Table Of ContentP1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
POWER DEFINITIONS
AND THE PHYSICAL
MECHANISM OF
POWER FLOW
Power Definitions and the Physical Mechanism of Power Flow Alexander Eigeles Emanuel
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-66074-4
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
POWER DEFINITIONS
AND THE PHYSICAL
MECHANISM OF
POWER FLOW
AlexanderEigelesEmanuel
WorcesterPolytechnicInstitute,USA
A John Wiley and Sons, Ltd., Publication
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Thiseditionfirstpublished2010
(cid:1)C 2010JohnWiley&Sons,Ltd
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto
reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com.
TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,
DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform
orbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,
DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailablein
electronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand
productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespective
owners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.Thispublicationisdesignedto
provideaccurateandauthoritativeinformationinregardtothesubjectmattercovered.Itissoldontheunderstandingthat
thepublisherisnotengagedinrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,
theservicesofacompetentprofessionalshouldbesought.
LibraryofCongressCataloging-in-PublicationData
Emanuel,AlexanderEigeles.
Powerdefinitionsandthephysicalmechanismofpowerflow/AlexanderEigelesEmanuel.
p.cm.
Includesindex.
ISBN978-0-470-66074-4(cloth)
1. Electricchargeanddistribution–Mathematics. 2. Wavemechanics. 3. Electricpowertransmission. I. Title.
QC581.E4E432010
621.319–dc22 2010013501
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN: 978-0-470-66074-4
Typesetin10/12ptTimesbyAptaraInc.,NewDelhi,India
PrintedinSingaporebyMarkonoPrintMediaPteLtd
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Thisbookisdedicated
toRodica,mylife-long love,
and
tothreegreatteachersofmine:
tomyfatherIng.Sigmund Eigeles
whotaughtmehowtorowaboat,
toProfessorConstantin I.Budeanu
whoopenedmyeyestothebeauty
ofenergyconversion,
andtoProfessorMichaelS.Erlicki
whoguidedmyfirststeps
intherealmofresearch.
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Contents
Foreword xi
Preface xiii
1 ElectricEnergyFlow:PhysicalMechanisms 1
1.1 Problems 16
1.2 References 18
2 Single-PhaseSystemsWithSinusoidalWaveforms 21
2.1 TheResistance 21
2.2 TheInductance 25
2.3 TheCapacitance 27
2.4 The R– L –C Loads 29
2.5 TheApparentPower 30
2.6 TheConceptofPowerFactorandPowerFactorCorrection 34
2.7 CommentsonPowerFactor 38
2.8 OtherMeansofReactivePowerControlandCompensation 41
2.9 SeriesCompensation 44
2.10 ReactivePowerCausedbyMechanicalComponentsthatStoreEnergy 45
2.11 PhysicalInterpretationofInstantaneousPowersbyMeans
ofPoyntingVector 48
2.12 Problems 57
2.13 References 60
3 Single-PhaseSystemswithNonsinusoidalWaveforms 63
3.1 TheLinearResistance 63
3.2 TheLinearInductance 68
3.3 TheLinearCapacitance 71
3.4 TheLinearSeries R−L−C Circuit 71
3.5 TheNonlinearResistance 74
3.6 TheNonlinearInductance 80
3.7 NonlinearLoad:TheGeneralCase 83
3.8 Problems 90
3.9 References 92
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
viii Contents
4 ApparentPowerResolutionforNonsinusoidalSingle-PhaseSystems 93
4.1 ConstantinI.Budeanu’sMethod 95
4.2 StanislawFryze’sMethod 99
4.3 ManfredDepenbrock’sMethod 102
4.4 LeszekCzarnecki’sMethod 106
4.5 TheAuthor’sMethod 110
4.6 ComparisonAmongtheMethods 115
4.7 PowerFactorCompensation 120
4.8 CommentsonSkinEffect,ApparentPower,andPowerFactor 128
4.9 TheAdditivenessProblem 131
4.10 Problems 135
4.11 References 137
5 Three-PhaseSystemswithSinusoidalWaveforms 139
5.1 Background:TheBalancedandSymmetricalSystem 140
5.2 TheThree-PhaseUnbalancedSystem 142
5.3 ThePowerFactorDilemma 145
5.4 PowersandSymmetricalComponents 149
5.4.1 HowSymmetricalComponentsareGenerated 149
5.4.2 ExpressingthePowersbyMeansofSymmetricalComponents 154
5.5 EffectiveApparentPowerResolutions 158
5.5.1 FBD-Method 158
5.5.2 L.S.Czarnecki’sMethod 165
5.5.3 IEEEStd.1459–2010Method 167
5.5.4 ComparisonBetweenTheTwoMajorEngineeringSchoolsofThought 169
5.6 Problems 182
5.7 References 184
6 Three-PhaseNonsinusoidalandUnbalancedConditions 185
6.1 TheVectorApparentPowerApproach 185
6.2 TheIEEEStd.1459–2010’sApproach 187
6.3 TheDIN40110’sApproach 192
6.3.1 TheIEEEStd.1459–2010Approach 195
6.3.2 TheDIN40110Approach 196
6.4 ObservationsandSuggestions 198
6.5 Problems 201
6.6 References 202
7 PowerDefinitionsforTime-VaryingLoads 205
7.1 Background:BasicExample 206
7.2 Single-PhaseSinusoidalCase 210
7.2.1 AnalyticalExpressionsofPowers:Single–PhaseSinusoidal 213
7.3 Single-PhaseNonsinusoidalCase 214
7.4 Three-PhaseSinusoidalandUnbalancedCondition 216
7.5 Three-PhaseSystemswithNonsinusoidalandUnbalancedCondition 220
7.6 Problems 225
7.7 References 227
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Contents ix
8 Appendices 229
8.1 AppendixI:TheElectrostaticFieldDistributioninaCoaxialCable 229
8.2 AppendixII:PoyntingVectorduetoDisplacementCurrent 231
8.3 AppendixIII:ElectricFieldCausedbyaTime-VaryingMagneticField 232
8.4 AppendixIV:TheElectromagneticWaveAlongtheThree-PhaseLine 235
8.5 AppendixV:Equation(5.99) 242
8.6 AppendixVI:MaximumActivePower(Three-Phase,Four-WireSystem) 243
8.7 AppendixVII:AbouttheRatioρ = R /R 247
s n
8.8 AppendixVIII:TheUseofVarmetersinthePresenceofNonsinusoidal
andAsymmetricalVoltagesandCurrents 249
8.9 References 258
Index 259
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Foreword
Energypolicyistodayanationalpriority.Conservation,renewableelectricitysourcesandcon-
vertingtransportationfromfossilfuelstoelectricityaremajorfociofactivity.Thisisthemost
opportunetimeforsomeonetoprovidethedefinitiveexpositionofwhatismeantby“power”
and how its various constituents are calculated and measured. Professor Alex Emanuel has
donejustthat.Thisbook,bygatheringandclearlypresentingtheevolutionoftheincreasingly
complexinterpretationoftheV-Iproduct,hasdoneagreatservicetotheengineeringprofes-
sion.Overtime,theincreasedsophisticationofelectricityuseandtheintroductionofsolidstate
converterswiththeirattendantharmonicshaverequiredthatthedefinitionandmeasurement
of “power” be subjected to ever greater scrutiny. The resulting proposals, counterproposals
and controversies evolved into a series of IEEE and DIN standards, each responding to the
nascenteffectsofnewtechnologiesoranincreasedemphasisoneconomicaccuracy.Intoday’s
restructuredelectricityindustry,withreal-timemarkets,theprospectofpriceresponsivede-
mand,andtheintroductionofanadvancedmeteringinfrastructure,accuracyofmeasurement
andinterpretationofpowerdataiscrucial.
Professor Emanuel promises an “in-depth understanding of the very physical mechanism
that governs energy flow,” and he delivers. He starts with the fundamental field description
ofpowerrepresentedbyPoynting’svector,thencarefullyandlogicallytransitionstolumped
physical systems, adding complexity until we arrive at all the components of “power” that
constitutetheV-Iproductsofthreephase,four-wire,unbalancedsystemswithnon-sinusoidal
currentsandvoltages.DuringtheentirejourneyhebuildsuponthecontributionsofBudeanu,
Fryze,DepenbrockandCzarnecki,pioneersinattemptingtoprovidearationalinterpretation
of the result of multiplying current by voltage. And the comparisons he draws among the
results of their proposed methods and that of the recent IEEE 1459-2010 standard is most
interesting.
FewengineersareaswellqualifiedasProfessorEmanueltoundertakethewritingofthis
monumentalwork.Hehasdedicatedhisentireprofessionallifetothestudyofenergyrelated
problems, and has been a leading authority and educator in the field of power systems. It is
clearthatwritingthisbookhasbeenalaboroflove,andwefellowelectricalengineersowe
ProfessorEmanueladebtofgratitudeforthefruitofthislabor.
JohnG.Kassakian
ProfessorofElectricalEngineeringandComputerScience
LaboratoryforElectromagneticandElectronicSystems
TheMassachusettsInstituteofTechnology,USA
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
Preface
Thesedaystheimplementationofan“AdvancedMeteringInfrastructure”willbedetermined
bythetechnologythatenablesthemanufacturingof“SmartMeters.”Thequestforthesmart
meterisanintegralpartofarevolutionarymovement,thebigimpetusfortheSmartGridand
energy management. When the flow and the use of electric energy is monitored by means
ofsmartmeters,theenergyproviderreceives,viareal-timedataacquisition,informationthat
enables the remote control of customer loads, the ability to adjust demand response, asset
management,variablepricingprograms,andmanymorecapabilitiesthatimprovetheenergy
transmissionefficiencybyreducingthepowerlossesandbylevelingtheloadcurves.Smart
metersalsobenefitcustomersbyincreasingthereliabilityofsupplyaswellastheabilityto
monitor the use and cost of energy. This technology will stimulate much needed behavioral
changesthatwillleadtoasignificantdecreaseinenergyuse.
Themeteringinstrumentationisdesignedtoconformtothemathematicaldefinitionofthe
electric quantity monitored; however, the definition on which such smart meters’ design is
based must be true to the law of physics and provide information that enables the accurate
determination of energy flow rate and quality, optimum power dispatching, and efficient
maintenanceplanning.
The meters in use today, even some of the most modern electronic meters, are designed
and built following a tradition rooted in the 1930s and 1940s. It is well known that meters
thatmeasureenergy(kWh)andactivepower(kW)provideaccuratemeasurementsalsounder
nonsinusoidal or unbalanced conditions; nevertheless, meters dedicated to apparent power
(kVA) and nonactive power (kvar) measurements are prone to significant errors when the
current and voltage waveforms are distorted. The main reason for such uncertainties stems
from the inadequate power definitions that dictate the conceptual design of such instrumen-
tation.Evidentlythissituationledtothesearchforapracticalsolution.Theprogresstoward
universallyaccepteddefinitionsisslowandhinderedbyeconomicfactorstiedtoanexisting
infrastructureoflargeproportions.Alivelydebateovertheapparentpowerdefinitionandits
resolutionstartedacenturyagoandhasnotyetreachedaconclusion.Iamanactiveparticipant
inthisongoingdebateandhavewitnessedhow,inthelastdecades,avigorous“technological
soulsearching”hasproducedtwosignificantstandards:
1. TheIEEEStd.1459–2010,DefinitionsfortheMeasurementofElectricPowerQuantities
UnderSinusoidal,Nonsinusoidal,Balanced,orUnbalancedConditions.
2. TheDIN40110-2:2002–11,QuantitiesUsedinAlternatingCurrentTheory–Part2:Multi-
conductorcircuits(PolyphaseCircuits).
P1:OTE/OTE/SPH P2:OTE
fm BLBK294-Emanuel June23,2010 16:57 PrinterName:YettoCome
xiv Preface
Bothstandardsprovideimprovedpowerdefinitionsthathavebeenscrutinizedandapproved
by large groups of experts and have triggered a multitude of engineering papers. This book
hasitsmainoriginwiththeIEEEStd.1459–2010.Manyusersofthisdocumentcomplained
aboutits“toughreading”andaskedforsupportdocumentation.Anotherimportantmotivation
for the production of this book stems from my desire to make a small contribution toward
the acceptance and proliferation of smart meters. The major goals of this book are as
follows:
1. Toprovideaclearunderstandingofthephysicalmechanismthatgovernstheelectricenergy
flow under different conditions: single- and three-phase, sinusoidal and nonsinusoidal,
balanced,andunbalancedsystems,
2. To be able to propose and advocate for recently developed power definitions that are
not mathematical artifacts, but expressions that help correctly describe the actual effects
and interactions between the energy sources, loads, equipment, and environment. Such
definitionsmustbebasedonthesolidunderstandingofthephysicalcharacteristicsofthe
differentcomponentsofenergy,
3. Toexplain,discuss,andrecommendpowerdefinitionsthatplayedasignificanthistorical
roleinpavingtheroadforthetwostandards,
4. Tocomparethetwostandards.
This book consists of eight chapters. The first explains electric energy flow. It introduces
the concept of power as the rate of flow of energy and emphasizes the fact that electric
energy is carried by an electromagnetic wave characterized by the power density (W/m2)
that is a function of time and space. Such electromagnetic waves travel (slide) along the
conductors and contain a host of components. The main tool, used through the entire book,
for recognizing the characteristics that help separate the actual elementary components of
energy, is the Poynting vector. It is shown, with the help of a set of solved problems, that
some components are active and carry unidirectional energy from sources to the loads, and
other components oscillate between the loads and the sources and do not contribute to the
net transfer of energy, but cause additional power loss in the conductors that connect loads
andsources.ThiskeychapterconcludesthatthePoyntingvectorisanexcellenttoolforthe
visualization of the power flow distribution in space and time; most importantly, it helps to
reveal the correct energy and power components that ultimately are reflected in the ways
the apparent power is resolved, thus leading to power definitions that are true to Nature’s
laws.
Thesecondchapterdealswiththesingle-phasesystemwithsinusoidalwaveforms.While
introducing new definitions, such as the intrinsic power, this chapter presents a needed
introductionandreviewofbasicpowerdefinitions.Amplespaceisdedicatedtothenotionof
apparentpower,provingthatitisadefined(convention)quantitythatgovernstheequipment
size, equipment losses, and the equipment aging and life-span. The power factor concept
is presented in detail. A major section in this chapter is occupied by the discussions about
the power oscillations between load and source, about the quantification of reactive and
nonactivepowers.Itisshownthatreactivepowerdoesnothavetobeproducedbyinductive
or capacitive loads, but can also be caused by any energy converter that has the ability to
store and return energy. It is also proved that the Poynting vector provides an excellent
vehicle to help the reader familiarize with the separation and grouping of different active
