaryofthetransformertobeadjusted from 0to250mA DC,from0 to250%ofthe valueRMSof nominalcurrent.TheIDCcurrentmainlyflowsthroughthesec- ondarywindingofthetransformerbecauseitsresistanceis1/50 oftheloadresistance.Thecurrentsintheprimaryandsecondary transformerare measuredby resistiveshunts,andthevoltage measurement points have voltage dividers that are appropri- atefornotexceedingthevoltagelimitsofthedataacquisition system.
The stray magnetic-flux density is measured with aHall- effectsensorthatislocatedintheexternalportionofthecore, atthecentrallegandparalleltothemagneticfluxthatispro- ducedbythetransformerwinding.Thislocalizationwaschosen
todeterminetheleakagefluxthatleavesthemagneticcorewhen GICsarepresent.ThetemperatureismeasuredwithanLM35 sensorthatisattachedtothemagneticcore.Thereasonforthe temperaturemeasurementinthemagneticcoreistodetermine the increase of heat produced by harmonics associated with GICs. The DCsource current, the Hall-effect sensor andthe temperaturemeterwerepoweredwithanindependentAC/DC source.
2.3. Instrumentation
Theinstrumentationis basedon acommercialdataacqui- sition system that digitizes the measured variables at a rate of20,000samples/second.Acontrol programthat was devel- opedingraphicallanguageallowstheinstrumenttoacquirethe waveformsofthemeasuredvariablessimultaneously.
Thecontrolprogramallowstheusertovisualizethebehavior ofthevariablesintimeandfrequencydomain.Thefrequency spectrumof the measured waveformsis spread out by using adiscreteFouriertransformvia aHammingwindow,andthe rootmeansquare(RMS)valuesandtheTHD(TotalHarmonic Distortion)ofthe involved variablesare also spreadout.The programalsoshowsthebehaviorofthesaturationcurveforeach operatingpoint. Thetemperaturebehaviorduringthe testcan beusedtoestimatethelossesassociatedwitheachsimulation execution.
3. Simulationresultsanddiscussion
3.1. Asymmetricnon-linearitywithGICsanditseffecton waveforms
Thevoltagewaveformintheprimarycorrespondstothesup- pliedACpower,whichisalow-impedancesource.Theprimary currentshowssignificantchangesastheIDCcurrentincreases inthesecondary.The averagevalueof theprimary currentis zero,butthewaveformindicateshalf-waveasymmetry.Thepeak valueofthecurrentishigherbyahalf-wavecomparedtothe other.Thisdifferencedemonstratesthedecreasingmagnetiza- tionimpedanceinthehalf-cycle,whenthepeakcurrentislarger.
Figure3showstwocurrentwaveformsthat areseenfromthe primary.TheredcurvehasnoIDCcomponent,whiletheblue curvecorrespondstotheprimarycurrentplusIDCcomponent inthesecondarywhichsimulatestheGICs.Thevoltagesatthe secondarypositiveandnegativepeaksaredeformedduetosym- metricalsaturationundernormalconditions.However,whenthe IDCcomponentispresent,thehalf-wavesymmetryislost,and thedutycycleisasymmetrical.
Figure4showsthecurrentwaveformsoftwoconditionson thesecondary,withandwithoutIDCcurrentthatweremeasured ontransformerwinding.
3.2. Thebehaviorofthegeneratedharmonics
Thevoltagesandcurrentswaveformsinthesecondaryofthe transformerduringnominaloperatingcondition,wherethefun- damentalfrequencycanbe50Hzor60Hz,havesymmetryof
80 70 60 50 40 30 20
Current mA
10 0 –10 –20 –30 –40 –50
0 0.005 0.01 0.015 0.02 Time
0.025 0.03 0.035 0.04
Fig.3.WaveformsoftheprimarycurrentswithandwithoutGICdepictedas redandbluelines,respectively.
400 350 300 250 200 150 100 50
–50 –100 –150 –200 –250 –300
0 0.005 0.01 0.015 0.02 Time
0.025 0.03 0.035 0.04 0
Current mA
Fig.4.WaveformsofthesecondarycurrentswithandwithoutGICillustrated asredandbluelines,respectively.
half-waveandareassociatedwithsymmetricsaturationof the magneticcore. Thisbehavior onlyhasodd-harmoniccompo- nents.Thus,theharmoniccomponentsof1,3,5,7,...represent the components thatpossess thesewaveformsandsatisfy the followingproperty:
f(x)=−f(x+T/2) (1)
whereTistheperiodoftheperiodicsignal.
WhentheGICsflowthrough the secondarywinding,even harmonicsaregeneratedasaproductofasymmetricnonlinear- ityandthemagnitudeoftheoddharmoniccomponentsremains constant.Evenharmoniccomponentsappearintheprimaryand secondarycurrent andsecondaryvoltage. Figure5 shows the harmonic components of the primary current with andwith- outGICs, depictedassolid redandbluecurves,respectively.
Figure6showsthechangingmagnitudesofthelargestharmon- icsasafunctionthemagnitudesoftheIDCs.
40 30 20 10 0 –10 –20
Amplitude dB
–30 –40 –50 –60 –70 –80
0 100 200 300 400 500
Frquency
600 700 800 900 1000
Fig. 5.Spectral behaviorof the primarycurrents with and withoutGICs, depictedasredandbluelines,respectively.
60
H0 H1
IDC
H2 H3 H4 H5 H6
50
40
30
20
Is dB 10
0
0 20 40 60 80 100 120 140
–10
–20
–30
Fig.6.BehavioroftheharmonicsmagnitudeasafunctionoftheDCcurrent magnitude.
3.3. Magnetic-coreoperatingpointandlossesfrom hysteresis
Theoperating pointofthe magneticcoreisobtained from thegraphicalrepresentationofthemagneticfluxdensity(B)and themagneticfieldintensity(H).TheBHcurveshowshowthe magneticfluxdensitychangesasthealignmentofthemagnetic domainschangeswithinthemagneticcircuit.Oncealldomains havebeenaligned,thesaturationpointisreached,andfurther increasesinmagneticfieldintensityhavelittlechangesofthe magnetic flux density. The areaof the hysteresisloop corre- spondstotheenergydissipatedasheatbythemagnetizationand demagnetizationprocessduringeachcycle.Figure7showstwo operationconditionswithandwithoutanIDCcomponent.These curvesareobtainedbyplottingtheintegralofthesecondaryvolt- age(proportionaltomagneticfluxdensity“B”)onthevertical axis and primary current on the transformer (proportional to ampere*turns“H”)onthehorizontalaxis.
2.5
2.0
1.5
1.0
0.5
0.0
B tesla
–0.5
–1.0
–1.5
–2.0
–60.0 –50.0 –40.0 –30.0 –20.0 –10.0 0.0 10.0 20.0 H au
30.0 40.0 50.0 60.0 70.0 80.0 90.0
Fig.7.TransformermagnetizationcurveswithandwithoutGICdepictedasred andbluelines,respectively,wherethehysteresiscurveisobserved.
Aqualitative analysisindicatedthatthesaturationcurveis symmetricabouttheverticalaxiswhennoDCcurrentispresent.
However,whentheDCcomponentispresent,thecurveshiftsto therightinthefirstquadrant,whichindicatesincreasingsatura- tion.Incontrast,thesaturationdecreasesinthethirdquadrant.
Nosignificantchangewasfoundintheareaofthehysteresis curvewhentheGICslevelsarepresent.However,whentheGICs levelishigher,theareaincreasedduetothelevelofharmonics increase.
3.4. Straymagneticfluxdensityanditsrelationshipwith themagnetizationcurrent
Thewaveformofthemagneticfluxdensitymeasuredinthe outer portion of the core is similar to the current waveform measuredinprimaryofthetransformer(Fig.3).Therefore,the magneticfluxdensityandthecurrentintheprimaryofthetrans- formerhavethesameharmoniccontent.Similarly,themagnetic fluxdensityhasaDCcomponentonlywhenGICsarepresent.
Figure8providesacomparisonofthetwowaveforms.Thecurve inbluecorrespondstothepresenceofGICs,andthecurvein redcorrespondstotheabsenceofGICs.
Themagneticfluxdensitycanbemeasuredinthefittingsand tankandwiththisinformation;lossesinthecriticalmechanical partsofthetransformercanbeestimated.
3.5. Impedanceasseenfromtheprimary
TherelationshipbetweenthevoltageandcurrentRMSval- uesgivesanideaoftheimpedancemagnitudewhentheGICs occur.WhenaDCcomponentispresentinthesecondary,the impedancevariesasfollows:
Z=a−b(IDC)2 (2)
whereaandbareparametersthatdependonthesupplyvoltage.
Figure 9 showsthe impedancebehavior as a functionof the
0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004
Flux density tesla
0.002
–0.002 –0.004 –0.006 –0.008 –0.01 –0.012
0 0.005 0.01 0.015 0.02 0.025
Time
0.03 0.035 0.04 0
Fig.8.StraymagneticfluxwaveformswithandwithoutGICdepictedasred andbluelines,respectively.
12 11 10 9 8 7 6
Impedance ohms
5 4 3 2
0 50 100 150 200 250 300
Zp80 Zp90 Zp100 Zp110 Zp125 Zp140 IDC
Fig.9.Impedanceofprimarywindingasafunctionofinputvoltageandsec- ondaryDCcurrent.
IDCsatdifferent inputvoltages. Thiswas obtained bycurve fittingbehavior.
3.6. Powerassociatedwiththetransformer
Instantaneouspowerisobtainedbymultiplyingthevoltage bythecurrentpointbypoint,whichresultsinatime-dependent function.Figure 10 showsthe instantaneous power basedon theprimary winding of thetransformer withandwithoutthe DCcurrentdepictedasredandbluelines,respectively,onthe secondarywinding.
Thepowerhasacomponentthatistwicethefrequency,even harmonic components, inthe absence of the IDC. However, whentheIDCispresent,thecomponentof thefirstharmonic appearsintheinstantaneouspowerandoddharmoniccompo- nents.
0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004
Flux density tesla
0.002
–0.002 –0.004 –0.006 –0.008 –0.01 –0.012
0 0.005 0.01 0.015 Time
0.02 0.025 0.03 0.035 0.04 0
Fig.10.Instantaneouspowerwaveformintheprimarywindingofthetrans- former.
7000
6000
5000
4000
3000
2000
1000
0
0 50 100 150
IDC
Sp VA
200 250 300
Vp80 Vp90 Vp100 Vp110 Vp120 Vp140
Fig.11.Apparentpowerasafunctionoftheinputvoltageandthesecondary DCcurrent.
TherealpowerisobtainedbyusingEq.(3).
Pr= 1 T
T
0
V(t)∗I(t)dt (3)
If the average real power transferred by the transformer without GICs is 100%, the real power is 68% when IDC is present. Consequently, the real power at the inputthe trans- formerdecreasesby32%whentheIDCispresent.Thereactive power changeis from100%to166%VARs (underthe same conditions), whichcorresponds to an increase of 66% in the absenceoftheIDC.Incontrast,thepeakinstantaneouspower valuesincreaseby29%.
Ifwe considertheproductof the“RMS”voltageandcur- rent,themagnitudeoftheapparentpowercanbeobtained.The behavioroftheapparentpowerbasedontheIDCandfordiffer- entsupplyvoltagesisshowninFigure11.Inaddition,Figure11
60
50
40
30
20
10
0
0 20 40 60 80
Time minutes
Temperature °C
100 120 140
Fig.12. Thetemperaturemeasurementresultsonthetransformercore.
displaysaparabolicbehaviorthatissimilartothebehaviorthat ispresentedinFigure9.
3.7. Thermalbehavior
Theamountofheatgeneratedbythecorelosses(inthewind- ingsandfittings)resultsinnon-uniformtemperatureincreases in the transformer. However, if the total concentrated losses areconsidered,thetemperatureincreasefollowsanexponential functionrelativetotheamountofheatgeneratedbyalllosses,the transformermass,theenvironmentaltemperatureandtimeevo- lution.Figure12showsthetemperaturemeasurementresultson thetransformercore.Duringthefirstperiod,onlylossesfromthe transformeroccurred.Thetemperaturetendstostabilizeduring thesecondperiod.Inaddition,whentheDCcurrentisapplied, thetemperatureofthetransformerincreases.
Theperformanceofthe coretemperaturewithandwithout theIDCcanbeapproximatedbyusingthefollowingequations:
T =6.6∗(1−e−0.06t)+23.6 (4)
T =25∗(1−e−0.017(t−52))+29.5 (5)
whereTrepresentsthetemperature(◦C)andtistime(min).Eq.
(4)isonlyvalidoverthetimeintervalof0<t<52,whileEq.(5) isonlyvalidfor t>52.ThetimeconstantsinEqs.(4)and(5) aredifferentbecausenewheatsourcesappearwhentheGICs arepresent.Forexample,theheatproducedby“eddycurrents losses”onthecoreandwindings.
4. Conclusions
Thesimulation of GICsusingareduced-scale transformer model provide insight into the effects that occur on parame- terssuchasvoltage,current,power,magneticfluxandthermal behavior.Thissimulationpermitstoobservetheharmonicscon- ductproducedattheoperating pointofthe magneticcore.In
addition,thelossesandthereactiveloadvariationscanbeesti- matedwhentheGICsarepresent.Changescanbeobservedin theoperating pointofthetransformerduetothe GICs,which mainlyaffectrealpowertransference,variationinitsimpedance andtheincreaseoflosses.Eachtransformerhasauniqueelectri- cal,magneticandmechanicaldesigninwhichthecharacteristics ofthematerialsareveryimportant.Therefore,toapplythepro- posedsolution,manufacturingascalemodelandthesimulation of its behaviorunder the effect of GICsis requiredfor each transformerdesign.Theinformationobtainedfromthesimula- tioncanbeusedtoobtaindesignrulesandvalidatemathematical simulationmodels.Consequently,designrulescanbeoptimized consideringtheGICs.Futurestudieswillaimtodevelopelab- orate scale models for real transformersinorder tosimulate theirbehaviorundertheinfluenceoftheGICs.Furtherstudies willexploretheeffectsofGICsinthree-phasetransformerswith three,four,fivelegsandpowerof100kVA,whichwillbecon- structedwithdifferentdesigncriteria.Onecurrenttechnological challenge is the establishment of test methodsfor evaluating theperformanceoftransformerswithmorethan1MVAwhen influencedbyGICs.
Conflictofinterest
Theauthorshavenoconflictsofinteresttodeclare.
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