Jan A. Melkebeek Electrical Machines and Drives Fundamentals and Advanced Modelling 123 Jan A.Melkebeek Faculty of Engineering andArchitecture GhentUniversity Zwijnaarde, Ghent Belgium ISSN 1612-1287 ISSN 1860-4676 (electronic) Power Systems ISBN978-3-319-72729-5 ISBN978-3-319-72730-1 (eBook) https://doi.org/10.1007/978-3-319-72730-1 LibraryofCongressControlNumber:2017962069 ©SpringerInternationalPublishingAG2018 Foreword It is remarkable to me that well over half of the subject matter in this book simply did not exist when I taught my first electric machines course in 1959. This is testimonytotheexpandingroleofelectromechanicalconversionsystems,fueledby demandsforimprovedenergymanagementandenabledbydevelopmentsinpower electronicdevicesandsystems.Italsospeakstothedepthandbreadthofthetopical coverage in the book. The organisation into four parts, Electric Machines, Power Electronics, Electric DrivesandDriveDynamics,providessubstantialflexibility.Viewedasatextbook, thefourpartstogetherprovidecomprehensivecontentsuitableforamulti-semester course sequence in electromechanical energy conversion. Alternatively, Part 1 can beusedaloneforaone-semester courseinElectricMachinesandportionsofParts 2–4 for a one-semester Electric Drives course and a more advanced course emphasising dynamics using Part 4. The book can also be viewed as a valuable referencebookbecauseofitscomprehensivecoverageofthesubjectareaincluding many special topics such as stepping motors, switched reluctance motors, small electric motor drives and voltage surges in electrical machines. I spent a semester in Gent as a Fulbright Lecturer and had the opportunity to collaborate with the author on the influence of magnetic saturation on electric machine dynamic behaviour. This experience left me with a deep appreciation oftheauthor'sdedicationtoaccuratebutcleardescriptionoftechnicalmattersthat has carried over to this text. Whether as a text or a reference, the content of this book provides a compre- hensivetreatmentofelectricmachinesanddrivesspicedwithagenerouscollection ofspecialtopicsnotusuallyincludedincontemporarybooks.Itisaworthyaddition to any collection of electric machines books. Donald Novotny Emeritus Professor, Department of Electrical and Computer Engineering University of Wisconsin— Madison, Madison USA Preface This work can be used as a comprehensive study and reference textbook on the most common electrical machines and drives. In contrast with many textbooks on drives, this book goes back to the fundamentals of electrical machines and drives, following in the footsteps of the traditional textbooks written by Richter and Bödefeld & Sequenz in German. Thebasicideaistostartfromthepureelectromagneticprinciplestoderiveboth the equivalent circuits and the steady-state equations of these electrical machines (e.g. in Part 1) as well as its dynamic equations in Part 4. In my view, only this approachleadstoafullunderstandingofthemachine,ofthesteady-statebehaviour ofadriveanditsdynamics.Muchattentionispaidtotheelectromagneticbasisand to analytical modelling. Intentionally, computer simulation is not addressed, although the students are required to use computer models in the exercises and projects, for example, for the section on power electronics or that on dynamic modelling and behaviour. I have successfully used this approach for more than 30 years,andIoftenreceivemailsandrequestsfromformerstudentsworkingabroad, who would like my course texts in electronic format. Indeed, few (if any) books offer a similar in-depth approach to the study of the dynamics of drives. The textbook is used as the course text for the Bachelor’s and Master’s pro- grammeinelectricalandmechanicalengineeringattheFacultyofEngineeringand Architecture of Ghent University. Parts 1 and 2 are taught in the basic course ‘FundamentalsofElectricDrives’inthethirdbachelor.Part3isusedforthecourse ‘Controlled Electrical Drives’ in the first master, while Part 4 is used in the spe- cialised master on electrical energy. Part 1 focuses mainly on the steady-state operation of rotating field machines. Nevertheless,thefirsttwochaptersaredevotedtotransformersandDCcommutator machines: the chapter on transformers is included as an introduction to induction and synchronous machines, their electromagnetics and equivalent circuits, while that on DC commutator machines concludes with the interesting motor and gen- erator characteristics of these machines, mainly as a reference. Chapters 3 and 4 offer an in-depth study of induction and synchronous machines, respectively. Starting from their electromagnetics, steady-state equations and equivalent circuits are derived, from which their properties can be deduced. In addition to the poly- phase machines, also special types such as capacitor motors and shaded-pole motors are discussed. The second part of this book discusses the main power electronic supplies for electrical drives, for example, rectifiers, choppers, cycloconverters and inverters. This part is not at all intended as a fundamental course text on power electronics and its design. For the design of power electronic circuits, much more in-depth textbooks are available. The only aim is to provide the basics required for their application in electrical machine drives. After an overview of power electronic components,thefollowingchaptersprovidearatherthoroughanalysisofrectifiers, DC and AC choppers, cycloconverters and inverters. Much attention is paid to PWM techniques for inverters and the resulting harmonic content in the output waveform. In the third part, electrical drives are discussed, combining the traditional (ro- tatingfieldandDCcommutator)electricalmachinestreatedinPart1andthepower electronicsofPart2.Part3beginswithachapteronDCcommutatormachinesand their characteristics. Next, the traditional constant frequency operation of rotating fieldmachinesistreatedindetail,includingits(limited)startingandvariablespeed operation possibilities. In the same chapter, the effect of voltage variations is also discussed, as is voltage adaptation to the load and power electronic starting of induction machines. The next chapter analyses ideal sinusoidal current supply of rotating field machines, with a special focus on main field saturation. After ideal variable frequency supply of rotating field machines is treated, the useful funda- mental frequency equivalent circuits for inverters (originally presented by the colleaguesofUW-Madison)arediscussed.Withtheseequivalentcircuits,themain properties of rotating field machines with variable frequency inverter supply are straightforwardly derived. Next, the basics of controlled drives are presented, includingfieldorientationofinductionandsynchronousmachines,aswellasdirect torquecontrol.Thetwosubsequentchaptersaredevotedtopowerelectroniccontrol of small electric machines and to AC commutator machines, respectively. To end, small synchronous machines are described (i.e. permanent magnet synchronous machines, reluctance machines and hysteresis motors), as are stepping motors and switched reluctance machines. Finally,Part4isdevotedtothedynamicsoftraditionalelectricalmachines.For the dynamics of induction and synchronous machine drives as well, the electro- magneticsareusedasthestartingpointtoderivethedynamicmodels.Throughout Part 4, much attention ispaid to thederivation ofanalytical models. Naturally,the basic dynamic properties and probable causes of instability of induction and syn- chronousmachinedrivesarediscussedindetailaswell,withthederivedmodelsfor stabilityinthesmallasthestartingpoint.Inadditiontothestudyofthestabilityin thesmall,onechapter isdevotedtolarge-scale dynamics (e.g.sudden short circuit ofsynchronousmachines).Anotherchapterisdedicatedtothedynamicsinvector- andfield-orientedcontrol,whilethelastchapterdiscussesvoltagesurgephenomena in electrical machines and transformers. In the appendices, additional background is provided on terminal markings of machines and transformers (Appendix A), static stability of a drive (Appendix B) andonphasorsandspacevectors(AppendixC).Somebasicknowledgeofterminal markings is of course required for the practical exercises. The notion of static stability is explained in Appendix B, and it is not repeated for each machine type. With regard to the appendix on space vectors and phasors, the first section is required for Parts 1 and 3, while the second section is required for Part 4. Ghent, Belgium Jan A. Melkebeek Contents Part I Transformers and Electrical Machines 1 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Transformer Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Basic Electromagnetic Description and Equations. . . . . 4 1.2.2 Phasor Equations and Equivalent Circuit for Sinusoidal Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Referred Values: Equations and Equivalent Circuit . . . . . . . . . . 10 1.4 Per-Unit Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Construction and Scaling Laws . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5.1 Specific Rated Quantities . . . . . . . . . . . . . . . . . . . . . . 12 1.5.2 Rated Per-Unit Impedances. . . . . . . . . . . . . . . . . . . . . 13 1.6 Alternative and Simplified Equivalent Circuits . . . . . . . . . . . . . 19 1.7 No-Load Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.8 Short-Circuit Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.8.1 Short-Circuit Impedance . . . . . . . . . . . . . . . . . . . . . . . 22 1.8.2 Procentual Short-Circuit Voltage . . . . . . . . . . . . . . . . . 23 1.8.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.9 Voltage Variation with Load . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.10 Parallel Operation of Transformers. . . . . . . . . . . . . . . . . . . . . . 26 1.11 Construction of Single-Phase and Three-Phase Transformers. . . 29 1.11.1 Single-Phase Transformers . . . . . . . . . . . . . . . . . . . . . 29 1.11.2 Three-Phase Transformers. . . . . . . . . . . . . . . . . . . . . . 29 1.12 Connection and Vector Group of a Three-Phase Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.12.1 Winding and Terminal Markings. . . . . . . . . . . . . . . . . 33 1.12.2 Modelling of a Three-Phase Transformer. . . . . . . . . . . 33 1.12.3 Connections and Vector Groups . . . . . . . . . . . . . . . . . 34 1.12.4 Asymmetrical Operation of 3-Phase Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.13 Autotransformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.14 Phase-Number Transformation. . . . . . . . . . . . . . . . . . . . . . . . . 41 1.14.1 Three to Six or Twelve Phases . . . . . . . . . . . . . . . . . . 41 1.14.2 Three to Two Phases . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.15 Voltage Regulation Transformers. . . . . . . . . . . . . . . . . . . . . . . 43 1.16 Measurement Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.16.1 Current Transformers . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.16.2 Voltage Transformers . . . . . . . . . . . . . . . . . . . . . . . . . 46 2 Direct Current Commutator Machines . . . . . . . . . . . . . . . . . . . . . . 49 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.2 Construction of the DC Machine . . . . . . . . . . . . . . . . . . . . . . . 50 2.2.1 Basic Construction - Operating Principle . . . . . . . . . . . 50 2.2.2 Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.2.3 Armature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.3 Electrical Power Conversion in a DC Machine. . . . . . . . . . . . . 58 2.3.1 Voltage Induction (emf) . . . . . . . . . . . . . . . . . . . . . . . 58 2.3.2 Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.3.3 Electrical Power Conversion . . . . . . . . . . . . . . . . . . . . 60 2.4 Armature Reaction and the Compensation Winding . . . . . . . . . 63 2.5 Commutation and the Commutation Poles . . . . . . . . . . . . . . . . 66 2.6 Steady-State Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.6.1 Introduction - Per-Unit . . . . . . . . . . . . . . . . . . . . . . . . 70 2.6.2 Basic Characteristics and Derivation Methods . . . . . . . 70 2.6.3 Generator Characteristics . . . . . . . . . . . . . . . . . . . . . . 73 2.6.4 Motor Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 78 3 Rotating Field Machines: mmf, emf and Torque . . . . . . . . . . . . . . 85 3.1 Generation of a Rotating Field. . . . . . . . . . . . . . . . . . . . . . . . . 85 3.1.1 Magnetic Field by (stator) Salient Poles with Concentrated Windings. . . . . . . . . . . . . . . . . . . . . . . . 85 3.1.2 Magnetic Field by Rotating Salient Poles with Concentrated Windings. . . . . . . . . . . . . . . . . . . . . . . . 87 3.1.3 Magnetic Field by a Distributed AC Winding . . . . . . . 90 3.1.4 Magnetic Field by a Multiphase AC Winding . . . . . . . 94 3.1.5 Current Layer - Linear Current Density . . . . . . . . . . . . 98 3.1.6 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . 102 3.2 Induced Voltage (Electromagnetic Force or emf) . . . . . . . . . . . 104 3.2.1 Sinusoidal Rotating Field . . . . . . . . . . . . . . . . . . . . . . 104 3.2.2 Alternating Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.2.3 Non-sinusoidal Field. . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.3 Magnetising Inductance of an Armature Winding . . . . . . . . . . . 109 3.3.1 Single-Phase Winding. . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3.2 Multiphase Winding. . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.4 Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.4.2 Alternating Field and Alternating Current Layer. . . . . . 112 3.4.3 Rotating Field and Rotating Current Layer. . . . . . . . . . 113 4 The Induction Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1 Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.2 Transformer Properties of the Induction Machine at Standstill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2.1 The Axes of Stator and Rotor Windings Are Co-linear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2.2 The Axes of Stator and Rotor Windings Are Displaced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.2.3 Energy Conversion and Forces for an Induction Machine at Standstill . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.2.4 Applications of the Rotating Field Transformer . . . . . . 127 4.3 The Rotating Induction Machine: Operating Principle . . . . . . . . 127 4.3.1 Motoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.3.2 Generating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.3.3 Frequency Converter . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4 Equations and Equivalent Circuit of an Induction Machine . . . . 130 4.5 Energy Conversion and Torque . . . . . . . . . . . . . . . . . . . . . . . . 134 4.6 Torque and Torque-Slip Characteristic . . . . . . . . . . . . . . . . . . . 137 4.7 The Current Locus of an Induction Machine . . . . . . . . . . . . . . 140 4.8 Per-Unit Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.9 Effect of s=r, xr and xm on Current and Torque . . . . . . . . . . . . 147 4.10 Scaling Laws - Rated Specific Values . . . . . . . . . . . . . . . . . . . 152 4.11 Single-Phase and Two-Phase Induction Machines. . . . . . . . . . . 153 4.11.1 Two-Phase Induction Machines. . . . . . . . . . . . . . . . . . 153 4.11.2 Single-Phase Induction Machines . . . . . . . . . . . . . . . . 154 5 The Synchronous Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 5.1 Introduction - Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 5.2 Smooth Rotor Synchronous Machines . . . . . . . . . . . . . . . . . . . 168 5.2.1 Field Curve and No-Load Characteristic . . . . . . . . . . . 168 5.2.2 Armature Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 5.2.3 Phasor Diagram of Voltages and Currents . . . . . . . . . . 174 5.2.4 Linearised Equivalent Circuit of a Smooth Rotor Synchronous Machine. . . . . . . . . . . . . . . . . . . . . . . . . 177 5.2.5 Torque - Power - Energy Flow . . . . . . . . . . . . . . . . . . 181 5.2.6 Per-Unit Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 5.2.7 The Current Locus for Constant Excitation . . . . . . . . . 185 5.2.8 Characteristics of Synchronous Machines. . . . . . . . . . . 187 5.3 Salient-Pole Synchronous Machines. . . . . . . . . . . . . . . . . . . . . 193 5.3.1 Emf Induced by a Salient-Pole Rotor with Concentrated DC Winding . . . . . . . . . . . . . . . . . . . . . 193 5.3.2 Armature Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 5.3.3 Equations and Phasor Diagram of the Salient Pole Synchronous Machine. . . . . . . . . . . . . . . . . . . . . . . . . 198 5.3.4 Equivalent Circuits for a Salient Pole Synchronous Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 5.3.5 Torque, Power and Energy . . . . . . . . . . . . . . . . . . . . . 202 5.3.6 Current Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 5.4 Synchronous Machines Connected to a Power Grid . . . . . . . . . 205 5.5 Synchronous Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Part II Basics of Power Electronics 6 Power Electronic Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 6.2 The Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.3 The Thyristor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 6.4 The Triac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.5 The GTO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.6 The IGCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.7 The BJT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.8 The Mosfet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.9 The IGBT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.10 SiC and GaN Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.11 Other Power Electronic Devices. . . . . . . . . . . . . . . . . . . . . . . . 224 6.12 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 7 Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.2 Basic Theory of the Rectifier. . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.2.1 Uncontrolled Diode Rectifier. . . . . . . . . . . . . . . . . . . . 233 7.2.2 Phase-Controlled Rectifier. . . . . . . . . . . . . . . . . . . . . . 239 7.2.3 Discontinuous Conduction Mode. . . . . . . . . . . . . . . . . 241 7.2.4 Rectifier with a Capacitive Load . . . . . . . . . . . . . . . . . 242 7.2.5 Non-ideal AC Source: Finite Commutation Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 7.2.6 Power Exchange Between Rectifier and Grid. . . . . . . . 247 7.3 Rectifier Supply of DC Machines . . . . . . . . . . . . . . . . . . . . . . 259 7.3.1 Anti-parallel Connection. . . . . . . . . . . . . . . . . . . . . . . 259 7.3.2 Cross Connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . 261