EMI PPT (UNIT-2).pdf

EMI PPT (UNIT-2)

1. ELECTRICAL MEASUREMENTS AND INSTRUMENTATION
UNIT –II: Analog Wattmetersand Power Factor Meters
M.SURESH
M.Tech(NITW)., (Ph.D)
Associate Professor
EEE Department
RISE Krishna SaiPrakasamGroup of Institutions
Ongole, PrakasamDt. AP

2. Content
•Electrodynamometer type wattmeter (LPF and UPF),
•Power factor meters: Dynamometer and M.I type
•(Single phase and Three phase),
•Construction, Theory, Torque equation,
•Advantages and Disadvantages
•Numerical Problems.
M.SURESH, EEE Dept

3. INTRODUCTION
•Measurementofelectricpowerisasessentialinindustryasincommercial
orevendomesticapplications.
•Priorestimationandsubsequentmeasurementsofinstantaneousand
peakpowerdemandsofanyinstallationaremandatoryfordesign,
operationandmaintenanceoftheelectricpowersupplynetworkfeeding
it.
•Whereasanunder-estimationofpowerdemandmayleadtoblowingout
ofpowersupplysideaccessories,ontheotherhand,over-estimationcan
endupwithover-designandadditionalcostofinstallation.
•Knowledgeaboutaccurateestimation,calculationandmeasurementof
electricpoweristhusofprimaryconcernfordesignersofnew
installations.
M.SURESH, EEE Dept

4. ELECTRODYNAMOMETER-TYPE INSTRUMENTS(Cont…)
•Theelectrodynamometerisatransfer-typeinstrument.Atransfer-type
instrumentisonethatmaybecalibratedwithadcsourceandthenused
withoutmodificationtomeasureac.
•Thisrequiresthetransfertypeinstrumentstohavesameaccuracyforboth
dcandac.
•Theelectrodynamicordynamometer-typeinstrumentisamoving-coil
instrumentbutthemagneticfield,inwhichthecoilmoves,isprovidedby
twofixedcoilsratherthanbypermanentmagnets.
•TheschematicdiagramofelectrodynamicinstrumentisshowninFig.(a)
andapracticalmeterisshowninFig.(b).
•Itconsistsoftwofixedcoils,whicharesymmetricallysituated.
•Itwouldhaveatorqueinonedirectionduringonehalfofthecycleandan
equaleffectinoppositedirectionduringtheotherhalfofthecycle.
•If,however,weweretoreversethedirectionofthefluxeachtimethe
currentthroughthemovablecoilreverses,aunidirectionaltorquewould
beproducedforbothpositivehalfandnegativehalfofthecycle.
•Inelectrodynamicinstruments,thefieldcanbemadetoreverse
simultaneouslywiththecurrentinthemovablecoilifthefixedcoilis
connectedinserieswiththemovablecoil.
M.SURESH, EEE Dept

5. ELECTRODYNAMOMETER-TYPE INSTRUMENTS
Fig. Electrodynamometer-type instrument
M.SURESH, EEE Dept

6. M.SURESH, EEE Dept
ELECTRODYNAMOMETER-TYPE INSTRUMENTS

7. ELECTRODYNAMOMETER-TYPE INSTRUMENTS (Cont…)
1.ControllingTorqueThecontrollingtorqueisprovidedbytwocontrol
springs.Thesespringsactasleadstothemovingcoil.
2.DampingAir-frictiondampingisemployedfortheseinstrumentsandis
providedbyapairofaluminumvanes,attachedtothespindleatthe
bottom.Thesevanesmoveinasector-shapedchamber.
M.SURESH, EEE Dept

8. Torque Equation of Electrodynamometer-type Instruments2
M.SURESH, EEE Dept
•Let, i
1= instantaneous value of current in the fixed coils, (A)
•i
2= instantaneous value of current in the moving coils, (A)
•L
1= self-inductance of fixed coils, (H)
•L
2= self-inductance of moving coil, (H)
•M = mutual inductance between fixed and moving coils (H)
•Flux linkage of Coil 1, ψ
1= L
1i
1+ Mi
2
•Flux linkage of Coil 2, ψ
2= L
2i
2+ Mi
1
•Electrical input energy,

9. Torque Equation of Electrodynamometer-type Instruments (Cont…)
•From the principle of conservation of energy,
•Total electrical input energy = Change in energy in energy stored +
mechanical energy
•The mechanical energy can be obtained by subtracting Eq. (2) from Eq. (1).
•Therefore, mechanical energy
•Now,theself-inductancesL
1andL
2areconstantsand,therefore,dL
1and
dL
2bothareequaltozero.Hence,mechanicalenergy=i
1i
2Dm
•SupposeT
iistheinstantaneousdeflectingtorqueanddθisthechangein
deflection,then,Mechanicalenergy=workdone=T
idθ
•Thuswehave
M.SURESH, EEE Dept

10. M.SURESH, EEE Dept

11. M.SURESH, EEE Dept
Torque Equation of Electrodynamometer-type Instruments (Cont…)

12. M.SURESH, EEE Dept
Torque Equation of Electrodynamometer-type Instruments (Cont…)

13. M.SURESH, EEE Dept
Torque Equation of Electrodynamometer-type Instruments (Cont…)

14. •Inanelectrodynamicammeter,thefixedandmovingcoilsareconnectedin
seriesasshowninFig.
•Ashuntisconnectedacrossthemovingcoilforlimitingthecurrent.
•Thereactance–resistanceratiooftheshuntandthemovingcoiliskeptnearly
sameforindependenceofthemeterreadingwiththesupplyfrequency.
•Sincethecoilcurrentsarethesame,thedeflectingtorqueisproportionalto
themeansquarevalueofthecurrent.Thus,thescaleiscalibratedtoreadthe
rmsvalue.
Fig. Electrodynamometer
ammeter
M.SURESH, EEE Dept
ElectrodynamicAmmeter

15. •Theelectrodynamicinstrumentcanbeusedasavoltmeterbyconnecting
alargenoninductiveresistance(R)oflowtemperaturecoefficientinseries
withtheinstrumentcoilasshowninFig.
Fig. Electrodynamometer
voltmeter
M.SURESH, EEE Dept
ElectrodynamicVoltmeter

16. •Theelectrodynamicwattmeterconsistoftwofixedcoils‘a’and‘b’placed
symmetricaltoeachotherandproducingauniformmagneticfield.
•TheyareconnectedinserieswiththeloadandarecalledtheCurrentCoils
(CC).
•Thetwofixedcoilscanbeconnectedinseriesorparalleltogivetwo
differentcurrentratings.
•Thecurrentcoilscarrythefull-loadcurrentorafractionoffullloadcurrent.
•Thusthecurrentinthecurrentcoilsisproportionaltotheloadcurrent.
•Themovingcoil‘c’,inserieswithahighnoninductiveresistanceR
vis
connectedacrossthesupply.
•Thusthecurrentflowinginthemovingcoilisproportionalto,andpractically
inphasewiththesupplyvoltage.
•ThemovingcoilisalsocalledthevoltagecoilorPressureCoil(PC).
•Thevoltagecoiliscarriedonapivotedspindlewhichcarriesthepointer,the
pointermovedoveracalibratedscale.
•Twohairspringsareusedforprovidingthecontrollingtorqueandforleading
currentintoandoutofthemovingcoil.
•Dampingisprovidedbyairfriction.
•Fig.showsthebasicarrangementofaelectrodynamicwattmeter.
M.SURESH, EEE Dept
ElectrodynamicWattmeter

17. Fig. Electrodynamicwattmeter
M.SURESH, EEE Dept
ElectrodynamicWattmeter

18. Torque Equation of Electrodynamometer-type Instruments
•Let, i
f= current in the fixed coil
i
m= current in the moving coil
i= load current
v = load voltage
T
in= instantaneous value of the deflecting torque
p = instantaneous power
•T
inαi
fx i
m
•But since i
fαI, i
mαv
•T
inαv x I αp
•Thus,theinstantaneousvalueofthedeflectingtorqueisproportionaltothe
instantaneouspower.
•Owingtotheinertiaofthemovingsystem,thepointerreadstheaverage
power.
•Indccircuits,thepowerisgivenbytheproductofvoltageandcurrent,and
hencethetorqueisdirectlyproportionaltothepower.
•Thus,theinstrumentindicatesthepower.
M.SURESH, EEE Dept

19. •Let, i
f = current in the fixed coil
•i
m= current in the moving coil
•i= load current
•v = load voltage
•T
in= instantaneous value of the deflecting torque
•p = instantaneous power
•T
inαi
fi
m
•But since i
fαiand i
mαv and T
inαvi αp
•Thus,theinstantaneousvalueofthedeflectingtorqueisproportionaltothe
•instantaneouspower.Owingtotheinertiaofthemovingsystem,the
pointerreadstheaveragepower.Indccircuits,thepowerisgivenbythe
productofvoltageandcurrent,andhencethetorqueisdirectly
proportionaltothepower.Thus,theinstrumentindicatesthepower.
•Forac,theinstrumentindicatestheaveragepower.Thiscanbeprovedas
follows:T
inαvi
M.SURESH, EEE Dept
Torque Equation of Electrodynamometer-type Instruments

20. •Average deflecting torque αAverage power
•Let, v = V
msin wt and I = I
msin (wt-Ф)
•Average deflecting torque αAverage value of V
msin wt ×I
msin (wt-Ф)
αVI cosФ
•If T
dbe the average torque, then T
dαVI cosФ
αTrue power = k P
•where P is the true power and k is the constant.
•For spring control T
C= k
sθ
1
•whereT
Cisthecontroltorque,
•k
sisthespringconstantand
•θ
1istheangleofdeflectionofthepointer.
•Forsteadydeflection,
•T
C=T
d
•k
sθ
1=kP
•k
sθ
1=(K/k
1)xP
•θ
1αP
•Hence,incaseofacalsothedeflectionisproportionaltothetruepowerinthe
circuit.
•Thescaleoftheelectrodynamometerwattmeteristhereforeuniform.
M.SURESH, EEE Dept
Torque Equation of Electrodynamometer-type Instruments

21. Advantages & Disadvantages of Electrodynamometer-type
Instruments
AdvantagesofElectrodynamometer-typeInstruments
➢Theycanbeusedonacaswellasdcmeasurements.
➢Theseinstrumentsarefreefromeddycurrentandhysteresiserror.
➢Electrodynamometer-typeinstrumentsareveryusefulforaccurate
measurementofrmsvaluesofvoltagesirrespectiveofwaveforms.
➢Becauseofprecisiongradeaccuracyandsamecalibrationforacanddc
measurementstheseinstrumentsareusefulastransfertypeand
calibrationinstruments.
DisadvantagesofElectrodynamometer-typeInstruments
✓Astheinstrumenthassquarelawresponse,thescaleisnon-uniform.
✓Theseinstrumentshavesmalltorque/weightratio,sothefrictionalerroris
considerable.
✓MorecostlythanPMMCandMItypeofinstruments.
✓Adequatescreeningofthemovementsagainststraymagneticfieldsis
essential.
✓Powerconsumptioniscomparablyhighbecauseoftheirconstruction.
M.SURESH, EEE Dept

22. Power Measurement In AC Circuits
•Inalternatingcurrentcircuits,theinstantaneouspowervaries
continuouslyasthevoltageandcurrentvarieswhilegoingthroughacycle.
•Insuchacase,thepoweratanyinstantisgivenbyP(t)=v(t)Xi(t)
•where,p(t),v(t),andi(t)arevaluesofinstantaneouspower,voltage,and
currentrespectively.
•Thus,ifbothvoltageandcurrentcanbeassumedtobesinusoidal,with
thecurrentlaggingthevoltagebyphase-angleφ,then
•where,V
mandI
marepeakvaluesofvoltageandcurrentrespectively,and
wistheangularfrequency.
M.SURESH, EEE Dept

23. where,VandIarermsvaluesofvoltageandcurrentrespectivelyandcosjispower
factoroftheload.
M.SURESH, EEE Dept

24. Power Measurement in DC Circuits
•Electricpower(P)consumedbyaload(R)suppliedfromadcpower
supply(V
S)istheproductofthevoltageacrosstheload(V
R)andthe
currentflowingthroughtheload(I
R):
•Thus,powermeasurementinadccircuitcanbecarriedoutusinga
voltmeter(V)andanammeter(A)usinganyoneofthearrangements
showninFig.(1).
Fig.(1) Two arrangements for power measurement in dc circuits
M.SURESH, EEE Dept

25. Power Measurement in DC Circuits (Cont..)
•Powerindccircuitscanalsobemeasuredbywattmeter.
•Wattmetercangivedirectindicationofpowerandthereisnoneedto
multiplytworeadingsasinthecasewhenammeterandvoltmeterisused.
•Thetypeofwattmetermostcommonlyusedforsuchpowermeasurement
isthedynamometer.Itisbuiltby(1)twofixedcoils,connectedinseries
andpositionedcoaxiallywithspacebetweenthem,and(2)amovingcoil,
placedbetweenthefixedcoilsandfittedwithapointer.
•Suchaconstructionforadynamometer-typewattmeterisshowninFig(2).
Fig(2). Basic construction of dynamometer-type wattmeter
M.SURESH, EEE Dept

26. •Itcanbeshownthatthetorqueproducedinthedynamometeris
proportionaltotheproductofthecurrentflowingthroughthefixedcoils
timesthatthroughthemovingcoil.
•Thefixedcoils,generallyreferredtoascurrentcoils,carrytheloadcurrent
whilethemovingcoil,generallyreferredtoasvoltagecoil,carriesa
currentthatisproportional,viathemultiplierresistorRV,tothevoltage
acrosstheloadresistorR.
•Asaconsequence,thedeflectionofthemovingcoilisproportionaltothe
powerconsumedbytheload.
•Atypicalconnectionofsuchawattmeterforpowermeasurementindc
circuitisshowninFig.(3).
Fig.(3) Connection of dynamometer-type wattmeter for power measurement in dc circuit
M.SURESH, EEE Dept

27. Electrodynamometer-type Wattmeter
•Construction of Electrodynamometer-type Wattmeter:
•Schematicdiagramdisplayingthebasicconstructionalfeaturesofa
electrodynamometertypewattmeterisshowninFig(3).
Fig.(3) Schematic of electrodynamometer-type wattmeter
M.SURESH, EEE Dept

28. Electrodynamometer-type Wattmeter (Cont..)
1. Fixed Coil System:
•Suchaninstrumenthastwocoilsconnectedindifferentwaystothesamecircuit
ofwhichpoweristobemeasured.
•Thefixedcoilsorthefieldcoilsareconnectedinserieswiththeloadsoasto
carrythesamecurrentastheload.
•Thefixedcoilsarehence,termedastheCurrentCoils(CC)ofthewattmeter.
•Themainmagneticfieldisproducedbythesefixedcoils.
•Thiscoilisdividedintwosectionssoastoprovidemoreuniformmagneticfield
nearthecentreandtoallowplacementoftheinstrumentmovingshaft.
•Fixedcoilsareusuallywoundwiththickwiresforcarryingthemainloadcurrent
throughthem.
•Windingsofthefixedcoilisnormallymadeofstrandedconductorsrunning
togetherbut,insulatedfromeachother.
•Allthestrandsarebroughtouttoanexternalcommutatingterminatorsothata
numberofcurrentrangesoftheinstrumentmaybeobtainedbygroupingthem
allinseries,allinparallel,orinaseries–parallelcombination.
•SuchstrandingofthefixedcoilsalsoreducesEddy-currentlossinthe
conductors.
•Stillhighercurrentorvoltageranges,however,canbeaccommodatedonly
throughtheuseofinstrumenttransformers.
•Fixedcoilsaremountedrigidlywiththecoilsupportingstructurestopreventany
smallmovementwhatsoeverandresultingfielddistortions.
•Mountingsupportsaremadeofceramic,andnotmetal,soasnottodisturbthe
magneticfielddistribution.
M.SURESH, EEE Dept

29. 2. Moving Coil System:
•Themovingcoilthatisconnectedacrosstheloadcarriesacurrent
proportionaltothevoltage.
•Sincethemovingcoilcarriesacurrentproportionaltothevoltage,itis
calledthevoltagecoilorthepressurecoilorsimplyPCofthewattmeter.
•Themovingcoilisentirelyembracedbythepairoffixedcoils.
•Ahighvaluenon-inductiveresistanceisconnectedinserieswiththe
voltagecoiltorestrictthecurrentthroughittoasmallvalue,andalsoto
ensurethatvoltagecoilcurrentremainsasfaraspossibleinphasewith
theloadvoltage.
•Themovingcoil,madeoffinewires,iswoundeitherasaself-sustaining
air-coredcoil,orelsewoundonanonmetallicformer.
•Ametallicformer,otherwisewouldinduceEddycurrentsinthemunder
influenceofthealternatingfield.
M.SURESH, EEE Dept
Electrodynamometer-type Wattmeter (Cont..)

30. 3. Movement and Restoring System:
•Themoving,orvoltagecoilalongwiththepointerismountedonan
aluminumspindleincasejewelbearingsareusedtosupportthespindle.
•Forhighersensitivityrequirements,themovingcoilmaybesuspended
fromatorsionheadbyametallicsuspensionwhichservesasaleadtothe
coil.
•Inotherconstructions,thecoilmaybesuspendedbyasilkfibretogether
withaspiralspringwhichgivestherequiredtorsion.
•Thephosphor-bronzespringsarealsousedtoleadcurrentintoandoutof
themovingcoil.
•Inanycase,thetorsionheadwithsuspension,orthespring,alsoserves
thepurposeofprovidingtherestoringtorquetobringthepointerbackto
itsinitialpositiononcemeasurementisover.
M.SURESH, EEE Dept
Electrodynamometer-type Wattmeter (Cont..)

31. 4. Damping System
•Dampinginsuchinstrumentsmaybeprovidedbysmallaluminumvanes
attachedatthebottomofthespindle.
•Thesevanesaremadetomoveinsideenclosedairchambers,therebycreating
thedampingtorque.
•Inothercases,themovingcoilitselfcanbestitchedonathinsheetofmica,
whichactsasthedampingvanewhilemovements.
•Eddy-currentdamping,however,cannotbeusedwiththeseinstruments.
•ThisisduetothefactthatanymetallicelementtobeusedforEddy-current
dampingwillinterfereanddistorttheotherwiseweakoperatingmagneticfield.
•Moreover,introductionofanyexternalpermanentmagnetforthepurposeof
Eddy-currentdampingwillseverelyhampertheoperatingmagneticfield.
5.ShieldingSystem
•Theoperatingfieldproducedbythefixedcoils,iscomparativelylowerin
electrodynamometer-typeinstrumentsascomparedtoothertypeof
instruments.
•Insomecases,eventheearth’smagneticfieldcanpollutethemeasurement
readings.
•Itisthusessentialtoshieldtheelectrodynamometer-typeinstrumentsfrom
effectsofexternalmagneticfields.
•Enclosuresofsuchinstrumentsarethusmadeofalloyswithhighpermeability
torestrictpenetrationofexternalstraymagneticfieldsintotheinstrument.
M.SURESH, EEE Dept
Electrodynamometer-type Wattmeter (Cont..)

32. Operation of Electrodynamometer-type Wattmeter
•V = voltage to be measured (rms) I = current to be measured (rms)
•i
P= voltage (pressure) coil instantaneous current
•i
C= current coil instantaneous current
•R
V= external resistance connected with pressure coil
•R
P = resistance of pressure coil circuit (PC resistance + RV)
•M = mutual inductance between current coil and pressure coil
•θ = angle of deflection of the moving system
•ω = angular frequency of supply in radians per second
•φ = phase-angle lag of current I with respect to voltage V
Fig.(5) Operational circuit of
electrodynamometer-type
wattmeter
M.SURESH, EEE Dept

33. •InstantaneoustorqueoftheelectrodynamometerwattmetershowninFig.(5)is
givenbyT
i=i
pi
c(dM/dθ)
•Instantaneous value of voltage across the pressure-coil circuit is vp=
•Ifthepressurecoilresistancecanbeassumedtobeveryhigh,thewholepressure
coilcanbeassumedtobebehavinglikearesistanceonly.Thecurrenti
Pinthe
pressurecoilthus,canbeassumedtoinphasewiththevoltagev
P,andits
instantaneousvalueis
•whereI
P=V/R
Pisthermsvalueofcurrentinpressurecoil.
•Assumingthatthepressure-coilresistanceissufficientlyhightopreventbranching
outofanyportionofthesupplycurrenttowardsthepressurecoil,thecurrentcoil
currentcanbewrittenas
M.SURESH, EEE Dept
Operation of Electrodynamometer-type Wattmeter (Cont..)

34. •Thus,instantaneoustorquecanbewrittenas
•Presenceofthetermcontaining2wt,variesattwicethefrequencyofvoltageand
current.
•Averagedeflectingtorqueoveracompletecycleis
M.SURESH, EEE Dept
Operation of Electrodynamometer-type Wattmeter (Cont..)

35. Operation of Electrodynamometer-type Wattmeter (Cont..)
➢WithaspringconstantK,thecontrollingtorqueprovidedbythespringforafinal
steady-statedeflectionofθisgivenbyT
C=Kθ
➢Understeady-statecondition,theaveragedeflectingtorquewillbebalancedbythe
controllingtorqueprovidedbythespring.Thus,atbalancedconditionT
C=T
d
➢where, P is the power to be measured and K
1= 1/KR
Pis a constant.
➢Steady-state deflection θ is thus found to be an indication of the power P to be
Measured.
M.SURESH, EEE Dept

36. Errors in Electrodynamometer-type Wattmeter
❖Error due to Pressure-Coil Inductance
❖Compensation for Pressure Coil Inductance
❖Error due to Pressure Coil Capacitance
❖Error due to Connection
❖Eddy-current Errors
❖Stray Magnetic Field Errors
❖Error Caused by Vibration of the Moving System
❖Temperature Errors
M.SURESH, EEE Dept

37. Errors in Electrodynamometer-type Wattmeter (Cont...)
1. Error due to Pressure-Coil Inductance
•Itwasassumedduringthediscussionssofarthatthepressurecoilcircuitispurely
resistive.
•Inreality,however,thepressurecoilwillhavecertaininductancealongwith
resistance.
•Thiswillintroduceerrorsinmeasurementunlessnecessarycompensationsare
takencareof.
•Tohaveanestimateofsucherror,letusconsiderthefollowing:
•V = voltage applied to the pressure coil circuit (rms)
•I = current in the current coil circuit (rms)
•I
P= current in the voltage (pressure) coil circuit (rms)
•r
P= resistance of pressure coil only
•L = inductance of pressure coil
•R
V= external resistance connected with pressure coil
•R
P= resistance of pressure coil circuit (PC resistance + RV)
•Z
P= impedance of pressure coil circuit
•M = mutual inductance between current coil and pressure coil
•ω = angular frequency of supply in radian per second
•φ = phase-angle lag of current I with respect to voltage V
M.SURESH, EEE Dept

38. Duetoinherentinductanceofthepressurecoilcircuit,thecurrentandvoltageinthe
pressurecoilwillnolongerbeinphase,ratherthecurrentthroughthepressurecoil
willlagthevoltageacrossitbyacertainanglegivenby
AscanbeseenfromFig(6),currentthroughthepressurecoillagsvoltageacrossitbya
phase-anglewhichislessthanthatbetweenthecurrentcoilcurrentandthepressure
coilvoltage.
Fig.(6) Wattmeter phasordiagram with pressure coil inductance
M.SURESH, EEE Dept
Errors in Electrodynamometer-type Wattmeter (Cont...)

39. Relating to R
P= Z
Pcosα in the pressure coil circuit, the wattmeter deflection can be
rewritten as VI dM
Intheabsenceofinductance,Z
P=R
Pandα=0;wattmeterinthatcasewillreadtrue
power,givenby,
Taking the ratio of true power indication to actual wattmeter reading, we get
True power indication can thus be obtained from the actual wattmeter reading using
the correction factor CF as True power indication = CF X Actual wattmeter reading
For leading power factor loads, however, the wattmeter phasordiagram will be as
shown in Fig.(7)
Fig.(7) Wattmeter phasordiagram with pressure coil inductance during leading load
M.SURESH, EEE Dept
Errors in Electrodynamometer-type Wattmeter (Cont...)

40. Errors in Electrodynamometer-type Wattmeter (Cont...)
2.CompensationforPressureCoilInductance
•Awattmetercanbecompensatedforpressurecoilinductanceby
connectingapresetvalueofcapacitanceacrossacertainportionofthe
externalresistanceconnectedinserieswiththepressurecoil,asshownin
Fig(8).
Fig(8). Compensation for pressure coil inductance
M.SURESH, EEE Dept

41. M.SURESH, EEE Dept
Errors in Electrodynamometer-type Wattmeter (Cont...)

42. Errors in Electrodynamometer-type Wattmeter (Cont...)
3. Error due to Pressure Coil Capacitance
•Thevoltageorpressurecoilcircuitmayhaveinherentcapacitancein
additiontoinductance.
•Thiscapacitanceeffectismainlyduetointer-turncapacitanceofthe
windingandexternalseriesresistance.
•Theeffectofstraycapacitanceofthepressurecoilisoppositetothatdue
toinductance.
•Therefore,thewattmeterreadslowonlaggingpowerfactorsandhighon
leadingpowerfactorsoftheload.
•Actualreadingofthewattmeter,thus,onceagainneedstobecorrected
bythecorrespondingcorrectionfactorstoobtainthetruereading.
•Theeffectofcapacitance(aswellasinductance)varieswithvariable
frequencyofthesupply.
M.SURESH, EEE Dept

43. Errors in Electrodynamometer-type Wattmeter (Cont...)
4. Error due to Connection:
•Therearetwoalternatemethodsofconnectionofwattmetertothecircuit
formeasurementofpower.TheseareshowninFig(9).
•Ineitheroftheseconnectionmodes,errorsareintroducedin
measurementduepowerlossesinpressurecoilandcurrentcoil.
Fig. (9) Wattmeter connections
M.SURESH, EEE Dept

44. •IntheconnectionofFig(9)(a),thepressurecoilisconnectedacrossthe
supply,thuspressurecoilmeasuresthevoltageacrosstheload,plusthe
voltagedropacrossthecurrentcoil.
•Wattmeterreadinginthiscasewillthusincludepowerlossincurrentcoil
aswell,alongwithpowerconsumedbytheload.
•Wattmeterreading=Powerconsumedbyload+PowerlossinCC
•IntheconnectionofFig(9)(b),thecurrentcoilisconnectedtothesupply
side;therefore,itcarriesloadcurrentplusthepressurecoilcurrent.
•Hence,wattmeterreadinginthiscaseincludes,alongwithpower
consumedbytheload,powerlossinthepressurecoilaswell.
•Wattmeterreading=Powerconsumedbyload+PowerlossinPC
•Inthecasewhenloadcurrentissmall,powerlossinthecurrentcoilis
smallandhencetheconnectionofFig(9)(a)willintroducecomparatively
lesserrorinmeasurement.
•Ontheotherhand,whenloadcurrentislarge,currentbranchingthrough
thepressurecoilisrelativelysmallanderrorinmeasurementwillbelessif
connectionofFig(9)(b)isused.
M.SURESH, EEE Dept
Errors in Electrodynamometer-type Wattmeter (Cont...)

45. Errors in Electrodynamometer-type Wattmeter (Cont...)
5. Eddy-current Errors:
•Unlessadequateprecautionsareadopted,Eddy-currentsmaybeinduced
inmetallicpartsoftheinstrumentandevenwithinthethicknessofthe
conductorsbyalternatingmagneticfieldofthecurrentcoil.
•TheseEddy-currentsproducespuriousmagneticfieldsoftheirownand
distortthemagnitudeandphaseofthemaincurrentcoilmagneticfield,
therebyintroducingerrorinmeasurementofpower.
•ErrorcausedbyEddy-currentsisnoteasytoestimate,andmaybecome
objectionableifmetalpartsarenotcarefullyavoidedfromnearthe
currentcoil.
•Infact,solidmetalincoilsupportsandstructuralpartshouldbekepttoa
minimumasfaraspracticable.
•Anymetalthatisusediskeptawayandisselectedtohavehighresistivity
soastoreduceEddycurrentsinducedinit.
•Strandedconductorsarerecommendedforthecurrentcoiltorestrict
generationofEddy-currentwithinthethicknessoftheconductor.
M.SURESH, EEE Dept

46. Errors in Electrodynamometer-type Wattmeter (Cont...)
6. Stray Magnetic Field Errors:
•Theoperatingfieldinelectrodynamometer-typeinstrumentsbeingweak,
specialcaremustbetakentoprotecttheseinstrumentsfromexternal
magneticfields.
•Hence,theseinstrumentsshouldbeshieldedagainsteffectsofstray
magneticfields.
•Laminatedironshieldsareusedinportablelaboratoryinstruments,while
steelcasingsareprovidedasshieldsinswitchboardmountedwattmeter.
•Precisionwattmeters,however,arenotprovidedwithmetalsshields,for
thatwillintroduceerrorsduetoEddy-current,andalsosomedcerrordue
topermanentmagnetizationofthemetalshieldunderinfluenceof
externalmagneticfield.
•Suchwattmetersaremanufacturedtohaveastaticsystemasshownin
Fig(10).
M.SURESH, EEE Dept

47. Fig(10) Astaticsystems for electrodynamometer wattmeter
M.SURESH, EEE Dept

48. •Astaticelectrodynamometerinstrumentsareconstructedwithtwosimilarsets
offixedandmovingcoilsmountedonthesameshaft.
•Thepairoffixedcoilsissoconnectedthattheirmagneticfieldsarein
opposition.
•Similarly,thepairofmovingcoilsisalsoconnectedtoproducemagneticfieldsin
oppositedirections.
•Thismakesthedeflectingtorqueactingonthetwomovingcoilstobeinthe
samedirection.
•Deflectionofthepointeristhusduetoadditiveactionofthetwomovingcoils.
•However,sincethetwofieldsinthetwopairsoffixedandmovingcoilsarein
opposition,anyexternaluniformfieldwillaffectthetwosetsofpairsdifferently.
•Theexternalfieldwillreducethefieldinonecoilandwillenhancethefieldin
theothercoilbyidenticalamount.
•Therefore,thedeflectingtorqueproducedbyonecoilisincreasedandthatby
theothercoilisreducedbyanequalamount.
•Thismakesthenettorqueonaccountoftheexternalmagneticfieldtozero.
M.SURESH, EEE Dept
Errors in Electrodynamometer-type Wattmeter (Cont...)

49. Errors in Electrodynamometer-type Wattmeter (Cont...)
7. Error Caused by Vibration of the Moving System:
•Theinstantaneoustorqueonthemovingsystemvariescyclicallyattwice
thefrequencyofthevoltageandcurrent.
•Ifanypartofthemovingsystem,suchasthespringorthepointerhas
naturalfrequencyclosetothatoftorquepulsation,thenaccidental
resonancemaytakeplace.Insuchacase,themovingsystemmayvibrate
withconsiderableamplitude.
•Thesevibrationsmayposeproblemswhilenotingthepointerpositionon
thescale.Theseerrorsduetovibrationsmaybeavoidedbydesigningthe
movingelementstohavenaturalfrequenciesmuchfurtherawayfrom
twicethefrequencyofthesupplyvoltage.
M.SURESH, EEE Dept

50. Errors in Electrodynamometer-type Wattmeter (Cont...)
8. Temperature Errors:
•Temperaturechangesmayaffectaccuracyofwattmeterbyalteringthe
coilresistances.
•Temperaturemychangeduetochangeinroomtemperatureorevendue
toheatingeffectsinconductorswithflowofcurrent.
•Changeintemperaturealsoaffectsthespringstiffness,thereby
introducingerrorinthedeflectionprocess.
•High-precisioninstrumentsarefittedwithtemperaturecompensating
resistorsthattendtoneutralisetheeffectsoftemperaturevariation.
M.SURESH, EEE Dept

51. LPF (Low Power Factor) Electrodynamictype wattmeter
M.SURESH, EEE Dept

52. M.SURESH, EEE Dept
LPF (Low Power Factor) Electrodynamictype wattmeter

53. M.SURESH, EEE Dept
LPF (Low Power Factor) Electrodynamictype wattmeter

54. M.SURESH, EEE Dept
LPF (Low Power Factor) Electrodynamictype wattmeter

55. M.SURESH, EEE Dept
Extension of Range of Wattmeter using Instrument Transformers

56. Three Phase Wattmeter
M.SURESH, EEE Dept

57. M.SURESH, EEE Dept
Three Phase Wattmeter

58. M.SURESH, EEE Dept
Power-Factor Meter

59. M.SURESH, EEE Dept
Power-Factor Meter

60. M.SURESH, EEE Dept
Power-Factor Meter

61. Single-Phase Dynamometer-type Power-Factor Meter
•Single-phasedynamometer-typepowerfactormeterisschematically
showninFigure.
M.SURESH, EEE Dept

62. M.SURESH, EEE Dept

63. M.SURESH, EEE Dept

64. M.SURESH, EEE Dept

65. M.SURESH, EEE Dept

66. •Ithastwofixedcoilsthatareconnectedinserieswiththeloadandthusactas
thecurrentcoils.
•Currentcoils,thus,carrythesamecurrentastheload.
•TwoidenticalcoilsAandBthatareconnectedtothespindleandplacedinthe
spacebetweenthetwofixedcoilsarethemovingcoils.
•CoilAhasahighvaluenon-inductiveresistanceRconnectedwithitandthecoil
BhasahighlyinductivechokecoilLconnectedtoit.
•BoththecoilsalongwiththeirrespectiveseriesconnectedRandLare
connectedparalleltothesupply,andarecalledthepressurecoils,sincecurrent
throughthesetwocoils,AandBareproportionaltothesupplyvoltage.
•ValuesofRandLaresoselectedthatatnormalfrequency,theirimpedances
becomeequal(R=ωL)andhencethetwocoils,AandBcarrythesame
current.
•CoilAbeinghighlyresistive,itscurrentisalmostinphasewiththesupply
voltageV.
•Similarly,thecoilBbeinghighlyinductive,itscurrentisalmostatanangleδ≈
90°withthesupplyvoltageV.
•TheaxesofthecoilsAandBarealsokeptatthesameangleδ≈90°with
respecttoeachother.
M.SURESH, EEE Dept
Single-Phase Dynamometer-type Power-Factor Meter

67. •Therewillbetwodeflectingtorques,oneactingonthecoilAandthe
otheronB.
•Thesetwocoilwindingsaresoarrangedthattheyexperiencetorquein
theoppositedirection.
•Thepointerwhichisattachedtothesetwocoilsjointly,willthusattaina
steadydeflectionwhenthesetwooppositetorquesoncoilsAandBare
equal.
•Letusconsideralaggingpowerfactorcosφoftheload.
•DeflectingtorqueonthecoilA,
•where θ = angular deflection from the reference horizontal plane
•M = mutual inductance between the fixed coils and coil A
M.SURESH, EEE Dept
Single-Phase Dynamometer-type Power-Factor Meter

68. •Deflecting torque on the coil B
•At equilibrium, T
A= T
B
•Therefore, the deflection (θ) of the instrument is a measure of the power-
factor angle.
•By proper calibration, the scale can be made to show the value of the
power factor directly.
M.SURESH, EEE Dept
Single-Phase Dynamometer-type Power-Factor Meter

69. Three Phase Dynamometer-type Power-Factor Meter
•Construction of Three-Phase Power Factor Meter
•Thisinstrumentisnotaffectedbythevariationsinfrequency.
•Thesepowerfactormetershavethesameconstructionasthesingle-
phasepowerfactormeter.
•Themaindifferenceofconstructionbetweenthesingle-phaseandthree-
phasepowerfactoristhatthemovingcoilsC
1andC
2areat120degreesto
eachotherandthesemovingcoilsC
1andC
2areconnectedacrossthetwo
variousphasesofthesupply.
•ThestationarycoilsSC
1andSC
2areconnectedinserieswiththirdphase.
ThecurrentI
1andI
2arenotdeterminedbythephasesplittingcircuit.
M.SURESH, EEE Dept

70. M.SURESH, EEE Dept
Three Phase Dynamometer-type Power-Factor Meter

71. •Working of Three Phase Power Factor Meter
•Itsworkingissameasthesingle-phasepowerfactormeterworks.The
maindifferenceisthatthecurrentlagswith120
0
inplaceof90
0
.
•Thecurrentisinphasewiththevoltagewhentheloadpowerfactoris
unity.
•ThecurrentI
1isinphasewiththecurrentIandthecurrentI
2lagsbehind
by120
0
.
•ThetorqueactsoncoilC
1andsetsitsplaneperpendiculartothemagnetic
axesofthestationarycoilsSC
1andSC
2.
•ThetorquedoesnotactonthemovingcoilC
2.
•Whenthepowerfactoriszero,thecurrentlagswithvoltageby120
0
.
•ThecurrentI
2isinphasewiththecurrentandthecurrentI
1willbe120
0
outofphaseandthereisnotorqueonthemovingcoilC
1butitactsonC
2.
•Itwillbringitsplaneperpendiculartothecommonmagneticaxisof
SC
1andSC
2.
•Advantages
•These meters are more reliable.
•These three-phase power factor meter provides actual readings.
M.SURESH, EEE Dept
Dynamometer-type Power-Factor Meter

72. Moving Iron Power Factor Meter
M.SURESH, EEE Dept

73. Rotating Field Type MI Power Factor Meter
M.SURESH, EEE Dept

74. M.SURESH, EEE Dept
Rotating Field Type MI Power Factor Meter

75. M.SURESH, EEE Dept
Rotating Field Type MI Power Factor Meter

76. Alternating Field Type MI Power Factor Meter
M.SURESH, EEE Dept

77. M.SURESH, EEE Dept

78. M.SURESH, EEE Dept
Alternating Field Type MI Power Factor Meter

79. M.SURESH, EEE Dept
Alternating Field Type MI Power Factor Meter

80. Advantages
•These meters are strong and cheap.
•Their scales are up to 360 degrees.
•There are no electrical connections in the moving parts.
Disadvantages
•These instruments have so many errors.
•These instruments are not accurate.
•These instruments have hysteresis losses and eddy current losses in
their iron parts.
M.SURESH, EEE Dept
Moving Iron Power Factor Meter