Alternating Current Multi-Circuit Electric Machines: A New Approach to the Steady-State Parameter Determination

920 Pages·2015·11.77 MB·English

by  Valentin Asanbayev (auth.)

Valentin Asanbayev
Alternating
Current Multi-
Circuit Electric
Machines
A New Approach to the Steady-State
Parameter Determination
Alternating Current Multi-Circuit Electric Machines

Valentin Asanbayev
Alternating Current
Multi-Circuit Electric
Machines
A New Approach to the Steady-State
Parameter Determination
ValentinAsanbayev
InstituteofElectrodynamics
NationalAcademyofScienceoftheUkraine
Kiev,Ukraine
ISBN978-3-319-10108-8 ISBN978-3-319-10109-5(eBook)
DOI10.1007/978-3-319-10109-5
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014948343
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This work is dedicated to the memory of my
mother Fedora and father Nicolay, who lived
and raised their many children in the
complicated years of the revolution and
formation of the Soviet Union, in the difficult
years of the long Civil War, Second World
War, and “Cold” War, and in the critical
yearsof“Glasnost”and“Perestroika”.They
were witness to, and in some ways
participantsin,thesecomplexhistoricevents.
Despite these terrible life circumstances, my
parents tried to find small moments of human
joy, and they tried to approach life with
humor and optimism. Simple manifestations
of goodness and decency and a respectful
attitude towards people were typical of their
daily life. All of this fostered and
strengthened in me a deep sense of respect
andlove for myparents. Iam very grateful to
them that these remarkable human values
became the basis of my perception of the
world.

Preface
Inthisbook,issuesareconsideredwithregardtoestablishingACelectricmachine
circuit loops and determining their parameters. Here, the accepted approach is
based on the use of the field decomposition principle, which is the foundation for
determining the parameters of the AC electric machine. Within the book, various
waysof implementingthefielddecompositionprinciplearedescribed.Methods,as
well as concrete techniques and procedures, are presented for establishing AC
electric machine circuit loops and determining their parameters. The proposed
methods are based on the use of the models of AC electric machine with both
laminatedandsolidrotors,andmodelswidelyusedinpracticehavebeenapplied.
Thecircuitloopsformachinesofvariousdesignsareestablishedandtheirparam-
eters aredeterminedfor both weakandstrongskin effects. Theanalyticalexpres-
sionsfortheparametersoftheACelectricmachinecircuitloopsarepresentedina
formconvenientforpracticaluse.
The book is designed for a wide range of electrical engineers and researchers,
university lecturers, graduate students, and students with an interest in electric
machineparameters.
Parameters are the basis of the engineering methods used to analyze electro-
magnetic processes taking place in AC electric machines. In this book, the resis-
tanceandreactancevaluesusedinthecircuitloopsvisualizedbyequivalentcircuits
andappliedinvoltageequationsdescribingthesecircuitloopsrepresenttheparam-
eters of the AC electric machine. These parameters allow the behavior of electric
machinestobepredeterminedundervariousoperatingconditions.Assuch,correct
determinationofelectricmachineparametersiscritical,especiallythoseofmodern
electricmachinescharacterizedbyarelativelyhighlevelofuseofactivematerials.
Thefielddecompositionprinciple,whichpresupposesthedecompositionofthe
resultingfieldofanelectricmachineintoitscomponents,isthebasisfordetermin-
ing parameters. The theory of electric machines utilizes two methods for
decomposing the resulting field into its components. With the first method, the
electric machine resulting field is decomposed into fields of self- and mutual
induction. With the second, the electric machine resulting field is decomposed
vii
viii Preface
intotheleakagefieldsofthestatorandrotorwindingsandthemagnetizingfield.It
is quite apparent froma physical point of view that these two methods of decom-
position are not supported at present by distinct methods of implementation. In
manycases,thissituationcreatesseriousdifficultyindeterminingelectricmachine
parameters,particularlythoserepresentingmulti-circuitelectromagneticsystems.
At the present time, the methods, concrete techniques, and procedures for
implementing the field decomposition principle are inadequate, and this creates a
serious barrier with respect to more intensive development of field methods of
researchandanalysistowardsachievingagreaterunderstandingofelectricmachine
parameters.Theproposalssetforthinthisbookareanefforttobridgetheexisting
gapinthefieldwithregardtodeterminationofACelectricmachineparameters.
Thisbookwaswrittenonthebasisoftheauthor’sworkperformedattheInstitute
ofElectrodynamicsoftheNationalAcademyofScienceofUkrainefrom1968to
1995,theresultsofwhichhaveappearedprimarilyinthepublicationsinitiatedby
thesciencecounseloftheInstitute.Thematerialscontainedintheauthor’spubli-
cations and those representing the contents of this book were properly processed,
summarized,andsupplemented.
Inthebook,variousmethodsforimplementingthefielddecompositionprinciple
are considered and proposed. The author strives to focus the reader’s attention on
the issues of developing techniques and procedures for establishing electric
machine circuit loops and determining their parameters. Therefore, the contents
of this book are conditioned by issues concerning the practical application of the
proposed methods and the need to demonstrate the process of establishing circuit
loopsanddeterminingparametersforelectricmachinesofvariousdesigns(electric
machines with single,- double-, and triple-cage rotors and solid rotors). These
methods were developed using well-known electric machine models, and as such
theanalyticalexpressionsfortheparametersarepresentedinaformconvenientfor
engineeringcalculations.
Kiev,Ukraine ValentinAsanbayev
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ACElectricMachines:TheEddyCurrentCircuits. . . . . . . . . . 1
1.1.1 TheSteadyStateParameterDetermination:
InitialProvisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 AnElectromagneticAnalysis:FeaturesofUsing. . . . . . . . . . . 5
1.3 AMulti-LayerRepresentationofACElectric
Machines:TheLadderCircuits. . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 FundamentalsoftheFieldDecompositionPrinciple. . . . . . . . . . . . 11
2.1 AnInductionMachinewithaSingle-WindingRotor:
VoltageEquationsThroughtheResulting
EMFoftheWindings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 TheResultingEMFastheSumoftheEMFs
ofSelf-InductionandMutualInduction. . . . . . . . . . . . 14
2.1.2 ResultingEMFastheSumofLeakageEMF
andEMFsofSelf-andMutualInduction. . . . . . . . . . . 17
2.1.3 ResultingEMFastheSumofLeakageEMF
andMagnetizingEMF:ThePhysicalBasis. . . . . . . . . 24
2.1.4 ResultingEMFastheSumoftheReferredEMF
ofSelf-andMutualInduction. . . . . . . . . . . . . . . . . . . 30
2.2 MagnetizingEMFEquations:Methods
forObtaining. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 CircuitLoopEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4 VoltageEquationswithReferredSecondaryValues. . . . . . . . . 42
2.5 TheBasicParameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6 AnInductionMachinewithMulti-WindingRotor:
ResultingEMFEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.6.1 ResultingEMFastheSumofLeakageEMF
andEMFofSelf-andMutualInduction. . . . . . . . . . . 50
ix