Transformer-Like Devices for High-Accuracy AC Current Measurements

63 Pages·2008·0.66 MB·English

by  T. M. Souders

NIST Technical Note 1473
Transformer-Like Devices for High-Accuracy AC
Current Measurements
T. M. Souders
NIST Technical Note 1473
Transformer-Like Devices for High-Accuracy AC
Current Measurements
T. M. Souders
June2008
U.S.DepartmentofCommerce
CarlosM.Gutierrez,Secretary
NationalInstituteofStandardsandTechnology
JamesM.Turner,DeputyDirector
Certaincommercialentities,equipment,ormaterialsmaybeidentifiedinthis
documentinordertodescribeanexperimentalprocedureorconceptadequately.Such
identificationisnotintendedtoimplyrecommendationorendorsementbythe
NationalInstituteofStandardsandTechnology,norisitintendedtoimplythatthe
entities,materials,orequipmentarenecessarilythebestavailableforthepurpose.
NationalInstituteofStandardsandTechnologySpecialPublication1473
Natl.Inst.Stand.Technol.Spec.Publ.1473,62pages(June2008)
CODEN:NSPUE2
TableofContents
FOREWORD………………………….……………….……………………………….. ix
ABSTRACT………………………………………………………………………………1
1. INTRODUCTION…………………….………………………………………….….……2
1.1 TheIdealTransformer………………………………………………………………2
1.2 TransformerErroranditsRepresentation……….………………………………….2
1.3 OtherErrorSources…………………………………………………………………3
1.4 Notation………………………………………………………………………....…..4
2. PHYSICALINTERPRETATIONOFTRANSFORMER ERROR ……………………...4
3. THECURRENTCOMPARATOR …………………………….…………………..….….7
3.1 TheCompensatedCurrentComparator…………………………………………...10
4. MAGNETICDESIGN EQUATIONSANDTHE
MEASUREMENTOFMAGNETICPROPERTIES………….…………………….…..11
4.1 Hysteresis,PermeabilityandCoreLoss………………………………………..…11
4.2 MagneticFlux DensityandSaturation Flux Density……….……………………. 13
4.3 MagnetizingImpedance andMagnetizingImpedanceperTurn-Squared………...13
4.4 DetectionSensitivityforCurrentComparators,andTunedDetection………..…. 14
4.5 CoreDemagnetization ………………………………………..……………………16
5. WINDINGTECHNIQUESAND THE
ESTIMATIONOFLEAKAGE IMPEDANCES ………….……………………..……. 16
5.1 NumberofTurns and WireSize…………………………..………………………16
5.2 WindingLayout……………………………………………..…………………….17
5.3 The“Single-Turn”Problem………………………………….…………………... 18
5.4 TurnsCounting…………………………………………….……………………...19
6. PASSIVEANDACTIVECORRECTIONTECHNIQUES…………….…………….. 20
6.1 PassiveTwo-StageCurrentTransformers…………………….…………………. 20
6.2 ActiveTwo-StageTransformers……………………………….………………… 23
6.3 ActiveCurrent-ComparatorCorrectionCircuits ………………………………… 25
6.4 ConstructionofTwo-StageTransformersandCompensated
CurrentComparators……………………………………….…………..…….…….27
6.5 RatioCascading…………………………………………………..………………..28
7. MAGNETICERROR:ITS MEASUREMENTANDMITIGATION………….………28
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7.1 SourceofMagneticError………………………………………………………... 29
7.2 TestMethod forMagneticError…………………………………………………. 30
7.3 MagneticShieldingtoReduceMagneticError………………………………….. 31
8. CALCULATIONANDMANAGEMENTOFCAPACITIVEERRORS…………….. 34
8.1 EvaluationofSign Factor,k ……………………………………………………. 35
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8.2 CalculatingCapacitiveErrors:Examples ……………………………………….. 35
8.3 TrimmingofCapacitiveErrorsinTransformers orCompensated
CurrentComparators……………………………………………………………… 40
8.5 AdditionalComments on CapacitiveErrors…………………………………….. 42
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9. CURRENTTRANSFORMER TESTING……………………………………………... 42
9.1 TransformerTestingUsingaStandardTransformer…………………………….. 43
9.2TransformerTestingUsingaCompensatedCurrentComparator………………… 45
9.3SecondaryFeedwithaCompensatedCurrent Comparator……………………….. 46
9.4TestingTransformers withRatiosLessThanUnity………………………………. 47
9.5MeasuringtheTestTransformerBurden………………………………………….. 48
10. CalibrationMethodsand DeterminationofUncertainties……………………………... 48
11. REFERENCES………………………………………………………………………… 50
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ListofFigures
Figure1.1 CurrentMeasurementUsingVoltage-Based Instrumentation…………………. 1
Figure1.2 TheIdealTransformer…………………………………………………………. 2
Figure1.3 Equivalent CircuitofTwo-WindingTransformer……………………………... 3
Figure1.4 NotationofCoresand Windings …………………………………………….… 4
Figure2.1 CurrentTransformerwithSquare-Cross-SectionToroidalCore (1/2shown)… 5
Figure3.1a SimpleCurrentComparator……………………………………………………. 7
Figure3.1b SchematicRepresentationofSimpleCurrentComparator…………………….. 8
Figure3.2 EquivalentCircuitofaSimpleCurrentComparator…………………………… 8
Figure3.3 CompensatedCurrentComparator…………………………………………….. 10
Figure3.4 CompensatedCurrentComparator:EquivalentCircuit……………………….. 11
Figure4.1 Hysteresis Loop……………………………………………………………….. 12
Figure4.2 TestSetupto MeasureMagnetizingImpedanceperTurn-Squared(left),
anditsEquivalentCircuit(right)………………………………………………. 14
Figure4.3 TunedDetectionCircuit(left),andEquivalentCircuit(right).……………….. 15
Figure4.4 CoreDemagnetization …………………………………………………………. 16
Figure5.1 Series-ParallelArrangementforPrimaryWinding(oneexample)……….…… 18
Figure5.2 Solutionfor “Single-Turn”Problem…………………………………………… 19
Figure5.3 TurnsCountingCircuit…………………………………………………………. 19
Figure6.1 Two-StageCurrentTransformerwith SeparateBurdens……………………… 20
Figure6.2 Two-StageTransformer withSeparateBurdens:EquivalentCircuit …………. 21
Figure6.3 Two-StageTransformer-ScaledResistor……………………………………… 22
Figure6.4a,b Two-StageTransformer withSingleBurden:EquivalentCircuits……………. 22
Figure6.4c Two-StageTransformer withSingleBurden: FinalEquivalentCircuit………. 23
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Figure6.5 Two-StageTransformer with FeedbackAmplifier……………………………. 24
Figure6.6 Amplifier-AidedTwo-StageTransformer…………………………………….. 24
Figure6.7 Self-BalancingCurrentComparator…………………………………………… 25
Figure6.8 Self-BalancingCurrentComparator:EquivalentCircuit……………………… 26
Figure6.9 Miljanic-So-MooreCircuit……………………………………………………. 26
Figure6.10 Miljanic-So-MooreEquivalentCircuit………………………………………... 27
Figure6.11 ConstructionofTwo-StageTransformersandCompensated
CurrentComparators………………………………………………………….. 28
Figure6.12 CascadingTwo-StageandAmplifier-AidedTwo-StageTransformers………. 28
Figure7.1 UnequalSensitivities DuetoMagneticError…………………………………. 29
Figure7.2 Manifestationof MagneticError………………………………………………. 29
Figure7.3 SourceofMagneticError……………………………………………………… 30
Figure7.4 TestMethod forAssessingMagneticError…………………………………… 31
Figure7.5 UseofMagneticShieldtoReduceMagneticError …………………………… 32
Figure7.6 MagneticShield–½ofShieldShowntoillustrateCrossSection……………. 32
Figure7.7 EddyCurrentShield–½ ofShield ShowntoillustrateCrossSection……….. 33
Figure8.1 CapacitiveCurrentin SecondaryWinding
ofaTransformerorCompensatedCurrent
Comparator,withaShieldConnectedtotheDefinedTerminal………………. 36
Figure8.2 CapacitiveCurrentin SecondaryWindingof a
TransformerorCompensatedCurrentComparator,
withaGrounded ShieldandMarkedTerminalatVirtualGround…………… 37
Figure8.3 Turn-to-TurnCapacitanceofSecondaryWinding……………………………. 38
Figure8.4 CapacitiveCurrentin PrimaryWindingofa
TransformerorCompensatedCurrentComparator,
withaGrounded ShieldandMarkedTerminalatVirtualGround…………… 39
Figure8.5 Turn-to-TurnCapacitanceofPrimaryWinding………………………………. 40
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Figure8.6 TrimmingCapacitiveErrorinaTwo-Stage
TransformerorCompensatedCurrentComparator ……………………………. 41
Figure9.1 TransformerTestingwithaTransformer-LikeStandard……………………… 43
Figure9.2 TestSetBasedon Measurementof
ErrorCurrentThroughaSmallResistance……………………………………. 44
Figure9.3 TestSetBasedon Measurementof
ErrorCurrentinaCurrentComparator Winding……………………………….. 44
Figure9.4 TransformerTestingwithaCompensatedCurrentComparator……………… 45
Figure9.5 TransformerTestingwithCompensated
CurrentComparatorUsingSecondaryFeed…………………………………… 47
Figure9.6 SpecialPurposeCompensatedCurrent
ComparatorforRatios LessThanUnity………………………………………. 48
Figure10.1 Calibrationofthe1/1BaseRatioofaTransformer…………………………… 49
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ListofTables
Table5.1 ApproximateCurrentCarryingCapacityofSelected Wire Sizes…………………. 17
Table7.1 LowestAchievableMagneticError forDifferentConfigurations………………… 34
Table8.1 EvaluationofSign Factor,k ……………………………………………………… 35
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FOREWORD
Between1967and1975, theauthorconductedthecalibrationservices forinstrumentcurrent
transformers attheNationalBureauofStandards(nowNationalInstituteof Standards and
Technology),andupgradedthefacilitiesusedinthoseservices. Inaddition,hedeveloped and
implemented anewmeasurementserviceforlow-valueacresistors. Much ofthematerialincluded
inthis TechnicalNotederivesfromworkduringthatperiod. Remarkably, thefieldhasnot
changeddramaticallyovertheinterveningyears.
Theperiodfromabout1958to1970sawrenewed interestintransformer-likedevices assolutions
toavarietyofelectrical measurementproblems, anddevelopmentprogramswereundertaken ata
numberofnationallaboratoriesanduniversities. Manyoftheseledtonewtypesofdeviceshaving
vastlyimproved accuracy, makingitpossibletoscaleand measureimpedances,acvoltageand
current,andpowerandenergy,withunprecedentedaccuracy. Duringthis period,anongoing
collaborationbetweenP. N.MiljanicoftheInstitutNikolaTeslainBelgrade,Yugoslaviaand N.
L. Kustersand W.J. M. MooreoftheNationalResearchCouncil(NRC)inOttawa,Canada,ledto
thedevelopmentofthemoderncurrentcomparator. Thisrepresentedanewclassoftransformer-
likedevices withremarkablyincreasedaccuracyoverconventional currenttransformers.O.
Petersons,alsowithNRC duringpartofthattime,extendedandappliedtheworkofthat group,
particularlytothefieldofhighvoltagemeasurements. Manyofthesedevelopmentswere
availabletotheauthor as hebeganthedesignofthenewmeasurementservicesatNBS. Around
1968PetersonsleftNRC totakeapositionatNBSandtheauthorwas fortunatetohavehim asa
mentorduringthefirstfew yearsofhis career. Manyoftheideas andapproachessetforthinthis
document,especiallyregardingmagneticshieldingandtheuseof equivalentcircuits,canbetraced
tohisinfluence. TheworkwasperformedunderthesupervisionofB.L.Dunfee,whoprovideda
supportive,nurturingworkenvironmentfor whichtheauthorhaseversincebeenthankful. In
addition,colleaguesD. FlachandR. Kahlerwerepartners duringpartofthis work, andcontributed
theirowndiligenceandinsights. Ofcourse,anyerrorsoromissions inthisdocumentaresolely
theauthor’s responsibility.
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