DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis: Practice Problems, Methods, and Solutions PDF
Preview DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis: Practice Problems, Methods, and Solutions
Mehdi Rahmani-Andebili DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis Practice Problems, Methods, and Solutions DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis Mehdi Rahmani-Andebili DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis Practice Problems, Methods, and Solutions MehdiRahmani-Andebili DepartmentofEngineeringandPhysics UniversityofCentralOklahoma Edmond,OK,USA ISBN978-3-031-08862-9 ISBN978-3-031-08863-6 (eBook) https://doi.org/10.1007/978-3-031-08863-6 #TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whetherthewholeor part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformationstorageand retrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafter developed. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbookarebelievedto betrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsortheeditorsgiveawarranty, expressedorimplied,withrespecttothematerialcontainedhereinorforanyerrorsoromissionsthatmayhavebeen made.Thepublisherremainsneutralwithregardtojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The courses of DC electric machines and electromechanical energy conversion principles are two of the fundamental courses of electric power engineering major that are taught for junior students.Thesubjectsincludemagneticcircuitsanalysis,inductanceofwindingsandinduced voltage in windings, energy loss in magnetic circuits, electromechanical energy conversion, separately excited DC electric machines, shunt DC electric machines, series DC electric machines, compound DC electric machines, and power loss and efficiency of DC electric machines. Like theauthor’s previously publishedtextbooks, this textbook includes very detailed and multiplemethodsofproblemsolutions.Itcanbeusedasapracticingtextbookbystudentsand asasupplementaryteachingsourcebyinstructors. To help students study the textbook in the most efficient way, the exercises have been categorizedinninedifferentlevels.Inthisregard,foreachproblemofthetextbook,adifficulty level (easy, normal, or hard) and a calculation amount (small, normal, or large) have been assigned.Moreover,ineachchapter,problemshavebeenorderedfromtheeasiestproblemwith thesmallestcalculationstothemostdifficultproblemswiththelargestcalculations.Therefore, students are suggested to start studying the textbook from the easiest problems and continue practicing until they reach the normal and then the hardest ones. On the other hand, this classification can help instructors choose their desirable problems to conduct a quiz or a test. Moreover,theclassificationofcomputationamountcanhelpstudentsmanagetheirtimeduring futureexamsandinstructorsgivetheappropriateproblemsbasedontheexamduration. Sincetheproblemshaveverydetailedsolutionsandsomeofthemincludemultiplemethods ofsolution,thetextbookcanbeusefulfortheunder-preparedstudents.Inaddition,thetextbook isbeneficialforknowledgeablestudentsbecauseitincludesadvancedexercises. Inthepreparationofproblemsolutions,anattempthasbeenmadetousetypicalmethodsof electrical circuit analysis to present the textbook as an instructor-recommended one. In other words,theheuristicmethodsofproblemsolutionhavenever beenusedasthefirstmethodof problem solution. By considering this key point, the textbook will be in the direction of instructors’ lectures, and the instructors will not see any untaught problem solutions in their students’answersheets. The Iranian University Entrance Exams for the master’s and PhD degrees of electrical engineering major is the main reference of the textbook; however, all the problem solutions havebeenprovidedbyme.TheIranianUniversityEntranceExamisoneofthemostcompeti- tiveuniversityentranceexamsintheworldthatallowsonly10%oftheapplicantstogetinto prestigiousandtuition-freeIranianuniversities. TheauthorhasalreadypublishedthebelowbooksandtextbookswithSpringer. v Textbooks DifferentialEquations:PracticeProblems,Methods,andSolutions,2022. Feedback Control Systems Analysis and Design: Practice Problems, Methods, and Solutions,2022. PowerSystemAnalysis:PracticeProblems,Methods,andSolutions,2022. AdvancedElectricalCircuitAnalysis:PracticeProblems,Methods,andSolutions,2022. ACElectricalCircuitAnalysis:PracticeProblems,Methods,andSolutions,2021. Calculus:PracticeProblems,Methods,andSolutions,2021. Precalculus:PracticeProblems,Methods,andSolutions,2021. DCElectricalCircuitAnalysis:PracticeProblems,Methods,andSolutions,2020. Books ApplicationsofArtificialIntelligenceinPlanningandOperationofSmartGrid,2022. Design,Control,andOperationofMicrogridsinSmartGrids,2021. ApplicationsofFuzzyLogicinPlanningandOperationofSmartGrids,2021. OperationofSmartHomes,2021. Planning and Operation of Plug-in Electric Vehicles: Technical, Geographical, and Social Aspects,2019. Edmond,OK,USA MehdiRahmani-Andebili Contents 1 Problems:MagneticCircuitsAnalysis. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 1 2 SolutionsofProblems:MagneticCircuitsAnalysis. . . . . . . . . . . . . . . . . . . . . 5 3 Problems:InductanceofWindingsandInducedVoltageinWindings. . . . . . 13 4 SolutionsofProblems:InductanceofWindingsandInducedVoltage inWindings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Problems:EnergyLossinMagneticCircuits. . . . . . . . . . . . . . . . . . . . . . . . . 29 6 SolutionsofProblems:EnergyLossinMagneticCircuits. . . . . . . . . . . . . . . . 33 7 Problems:ElectromechanicalEnergyConversion. . . . . . . . . . . . . . . . . . . . . . 41 8 SolutionsofProblems:ElectromechanicalEnergyConversion. . . . . . . . . . . . 55 9 Problems:SeparatelyExcitedDCElectricGenerator. . . . . . . . . . . . . . . . . . . 81 10 SolutionsofProblems:SeparatelyExcitedDCElectricGenerator. . . . . . . . . 85 11 Problems:ShuntDCElectricGenerator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 12 SolutionsofProblems:ShuntDCElectricGenerator. . . . . . . . . . . . . . . . . . . 97 13 Problems:SeriesandCompoundDCElectricGenerators. . .. . . . . . . . . .. . . 103 14 SolutionsofProblems:SeriesandCompoundDCElectricGenerators. . . . . . 105 15 Problems:SeparatelyExcitedandShuntDCElectricMotors. . . . . . . . . . . . . 111 16 SolutionsofProblems:SeparatelyExcitedandShuntDCElectricMotors. . . 119 17 Problems:SeriesDCElectricMotor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 18 SolutionsofProblems:SeriesDCElectricMotor. . . . . . . . . . . . . . . . . . . . . . 157 19 Problems:CompoundDCElectricMotor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 20 SolutionsofProblems:CompoundDCElectricMotor. . . . . . . . . . . . . . . . . . 175 21 Problems:PowerLossandEfficiencyofDCElectricMachines. . . . . . . . . . . 183 22 SolutionsofProblems:PowerLossandEfficiencyofDCElectric Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 vii About the Author Mehdi Rahmani-Andebili is an assistant professor in the Department of Engineering and PhysicsattheUniversityofCentralOklahoma,OK,USA.Beforethat,hewasalsoanassistant professorintheElectricalEngineeringDepartmentatMontanaTechnologicalUniversity,MT, USA,andtheEngineeringTechnologyDepartmentatStateUniversityofNewYork,Buffalo State, NY, USA, during 2019–2022. He received his first MSc and PhD degrees in electrical engineering(powersystem)fromTarbiatModaresUniversityandClemsonUniversityin2011 and 2016, respectively, and his second MSc degree in physics and astronomy from the UniversityofAlabamainHuntsvillein2019.Moreover,hewasapostdoctoralfellowatSharif UniversityofTechnologyduring2016–2017.Asaprofessor,hehastaughtmanycoursesand labs,includingpowersystemanalysis,DCandACelectricmachines,feedbackcontrolsystems analysisanddesign,renewabledistributedgenerationandstorage,industrialelectronics,analog electronics,electricalcircuitsanddevices,ACelectricalcircuitsanalysis,DCelectricalcircuits analysis, essentials of electrical engineering technology, and algebra- and calculus-based physics.Dr.Rahmani-Andebilihasmorethan200single-authorandfirst-authorpublications, including journal papers, conference papers, textbooks, books, and book chapters. He is an IEEESeniorMemberandthepermanentreviewerofmanycrediblejournals.Hisresearchareas includesmartgrid,powersystemoperationandplanning,integrationofrenewablesandenergy storagesintopowersystem,energyschedulinganddemand-sidemanagement,plug-inelectric vehicles, distributed generation, and advanced optimization techniques in power system studies. ix 1 Problems: Magnetic Circuits Analysis Abstract In this chapter, Kirchhoff’s Magnetomotive Force Law (KML) and Kirchhoff’s Flux Law (KFL) are applied on the equivalent electrical circuits of the magnetic circuits to analyze their basic and advanced problems. In this chapter, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large). Additionally, the problems are ordered from the easiest problem with the smallest computationstothemostdifficultproblemswiththelargestcalculations. 1.1. Figure1.1.ashowsamagneticcorethatitsmagnetizationcurveisillustratedinFig.1.1.a.Thecross-sectionalareaand theaverageperimeterofthecoreareabout20cm2and50cm,respectively.DeterminethenumberofturnsofcoilCto createthemagneticfluxof3.5mWbinthecore.Herein,assumethatμ (cid:1)10(cid:3)6H/m. 0 Difficultylevel ○Easy ●Normal ○Hard Calculationamount ○Small ●Normal ○Large 1) 275 2) 150 3) 350 4) 125 Fig.1.1 Themagneticcircuitandgraphofproblem1.1 #TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2022 1 M.Rahmani-Andebili,DCElectricMachines,ElectromechanicalEnergyConversionPrinciples,andMagneticCircuitAnalysis, https://doi.org/10.1007/978-3-031-08863-6_1 2 1 Problems:MagneticCircuitsAnalysis 1.2. InthemagneticcircuitshowninFig.1.2,therelativepermeabilityofthecoreisabout20,000.Determinetheampere-turn ofthecoiltocreatethemagneticfluxdensityof1Tinthecore.Herein,assumethatthefringingfactorisabout1.05. Difficultylevel ○Easy ●Normal ○Hard Calculationamount ○Small ●Normal ○Large 1) 2796AT 2) 3876AT 3) 3020AT 4) 7608AT Fig.1.2 Themagneticcircuitofproblem1.2 1.3. Inacircularobjectmadefromamagneticmaterialwiththerelativepermeabilityof1000,anairgapof2mmiscreated. To keep the primary magnetic flux unchanged, what must be the ratio of the new magnetomotive force (mmf) to the primaryvalueiftheaverageperimeteroftheobjectis1m? Difficultylevel ○Easy ●Normal ○Hard Calculationamount ○Small ●Normal ○Large 1) 3 2) 2 3) 1 4) 1.5 1.4. InthemagneticcircuitshowninFig.1.3,thenumberofturnsofthecoilandtheaveragelengthofthecoreare500and 360mm,respectively.Iftherequiredmagneticfluxdensityandmagneticfieldintensityfortheoperationoftherelayare about0.8Tand510AT/minthecore,respectively,calculatetheratioofthecurrent,whentherearetwoairgapsof1.5 mm,tothecurrent,whenthereisnoairgapinthemagneticcircuit. Difficultylevel ○Easy ●Normal ○Hard Calculationamount ○Small ●Normal ○Large 1) 8 2) 13 3) 11 4) 15 Fig.1.3 Themagneticcircuitofproblem1.4
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