DC Electric Machines, Electromechanical Energy Conversion Principles, and Magnetic Circuit Analysis: Practice Problems, Methods, and Solutions

188 Pages·2022·6.933 MB·English

by  Mehdi Rahmani-Andebili

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
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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