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 ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerpts inconnectionwithreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeing enteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplication ofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthe Publisher’s location, in its current version, and permission for use must always be obtained from Springer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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