Electric Powertrain

John G. Hayes, PhD, MSEE, MBA, lectures at University College Cork, Ireland, and specialises in automotive, industrial and renewable energy systems and related power electronics, machines and electromagnetism. He previously worked in Southern California for ten years at General Motors' Hughes Aircraft subsidiary developing EV propulsion and inductive charging systems for the General Motors EV1, the first modern production EV. John's recent focus has been on the development of integrated and holistic EV teaching materials for the engineering student and the automotive professional. G. Abas Goodarzi, PhD, P.E., is the Chief Executive Officer and President of US Hybrid Corporation, Torrance, California, which he founded in 1999. He is also the President of US FuelCell, a company formed with the acquisition by US Hybrid of the United Technologies PEM fuel cell transportation division. He served as Senior Scientist at General Motors' Hughes Aircraft subsidiary, and as Technical Director for the General Motors EV1. He has designed various EV, HEV, and FCEV powertrain systems for light, medium, and heavy-duty, on-road, off-road, and special-purpose vehicles.

Preface xix

Acknowledgments xxi

Textbook Structure and Suggested Teaching Curriculum xxii

About the Companion Web Site xxiv

Part 1 Vehicles and Energy Sources 1

1 Electromobility and the Environment 3

1.1 A Brief History of the Electric Powertrain 4

1.1.1 Part I – The Birth of the Electric Car 4

1.1.2 Part II – The Resurgent Electric Powertrain 5

1.1.3 Part III – Success at Last for the Electric Powertrain 6

1.2 Energy Sources for Propulsion and Emissions 10

1.2.1 Carbon Emissions from Fuels 12

1.2.2 Greenhouse Gases and Pollutants 13

1.3 The Advent of Regulations 15

1.3.1 Regulatory Considerations and Emissions Trends 17

1.3.2 Heavy-Duty Vehicle Regulations 18

1.4 Drive Cycles 19

1.4.1 EPA Drive Cycles 19

1.5 BEV Fuel Consumption, Range, and mpge 24

1.6 Carbon Emissions for Conventional and Electric Powertrains 25

1.6.1 Well-to-Wheel and Cradle-to-Grave Emissions 27

1.6.2 Emissions due to the Electrical Grid 28

1.7 An Overview of Conventional, Battery, Hybrid, and Fuel Cell Electric Systems 29

1.7.1 Conventional IC Engine Vehicle 30

1.7.2 BEVs 30

1.7.3 HEVs 31

1.7.4 FCEV 33

1.7.5 A Comparison by Efficiency of Conventional, Hybrid, Battery, and Fuel Cell Vehicles 34

1.7.6 A Case Study Comparison of Conventional, Hybrid, Battery, and Fuel Cell Vehicles 35

1.8 A Comparison of Automotive and Other Transportation Technologies 36

References 37

Further Reading 38

Problems 38

Assignments 39

2 Vehicle Dynamics 40

2.1 Vehicle Load Forces 40

2.1.1 Basic Power, Energy, and Speed Relationships 41

2.1.2 Aerodynamic Drag 42

2.1.3 Rolling Resistance 45

2.1.4 Vehicle Road-Load Coefficients from EPA Coast-Down Testing 46

2.1.5 Battery Electric Vehicle Range at Constant Speed 49

2.1.6 Gradability 51

2.2 Vehicle Acceleration 52

2.2.1 Regenerative Braking of the Vehicle 54

2.2.2 Traction Motor Characteristics 54

2.2.3 Acceleration of the Vehicle 57

2.3 Simple Drive Cycle for Vehicle Comparisons 60

References 62

Further Reading 62

Problems 62

Sample MATLAB Code 63

Assignment: Modeling of a BEV 66

3 Batteries 68

3.1 Introduction to Batteries 68

3.1.1 Batteries Types and Battery Packs 68

3.1.2 Basic Battery Operation 73

3.1.3 Basic Electrochemistry 74

3.1.4 Units of Battery Energy Storage 76

3.1.5 Capacity Rate 77

3.1.6 Battery Parameters and Comparisons 79

3.2 Lifetime and Sizing Considerations 81

3.2.1 Examples of Battery Sizing 84

3.2.2 Battery Pack Discharge Curves and Aging 86

3.3 Battery Charging, Protection, and Management Systems 88

3.3.1 Battery Charging 88

3.3.2 Battery Failure and Protection 88

3.3.3 Battery Management System 89

3.4 Battery Models 90

3.4.1 A Simple Novel Curve Fit Model for BEV Batteries 92

3.4.2 Voltage, Current, Resistance, and Efficiency of Battery Pack 95

3.4.3 A Simple Curve-Fit Model for HEV Batteries 96

3.4.4 Charging 97

3.4.5 Determining the Cell/Pack Voltage for a Given Output/Input Power 99

3.4.6 Cell Energy and Discharge Rate 100

3.5 Example: The Fuel Economy of a BEV Vehicle with a Fixed Gear Ratio 102

References 105

Further Reading 106

Problems 106

Appendix: A Simplified Curve-Fit Model for BEV Batteries 108

4 Fuel Cells 111

4.1 Introduction to Fuel Cells 111

4.1.1 Fuel Cell Vehicle Emissions and Upstream Emissions 113

4.1.2 Hydrogen Safety Factors 113

4.2 Basic Operation 114

4.2.1 Fuel Cell Model and Cell Voltage 116

4.2.2 Power and Efficiency of Fuel Cell and Fuel Cell Power Plant System 118

4.2.3 Fuel Cell Characteristic Curves 119

4.3 Sizing the Fuel Cell Plant 120

4.3.1 Example: Sizing a Fuel Cell 121

4.3.2 Toyota Mirai 121

4.3.3 Balance of Plant 121

4.3.4 Boost DC-DC Converter 122

4.4 Fuel Cell Aging 122

4.5 Example: Sizing Fuel Cell System for Heavy Goods Tractor–Trailer Combination 124

4.6 Example: Fuel Economy of Fuel Cell Electric Vehicle 125

References 129

Problems 129

Assignments 130

5 Conventional and Hybrid Powertrains 131

5.1 Introduction to HEVs 131

5.2 Brake Specific Fuel Consumption 134

5.2.1 Example: Energy Consumption, Power Output, Efficiency, and BSFC 135

5.3 Comparative Examples of Conventional, Series, and Series-Parallel Hybrid Systems 138

5.3.1 Example: Fuel Economy of IC Engine Vehicle with Gasoline or Diesel Engine 138

5.3.2 Example: Fuel Economy of Series HEV 144

5.3.3 Example: Fuel Economy of Series-Parallel HEV 146

5.3.4 Summary of Comparisons 148

5.4 The Planetary Gears as a Power-Split Device 148

5.4.1 Powertrain of 2004 Toyota Prius 150

5.4.2 Example: CVT Operating in Electric Drive Mode (Vehicle Launch and Low Speeds) 151

5.4.3 Example: CVT Operating in Full-Power Mode 153

5.4.4 Example: CVT Operating in Cruising and Generating Mode 154

References 155

Problems 155

Assignments 156

Part 2 Electrical Machines 159

6 Introduction to Traction Machines 161

6.1 Propulsion Machine Overview 161

6.1.1 DC Machines 162

6.1.2 AC Machines 163

6.1.3 Comparison of Traction Machines 167

6.1.4 Case Study – Mars Rover Traction Motor 169

6.2 Machine Specifications 170

6.2.1 Four-Quadrant Operation 170

6.2.2 Rated Parameters 171

6.2.3 Rated Torque 172

6.2.4 Rated and Base Speeds 172

6.2.5 Rated Power 172

6.2.6 Peak Operation 173

6.2.7 Starting Torque 173

6.3 Characteristic Curves of a Machine 173

6.3.1 Constant-Torque Mode 173

6.3.2 Constant-Power Mode 174

6.3.3 Maximum-Speed Mode 174

6.3.4 Efficiency Maps 174

6.4 Conversion Factors of Machine Units 176

References 177

7 The Brushed DC Machine 178

7.1 DC Machine Structure 178

7.2 DC Machine Electrical Equivalent Circuit 180

7.3 DC Machine Circuit Equations 182

7.3.1 No-Load Spinning Loss 183

7.3.2 No-Load Speed 184

7.3.3 Maximum Power 184

7.3.4 Rated Conditions 184

7.4 Power, Losses, and Efficiency in the PM DC Machine 185

7.5 Machine Control using Power Electronics 186

7.5.1 Example: Motoring using a PM DC Machine 186

7.6 Machine Operating as a Motor or Generator in Forward or Reverse Modes 189

7.6.1 Example: Generating/Braking using a PM DC Machine 190

7.6.2 Example: Motoring in Reverse 191

7.7 Saturation and Armature Reaction 191

7.7.1 Example: Motoring using PM DC Machine and Machine Saturation 192

7.8 Using PM DC Machine for EV Powertrain 193

7.8.1 Example: Maximum Speeds using PM DC Machine 194

7.9 Using WF DC Machine for EV Powertrain 195

7.9.1 Example: Motoring using WF DC Machine 197

7.10 Case Study – Mars Rover Traction Machine 199

7.11 Thermal Characteristics of Machine 201

7.11.1 Example of Steady-State Temperature Rise 202

7.11.2 Transient Temperature Rise 203

7.11.3 Example of Transient Temperature Rise 203

References 204

Problems 204

8 Induction Machines 206

8.1 Stator Windings and the Spinning Magnetic Field 207

8.1.1 Stator Magnetic Flux Density 209

8.1.2 Space-Vector Current and the Rotating Magnetic Field 211

8.2 Induction Machine Rotor Voltage, Current, and Torque 216

8.2.1 Rotor Construction 216

8.2.2 Induction Machine Theory of Operation 216

8.3 Machine Model and Steady-State Operation 219

8.3.1 Power in Three-Phase Induction Machine 222

8.3.2 Torque in Three-Phase Induction Machine 223

8.3.3 Phasor Analysis of Induction Motor 225

8.3.4 Machine Operation When Supplied by Current Source 225

8.4 Variable-Speed Operation of Induction Machine 234

8.4.1 Constant Volts per hertz Operation 235

8.4.2 Variable-Speed Operation 235

8.5 Machine Test 240

8.5.1 DC Resistance Test 240

8.5.2 Locked-Rotor Test 240

8.5.3 No-Load Test 242

References 244

Further Reading 244

Problems 245

Sample MATLAB Code 246

9 Surface-Permanent-Magnet AC Machines 249

9.1 Basic Operation of SPM Machines 249

9.1.1 Back EMF of a Single Coil 249

9.1.2 Back EMF of Single Phase 250

9.1.3 SPM Machine Equations 253

9.2 Per-Phase Analysis of SPM Machine 255

9.2.1 Per-Phase Equivalent Circuit Model for SPM Machine 256

9.2.2 Phasor Analysis of SPM Machine 257

9.2.3 Machine Saturation 263

9.2.4 SPM Torque–Speed Characteristics 264

9.2.5 High-Speed Operation of SPM Machine above Rated Speed 266

9.2.6 Machine Characteristics for Field-Weakened Operation 270

References 272

Further Reading 273

Problems 273

MATLAB Code 274

10 Interior-Permanent-Magnet AC Machine 276

10.1 Machine Structure and Torque Equations 276

10.2 d- and q-Axis Inductances 278

10.2.1 Example: Estimating the d-axis and q-axis Inductances for 2004 Toyota Prius Motor 281

10.3 IPM Machine Test 281

10.3.1 No-Load Spin Test 282

10.3.2 DC Torque Test 282

10.4 Basic Theory and Low-Speed Operation 286

10.4.1 Example: Motoring at Rated Condition 287

10.4.2 Maximum Torque per Ampere (MTPA) 289

10.4.3 Maximum Torque per Volt (MTPV) or Maximum Torque per Flux (MTPF) 289

10.5 High-Speed Operation of IPM Machine 289

10.5.1 Example: Motoring at High Speed using IPM Machine 289

10.6 dq Modeling of Machines 291

10.6.1 Constant Current Transformation 292

10.6.2 Constant Power Transformation 294

References 295

Further Reading 295

Problems 296

Assignments 298

Part 3 Power Electronics 299

11 DC-DC Converters 301

11.1 Introduction 301

11.2 Power Conversion – Common and Basic Principles 304

11.2.1 The Basic Topologies 306

11.2.2 The Half-Bridge Buck-Boost Bidirectional Converter 307

11.3 The Buck or Step-Down Converter 307

11.3.1 Analysis of Voltage Gain of Buck Converter in CCM 309

11.3.2 BCM Operation of Buck Converter 317

11.3.3 DCM Operation of Buck Converter 319

11.4 The Boost or Step-up Converter 325

11.4.1 Analysis of Voltage Gain of Boost Converter in CCM 326

11.4.2 BCM Operation of Boost Converter 330

11.4.3 DCM Operation of Boost Converter 332

11.5 Power Semiconductors 336

11.5.1 Power Semiconductor Power Loss 337

11.5.2 Total Semiconductor Power Loss and Junction Temperature 341

11.6 Passive Components for Power Converters 342

11.6.1 Example: Inductor Sizing 342

11.6.2 Capacitor Sizing 343

11.7 Interleaving 343

11.7.1 Example: Two-Phase Interleaved Boost Converter 345

References 346

Further Reading 346

Problems 346

Assignments 349

Appendix I 349

Appendix II: Buck-Boost Converter 349

Appendix III: Silicon Carbide Converters and Inverters 352

12 Isolated DC-DC Converters 353

12.1 Introduction 353

12.1.1 Advantages of Isolated Power Converters 353

12.1.2 Power Converter Families 354

12.2 The Forward Converter 355

12.2.1 CCM Currents in Forward Converter 357

12.2.2 CCM Voltages in Forward Converter 362

12.2.3 Sizing the Transformer 365

12.3 The Full-Bridge Converter 365

12.3.1 Operation of Hard-Switched Full-Bridge Converter 367

12.3.2 CCM Currents in Full-Bridge Converter 370

12.3.3 CCM Voltages in the Full-Bridge Converter 376

12.4 Resonant Power Conversion 377

12.4.1 LCLC Series-Parallel Resonant Converter 377

12.4.2 Desirable Converter Characteristics for Inductive Charging 378

12.4.3 Fundamental-Mode Analysis and Current-Source Operation 381

12.4.4 Simulation 385

References 388

Further Reading 388

Problems 388

Assignments 390

Appendix I: RMS and Average Values of Ramp and Step Waveforms 390

Appendix II: Flyback Converter 391

13 Traction Drives and Three-Phase Inverters 392

13.1 Three-Phase Inverters 392

13.2 Modulation Schemes 393

13.2.1 Sinusoidal Modulation 395

13.2.2 Sinusoidal Modulation with Third Harmonic Addition 396

13.2.3 Overmodulation and Square Wave 398

13.3 Sinusoidal Modulation 398

13.3.1 Modulation Index m 399

13.3.2 Inverter Currents 401

13.3.3 Switch, Diode, and Input Average Currents 401

13.3.4 Switch, Diode, DC Link, and Input Capacitor RMS Currents 403

13.3.5 Example: Inverter Currents 404

13.4 Inverter Power Loss 405

13.4.1 Conduction Loss of IGBT and Diode 405

13.4.2 Switching Loss of IGBT Module 405

13.4.3 Total Semiconductor Power Loss and Junction Temperature 407

13.4.4 Example: Regenerative Currents 408

References 409

Further Reading 409

Problems 410

Assignments 411

14 Battery Charging 412

14.1 Basic Requirements for Charging System 412

14.2 Charger Architectures 414

14.3 Grid Voltages, Frequencies, and Wiring 416

14.4 Charger Functions 418

14.4.1 Real Power, Apparent Power, and Power Factor 419

14.5 Charging Standards and Technologies 422

14.5.1 SAE J1772 422

14.5.2 VDE-AR-E 2623-2-2 425

14.5.3 CHAdeMo 425

14.5.4 Tesla 425

14.5.5 Wireless Charging 425

14.6 The Boost Converter for Power Factor Correction 427

14.6.1 The Boost PFC Power Stage 428

14.6.2 Sizing the Boost Inductor 430

14.6.3 Average Currents in the Rectifier 431

14.6.4 Switch and Diode Average Currents 432

14.6.5 Switch, Diode, and Capacitor RMS Currents 434

14.6.6 Power Semiconductors for Charging 434

References 438

Further Reading 438

Problems 439

Assignments 440

15 Control of the Electric Drive 441

15.1 Introduction to Control 441

15.1.1 Feedback Controller Design Approach 442

15.2 Modeling the Electromechanical System 443

15.2.1 The Mechanical System 443

15.2.2 The PM DC Machine 446

15.2.3 The DC-DC Power Converter 447

15.2.4 The PI Controller 447

15.3 Designing Torque Loop Compensation 448

15.3.1 Example: Determining Compensator Gain Coefficients for Torque Loop 449

15.4 Designing Speed Control Loop Compensation 449

15.4.1 Example: Determining Compensator Gain Coefficients for Speed Loop 451

15.5 Acceleration of Battery Electric Vehicle (BEV) using PM DC Machine 451

15.6 Acceleration of BEV using WF DC Machine 452

References 455

Problems 455

Assignment and Sample MATLAB Codes 456

Part 4 Electromagnetism 459

16 Introduction to Electromagnetism, Ferromagnetism, and Electromechanical Energy Conversion 461

16.1 Electromagnetism 462

16.1.1 Maxwell’s Equations 462

16.2 Ferromagnetism 467

16.2.1 Magnetism and Hysteresis 467

16.2.2 Hard and Soft Ferromagnetic Materials 470

16.3 Self-Inductance 473

16.3.1 Basic Inductor Operation 474

16.3.2 Inductor Equations 475

16.3.3 Reluctance 478

16.3.4 Energy Stored in Magnetic Field 481

16.3.5 Core Loss 482

16.3.6 Copper Loss 484

16.3.7 Inductor Sizing using Area Product 487

16.3.8 High-Frequency Operation and Skin Depth 488

16.4 Hard Ferromagnetic Materials and Permanent Magnets 489

16.4.1 Example: Remanent Flux Density 490

16.4.2 Example: The Recoil Line 492

16.4.3 Example: Air Gap Flux Density due to a Permanent Magnet 494

16.4.4 Maximum Energy Product 494

16.4.5 Force due to Permanent Magnet 494

16.4.6 Electromagnet 497

16.5 The Transformer 498

16.5.1 Theory of Operation 498

16.5.2 Transformer Equivalent Circuit 500

16.5.3 Transformer Voltages and Currents 501

16.5.4 Sizing the Transformer using the Area-Product (AP) Method 505

16.6 The Capacitor 506

16.6.1 Sizing Polypropylene High-Voltage Capacitor 508

16.7 Electromechanical Energy Conversion 509

16.7.1 Ampere’s Force Law 509

16.7.2 General Expression for Torque on Current-Carrying Coil 510

16.7.3 Torque, Flux Linkage, and Current 511

16.7.4 Faraday’s Law of Electromagnetic Induction 512

16.7.5 Lenz’s Law and Fleming’s Right Hand Rule 512

References 513

Further Reading 514

Further Viewing 515

Problems 515

Assignments 518

Reference Conversion Table 519

Index 521