Power Transformers (Power Engineering) - 1st edition (April 12, 2002)

286 Pages·2002·2.02 MB·English

by  John Winders

Power
Transformers
Principles and Applications
John J. Winders, Jr.
PPL Electric Utilities
Allentown, Pennsylvania
Marcel Dekker, Inc. New York Basel
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Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Series Introduction
Powerengineeringistheoldestandmosttraditionalofthevariousareaswithin
electrical engineering, yet no other facet of modern technology is currently
experiencing a greater transformation or seeing more attention and interest
fromthepublicandgovernment.Butwhilepublicconcernandpoliticaldeci-
sions about de-regulation and energy trading may reshape the electric utility
industry’smannerofdoingbusiness,itsfuturelikeitspastrestsonthecapabil-
ity of its transmission and distribution systems to convey safe, reliable, and
economical electric power to homes, businesses, and factories. Nothing is
moreessentialtothisperformancethanthetransformer,whichenablesmodern
power and industrial systems to function.
IamparticularlydelightedtoseethislatestadditiontoMarcelDekker’s
Power Engineering series. Power Transformers: Principles and Applications
is a comprehensive compendium of theory and practices for electric power
transformers. This book provides a concise but thorough treatment of basic
transformertheory,itsapplicationtovarioustypesoftransformerdesignsand
theirapplicationinutilityandindustrialpowersystems.Itseasytoreadstyle
andlinearorganizationmakeitparticularlysuitableasatutorialforthosewho
needtolearnthematerialindependently,outsideoftheclassroom,orasatext
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
for formal courses.Thisbookalso makesaverygood practicalreferencefor
utility and industrial power engineers.
In addition to having concise summaries of all the basics, the text pro-
videsanexcellentdescriptionofthevariousancillaryequipmentandsystems,
whichareoftenthemostdifficulttopreciselyengineerandfitintothesystem.
JohnWindershasalsoprovidedexcellentcoverageofhowtoread,interpret,
andapplyapowertransformer’snameplatedata,notalwaysastraightforward
orunambiguoustaskandonewhereasurprisingnumberofmistakesaremade
byinexperiencedengineers.Chapter8willbeparticularlyusefultopracticing
engineers and power system operators, covering maintenance needs, testing
options,andtroubleshootingtechniquesandtheiruse,anddiscussingreliabil-
ity of transformers.
As the editor of the Power Engineering series, I am proud to include
PowerTransformers:PrinciplesandApplicationsamongthisimportantgroup
of books. Like all the books in Marcel Dekker’s Power Engineering series,
thisbookprovidesmodernpowertechnologyinacontextofproven,practical
application,usefulasareferencebookaswellasforself-studyandadvanced
classroomuse.MarcelDekker’sPowerEngineeringseriesincludesbookscov-
ering the entire field of power engineering, in all of its specialties and sub-
genres, each aimed at providing practicing power engineers with the knowl-
edge and techniques they need to meet the electric industry’s challenges in
the 21st century.
H. Lee Willis
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Preface
ThisbookisbasedonnotesfortheTransformerApplicationsCourseoffered
by the Center for Power System Study at Lehigh University. The key word
in both the title of that course and the title of this book is applications. The
material presented in the following chapters was obtained from various
sources: textbooks, industry standards, and established utility practices and
procedures.Muchofthismaterialalsocomesfrommypersonalfilesrelating
to actual events and case studies that were observed during my career in the
utility industry spanning 30 years.
There are many kinds of transformers, and all share the same set of
fundamentaloperatingprinciples.Sincethisbookfocusesonpowertransform-
ers, it is fair to ask, ‘‘What exactly is a power transformer?’’ By definition,
a power transformer is a transformer which transfers electric energy in any
partofthecircuitbetweenthegeneratorandthedistributionprimarycircuits.*
This definition of power transformer in the IEEE standard appears under the
*IEEEStd.C57.12.80-1978.IEEEStandardTerminologyforPowerandDistributionTransform-
ers.InstituteofElectricalandElectronicsEngineers,Inc.,1978,NewYork,p.8.
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
heading of ‘‘Size’’ and does not indicate how the transformer is used in the
power system. Thus, this book uses this definition in the broadest sense to
include discussions of specialty applications such as step voltage regulators,
phase shifters, and grounding transformers, as well as the usual step-up and
step-downapplications.Sincethelinebetweenpowertransformersanddistri-
butiontransformersissomewhatblurry,manyofthebasicprinciplespresented
can be applied to distribution transformers as well.
Thefirstseveralchaptersbuildasolidtheoreticalfoundationbydescrib-
ingtheunderlyingphysicsbehindtransformeroperation.Atheoreticalfounda-
tion is absolutely necessary in order to understand what is going on inside a
transformerandwhy.Themagneticpropertiesofmaterials,areviewofmag-
neticunits,andanalysisofmagneticcircuitsarediscussedwithenoughmathe-
maticalrigorfortheinterestedreadertogainfullcomprehensionofthephysics
involved. Whenever a detailed mathematical treatment is presented, it is al-
waysdonewithapracticalobjectiveinmind.Eachchapterincludesanumber
ofpracticeproblemstoclearlyillustratehowthetheoryisappliedineveryday
situations. Many of these practice problems are based on actual events.
Several things set this book apart from other transformer reference
books.First,thisbookemphasizestheimportanceofmagneticpropertiesand
howthechoiceofacoredesigncanaffectthetransformer’selectricalproper-
ties,especiallyduringfaultsandunbalancedoperations.Manyreferencebooks
overlook this critical aspect of transformer applications.
Next,thisbookdiscussesspecialtypesoftransformerconnections,such
as the zigzag, Scott, and tee connections, as well as the more common wye
and delta types. The Scott and tee connections, which transform three-phase
voltages into two-phase voltages, are seldom covered in modern transformer
referencebookseventhoughtwo-phasesystemsstillexisttoday.Tapchanging
under load and variable phase shifting transformers are covered. Different
typesoftransformercoilandcoilconstructionarecompared,withdiscussion
of the particular advantages and disadvantages of each with respect to the
various transformer connections. The reader will also gain insight into some
of the economic trade-offs of different transformer design options.
Abrieftutorialonsymmetricalcomponentsisalsoincluded.Thetopic
iscoveredinotherreferencebooksbutseldominsuchacompactandstraight-
forwardway,enablingthereadertoimmediatelyapplythetechniqueinpracti-
cal problems.
A section of the book defines a transformer’s nameplate rating versus
its thermal capability and describes how to calculate a transformer’s rate of
loss of life. An entire chapter is devoted to describing abnormal operating
conditions that can damage power transformers, including overloads, short
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
circuits, single phasing from primary fuse operations, ferroresonance, and
voltage surges. The chapter describes ways to avoid these conditions, or at
least ways to mitigate them through proper system design and selection of
appropriate transformer designs.
Thereader will learnhow tointerpretand useatransformer testreport
aswellastheinformationonthetransformernameplate.Thebookconcludes
with a comprehensive discussion of preventive and predictive maintenance,
good utility practices, factory and field testing, and failure rate analysis.
This book is intended primarily for readers having an electrical engi-
neering background although training as an electrical engineer is not neces-
sary,andotherswillalsobenefitfromtheconclusionsthatcanbedrawnfrom
the practical examples. Mastery of the principles presented in this book will
provideasoundworkingknowledgeofhowtospecify,operate,andmaintain
power transformers in a utility or plant environment.
IwishtothankAnthonyF.Slevafor histhoroughreviewofthemanu-
script and his many helpful suggestions for improving it, and for making it
possible to publish this book. I am indebted to the late Charles H. Morrison,
whopatientlysharedwithmesomuchofhisextensivetheoreticalandpracti-
cal knowledge about power transformers.
John J. Winders, Jr.
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Contents
SeriesIntroduction H.LeeWillis
Preface
1BasicTransformerTheory
1.1Definitionof aTransformer
1.2MagneticUnitsandConversionFactors
1.3CurrentsandMagneticFields
1.4MagneticInduction
1.5ConstructingaSimpleTransformer
1.6TheMagneticCircuit
1.7The B-H Curve
1.8The B-H CurveandHysteresis
1.9MagnetizingCurrentsandHarmonics
1.10TransformerCoreDesignandConstruction
1.11Magnetostriction
1.12 Completing the Transformer by Adding a Second
Winding
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
1.13PlacementoftheWindings
References
2Two-WindingTransformerConnections
2.1Introduction
2.2TheY-YConnectioninThree-PhaseSystems
2.3AdvantagesoftheY-YConnection
2.4DisadvantagesoftheY-YConnection
2.5TheY- ∆ Connectionandthe ∆-YConnection
2.6PhaseAngleDisplacementandPhaseRotation
2.7TheY- ∆ GroundingBank
2.8TheZigzagConnection
2.9 Comparisons of Economy of the Different Winding
Configurations
2.10 Trade-Off Between Steel and Copper in the Design of a
Transformer
2.11 Connecting Three-Phase Banks Using Single-Phase
Transformers
2.12 Transforming Three-Phase Voltages into Two-Phase
Voltages
2.13TheScottTransformerConnection
2.14Three-PhaseTransformerDesigns
2.15StandardTerminalMarkingsforTransformers
References
3TransformerImpedanceandLosses
3.1LeakageFluxandLeakageReactance
3.2ConductorLosses
3.3No-LoadLosses
3.4MagnetizingReactance
3.5EquivalentCircuitofaTwo-WindingTransformer
3.6ABriefTutorialonSymmetricalComponents
3.7 Transformer Equivalent Circuits Modeled in Zero Phase
SequenceNetworks
3.8SeriesImpedanceandRegulation
3.9 Matching Transformers for Parallel and Bank
Operations
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
3.10 Impedance Mismatch in Three-Phase Transformer
Banks
3.11TemperatureRiseandtheThermalCapability
3.12InterpretingTransformerTestReports
3.13 Calculating the Hot-Spot Temperature Using the IEEE
Method
3.14CalculatingtheLossofLife
References
4AutotransformersandThree-WindingTransformers
4.1AutotransformerConnections
4.2ImpedanceofanAutotransformer
4.3LimitationsoftheAutotransformerConnection
4.4AutotransformerVoltageswithShortCircuitsApplied
4.5ImpulseVoltagesAppliedtoAutotransformers
4.6 Autotransformer Core and Coil Designs and Terminal
Configurations
4.7 Advantages and Disadvantages of the Autotransformer
Connection
4.8Three-WindingTransformers
4.9ModificationofTransformerLawswithThreeWindings
4.10EquivalentCircuitofaThree-WindingTransformer
4.11 Core and Coil Construction of Three-Winding
Transformers
4.12ThermalCapabilityofThree-WindingTransformers
4.13TheStabilizingEffectof a ∆ TertiaryWinding
Reference
5ShortCircuits,InrushCurrents,andOtherPhenomena
5.1EffectsofShortCircuitsonTransformers
5.2 Comparisons of Short-Circuit Currents for Various
Faults
5.3MechanicalForcesinTransformers
5.4ForcesbetweenTransformerWindings
5.5Short-CircuitForcesinThree-WindingTransformers
5.6ExcitingCurrentInrush
5.7TankOverheatingfromZero-SequenceCurrents
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.