General Airgap Field Modulation Theory for Electrical Machines Principles and Practice

Introducing a new theory for electrical machines

Air-gap magnetic field modulation phenomena have been widely observed in electrical machines. This book serves as the first English-language overview of these phenomena, as well as developing systematically for the first time a general theory by which to understand and research them. This theory not only serves to unify analysis of disparate electrical machines, from conventional DC machines, induction machines, and synchronous machines to unconventional flux-switching permanent magnet machines, Vernier machines, doubly-fed brushless machines etc., but also paves the way towards the creation of new electrical machine topologies.

General Airgap Field Modulation Theory for Electrical Machines includes both overviews of key concepts in electrical machine engineering and in-depth specialized analysis of the novel theory itself. It works through the applications of the developed theory before proceeding to both qualitative analysis of the theory’s operating principles and quantitative analysis of its parameters.

Readers will also find:

• The collective experience of four award-winning authors with long records of international scholarship on this subject
• Three separate chapters covering the principal applications of the theory, with detailed examples
• Discussion of potential innovations made possible by this theory

General Airgap Field Modulation Theory for Electrical Machines is an essential introduction to this theory for postgraduates, researchers, and electrical engineers.

Ming Cheng, Ph.D. is the Endowed Chair Professor of Electrical Engineering and Director of the Research Center for Wing Power Generation at Southeast University, China. He has B.Sc. and M.Sc. degrees from Southeast University and a Ph.D. in electrical engineering from Hong University. He has been the recipient of the National Technology Invention Award of China, the IET Achievement Award, and an IEEE IAS Distinguished Lectureship, among others.

Peng Han, Ph.D. is a Senior Application Engineer at Ansys Inc., USA. He holds both B.Sc. and Ph.D degrees in electrical engineering from Southeast Unniversity.

Yi Du, Ph.D. is a Professor of Electrical and Information Engineering at Jiangsu University, China. He holds B.Sc. and M.Sc. degrees from Jiangsu University and Ph.D. in electrical engineering from Southeast University.

Honghui Wen, Ph.D., is a Research Assistant at Southeast University, China. He received B.Sc. and Ph.D. degrees in electrical engineering from Southeast University. He received second prize in the IEEE IAS Myron Zucker Undergraduate Student Design Contest in 2017.

Preface xi

About the Authors xv

About the Companion Website xvii

1 Introduction 1

1.1 Review of Historical Development of Electrical Machines 1

1.2 Limitations of Classical Electrical Machine Theories 7

1.2.1 Fragmentation of Electrical Machine Theories 7

1.2.2 Limitations in Analysis of Operating Principles 8

1.2.3 Lack of Uniformity in Performance Analysis 9

1.3 Overview of Magnetic Field Modulation Machines and their Theories 11

1.4 Scope and Organization of the Book 14

References 16

2 Airgap Magnetic Field Modulation Phenomena in Electrical Machines 23

2.1 Traditional Electrical Machines 23

2.1.1 Brushed Direct Current Machines 24

2.1.2 Induction Machines 26

2.1.3 Synchronous Machines 29

2.2 Field Modulation Magnetic Gears 33

2.2.1 Construction and Operating Principle 34

2.2.2 Airgap Magnetic Field Modulation Behaviors 36

2.2.3 Other MG Types 42

2.3 Magnetically Geared Machines 45

2.3.1 Evolution of MGMs 46

2.3.2 Airgap Magnetic Field Modulation Behaviors 48

2.4 PM Vernier Machine 50

2.4.1 Machine Construction 50

2.4.2 Airgap Magnetic Field Modulation Behaviors 50

2.5 Linear PMV Machine 52

2.5.1 Machine Construction 53

2.5.2 Airgap Magnetic Field Modulation Behaviors 54

2.6 Flux-switching PM Machine 57

2.6.1 Magnetic Field Modulation Mechanism of PM Field 58

2.6.2 Magnetic Field Modulation Mechanism of Armature Field 62

2.7 Doubly-Fed Machines 66

2.7.1 Classification and Operating Principles 67

2.7.2 Cascaded Type 70

2.7.3 Modulation Type 71

2.7.4 Commonalities and Differences of Existing Brushless Doubly-fed Machines 78

2.8 Uniformity of Machine Operating Principles 79

References 82

3 Three Key Elements Model for Electrical Machines 87

3.1 Introduction 87

3.2 Classical Winding Function Theory and Its Limitations 89

3.2.1 Winding MMF 89

3.2.2 Classical Winding Function Theory 92

3.2.3 Limitations of Classical Winding Function Theory 95

3.3 Three Key Elements 99

3.3.1 Source of Excitation 101

3.3.2 Modulator 101

3.3.3 Filter 103

3.4 Mathematical Representation of Three Key Elements 103

3.4.1 Source MMF 104

3.4.2 Modulation Operator 108

3.4.3 Filter 120

3.4.4 Unified Airgap Model 121

3.4.5 Duality Between Electrical Machines and Switching Power Converters 124

3.5 Torque Decomposition 129

3.5.1 General Torque Equation 129

3.5.2 Wound-Field Salient-Pole SM 132

3.5.3 SynRM 135

3.5.4 Squirrel-Cage IM 135

3.5.5 Bdfrm 136

3.5.6 Bdfim 138

3.5.7 FSPM Machine 139

3.5.8 PMV Machine 151

3.5.9 Axial-Flux PMV Machine 155

References 158

4 Analysis of Magnetic Field Modulation Behaviors 163

4.1 Introduction 163

4.2 Magnetic Field Modulation Behaviors and Torque Components 163

4.2.1 Asynchronous and Synchronous Modulation Behaviors 164

4.2.2 Asynchronous and Synchronous Torque Components 166

4.3 Characterization of Modulation Behaviors in Typical Machine Topologies 167

4.3.1 Brushed DCM 168

4.3.2 Wound-Field Salient-Pole SM 168

4.3.3 Wound-Field Non-Salient-Pole SM and Slip-Ring Doubly-Fed Induction Machine 169

4.3.4 Squirrel Cage IM and BDFIM 170

4.3.5 Synchronous Reluctance Machine and Brushless Doubly-Fed Reluctance Machine 171

4.3.6 Surface-Mounted PMSM and FRPM Machine 173

4.3.7 Interior PMSM and FSPM Machine 174

4.3.8 Switched Reluctance Machine and Vernier Machine 175

4.3.9 Magnetically-Geared Machine and PM Vernier Machine 176

4.4 Torque Composition of Typical Machine Topologies 177

4.4.1 Case Study I – BDFIM 179

4.4.2 Case Study II – BDFM with a Hybrid Rotor 183

4.4.3 Case Study III – FSPM Machine 186

4.5 Magnetic Field Modulation Behaviors of Various Modulators 188

4.5.1 Salient Reluctance Pole Modulator 188

4.5.2 Multilayer Flux Barrier Modulator 197

4.5.3 Short-Circuited Coil Modulator 202

4.6 Interchangeability of Modulators 213

4.6.1 Comparison of Three Basic Modulator Types 213

4.6.2 Influence of Modulators on Machine Performance 217

References 225

5 Performance Evaluation of Electrical Machines Based on General Airgap Field Modulation Theory 227

5.1 Introduction 227

5.2 Squirrel-Cage IM 227

5.2.1 Airgap Magnetic Field Analysis 229

5.2.2 Inductance and Torque Characteristics 231

5.3 Brushless Doubly-fed Machines 234

5.3.1 Stator Winding MMF 235

5.3.2 Airgap Magnetic Field and Inductances 238

5.3.3 Quantitative Analysis of 4/2 BDFRM 250

5.3.4 Quantitative Analysis of 4/2 BDFIM 264

5.4 SynRM 272

5.4.1 Inductances 272

5.4.2 Torque Characteristic 274

5.5 FRPM Machine 276

5.5.1 Magnetic Field Modulation Behavior 276

5.5.2 Influence of Key Topological Parameters 279

5.5.3 Experimental Validation 280

5.6 Comparison of Representative Machine Topologies 284

References 288

6 Innovation of Electrical Machine Topologies 293

6.1 Innovation Methods 293

6.1.1 Change of Source MMF 294

6.1.2 Change of Modulator 296

6.1.3 Change of Filter 296

6.1.4 Change of Relative Position of Three Key Elements 297

6.1.5 Change of Relative Motion of Three Key Elements 297

6.2 DSPM Machine with Π-Shaped Stator Core 298

6.2.1 Machine Construction and Operating Principle 299

6.2.2 Performance Analysis and Comparison 308

6.2.3 Prototype and Experimental Results 310

6.3 Stator-PM Variable Reluctance Resolver 313

6.3.1 Machine Construction and Operating Principle 315

6.3.2 Odd-Pole Issue and Solutions Based on GAFMT 318

6.4 FRPM Machine 322

6.4.1 Operating Principle 324

6.4.2 Analysis of Open-Circuit Back-EMF Based on GAFMT 330

6.5 FSPM Machine with Full-Pitch Windings 332

6.5.1 Machine Construction and Operating Principle 334

6.5.2 Influence of Key Geometric Parameters 336

6.5.3 Comparative Study 340

6.6 Rotor-PM FSPM Machine 341

6.6.1 Machine Construction and Operating Principle 342

6.6.2 Winding Consistency and Complementarity 345

6.6.3 Fundamental Electromagnetic Performance 347

6.7 Dual-Rotor Magnetically-Geared Power Split Machine 359

6.7.1 Machine Construction and Operating Principle 360

6.7.2 Modes of Operation 362

6.7.3 Asymmetry in Magnetic Circuits 365

6.7.4 Complementary MGPSM and Experimental Validation 370

6.8 Stator Field-Excitation HTS Machines 383

6.8.1 Stator Field-Excitation HTS Flux-Switching Machine 385

6.8.2 Double-Stator Field Modulation Superconducting Excitation Machine 387

6.8.3 Technical Challenges and Outlook of Field Modulation HTS Machines 391

6.9 Brushless Doubly-Fed Reluctance Machine with an Asymmetrical Composite Modulator 393

6.9.1 Phase Shift Phenomenon of Modulated Harmonics 394

6.9.2 Asymmetrical Composite Modulator 398

6.9.3 Experimental Verification 400

References 402

7 Other Applications of General Airgap Field Modulation Theory 409

7.1 Introduction 409

7.2 Analysis of Radial Forces in Brushless Doubly-fed Machines 410

7.2.1 Electromagnetic Vibration and Noise in Electrical Machines 410

7.2.2 Analysis of Radial Forces 410

7.2.3 Calculation of Radial Forces 411

7.2.4 Pole-Pair Combinations Without UMP 422

7.3 Design of Suspension Windings for Bearingless Homopolar and Consequent Pole PM Machines 423

7.3.1 Design Principle of Pole-Changing Windings 424

7.3.2 Solution 1: Coil Span y = 4 427

7.3.3 Solution 2: Coil Span y = 5 427

7.4 Loss Calculation 427

7.4.1 Stray Load Loss Calculation for IMs 432

7.4.2 Computationally Efficient Core Loss Calculation for FSPM Machines Supplied by PWM Inverters 449

7.5 Optimization of Salient Reluctance Pole Modulators for Typical Field Modulation Electrical Machines 472

7.5.1 Typical Salient Reluctance Poles 473

7.5.2 Optimization for Magnetically-Geared PM Machine 477

7.5.3 Optimization for FRPM Machine 482

7.5.4 General Guidelines 487

7.6 Airgap-Harmonic-Oriented Design Optimization Methodology 488

7.6.1 Airgap-Harmonic-Oriented Design Optimization Concept 490

7.6.2 Sensitivity Analysis 495

7.6.3 Multi-Objective Optimization 498

7.6.4 Optimization Results and Experimental Validation 501

References 508

Appendix A Derivation of Modulation Operators 513

A. 1 Derivation of Modulation Operator for Short-circuited Coils 513

A. 2 Derivation of Modulation Operator for Salient Reluctance Poles 514

A. 3 Derivation of Modulation Operator for Multilayer Flux Barriers 516

Appendix B Magnetic Force of Current-Carrying Conductors in Airgap and in Slots 521

References 524

Appendix C Methods for Force and Torque Calculation 525

C.1 Maxwell Stress Tensor Method 525

C.2 Principle of Virtual Work 530

C.2.1 Torque Derived from Magnetic Stored Energy and Virtual Displacement 530

C.2.2 Torque Derived from Co-energy and Virtual Displacement 532

References 533

Index 535

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