Design, Analysis and Implementation of a Novel Double Sided E-Core

DESIGN, ANALYSIS AND IMPLEMENTATION OF A NOVEL DOUBLE SIDED E-CORE

TRANSVERSE FLUX MACHINE WITH AXIAL AIRGAP

A Dissertation

Presented to

The Graduate Faculty of the University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy

Tausif Husain

August, 2017 DESIGN, ANALYSIS, AND IMPLEMENTATION OF A NOVEL DOUBLE SIDED

E-CORE TRANSVERSE FLUX MACHINE WITH AXIAL AIRGAP

Tausif Husain

Dissertation

Approved: Accepted:

______Advisor Interim Department Chair Dr. Yilmaz Sozer Dr. Joan Carletta

______Committee Member Interim Dean of the College Dr. Malik E. Elbuluk Dr. Donald P. Visco Jr.

______Committee Member Dean of the Graduate School Dr. Igor Tsukerman Dr. Chand Midha

______Committee Member Date Dr. Dane Quinn

______Committee Member Dr. Kevin Kreider

ABSTRACT

Direct drive applications are an attractive alternative to geared systems due to their high efficiency. This type of application requires electric machines operating at low speed with high torque. As a result, electric machines with high torque densities are preferred in this application. Machines with high torque densities typically employ rare- earth based NdFeB magnets. However, rare earth material is limited and their prices are volatile. Therefore, it is important to develop alternative high torque density machines that do not require rare-earth materials.

Axial flux and Transverse flux machines (TFM) offer high torque densities.

However, they suffer from low power factor due to high flux leakage. To improve the power factor rare earth based NdFeB magnets are used traditionally. This dissertation presents a double-stator single rotor E-cored TFM that can reduce leakage flux and improve power factor without needing rare-earth magnets. The machine uses ferrite magnets that are arranged in a flux-concentrating manner in the rotor. The novel topology is analyzed by developing analytical sizing equations, performing detailed 3D finite element analysis (FEA) based machine design and cogging torque minimization. The characteristics of the TFM are determined from FEA model and used to analyze the dynamic stability and performance. A novel winding configuration for wide speed operation of the proposed machine is also presented.

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The proposed machine has an airgap flux in the axial direction, winding current in the circumferential direction and the flux is linked between the stator and the rotor in the transverse plane. These flux paths require 3D FEA for the design of the machine.

However, 3D FEA is time-consuming. The first section of the dissertation involves the development of simplified analytical sizing equations for the proposed machine topology.

Detailed FEA analysis is then performed on the machine to characterize the effect of different geometric parameters on the machine.

Cogging torque is a critical issue in the design of TFMs. Different cogging torque minimization techniques and their applicability to the proposed machine are presented.

Key methods of cogging torque minimization are identified and used as design variables for the optimization using the design of experiments (DOE), based on Taguchi method.

Different winding configurations and their associated drive for the proposed dual stator machine is also investigated. A new winding structure through manipulation of the end connections is then proposed. The proposed structure offers greater flexibility in torque profiling and greater flux weakening region. A rotating reference frame model of the machine is presented. This model aids the stability and performance analysis.

The proposed machine topology is verified with 3D FEA and an experimental prototype built at the Alternative Energy Laboratory of the University of Akron. The experimental results of the proof of principle machine further validated the different concepts presented in this dissertation.

DEDICATION

I dedicate my work to my parents, wife, sister, grandmother and advisor who supported me throughout the course of my degree.

ACKNOWLEDGMENTS

I wish to express my sincere gratitude to my advisor, Dr. Yilmaz Sozer, for his guidance, encouragement, and support during my graduate studies. His technical knowledge, managerial skills, and human qualities have been a source of inspiration. His hands-on teaching method helped me to be the type of engineer I am.

I would like to thank the National Science Foundation (NSF Award No. 1307693,

1307846) for funding this research. NREL’s contribution to this work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the

National Renewable Energy Laboratory. I am grateful to Dr. Ed Muljadi from NREL and

Dr. Husain from NC State University for their valuable advice and deep insights. The initial group meetings helped shape the content of the dissertation.

I am grateful to my professors, Dr. Malik Elbuluk, Dr. Igor Tsukerman, Dr.

Alexis De Abreu-Garcia and Dr. Robert Veillette for their help and guidance during my studies at the University of Akron. I wish also to thank my committee member, Dr. Dane

Quinn and Dr. Kevin Kreider for their valuable comments and suggestions to improve the quality of the dissertation.

I am grateful Mr. Dale Ertley for the time and effort he put into prototyping the machine. I learned a lot of regarding manufacturing; tolerances and machining process, which helped make me a more well-rounded engineer. It would have been extremely hard

vi to prototype the machine without his help and insights into making the machine. His advice helped refine the prototyping procedure. I would like to thank Mr. Eric Rinaldo and Mr. Max Fightmaster for their prompt help and advice during the time at Akron in multiple projects.

I would like to acknowledge my colleagues at the Alternative Energy Laboratory for their continuous help and for providing the best educational atmosphere and enjoyable moments that we spent together during our work. I would like to particularly thank Dr.

Ali Elrayyah and Dr. Mohammed Badawy for their valuable advice and the thought provoking discussions that helped me improve as a researcher. Drs. Fatih Cingoz, Burak

Tekgun, Adeeb Ahmed and Wasi Uddin for their company and valuable advice regarding different aspects of this project. I would also like to thank Iftekhar Hasan who worked with me closely in this project. His insights and knowledge helped to improve the quality of this work.

Finally and most importantly, I would like to thank my wife Nashita, my mother, father, grandmonther, sister, uncle and friends for their unconditional help and encouragement all the time. My wife has been patient with me during the course of my studies and her support and inspiration were instrumental to my work. I would not have gone through with a dissertation without my father’s insistence and I am grateful that he encouraged me continuing in this path.

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TABLE OF CONTENTS

Page

Abstract ...... iii

Dedication ...... v

Acknowledgement ...... vi

List of Tables...... xiii

List of Figures ...... xv

CHAPTER

I. INTRODUCTION ...... 1

1.1. Background ...... 1

1.2. Permanent Magnet Machines ...... 2

1.3. Research Motivation and Objectives ...... 5

1.4. Dissertation Outline ...... 7

II. LITERATURE REVIEW ...... 10

2.1. Introduction ...... 10

2.2. Radial Flux Machines ...... 10

2.2.1.Non-PM Machines ...... 12

2.2.2. PM Machines ...... 17

2.3. Axial Flux Machines ...... 21

2.3.1.Non-PM Machines ...... 23

2.3.2.PM Machines ...... 25

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2.4. Transverse Flux Machines ...... 33

2.4.1. Single-sided TFM ...... 34

2.4.1.1. Surface Mounted TFM...... 34

2.4.1.2. Flux Concentrating TFM ...... 39

2.4.2.Double-sided TFM ...... 41

2.4.2.1. Surface Mounted TFM...... 41

2.4.2.2. Flux Concentrating TFM ...... 42

2.5. Cogging Torque in PM Machines...... 44

2.6. Modeling, Sizing and Optimization of AFM and TFM ...... 46

2.7. Flux Weakening Control of AFM and TFM ...... 48

2.8. Summary ...... 49

III. DESIGN OF E-CORE TRANSVERSE FLUX MACHINE ...... 50

3.1. Introduction ...... 50

3.2. Direct Drive Application ...... 51

3.3. U-core TFM ...... 52

3.4. Analysis of Power Factor and Motivation for E-Core Stator ...... 55

3.5. Proposed E-Core Transverse Flux Machine Structure...... 61

3.6. Design of E-Core Transverse Flux Machine Structure ...... 65

3.6.1.Initial Machine Design ...... 67

3.6.2.Specifications ...... 68

3.6.3.Choice of Pole Numbers ...... 69

3.6.4.Initial Dimensions in Radial Length (Peripheral Length) ...... 70

3.6.5.Rotor Design ...... 71

3.6.6.Turn Number Selection ...... 72

3.6.7.Stator Design ...... 72

3.6.8.Effect of Key Design Parameters ...... 73

3.6.9.Material Considerations ...... 77

3.6.10.Multiphase Machine ...... 81

3.7. Cogging Torque Reduction in Proposed Machine...... 82

3.7.1.Cogging Torque Minimization and Preliminary Results...... 82

3.7.1.1. Rotor and Stator Pole Numbers ...... 83

3.7.1.2. Pole Width ...... 83

3.7.1.3. Skewing...... 84

3.7.1.4. Stator Displacement ...... 86

3.7.1.5. Dummy Slots in Stator Teeth ...... 83

3.7.2.Design of Experiment Based Optimization ...... 84

3.8. Conclusion ...... 94

IV. ANALYSIS AND COMPARISON OF E-CORE MACHINE ...... 95

4.1. Introduction ...... 95

4.2. Electromagnetic Analysis With 3D FEA ...... 95

4.3. Comparison at High Torque Low Speed Applications ...... 107

4.4. Comparison At Medium Torque And Medium Speed Applications ...... 111

4.5. Conclusions ...... 116

V.WINDING CONFIGURATION, MODELING, AND ANALYSIS OF E-CORE TFM ...... 117

5.1. Introduction ...... 117

5.2. Winding Configuration for Flux Weakening ...... 117

5.2.1.Proposed Winding Configurations ...... 118

5.2.2.Machine Models ...... 120

5.2.3.Three Phase Machine Drive and Model ...... 123

5.2.4.Inductance of E-Core Machine ...... 126

5.2.5.Simulation Results...... 127

5.3. Rotating Reference Frame Model of Two Phase E-Core Machine ...... 130

5.4. Control of E-Core Machine ...... 134

5.4.1.Id=0 Control ...... 134

5.4.2.Maximum Torque Per Ampere Control (MTPA) ...... 135

5.4.3.Flux Weakening Control ...... 136

5.4.4.Maximum Torque Per Voltage Control (MTPV) ...... 137

5.4.5.Unity Power Factor Control ...... 137

5.5. Characteristic Curves and Dynamic Simulation of E-Core Machine ...... 137

5.6. Stability Analysis of E-Core Machine ...... 143

5.7. Conclusion ...... 149

VI.EXPERIMENTAL PROTOTYPING AND RESULTS ...... 151

6.1. Introduction ...... 151

6.2. Mechanical Prototype Development ...... 151

6.3. Development of TFM Drive ...... 158

6.4. Motor Controller ...... 161

6.5. Experimental Results ...... 163

6.5.1.Discrepancies in Construction ...... 164

6.5.2.Experimental Verification ...... 168

6.5.2.1. Case 1: Single Phase Machine at 2.8 mm Airgap ...... 168

6.5.2.2. No-Load Back-emf Voltage At Different Airgap ...... 171

6.5.2.3. Cogging Torque at Different Airgap and Stator Displacement...... 172

6.5.2.4. Winding Inductance and Flux Weakening ...... 173

6.5.2.5. Case 5: Two phase machine at 1.28 mm airgap ...... 174

6.6. Conclusion ...... 179

VII.CONCLUSION AND FUTURE WORK...... 181

7.1. Conclusions ...... 181

7.2. Future Work ...... 183

References ...... 184

Appendix I: Matlab Scripts ...... 206

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List of Tables

Table Page

2.1 TFM type and corresponding references ...... 44

3.1 Specification of wind turbine ...... 52

3.2 Design parameters and performance metric of designed U core TFM ...... 54

3.3 Parametric definitions ...... 65

3.4 Design specifications ...... 69

3.5 First pass machine design parameters ...... 73

3.6 Final design of case study machine ...... 77

3.7 Design comparisons with arc and without arc shapes...... 79

3.8 Performance of E-core machine with different magnets ...... 80

3.9 Performance with different pole numbers ...... 83

3.10 Design variable levels for optimization in Stage 1 ...... 88

3.11 L16 orthogonal array and results(Stage 1)...... 89

3.12 Analysis of means after Stage 1 of DOE ...... 89

3.13 SN ratio for after Stage 1 of DOE ...... 89

3.14 Orthogonal array and results (Stage 2) ...... 91

3.15 Orthogonal array and results (Stage 2) ...... 92

3.16 Key parameters of reference machine ...... 93

4.1 Key parameters in comparisons of different machines ...... 111

4.2 Motor specifications ...... 112

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4.3 Comparison of the motors for compressor application ...... 113

4.4 Comparison of the back-emf, cogging torque and airgap flux densities ...... 114

4.5 Comparison of electrical parameters of different machines ...... 115

5.1 Aligned and unaligned inductances for winding configuration A and B...... 127

5.2 Key electrical parameters of the machine ...... 138

6.1 No-load voltages at different speeds ...... 169

6.2 No load voltage at different airgap ...... 171

6.3 Cogging torque at different airgap and stator displacement ...... 173

6.4 Measured winding inductance with different winding configuration...... 173

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List of Figures

Figure Page

1.1. Types of electric machines ...... 2

1.2. Types of PM machines...... 2

1.3. Outline of proposed dissertation...... 9

2.1. Flux paths in different machine topologies ...... 11

2.2. Classification of radial flux machines ...... 12

2.3. Induction machine (IM) ...... 13

2.4. Different structures of switched reluctance machines ...... 14

2.5. 2D view of a synchronous reluctance machine...... 16

2.6. Other types of Non-PM machines ...... 16

2.7. Classification of PM machines ...... 17

2.8. 2D and 3D view of surface PM machines ...... 18

2.9. 2D structure of interior permanent magnet machine ...... 19

2.10. 2D structure of a flux switching machine ...... 20

2.11. First axial flux machine ...... 22

2.12. Classification of AFMs ...... 23

2.13. Single rotor single stator configuration of axial flux induction machine ...... 23

2.14. Double rotor single stator configuration of axial flux induction machine ...... 23

2.15. Pancake shaped axial flux switched reluctance machine ...... 24

2.16. 3D view of a 12-16 axial flux segment rotor SRM ...... 25

2.17. Single stator single rotor AFM ...... 26

2.18. Dual stator single rotor AFM ...... 26

2.19. Flux path in (a) Surface PM AFM (b) Buried PM structure

2.20. 3D view of a DSSR AFM with ring windings ...... 27

2.21. 2D plane view of DSSR AFM with ring windings ...... 27

2.22. Single stator dual rotor AFM ...... 28

2.23. Flux paths in DSSR and SSDR AFM ...... 29

2.24. 3D view of a dual rotor AFM with torus DC winding ...... 32

2.25. Configuration of a multi-stage AFM ...... 32

2.26. Classification of TFM topologies ...... 34

2.27. Single-sided surface mount TFM ...... 35

2.28. TFM with iron bridges ...... 36

2.29. A claw pole TFM ...... 36

2.30. 3D view of three consecutive stator poles and rotor for one phase with flux paths . 37

2.31. TFM which uses U and I shaped laminations ...... 38

2.32. Z-cored surface magnet TFM ...... 38

2.33. Single-sided flux concentrating TFM with U core stator ...... 39

2.34. Flux concentrated TFM topology in recent literature ...... 39

2.35. TFM with axially magnetized PM rings ...... 40

2.36. U-core FC TFM with stator bridges ...... 40

2.37. U-core FC TFM with stator bridges and tooth modification for low leakage...... 40

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2.38. Different flux concentrating magnet structures in TFMs...... 41

2.39. Double-sided surface magnet TFM with U-core stator ...... 42

2.40. Different topologies of FC TFM ...... 42

3.1. Shaft speed of turbine for different power ratings and wind speed ...... 52

3.2. Rotor radius of the turbine for different power ratings and wind speed ...... 52

3.3. Single pole pair of double-sided U-core TFM ...... 53

3.4. Rotor and magnet structure of U-core TFM ...... 53

3.5. Flux path of the U-core machine ...... 54

3.6. Phasor diagram with q-axis current for maximum torque per ampere ...... 56

3.7. Simplified MEC of the two machines ...... 58

3.8. MEC of U-core with leakage flux ...... 59

3.9. Airgap flux density of the two machines ...... 59

3.10. Flux lines of two machines from 2D FEA...... 60

3.11. Airgap flux density from 2D FEA ...... 60

3.12. Airgap flux density from 3D FEA ...... 61

3.13. 2D of one pole of the proposed TFM...... 61

3.14. Isometric view of one pole-pair ...... 62

3.15. Exploded view of the complete motor assembly ...... 63

3.16. Stator with semi-ring windings ...... 64

3.17. Geometric parameters of the proposed machine ...... 65

3.18. Design flowchart for first pass design...... 68

3.19. Effect of pole numbers in a single phase E-core TFM...... 70

3.20. Effect of 휆 on machine performance ...... 74

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3.21. Effect of 푘푓 on machine performance ...... 75

3.22. Effect of 푘푚...... 75

3.23. Effect of 푘푙푐 ...... 75

3.24. Effect of 푃푒푚푏 on machine performance ...... 76

3.25. Effect of 푃푒푚푏 on back-emf voltage ...... 77

3.26. (a) BH curve of laminated steel and SMC used in study

(b) Magnetic characteristic of permanent magnets ...... 78

3.27. Isometric of view of two design structure of E-core TFM...... 79

3.28. Two phase E-core TFM by stator shift...... 82

3.29. Effect on average torque and peak cogging torque ...... 84

3.30. Effect on average torque and peak cogging torque ...... 84

3.31. Top view of machine structure with stator skewing (Top view) ...... 85

3.32. Effect of skew angle on average torque and peak cogging torque ...... 85

3.33. Structure for cogging torque reduction with stator displacement on two sides ...... 86

3.34. Effect on average torque and peak cogging torque ...... 86

3.35. Possible slotting structures ...... 87

3.36. Effect of slot height and slot width on peak cogging

torque for slotting on x-axis ...... 87

3.37. Analysis after first stage of DOE ...... 90

3.38. Top view of machine structure with stator skew in opposite sides ...... 91

3.39. Analysis of means after second stage of DOE ...... 92

3.40. Cogging torque of final optimized machine with second order mesh ...... 93

4.1. Flux lines of one pole with 2D FEA...... 96

xviii

4.2. Flux path of single phase E-core TFM at aligned position...... 96

4.3. Flux density at aligned position ...... 97

4.4. Air gap flux density at aligned position...... 97

4.5. Flux vectors in cut planes for with rated current...... 98

4.6. No load characteristic of top stator ...... 99

4.7. Flux density surface plots of magnets under different current conditions ...... 101

4.8. Effect of current in windings ...... 102

4.9. Torque, current and voltage waveform at rated speed and current of single phase

motor...... 103

4.10. Efficiency plot for the entire speed range ...... 104

4.11. Torque per ampere plot for the entire speed range ...... 104

4.12. No load characteristic of two phase motor...... 105

4.13. Torque and current waveform at rated speed and current of two phase motor...... 105

4.14. FEA model and flux density distribution of three phase E-core TFM...... 106

4.15. Air gap flux density and back-emf waveform of three phase E-core TFM ...... 107

4.16. Torque and current waveforms at rated speed and current ...... 107

4.17. Cross section and flux density distribution of comparison machines ...... 109

4.18. Torque-speed characteristics of designed machines ...... 115

5.1. a) Coils for standard configuration A, b) Coils for configuration B...... 118

5.2. Standard connection of coils ...... 119

5.3. Winding configuration A ...... 119

5.4. Winding configuration B ...... 120

5.5. Three phase inverter for standard connection of TFM ...... 123

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5.6. Two sets of inverters for winding configuration A...... 124

5.7. Two sets of inverters for winding configuration B ...... 125

5.8. Effect of current advance angle of once coil on terminal voltage on second coil .129

5.9. Effect of winding configuration on torque-speed curve ...... 130

5.10. Effect of winding configuration on torque per ampere at rated current ...... 130

5.11. Power-speed curve at rated configuration for different winding configuration .... 130

5.12. Space vector representation of two phase machine ...... 131

5.13. Steady state vector diagram of machine in dq reference frame ...... 134

5.14. Phase plane characteristics of E-core machine ...... 139

5.15. Torque-speed curve of proposed machine at different current levels ...... 140

5.16. Torque per ampere curve of proposed machine for entire operating ...... 140

5.17. Phase current in ab domain in dynamic simulation with dq model ...... 141

5.18. Phase current in dq domain in dynamic simulation with dq model...... 141

5.19. Torque in dynamic simulation with dq model ...... 141

5.20. Torque, speed currents from transient simulation ...... 142

5.21. Phase current in ab domain in dynamic simulation with LUT model ...... 143

5.22. Phase current in dq domain in dynamic simulation with LUT model ...... 143

5.23. Torque waveform in dynamic simulation with LUT model ...... 143

5.24. Eigen value plot with different frequency at no load ...... 147

5.25. Zoom into the rotor poles at no load...... 147

5.26. Eigen value plot with different frequency at different loading conditions ...... 148

5.27. Zoom into the rotor poles at different loads ...... 149

6.1. Exploded view of the machine with mechanical supports ...... 152

6.2. Cut view of the machine with mechanical supports...... 152

6.3. Rotor cores of the prototype ...... 153

6.4. Ferrite magnets of the prototype ...... 153

6.5. Rotor housing with shaft and bearing ...... 153

6.6. Single stack of rotor with three rotor cores and two magnets ...... 154

6.7. Rotor assembly gig machine from a block of delrin ...... 154

6.8. Process of assembling rotor stacks to rotor housing with rotor gig ...... 155

6.9. Leakage flux reduction magnets and plastic spacers inserted to complete rotor.... 156

6.10. Complete rotor after epoxying...... 156

6.11. Setup for smoothing rotor surface ...... 156

6.12. Complete rotor after sanding...... 156

6.13. Stator back stand ...... 157

6.14. Back stand with the stator cores epoxied in...... 157

6.15. Stator after insulating E-core ...... 158

6.16. Form wound coils by hand winding...... 158

6.17. Final Stator core with windings and insulation ...... 158

6.18. Complete prototyped machine...... 158

6.19. Drive for testing TFM ...... 158

6.20. Interface board for testing TFM ...... 160

6.21. dSpace controller for testing TFM ...... 160

6.22. Complete drive and controller setup for testing TFM ...... 160

6.23. Mechanical setup of TFM coupled with servomotor through torque transducer. .. 161

6.24. Block diagram of a single phase TFM controller...... 162

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6.25. Inverter configuration for a single phase TFM...... 162

6.26. Dual band hysteresis current regulator for single phase TFM ...... 162

6.27. dq based field oriented controller (FOC) for two phase TFM ...... 163

6.28. Current regulator for two-phase machine in dq domain ...... 163

6.29. Rotor structure of proposed machine and built prototype ...... 164

6.30. Setup for measuring BH curve ...... 166

6.31. Schematic of setup for measuring BH curve ...... 166

6.32. BH curve from experiment...... 167

6.33. Static magnetic characteristics of expected

and experimentally evaluated material...... 167

6.34. Back-emf voltage from experiment and FEA ...... 169

6.35. Average torque vs peak reference current...... 170

6.36. Average torque vs rms current...... 170

6.37. Current at a 4.65 Nm average torque ...... 171

6.38. Current at 1.18 Nm average torque ...... 171

6.39. Comparison of back-emf voltage in experiment with FEA results

at different airgap at 400 rpm...... 172

6.40. Fundamental of the back-emf voltage in open coil when coil 1 is advanced...... 174

6.41. Back-emf voltage of two phase machine at 400 rpm...... 175

6.42. Frequency spectrum of back-emf voltage of two phase machine at 400 rpm...... 175

6.43. Current waveforms with different current regulators at two sample load points ... 176

6.44. Phase current at 400 rpm and 9.4 Nm torque...... 177

6.45. Torque at 400 rpm with peak current reference of 44 A...... 177

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6.46. Average torque vs rms current at 400 rpm...... 178

6.47. Torque per ampere vs rms current at 400 rpm ...... 178

6.48. Power factor vs rms current at 400 rpm ...... 178

6.49. Average torque vs rms current at 600 rpm...... 179

6.50. Torque per ampere vs rms current at 600 rpm ...... 179

6.51. Power factor vs rms current at 600 rpm ...... 179

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CHAPTER I

INTRODUCTION

1.1. Background

Increased demand for energy security and greater environmental awareness has led to greater investment in renewable energy and electric transportation systems. A key component in enabling greater adoption of these systems is more efficient and compact electric machine. Electric machines in direct drive applications such as wind generators or in-wheel traction have the advantage of reducing the losses due to the absence of gears.

The machine requirements for these applications are lower cost and weight while maintaining a high torque and wide speed range of operation. Direct drive machines operate at low speeds and high torque to deliver the same amount of power as a geared indirect drive. In a conventional indirect drive system, a high-speed machine is used with speed reduction gearbox. The machine in the indirect drive operates at lower torque but higher speed. The gearbox places additional strains on space and system efficiency.

Typically, a mechanical gearbox has an efficiency in the range of 40% to 80% in wind generators and approximately 80% to 97% in automotive applications. The higher efficiencies in these applications are at lower gear ratios.

The torque density of an electric machine depends on its topology and size. Electric machines can be subdivided into two main types as shown in Fig 1.1. Typically, permanent

1 magnet motors with rare earth magnets attain the highest torque density among electric machines due to permanent magnet flux.

Figure 1.1: Types of electric machines. 1.2. Permanent Magnet Machines

Permanent magnet electric machines can generally be categorized into three basic types’ of machines as shown in Fig. 1.2. In Radial Flux Machines (RFMs), the flux crosses the air gap in the radial direction and has longitudinal flux direction. In AFMs, the air gap flux is in the axial direction and has longitudinal flux direction in the core. TFMs have transverse flux configuration. The air gap flux in TFMs can be radial or axial. Thus, TFMs with axial airgap flux are also termed as AFMs in some literature. Each category consists of a broad array of machine types each with its own advantages and disadvantages.

Figure 1.2: Types of PM machines.

In permanent magnet machines, the magnets can be placed in one of two ways:

 Surface mounted on the rotor surface.

 Flux concentrated configuration inside the rotor structure.

Surface magnets require high-energy rare earth magnets for producing the required air gap flux density. However, they exhibit extremely low torque ripple and are ideal for low-speed operation. Flux concentrated configurations are more widely used in machines requiring a wider operating speed range as it offers a greater saliency. It also enables the use of low energy magnets. RFMs and TFMs have machines with both magnet configurations. AFMs on the other hand mostly employ surface mounted magnets.

AFMs are one of the oldest electric machines. In fact, the earliest electric machine by M.

Faraday in 1831 is an AFM [1]. However, due to construction difficulties, AFMs were ignored in industrial applications for the next 150 years. Recent advancements in manufacturing have encouraged renewed work in AFMs. AFMs are also known as disc type PM machines due to their short stack length and large diameters. The disc type geometry makes the machine attractive in applications where the axial length is limited such as in-wheel motors. There are several types of AFMs depending on the number of stators and rotors. The main advantages of AFMs are:

 They exhibit a high torque density.

 AFMs are smaller than RFMs. Thus, their compactness makes them suitable for

large power drives.

 They have an adjustable air gap.

 The machine can be stacked axially resulting in simpler and modular construction.

 They exhibit a low cogging torque.

 Short-pitch windings are employed which have small end turns.

 Noise and vibration levels are less than conventional PM machines.

AFMs also have some disadvantages such as:

 Difficulty in maintaining the air gap in large diameters.

 High leakage flux.

 Structural instability.

W.M. Morday first introduced the concept of TFM in 1885 [2]. Although the machine gained more attention since the late 1980s after it was reintroduced and named as such by

Weh[2]. In TFMs, the pole number can be increased without sacrificing armature-winding space. This results in machines with high electric loading and high fundamental frequencies. This makes TFMs an excellent machine for direct conversion of high- frequency input into low speed or vice-versa. TFMs can be designed as single-sided or double-sided machines. In TFMs a single ring-shaped winding embraced by the U-shaped cores are employed. The advantages of TFMs can be summarized as:

 High torque density.

 Lower copper losses.

 Simple Winding.

TFMs, however, have the following disadvantages:

 Complicated construction.

 Low power factor.

 Narrow speed range.

 High leakage flux.

1.3. Research Motivation and Objectives

Direct drive machines are generally low speed, high torque machines where torque density is the preferred parameter when comparing performances. The torque density is proportional to the magnetic and electric loadings of the machine. It is possible to increase magnetic loading by increasing the air gap flux density. High torque density electric machines typically employ rare earth magnets such as NdFeB that has a large remnant flux density and contributes towards a high air gap flux density. However, this type of magnet depends on a material that is only available in a small region in the world and thus their prices are very volatile. In the past years, the price of a Toyota Prius permanent magnet machine for the traction application was increased from 200 $ to 600 $. This price increase is largely due to the increase in the price of NdFeB. The amount of magnet in wind generator applications are typically more than machines used in traction applications. Thus, it is important to achieve a high air gap flux density without using rare earth magnets.

Another method of increasing the torque density is by increasing the electric loading of the machine. This is achieved by increasing the line current density by increasing the number of poles or MMF per pole. In electric machines, it is necessary for the magnetic flux and the torque producing current to be perpendicular to each other. Thus, the flux lines are either parallel (longitudinal) or perpendicular (transversal) to the moving direction of the rotor. These can be established through four winding variants, Gramme-, Drum-, Pole- and Ring- windings. Pole and Ring-windings result in lower end windings.

TFMs and AFMs take advantage of short pitched windings to increase the torque density. Short pole pitch machines have the advantages of low end-turn and reduced back iron depth. This also results in short current paths and reduced conduction losses. TFMs, 5 in particular, can increase the current loading even more by simply increasing the pole pairs without increasing the armature ampere-turns. TFMs and AFMs also have smaller stack lengths and large diameters making them ideal for direct drive applications. However, magnet utilization and high leakage flux is a prime problem in TFMs and AFMs.

Direct drive machines also need to be variable speed machines capable of operating in a wide speed range. The saliency and inductance of the machine are key parameters, which dictate the speed range of the machine. The electromagnetic design of the machine is important as machine geometry and winding configuration affects the wide speed operation. A better wide speed operation is achieved by integrating both design and control techniques. The design objective for wide speed operation is to attain a higher saliency without sacrificing the machine performance at the rated conditions. The objective for the controller is to get wider speed operation with minimum current and demagnetization of the permanent magnets.

The main objectives of this research can be summarized as:

 Develop a modular, high torque density, direct-drive, non-rare earth PM TFM with flux

concentration.

 Develop analytical sizing equations and design procedure for the machine. The

machine is designed to be modular in structure and capable of wide speed operation.

The modular structure is key in addressing the manufacturing and assembly issues.

 Develop a methodology to reduce cogging torque in TFMs. Due to their different

electromagnetic flux paths; TFMs require different approaches for cogging torque

reduction. The objective is to investigate different cogging torque reduction in TFMs

and develop a design methodology for low cogging torque TFM design.

 Develop a control/winding strategy for wide speed operation. The dissertation

investigates different winding configurations for double-sided TFMs. A novel winding

configuration in double sided TFMs for wide speed operation and greater control

flexibility is desired.

1.4. Dissertation Outline

This dissertation initially investigates a modular TFM having a double-sided U- core stators and a rotor with ferrite magnets acting as flux concentrators. The winding structure has two alternate stators poles beside each other. This configuration is mirrored on the other side. However, this machine suffers from low power factor.

A novel E-core TFM is then proposed to mitigate the issue of low power factor in the initial machine. The machine has a double stator-single rotor configuration with flux concentrating ferrite magnets. The machine has pole windings across each leg of an E-core stator. E-core stators with the proposed flux-concentrating rotor arrangement result in better magnet utilization and as a result higher torque density and power factor. The machine also has a modular structure for simpler construction. The proposed machine is different from standard TFM in the sense that it has axial airgap flux instead of radial air gap flux. Multi-phase versions of the proposed machine can be attained on a single stack due to the use of pole windings. The novel E-core TFM topology is the core contribution of this dissertation.

Analytical sizing equations and a systematic design approach is proposed for the novel E-core machine. Detailed electromagnetic analysis for the machine is performed to investigate the machines performance at loaded and unloaded conditions. A three-stage optimization method reducing cogging torque in the E-core machine is also proposed.

A novel approach for wide speed range operation through electrical flux weakening on these machines is also proposed. Dual stator machines offer a new degree of flexibility in the control in the sense that the two stators can be controlled separately. The winding configurations in stators are an important aspect of this machine. Two winding strategies are proposed and studied for their effectiveness in flux weakening operation. Each set of the winding structure has its own set of advantages and disadvantages and the right winding configuration should be selected based on the desired application.

The structure of the dissertation is shown in Fig 1.3. Literature reviews were conducted on the state of the art in permanent magnet machines. The literature review covers each sub-section that is proposed or investigated. Thus, modeling, cogging torque, flux weakening operation and comparison of machines are also covered in the literature review section. In the dissertation, the U-machine TFM is found to have low power factor due to low core utilization as the main drawback. To mitigate this the E-cored stator is proposed. The rotor of the proposed machine is flux concentrated in nature to improve airgap flux density and achieve a high torque density with ferrite magnets. The machine is analyzed through finite element analysis (FEA) in terms of pole number selection and machine sizing. Analytical equations for sizing the machine are presented. The next section in the dissertation discusses different cogging torque reduction strategies and proposes a 3- step design of experiment based optimization method. Detailed electromagnet analysis and

8 comparisons with different machine topologies are then presented. The FEA data is used to develop a rotating dq model of the two-phase variant of the proposed machine. The dq model is used for stability and performance analysis of the proposed machine. A novel field weakening method for double-stator machines is also proposed. The preceding section of the dissertation presents the prototyping procedure and experimental results of the machine.

Literature review

Investigation of U-core TFM

E-core TFM: Design and analysis

Analytical sizing Cogging torque and design reduction procedure

Electromagnetic Analysis and Comparison

E-core TFM: Winding configuration, Control and analysis

Winding dq modeling configuration and stability for enhanced analysis flux weakening

Prototyping and experimental evaluation

Conclusions and future work

Figure 1.3: Outline of proposed dissertation.

CHAPTER II

LITERATURE REVIEW

2.1. Introduction

In order to improve on existing direct drive machines for the wind power generation and automotive applications, a thorough literature review on available machine topologies has been conducted. The first three sections of the review are focused on the design and topology of the machine. Machines with radial, axial and transverse flux topologies are presented. The machine topologies are defined according to the electromagnetic flux paths responsible for torque production. Figure 2.1 illustrates the different flux paths. A review on issues and solutions concerning cogging torque, modeling, and control of permanent magnet machines are then presented.

2.2. Radial Flux Machines

Radial flux machines (RFM) are the most common and widely used machine topology due to their straightforward and established fabrication methods. The air gap flux in this topology is radial and back iron flux is circumferential as shown in Fig 2.1a. Radial flux machines can be divided into two wide categories: with permanent magnets (PM) and without permanent magnets. Examples of non-PM machines are induction machines and reluctance machines. These machines offer a more cost effective solution. However, PM machines offer higher performance and have greater torque density that is ideal for direct drive applications. Permanent magnet machines can generally be subdivided into two

10 types: surface permanent magnet machines and interior permanent magnet machines. There are further sub-categories in these machines based on the magnet shapes and winding types.

Non-PM and PM versions exist for more novel electric machines such as flux switching machines and vernier machines. The classification of radial flux machines is given in Fig.

2.2.

Rotor core Stator core Shaft Magnets Winding Direction of Direction of airgap airgap Direction of rotation Direction of rotation and flux in core and flux in core

Full machine One section of AFM

(a) Radial flux PM machine (b) Axial flux PM machine Direction of airgap

Direction of rotation

Full machine One pole pair (c) Transverse flux PM machine

Figure 2.1: Flux paths in different machine topologies.

Figure 2.2: Classification of radial flux machines.

2.2.1. Non-PM machines

The use of magnet free machines is a very attractive concept as it reduces overall cost. There are several types of machines, which does not use any permanent magnets.

Common magnet free machines are the induction machine, switched reluctance machine

(SRM), and synchronous reluctance machine (Syn-RM).

Induction machines are the most common type of electric machines. It has the capability of running directly on the grid supply. The AC current in the stator of the motor creates a magnetic field that rotates with time. The rotor winding is shorted circuited by the end rings. The flux from the stator will induce an electromagnetic current in the rotor windings. The current in the rotor windings will generate another flux. The rotor flux will lag the stator flux and due to this, the rotor will produce torque and try to synchronize itself with the stator flux. Thus, the speed of the rotor will depend on the stator current frequency.

2D and 3D images of an induction machine are shown in Fig. 2.3.

2D view of an Induction Machine. 3D view of dissected induction machine.

Figure 2.3: Induction machine (IM). The use of induction machines in direct drive applications are limited due to their operating principle. A direct drive application using a doubly fed induction machine was proposed and studied in [3]. Direct drive induction machines were also considered in [4].

In this paper, an outer rotor induction machine was proposed.

SRMs, as its name suggests, operates on the principle of reluctance that is the tendency of an electromagnetic system to attain a stable equilibrium position of minimum reluctance. When a phase is excited the flux induced in the stator pole flows through the rotor structure. This results in the rotor being attracted towards the stator to achieve minimum reluctance. The movement of the rotor poles with respect to the stator poles results in gradual increase and decrease of the reluctance and flux linkage. The minimum reluctance position also is known as the aligned position. The inductance and flux linkage is maximum at this position. The rotor has minimum inductance and flux linkage when the rotor and stator are completely unaligned i.e. the rotor is exactly between two stator poles.

The unequal number of stator and rotor poles is important since this ensures that not all poles are aligned or unaligned at the same instant. The winding structure determines the

13 type of machine. It can be short-pitched winding where self-inductance plays a crucial role in torque production or it can be full-pitched where mutual inductance dominates in the production of torque. The machine structures are shown in Fig. 2.4. SRM with DC windings is also used.

DC- DC+ C+ A+ A+ DC+ DC- B- B+ C+ A- C- A- DC DC C- B- - C- A+ + B- B- DC DC + D+ D- -

DC D- D+ DC B+ B+ - + A+ C- B+ C+ DC DC A+ C+ + - A- C+ B+ B- A- C- A- DC- DC+ DC+ DC-

(a) Winding of SRM (b) Winding of MCSRM (c) Winding of SRM with DC

(d) 3D view of SRM

Figure 2.4: Different structures of switched reluctance machines. SRM in direct drive wind applications is presented in [5-7]. The design and performance of an SRM for a 20 kW direct drive application were studied in [7]. Control aspects for wind generators were studied in [5]. In-wheel traction application is another area where

SRMs were reported in the literature [8-11]. Optimization and design of SRMs were carried out in [11]. Different structures of SRMs were also studied [6,8,10]. Outer rotor SRMs for in wheel applications were proposed in [10]. Segmental rotor SRMs is another promising

14 machine type for direct drive applications. The high number of rotor poles and torque density indicate that segmental rotor SRMs are more suited to direct drive applications [6].

The design of Segmental rotor SRMs was presented in [8]. Off-road vehicle applications of SRMs have also been reported in the literature [12].

Mutually coupled SRM (MCSRM) is another topology of SRM that is suited more towards direct drive applications. In [13] the author showed that fully pitched winding SRM needs multiple phase excitation and it uses the magnetic circuit more effectively. It is able to produce at least 30% more torque than the CSRM [14,15].

Synchronous reluctance (Syn-RM) is another topology of motors, which depends on the principle of reluctance for torque production. These motors are synchronous in nature thus it is possible to drive these motors directly without any power electronic devices. The efficiency of these motors are also higher than induction machines. The synchronous nature of the motor also negates the issues related to torque ripple and acoustic noise that are typically associated with reluctance motors. Synchronous motors, however, suffer from structural issues. Solving these structural issues lead to lower power density and machine performance.

In Syn-RMs, the stator has a distributed stator winding (similar to those used in IMs), and the rotor is cylindrical but with an anisotropic magnetic structure (magnetic reluctance varies with the flux direction) [16-18]. One standard form of synchronous reluctance machines is shown in Fig. 2.5.

Figure 2.5 2D view of a synchronous reluctance machine.

Other types of radial magnet free machines include vernier machines [19-22] and flux switching machines [22-28] (Fig.2.6). Vernier reluctance machines were first proposed and studied in the

1970s. However, they suffer from low power factor. These machines attain very high torque density but power factor is a major drawback.

Flux switching machines are a promising solution to attain high torque density with a simple rotor.

The excitation exists only in the stator of the machine. This excitation could be provided by magnets or field windings. The purposes of these windings are to switch the flux path in every alternate pole by acting as flux guides. The use of magnets in flux switching machines results in complicated stator construction. A variety of flux switching machines with only field windings is presented in

[22-28].

(b) (a) Vernier Reluctance Machine (b) DC excited Flux Switching Machine

Figure 2.6: Other types of Non-PM machines.

2.2.2. PM Machines

Radial flux permanent magnet (RFPM) machines are the machine of choice for high-performance applications due to their high torque density, low torque ripple, and low acoustic noise. RFPM machines can generally be classified into four types as shown in Fig

2.7. The most common types of PM machines among them are surface mount permanent magnet synchronous machines (SMPMSM) and interior permanent magnet synchronous machines (IPMSMS). These types could also be further subdivided based on magnet shape, magnet position, and winding structure. Two other types of PM machines such as Vernier machines and flux switching machines (FSM) also exists. Vernier machines have been proposed for direct drive applications due to their high torque density. Flux switching machines offer a machine with a simple rotor and high torque density.

Figure 2.7: Classification of PM machines.

Radial surface and interior permanent magnet machines have been researched extensively over the past two decades. [28] presents an in-depth review of the design issues of radial permanent magnet machines. Slotted stators and surface mount magnets on the rotors are the hallmarks of a surface mounted permanent magnet machine (SMPMSM) as shown in Fig 2.8.

Figure 2.8: 2D and 3D view of surface PM machines. The use of surface magnet radial flux machines in direct drive applications have been reported extensively in the literature [29,30]. A 500 kW SMPMSM for direct drive wind applications was designed and presented in [31]. The authors in [30] studied different stator and rotor windings to identify the ideal combination of wind generators. Optimization to attain the highest torque density was discussed in [32]. In this paper, the optimum ratio of axial length to air gap diameter was determined for highest torque density. Outer rotor designs have also been discussed in [33-36]. [33] presented the optimization of a 20 kW machine with the objective of reducing cogging torque and improved performance. The optimization was carried on different numbers of poles and lamination and magnet types.

Several advantages of the outer rotor machine were presented in Chen [34].

The winding structure is another key aspect to the design of SMPMSMS. Typically these machines have distributed windings with integer slots. This configuration limits the speed range. [37] presented the opportunities and challenges of using fractional-slot concentrated windings. This structure has the benefits of an increased flux weakening range. [38] presented a Rosenberg based optimization of fractional slot pitches in SMPMSMs.

Research in SMPMSMs also focused on a variety of different aspects such as mechanical flux weakening in [39], unbalanced magnetic forces in [40], the influence of slot and rotor

18 pole combinations on vibro-acoustics [41]. The design techniques with respect to cogging torque reduction will also be discussed in a separate section.

The other type of radial flux machines with permanent magnets in the interior permanent magnet (IPM) machine. The magnets in this type of machine are buried into the rotor structure. The structure of an IPM is shown in Fig. 2.9. The rotors in IPM machines can be

V-shaped, tangentially shaped or spoke-shaped. These shapes give the benefits of flux concentration that result in high air gap flux densities. The machine also has high saliency that enables better flux weakening.

Their use in direct drive applications has been reported in [42,43]. In [42] a ferrite magnet based modular IPM was presented. Modular structures are also presented in [44-46]. The modular structure consisted of E-core stators each carrying a coil which is wound on a bobbin and fitted prior to assembly. The magnets in this structure were tangentially magnetized. Researchers also focused on design IPMS with better mechanical structure

[47] and flux weakening [48]. Some novel interior permanent magnet machines such as variable leakage flux IPM [49] have also been proposed.

Figure 2.9: 2D structure of interior permanent magnet machine.

The authors in [50] compared the merits and demerits of different interior and spoke type

IPM machines with a thorough multi-objective optimization. In [51], a comparison of surface and flux concentrating PM machines are presented. In [52], five different direct drive radial permanent magnet machines are investigated and compared. According to [52], the V-shaped magnets is not appropriate with high pole numbers and the outer rotor type had the highest torque density. The best performing motor was the tangentially magnetized

IPM machine.

Another type of RFPM machine that holds a lot promise is the flux switching machine as shown in Fig. 2.10. The magnets are buried in the stator making the rotors simple. The winding configuration and pole configurations of flux switching machines were studied in

[54]. [55] proposed the use of a reduced rare earth flux switching machine for EV applications. The machine was designed and experimentally tested. Some other notable works related to FSMs are [56-58].

Figure 2.10: 2D structure of a flux switching machine. PM assisted synchronous reluctance machines are another type of interior permanent magnet machine. In this type of machine, magnets are inserted in the flux barriers of

20 synchronous reluctance machines to enhance the saliency and increase PM torque [108].

However, difficult construction and weak structural strength are key barriers in this machine.

Vernier permanent magnet (VPM) machines are another novel branch of radial PM machines which hold promise in direct drive applications due to high torque density and efficiency [60-65]. However, they are also limited in their industrial adoption due to complicated construction and low power factor. This type of machine needs to be investigated and developed in detail to mature into a viable solution for direct drive applications.

RFPM machines are simple to construct and are widely used. Most low-speed megawatts rated wind generators are RF machines. The use of PMs enable the machines to operate with a high performance over a wide speed range. However, all PM machines with high torque densities employ the rare-earth NdFeB magnets.

2.3. Axial Flux Machines

AFMs (AFM) are one of the first ever machines patented. Faraday invented the first AFM in 1831 [1] preceding the first RFM patent by Davenport [66] (Fig.2.11). In AFM, the flux crosses the air gap axially and passes through the back iron in the circumferential direction as shown in Fig 2.1b. The axial air-gap allows for higher air gap diameters that result in higher torque density. The adoption of AFMs has not been as profound as radial flux machines due to limitations in motor fabrication technology. However, with the advent of powdered iron cores and development in lamination technology AFMs are gaining greater

21 industrial acceptance. Over the past decade, AFMs have been used in numerous applications from direct drive applications to elevators and vacuum pumps.

Figure: 2.11: First axial flux machine [66]. The main advantages of AFMs are that they have a low active mass that results in high torque density and efficiency. The machines are also smaller and disc-shaped in nature.

This makes them ideal for direct drive applications such as wind generators and in-wheel vehicle traction motors. Axial machines also have a distinct advantage in the sense that their air gap can be mechanically adjusted. This gives greater flexibility in flux weakening which would enhance the machine's operating speed range. AFMs can also be classified into two broad types: Magnet free AFMs and permanent magnet AFMs. AFMs without permanent magnets are rare and only limited literature is available in axial flux induction motors and axial flux reluctance motors. Axial flux permanent magnet machines are more widely used. They are classified on the number and types of stator and rotor cores. The classification of AFMs is shown in Fig 2.12.

Figure 2.12: Classification of AFMs. 2.3.1. Non-PM Machines

Axial Flux Induction Machines (AFIM) are presented in [67-72]. The machines presented

have either a single rotor or two rotors. The single rotor AFIMs has one stator core and one

cage rotor with winding in the slots. The operating principle is similar to radial flux

induction machines. The single sided AFIM as shown in Fig. 2.13 suffers from imbalanced

axial forces. The double cage rotor AFIM is shown in Fig. 2.14. The machines can be

classified as NN or NS depending on the main flux direction. In this type of motor, the end-

windings are small but the stator yoke is quite large as there is flux from both the stator

cores. The rotors have squirrel cage winding which is produced by inserting bars in the

rotor slots that are then short-circuited by end windings.

Stator Stator

Rotor Rotor Rotor

Figure 2.13: Single rotor single stator Figure 2.14: Dual rotor single stator configuration of axial configuration of axial flux induction machine. flux induction machine.

Axial Flux Switched Reluctance Machines (AFSRM) have also been proposed in the literature. In [73] the authors proposed a pancake shaped five phase AFSRM shown in Fig

2.15. Magnetic equivalent circuits were developed and used for determining the machine performance and then used for sizing the machine. Skin depths of the coils were studied in detail in this machine. [74] studied the machine about approaches towards leakage flux reduction. It was shown that the use of magnetic shielding improved the machine saliency and as a result improved torque out.

Figure 2.15: Pancake shaped axial flux switched reluctance machine. In [75-76] the authors suggested an axial flux segmented rotor SRMs. [77] proposed the concept of segment rotors in AFSRM machines. The paper also utilized the concept of having a higher number of rotor poles than stator poles [77] The structure of the machine is shown in Fig 2.16. The designed 1.83 kW machine attained a torque density of 1.83

Nm/Kg. Torque ripple reduction in AFSRMs in of this structure was proposed in [75]. The method proposed to displace the rotors on the two rotor sides to reduce torque ripple.

Figure 2.16: 3D view of a 12-16 axial flux segment rotor SRM [77]. 2.3.2. PM Machines

The simplest form of Axial Flux Permanent Magnet (AFPM) machine is the single stator single rotor (SSSR) machine as shown in Fig 2.17 [78]. The application of this motor is varied from pumps, elevators to industrial traction [84,79-80] The main disadvantage of this machine is the imbalanced axial forces. The machine also has a high static eccentricity that has been studied in [81]. The machine, however, is easier to manufacture and simpler to model. In [82] the author presented a quasi 3D modeling of AFPM with SSSR structures using 2D cut planes. The performance of an air-cored stator (SSSR) with overlapping and non-overlapping windings were studied in [83]. It was observed that concentrated-coil machines that did not have overlapping windings had a performance similar to machines with overlapping windings. The paper also showed that higher pole numbers further enhance the performance of concentrated winding AFMs. The use of magnetic wedges in

AFMs and their effect in losses and cogging torque was studied in [85]. The effect of SMC rotors for loss reduction was studied in [86]. This paper made a case for SMC rotor and

AFMs with concentrated windings for increasing efficiency.

Stator

Windings

Rotor

Magnets

Figure 2.17: Single stator single rotor AFM. The second category of AFPMs is the double stator single rotor (DSSR) machines. An example of a DSSR AFPM is shown in Fig 2.18. The DSSRs can also be of several types depending on the magnet configuration as shown in Fig 2.19.

Stator

Windings Rotor

Magnets Stator Windings

Figure 2.18: Dual stator single rotor AFM.

Figure 2.19: Flux path in (a) Surface PM AFM (b) Buried PM structure (c) Interior PM structure without steel. Another type of DSSR is proposed by Muljadi Et Al in [87]. In this structure, flux concentrating inset rotor magnets are used with toroidal ring windings. The flux direction in the airgap is axial and transverse in the back iron so this machine could also be classified

26 as TFMs. The design allowed for the use of low remnant flux density permanent magnets.

3D view and 2D plane view of the machine is shown in Fig 2.20-2.21.

Figure 2.20: 3D view of a DSSR AFM with ring Figure 2.21: 2D plane view of DSSR AFM with ring windings [87]. winding [87].

The rotor in DSSR machine could be located between two slotted stators forming SS type machine or be between two slotless stators forming NS type. In the non-slotted version, the stators strip is steel with sinusoidal distributed back-to-back windings placed across the core [88]. In [89] it was shown that the leakage fluxes in DSSR AFPMS result in higher leakage flux of the PM ends and armature reaction. The main advantage is that the rotor

PMs is protected against mechanical impact, wear, and corrosion. The authors in [88] proposed the DSSR structure where the steel rotor disc is eliminated. In this machine, aluminum was used to increase structural rigidity. The machine had a high power to inertia ratio. A major drawback of DSSR is the high copper loss. The slotted structure has a lower copper loss due to smaller end windings and better flux guides. This resulted in increased machine efficiency [90].

Increased efficiency was proposed by using a coreless AFPM in [91]. The paper also proposed the use of epoxy resin to fill the spaces of the stator slots to attain increased

27 structural rigidity and robustness. The machine in [99,93] made the case for the use of SMC materials. It was shown that powder iron machines exhibit a lower back-emf and torque.

To compensate these losses larger magnets need to be used.

Another interesting use of AFM is in a micro power generation application [94]. A multiobjective design procedure was followed in the design of a 3 kW 400 rpm DSSR AFM for an e-scooter in [96]. A DSSR in EV and HEV applications were also proposed in [98,101].

The influence of slot pole configurations on the machines inductances was studied in [97].

The third type of AFPM is the single stator double rotor (SSDR) type. In this machine, two rotors with surface mount permanent magnets sandwich a slotted or slotless stator. An example of one such machine is shown in Fig. 2.22.

Rotor

Windings Stator

Rotor Magnets

Figure 2.22: Single stator dual rotor AFM. In this structure, the main flux travels either circumferentially (NN) or through the stator

(NS) [102]. A slotless torus stator with toroidal stator windings is used in the torus concept as researched in great depth by Carrichi et al in [103-110]. It was shown that leakage and mutual inductance is lower in the slotless structure. The end windings are also shorter which resulted in higher efficiency. The slotless structure also has the advantage of lower torque ripple and cogging torque. The yoke thickness in the NN structure is higher as the flux travel circumferentially in the stator core. To attain this flux direction, the coils are phase wound with ring windings around the stator core. The longer flux path in this

28 machine structure increases the machine weight and iron loss. In the NS structure the flux flow is through the stator, thus the stators are thinner. This structure also has a shorter flux path and thus lower iron loss. The flux paths for NS and NN structures in SSDR and DSSR are shown in Fig. 2.23. In [103] mechanical flux weakening through displacement of the rotor cores was proposed to increase the constant power range.

Stator back iron Stator back iron

A C B A C A C B A C

Rotor back iron Rotor back iron

B C A C B A C A C A

Stator back iron Stator back iron (a) NN DSSR AFM (b) NS DSSR AFM.

Rotor back iron Rotor back iron

A C B A C A C B A C

Stator back iron Stator back iron

A C B A C A C B A C

Rotor back iron Rotor back iron

(c) NN SSDR AFM (d) NS SSDR AFM Figure 2.23: Flux paths in DSSR and SSDR AFM. An inverse saliency AFM with a DSSR structure cable of field weakening was designed for HEV applications in [92]. The concept of using an inverse saliency was first proposed in [99]. A 25 kW version of the non-slotted torus machine is prototyped for direct drive in wheel applications in [104]. In [127], a 25 kW SSDR was developed for in wheel

29 applications and tested on GM’s S10 mule vehicle to demonstrate the performance.

Another in wheel application is presented in [109]. An AFM for a three-wheel electric vehicle was designed and tested in [128]. The effect of armature reaction on an AFM developed for an electric two-wheeler was presented in [129].

The torus machine has been designed for elevator applications [110,118]. The design of the magnets in slotless torus machines was discussed in [105]. Slotted and non-slotted torus machines are optimally designed and compared in [114]. Drum windings are required for the NS type of SSDR machines. This winding structure is easier to produce but increases end windings and machine outer diameter [111].

A key aspect of the design of torus machines is the selection of the diameter ratio, axial length and airgap flux density for maximizing the power density and efficiency. A guide on machine sizing and optimization before prototyping are presented in [121]. A more detailed design optimization with genetic algorithms is presented in [123].

Comparative designs with integer slot and fractional slot windings are investigated in

[115]. It was found that the cogging torque is higher in integer slot machines. Fractional slot machines had a lower cogging torque and higher CPSR but the rotor and PM losses are high. An optimized design of an AFM with concentrated pole windings is presented in

[130]. The authors in [131] proposed a concentrated pole winding AFPM with a radially varying air gap for attaining a level magnetic flux density radially. The slots in slotted torus machines result in ripple torque, demagnetization due to armature reaction and higher core loss due to air gap flux density pulsations. The authors in [117] investigated the use of magnetic wedges and its effects in machine performance. Cogging torque is another

30 important issue in SSDR AFMS. A review of different techniques for cogging torque reduction is presented in [120]. The authors in [133] proposed the use of amorphous metal cores for increased efficiency.

Coreless SSDR AFMS are also proposed and discussed in [83,91,126] Different winding structures for coreless AFPMs were discussed in [83]. In [112] it was mentioned that the efficiency in coreless machines was extremely high. A coreless low power AFPM was proposed in [122]. Innovations such as having the rotors configured as two counter-rotating propellers are proposed and investigated in [107].

It has been mentioned that AFMs are ideal for direct drive applications but the structure of such machines are sensitive to manufacturing process [116]. In the study, it was found that manufacturing imperfections led to disk tilts or air gap offsets which led to bending torques due to unbalanced axial forces.

Most of the AFMs discussed in the literature are three phase machines but higher phase machines are also possible as shown in [124,132]. Line start versions of the AFM have been proposed in [125]. Other interesting variations of the SSDR AFPM include a Vernier type machine proposed in [134].

The authors in [119] proposed an electrical field-weakening scheme of slotted SSDR machines. An SSDR with a DC field winding was proposed in [113]. The machine shown in Fig 2.24 has a slotted stator, two rotor discs with surface mount permanent magnets and a DC winding that is capable of field weakening.

Figure 2.24: 3D view of dual rotor AFM with torus DC winding [113]. Another category of AFPMs is multistage AFPM machines. A multistage AFPM machine can have either DSSR or SSDR configurations. In this type of machine, two machines are stacked together using as shown in Fig 2.25. It results in the saving of one stator or rotor depending on rotor-stator configuration. The machine serves to increase torque density and power output when machine outer diameter is limited [135]. These types of machines have been proposed in applications such as ship propulsion, pumps, and high-speed generators.

Other examples of study on multi-stage AFPMs are presented in [136,137].

Figure 2.25: Configuration of a multi-stage AFM [136].

2.4. Transverse Flux Machines

The concept of transverse flux machines (TFM) was first introduced in 1885 by W.M.

Morday. The machine gained more attention since the late 1980s after it was reintroduced and named as such by Weh [138-140]. In longitudinal flux machines, the space for the windings is directly coupled with the number of slots and pole pitch. Thus, if high pole numbers are utilized the electrical loading and current density gets adversely affected as they both are competing for the same space. In TFMs, the electric loading is decoupled from the current density, allowing for high pole numbers and pole pitches. As a result,

TFMs can achieve higher torque densities at low speeds in comparison to longitudinal flux machines. However, TFMs suffers from a low power factor and construction difficulties.

TFMs can be classified into two main broad categories based on the arrangement of the stator cores with rest to the rotor. A single-sided machine only has stator cores on one side of the rotor, resulting in an incomplete utilization of the magnets. Double-sided machines have stator cores on both sides of the rotor, leading to a better magnet utilization. Single- sided machines are easier to manufacture in comparison to double-sided machines in traditional radial air gap structures. There exists further classification of TFMs based on the rotor structure. The permanent magnets in the rotors can have magnetization directions parallel either to the airgap (surface mounted) or perpendicular to the airgap (flux concentrating). The different topologies of PM-TFMs are shown in Fig. 2.26.

Permanent Magnet Transverse Flux Machines

Single Sided Double Sided

Rotor Flux Flux Surface PM concentrating Structure concentrating Surface PM PM PM

U core stator Z shaped Z shaped U core stator with Iron C core intermediate intermediate Bridges pole pole

U core stator Stator U core stator with Iron Claw pole Bridges structure

Figure 2.26: Classification of TFM topologies.

2.4.1. Single-sided TFM

2.4.1.1.Surface Mounted TFM

The most common type of single-sided surface mount PM-TFM is shown in Fig. 2.27

[138,141,142]. The structure has U-Core stators. However, in this topology, the alternate magnet poles are not utilized. Thus, the magnet utilization in this topology is 50%. The leakage reactance is also high in this topology of the motor. An exterior stator version of this motor topology was presented in [143]. The authors in [142] performed FEA analysis on a single sided surface mounted TFM showing that the stator flux not being linked to the rotor is very high and this result in high reactance in the q-axis. The authors also showed the presence of opposing fringing fluxes that resulted in reducing the back-emf. These are two of the main causes for low power factor in TFMs. However, TFMs are capable of delivering very high specific torque and the authors in [142] demonstrated that TFMs with rare earth magnets could obtain a power density of 35 kNm/m3.

In [143], the authors developed a static analytical model for calculating the torque per volume and mass. The average torque in this model is expressed as

푆 = 푘퐵, 퐵푎푣퐼푚푎푔퐿푒푓푓 (2.1) where, 푆 is the average net positive force, 퐵푎푣 is the average normal flux density under the tooth head, 퐼푚푎푔 is equivalent to the effect of the magnets, 퐿푒푓푓 is the effective axial length and 퐾푏 is a factor dependent on the number of poles and machine geometry. It is always less than unity. In this paper the authors demonstrated that this topology has a torque density 4.9 times higher by volume and 7 times greater by mass compared to an induction machine.

Winding U-Core Stator

Magnets

Figure 2.27: Single sided surface mount TFM.

The use of iron bridges in the stator to increase magnet usage was proposed in [153] as shown in Fig 2.28. In TFMs, the flux is transverse in both the rotor and the stator. However, the authors in [153] discovered that the flux in the rotor back iron is guided in the longitudinal plane due the magnets and the iron bridge offering a lower reluctance path.

This led to the development of the TFM without the core in the middle portion and offered the advantage of higher torque density and the use of laminated steel in the rotor core with a simpler construction. The machine in this study achieved a torque density of 16 Nm/kg

35 and power factor of 0.4 using rare earth magnets in a18 kW machine. The authors in

[141,151,152] further studied this model and compared it with the traditional TFM through

3D FEA, and according to their analyses, the TFM with iron bridges are superior by increasing the magnet utilization by 84%.

Winding U-Core Stator

Iron bridge

Figure 2.28: TFM with iron bridges. A claw-pole single sided TFM as shown in Fig 2.29 was proposed in [156] to improve magnet utilization. The claw pole structure was made with SMC material. The machine was optimized through FEA and analytical methods and attained a torque density of 9.3

Nm/kg.

Figure 2.29 A claw pole TFM [156].

A recent advance in the single-sided surface mount TFM is the use of non-overlapping stator poles as proposed in [172]. The novel stator configuration in [172] improved magnet and winding utilization to 100% without decreasing space for the windings. The authors also employed the rotor back iron construction principle developed in [153].

Figure 2.30 3D view of three consecutive stator poles and rotor for one phase with flux paths [172]. The pole thickness in this geometry is given by

푂 휋 푃표푙푒 푡ℎ𝑖푐푘푛푒푠푠 = 2 푅 sin ( 푠 ) 푖푛 푃 (2.2) where, 푅푖푛 is the radius of the airgap, 푃 is the number of poles and 푂푠 is the over span factor. In conventional TFMs the over-span factor is less than 1. However, for the proposed structure the over-span factor is greater than 1.5. Furthermore, an outer rotor structure was employed to improve machine performance. The only other way of not being limited by the overspan factor is by utilizing an axial airgap transverse flux machine.

The use of soft magnetic composites (SMC) for cores of this topology of machines has been reported in [144]. A comparison between claw pole machines and TFM with SMC cores also illustrated the benefits of TFM in terms of power density in [145]. The use of laminations and SMC material together has also been presented in [146] with an exterior rotor surface PM TFM. The 3D flux path makes the use of laminations difficult in TFMs.

However, innovative concepts of using laminations in TFM to ease construction difficulties are presented in [147-149]. In [148,149] the stator of the machine consists of U-shaped and

I-shaped laminated iron cores and rings and the rotor had a steel back iron core with surface mount PMs as shown in Fig. 2.31. A comparison between these three possibilities presented in [150] concludes that SMC based TFMs have the highest efficiency due to low iron losses.

Figure 2.31: TFM which uses U and I-shaped laminations [149]. Single-sided TFMS with hollow rotors and surface magnets and laminated slotted stacks was proposed in [151]. The TFMs were designed for direct-drive wind generator applications.

Figure 2.32: Z-cored surface magnet TFM [157]. Another interesting type of TFM is the Z-TFM discussed in [157]. In the Z-TFM, surface

PMs and alternate intermediate poles are used to maximize magnet usage. The output of

38 the machine is twice that of conventional surface mount TFMs. However, flux leakage and iron losses are much higher in this machine topology. The schematic of this machine is shown in Fig. 2.32. A similar concept was also used for free piston generators [173].

2.4.1.2.Flux Concentrating TFM

Flux concentrating (FC) TFM is the other widely used type of TFMs. This kind of machine is preferred due to their higher power factor, air gap flux density and as a result high torque density. A flux concentrating single-sided TFM is shown in Fig. 2.33.

Winding U-Core Stator

Magnets

Figure 2.33: Single-sided flux concentrating TFM with U-core stator.

Some recent work in TFMs [154] focused on this type of TFMs. The three phase TFMs developed in this paper employed SMC materials and rare earth magnets. A number of prototypes for this TFM has also been developed. It is a 500 W TFM for electric bicycle applications.

Flux concentrating magnets SMC based Rotor core

Ring Windings SMC based Stator core

Figure 2.34: Flux concentrated TFM topology in recent literature [154].

A different topology with laminated U-core stators and stator bridges, ring windings and axially magnetized PM rings as shown in Fig. 2.35 was proposed in [155].

Figure 2.35: TFM with axially magnetized PM rings [155]. A single sided TFM with FC magnets and stator bridges shown in Fig. 2.36 was proposed in [153]. Different types of TFMS with surface PMS and FC PMs was discussed in [164].

This paper further optimized the design in [153] by modifying the tooth shape to reduce leakage shown in Fig. 2.37. The modification also included an increase in the magnet overhang region to increase magnetic loading. The use of FC topology in the claw pole version have also been proposed in [165].

Figure 2.36: U-core FC TFM with stator Figure 2.37: U-core FC TFM with stator bridges and bridges [153]. tooth modification for low leakage [164].

Various FC magnet arrangement such as V-type embedded PMs like IPMS have been presented in [171]. The different FC concentrated structures is demonstrated in Fig. 2.38.

The machines in [171] were a designed for a 5 MW wind turbine. Comparisons between the different TFM structures were conducted and it was found that the V-shaped TFM with claw pole type stators achieved the highest force densities.

Iron core Flux barrier Magnet

Non-magnetic support Non-magnetic support Non-magnetic support

Longitudinal direction Transverse direction Longitudinal direction

Figure 2.38: Different flux concentrating magnet structures in TFMs. The uses of E-cores in TFMS have also been reported in the literature. An E-cored FC TFM was proposed in [159]. Modularity in TFMs with E-core stators was proposed in TFM

[166,167]. The machines are reluctance machines and use pole windings. TFMs generally result in high torque density due to transverse flux paths.

2.4.2. Double-sided

2.4.2.1.Surface Mounted TFM

Double-sided versions of TFMs have also been proposed in the literature. An example of a double-sided surface TFM with U-core stators is shown in Fig. 2.39. In double-sided

TFMs the magnet utilization is increased, and this results in increased torque density.

U-Core Winding Stator

Magnets

Figure 2.39: Double-sided surface magnet TFM with U-core stator.

2.4.2.2.Flux concentrating TFM

Weh proposed the first double sided flux concentrating (FC) TFM in [158,159]. A U-core concept with double stator windings was proposed in [159]. A variation with single windings on one side and stator bridges on the other side was proposed in [159]. The author proposed a further variation with C-cores and single windings. These machines are shown in Fig. 2.40.

Winding U-Core Stator

Magnets

(a) Double sided FC TFM (b) C-cored TFM

Figure 2.40: Different topologies of FC TFM

The C-type core with single windings was also proposed [160] for electric ship propulsion applications. It was a 20 MW water cooled TFM operating at 180 rpm. The machine was also multiphase in nature through stacking as it was 16 phases. The paper also concluded that the TFM offers high mechanical integrity and a low noise and vibration. Another TFM with the same topology and rated at 2 MW for ship propulsion was presented in [161]. The two types of double-sided FC TFMS was discussed in [162]. The machines were 20 kW 2 phase motors. A design procedure where the number of poles was first selected from the excitation frequency and operating speed was developed. The analysis in the paper concluded towards the superiority of the C-type arrangement for ship propulsion. A double sided FC TFM with passive rotor and single windings were analyzed in [163]. The dimensions for optimum performance were discussed in this paper.

The advantages and disadvantages of different topologies of TFMs were discussed in [168].

The FC type of TFM has a higher torque density and power factor in comparison to other types. The power factor is one the major drawbacks of TFMs [169,170]. The analysis and comparison in [170] concluded that the FC type is superior in terms of power factor. It also noted that higher MMF of higher electrical loading resulted in lowering the power factor.

TFMs are generally analyzed in single phase topologies. Multiphase versions are realized through stacking as discussed in AFMs and presented in [152,172] for TFMs.

Segmentation of the stator cores to make a multiphase machine has been proposed in

[155,173]. Authors also explored the possibility of using distributed windings in [174].

The machine proposed by Muljadi in [87] is also a form of TFM as the flux in the core is in the transverse plane. Classification of the literature presented based on core type, materials; magnet orientation is shown in Table 1.1.

Table 2.1: TFM type and corresponding references

Type Reference Reluctance [159,166,167] E-core [159,166,167] Claw pole [156,171] U-core [138,141,144,146,147,149,148,151,87,159,161,153,142,143,145] Iron Bridges [154,155,164] Surface PM [138,141,144,146,151,156,148,143,148,154,157] Flux concentrating PM [158,159,161,162,163,153,171] Axial (Longitudinal ) flux [155,87] concentrating PM Axial Airgap TFM [87,171] Double sided TFM [157,138,87,158,159,161,162] SMC materials in core [144,145,154] Laminations in core [147,149,148,151,155] SMC/Laminations used [146,153] together Z TFM [157] Multiphase TFMs [154,172,174]

2.5. Cogging Torque in PM Machines

PM machines with slotted stators exhibit a variation of the magnet energy as the PMs rotate.

This is due to the interaction of the PM field and the slotted stators. This is illustrated in the equation of cogging torque as given by Eqn. 2.3. Where 휑푔 is the air gap flux, R is the air gap reluctance and 휃 is the rotor position. Due to the slotted nature of the stator, the airgap reluctance varies periodically. Thus, it can be described by a Fourier series as shown

th in Eqn. 2.4. Where 푇푘 and 휃푘 are the amplitudes and phase of the k harmonic and 푁퐶 is the least common multiple of the number of rotor poles and stator slots. The cogging torque waveform could be determined both analytically and by using finite element analysis.

∞ 1 푑푅 푇 = 휙2 (2.3) 푇 = ∑ 푇 sin (푘푁 휃 + 휃 ) (2.4) 푐표푔푔푖푛푔 2 푔 푑휃 푐표푔푔푖푛푔 푘 퐶 푘 푘=1

It is evident from Eqn. 1 that the reluctance or the airgap flux needs to be reduced for the reduction of cogging torque. However, reducing the air gap flux would result in decreasing the machine's performance output. Thus, reducing the change of reluctance with respect to

44 rotor position is the best way to reduce cogging torque. From Eqn. 2 it is evident that the torque from each magnet is in phase with the others resulting in harmonic addition. Another method of cogging torque reduction would be to design the machine so that the harmonics sum up to a lower peak cogging torque.

Cogging torque is an important issue in direct drive applications e.g. in small wind turbines cogging torque results in startup difficulties and compromises the overall structural integrity of system [175]. Various techniques have been reported in the literature addressing the issue cogging torque. The common method of cogging torque reduction in surface PM machines is reported in [176]. The methods range from the use of notches, pole width optimization, and skewing. A review of these techniques applied to interior permanent magnet machines is presented in [177]. Slot and pole number selection also play an important role in cogging torque minimization [178]. AFMs also received a fair bit of attention in cogging torque reduction [178,179].

The concept of magnet skewing and different magnet shapes is discussed in [180]. The authors concluded that skewing is a cost effective method of cogging torque reduction in surface PM AFMs. The shapes of magnets played an important role in cogging torque reduction with circular magnets having the highest reduction in cogging torque.

The use of alternate magnet pole arcs is proposed in [181]. In this paper, the authors proposed using different pole arcs for alternate magnets to alter the harmonic spectrum of the cogging torque. A careful optimization led to a reduction of cogging torque. The concept of stator displacements in double-sided machines has also been proposed in

[182,183]. This method was very effective in cogging torque reduction. However, the currents in the two phases need to be adjusted accordingly to maintain no reduction in

45 cogging torque. The authors in [184] presented detailed experimental results showing the benefits of skewing. Skewing has also been employed in TFMs[185,186]. The symmetrical and asymmetrical shift of the stators were presented in [187] as a method of torque ripple reduction. Cogging torque reduction in double C-hoop stator TFMs through optimization of slot widths is presented in [188]. The stator tooth shapes are also optimized to reduce cogging torque and are presented in [189]. Cogging torque reduction in a unique flux switching TFM was presented in [190].The effects of cogging torque reduction have been studied both analytically and through FEA [191-196]. Different methods of optimizing machines for low cogging torque have also been researched. A particle swarm based method for cogging torque minimization in TFM was proposed in [197]. The design of experiment based methods such as the Taguchi method and response surface methodology has also been reported [198-202].

2.6. Modeling, Sizing, and Optimization of AFM and TFM

This section discusses the literature regarding initial sizing, modeling, and optimization of

AFM and TFMs. The first step in an electric machine design is sizing the machines base dimensions. In the most traditional sizing equation [203], the designer had to select the magnetic loading, electric loading, and efficiency based on various factors. The machine

2 power was directly proportional to 퐷푔 퐿푠푡푘 where 퐷푔 is the airgap diameter and 퐿푠푡푘 is the stack length.

The use of sizing equations also helps in comparison of different types of machines. Huang et al worked extensively in this regard [204-207]. In [204] the author's developed sizing equations for radial machines dependent the magnetic loading, electric loading, air gap

46 diameter, and efficiency. The sizing equations also incorporated the shapes of the back- emf and excitation current. This method was used for comparison between different

3 machines. The authors elaborated on this for AFMs in [205] resulting in a 퐷푔 proportionality with the machine output power. The method also was capable of incorporating different types of AFMs. The same authors also investigated TFMs with the same approach in [206,207]. Another variation on using analytical sizing equations for

TFMs are presented in [208]. In [222] the authors presented analytical methods for designing of a single stator surface magnet TFM and compared 3 different machine topologies.

After the initial sizing process, a more detailed analysis using further analytical tools such as magnetic equivalent circuits are used. Several MEC models for AFMs and TFMs have been developed. In [209] an MEC based sizing and design of claw pole alternators is presented. This method of machine design significantly reduced computation and machine design time. MEC based approaches for AFMs are presented in [210-212]. TFMs incorporating the MEC approach are presented in [213-216]. The 3D nature of these machines makes modeling them computationally more intensive in FEA. A unique approach to this was presented by [217]. The authors proposed to use a 2D cut section of one pole pair to approximate the 3D performance. This reduced the computation time in the design process significantly. The authors in [218-221] used FEA computation at only the aligned position to model the machine performance through the entire mechanical cycle.

2.7. Flux Weakening Control of AFM and TFMs

Research in AFM and TFMs mostly focuses on the design and modeling aspects of the machine as well as on the torque ripple minimization. Field weakening operation of AFM and TFMs for wider speed range operation would make these machines more attractive in renewable energy applications [223]. The most widely used form of flux weakening in radial machines is through electrical phase shift of the armature currents. This was proposed and investigated in [224]. In [225] a flux-weakening scheme for radial machines by a method of winding switching is proposed. Fractional slots have also been proposed an effective way of improving flux weakening in concentrated winding surface magnet radial machines [226].

Flux-weakening for AFMs has been studied [227,228]. In [227-231], the authors proposed using a field winding for achieving a field control in a two stator-two rotor AFM. This topology has a dual rotor-dual stator topology. The field windings are located between two concentric stators. The topology predicted a CPSR of 3.75:1. In [232-234] a negative saliency machine is proposed to achieve 3:1 CPSR with a lower d-axis current that reduced risks of PM demagnetization. In [235] different design aspects such as slotted stators and magnetic wedges were incorporated to achieve a CPSR of 3:1. Flux-weakening in slotless axial machines through electrical phase advancing is not possible. The authors in [236-

240] proposed a mechanical phase shifting mechanism for achieving the required flux weakening for wide speed range operations. [236-238] are dual rotor machines where a mechanical shift between the two rotors is applied to weaken the flux. A CPSR of 5:1 was achieved. Stator mechanical shifts were employed in [240] and a higher CPSR of 8.25:1 was achieved experimentally. Modeling a dual stator AFM for sensorless operation and

48 flux control was covered in [241,242]. The paper employed an electrical flux weakening through vector control.

2.8. Summary

This chapter presented the state of the art review of electric machines used in direct drive applications. The advantages of TFMs and AFMs resulted in a greater focus on these machines in the literature review. Different aspects of these machines such as cogging torque reduction, initial sizing, and flux weakening control have also been reviewed. From the reviews, it is evident that there is room for progress in the development of a TFM with a high torque density with non-rare earth magnets. The machine also needed to exhibit high power factor and wide speed operation.

CHAPTER III

DESIGN OF E-CORE TRANSVERSE FLUX MACHINE

3.1. Introduction

The literature review revealed that the majority of direct drive machines with high torque density are rare earth based PM machines. This is due to the high remanence flux of the

NdFeB. Non-rare earth PM such as ferrites and Alnico has significantly lower remanence flux or coercive force. In this dissertation, a novel double sided E-core TFM with flux concentrating magnets and axial airgap is proposed. The flux concentrated magnet structure facilitates a high airgap flux density with non-rare earth magnets. The machine has a double stator-single rotor configuration with flux concentrating ferrite magnets and pole/semi ring windings in the stator. The machine also has modular structure facilitating simpler construction. This chapter presents the specifications of a direct drive application for the case study in this dissertation, the advantages of the proposed structure in terms of power factor improvement, analytical sizing equations, design methodology, design considerations, cogging torque minimization techniques and cogging torque minimization optimization for the proposed novel E-core machine.

3.2. Direct Drive Application

Wind generator systems are slowly moving away from geared single speed drives to a direct drive configuration. This increases the system efficiency by avoiding the mechanical losses in the gears. It also increases the system reliability by reducing failures in the gearbox and lowering maintenance downtime. Direct drive system requires a low-speed high-torque machine and a power electronic converter for grid connection. Direct drive generators with permanent magnet excitation offer an added advantage of eliminating excitation losses and a reduction in the active weight of the system. The power generation equation for a wind turbine is given in (3.1)

1 푉 푃 = 휌휋푅2푉3퐶 (3.1) 휔 = 휆 (3.2) 2 푝 푚 푅 where, 휌 is the air density, 푅 is the radius of the turbine blade, 푉 is the wind velocity, and

퐶푝 is aerodynamic conversion factor, λ is the tip speed ratio. 휔푚 is the generator speed obtained from (2). Typically, the optimum λ is between 6 and 8 and the optimum 퐶푝 is

0.45. The design parameters, which effect the motor speed, are dependent on the power of wind turbine. This is illustrated in Fig. 3.1 and 3.2 where it is seen that as the rating of the turbine increases, the speed decreases. 퐶푝 and λ were chosen to be fixed at 0.45 and 7 respectively. Thus, machines with high torque at low speeds are ideal for wind generator applications. The Swift 1 kW turbine with a generator speed of 400 rpm at NREL is selected as the case study application. The specifications of the turbine is given in table I

Figure 3.1: Shaft speed of turbine for different power Figure 3.2: Rotor radius of the turbine for different ratings and wind speed. power ratings and wind speed.

Table 3.1 Specification of wind turbine

Axis Vertical No of blades 5 Rotor radius 1.05 m Cut-in Speed 3.4 m/s Rated Wind Speed 11 m/s Rated Rotor Speed 400 rpm Rated Power 1 kW

3.3. U-Core TFM

This section investigates a modular TFM having a double-sided double ring winding system with ferrite magnets acting as flux concentrators. The machine structure has two alternate stators poles beside each other. This configuration is mirrored on the other side.

This type of stator structure maximizes the utilization of the stator core and reduces the end winding space that reduces the leakage flux. The stator in this machine is based on the Z-

TFM proposed in [175] to maximize magnet utilization. The machine is double-sided and employs transverse magnetized magnets in the rotor similar to [87]. The rotor structure includes an additional magnet and iron core to facilitate the U-core stator with intermediate

52 poles and improve torque density. A systematic approach to the design considerations for this type of machine that includes initial sizing, pole number selection, and pole shaping are discussed in [245].

The investigated TFM structure is shown in Fig. 3.3 where the flux is concentrated into the center of the rotor by two ferrite magnets. Here the electromagnetic force vector is perpendicular to magnetic flux lines.

Winding window

Stator core Rotor core Shaft Leakage reduction magnet Flux focusing magnet

Winding window

Figure 3.3: Single pole pair of the double-sided U-core TFM.

(a) Top view of the rotor slice (b) Magnetization direction of the magnets. Figure 3.4: Rotor structure and magnet structure of U-core TFM.

The magnets are mainly used for concentrating the flux. This facilitates the use of cost- effective ferrite magnets. This particular orientation of the magnets also ensures a high air gap flux density. The length of the rotor can thus be just increased to increase the level of the flux focusing at the air gap. As the TFMs suffer from high leakages, magnets with orthogonal magnetization are added between the poles to reduce the leakage flux. The rotor structure and the magnetic orientation are shown in Fig. 3.4.

Winding Window

Flux Magnet Core path Figure 3.5: Flux path in the U-core machine. There are two stator cores which consist of single-phase ring windings through U-shaped stator cores. The stator cores are of two types. One core carries the flux from the center rotor to the outer rotor and the other stator carries the flux from the center rotor to the inner rotor. These are alternately arranged on both upper and lower sides. The preferred flux path with stator cores is shown in Fig. 3.5. The machine according to the specifications listed

54 in Table 3.1 was designed and the design parameters and performance metrics are shown in Table 3.2.

Table 3.2 Design parameters and performance metric of designed U core TFM

Description Value Description Value

Output power 1.2 kW Rotor Height 26 mm

Rated speed 400 rpm Stator clearance 5 mm

Current density 5 A/mm2 Winding height 16 mm

Air gap length 1 mm Pole number 30

Axial length 102 mm DC bus 48 V

Outer diameter 225 mm Frequency 100 Hz

Rotor core length 8 mm RMS current 107 A

Magnet length 10 mm Average Torque 28.6 Nm

Shaft length 68.5 mm Power factor 0.202

Stator pole width 8.25 mm Weight 8.69 kg

Rotor pole width 8.25 mm Torque density 3.28 Nm/kg

3.4. Analysis of Power Factor and Motivation for E-Core Stator

A detailed investigation of the machine indicates the potential of high torque density with non-rare earth magnets. It was observed that though the machine achieves a high torque density power factor was still low when utilizing non-rare earth magnets. The power factor

(PF) in a PM based electric machine with reluctance torque can be defined as:

푃 + 푃 푃퐹 = 퐶표푠휃 = 퐶푢푙표푠푠 푚푒푐ℎ (3.3) 푆

55 where, 푃퐶푢푙표푠푠 is the copper loss and 푃푚푒푐ℎ is the total power output of the machine. The total output power as two components: one due to the permanent magnet torque and the other due to the reluctance torque. The torque due to the permanent magnet depends on the back-emf voltage. In this machine structure there is little saliency. Thus, the armature current is in phase with the back-emf voltage. Hence, the mechanical power due to the PM torque can be expressed as

푃푚푒푐ℎ = 퐸퐼푞 (3.4) where, 퐼푞 is the current in the q-axis, E is the back emf voltage. The apparent power of the converter also represents is given by

푆 = 푉푟푚푠퐼푟푚푠 (3.5)

This includes real power and the reactive power due to the machines inductance. The steady state terminal voltage of the machine can also be used for power factor calculation and is given by

푉 = 퐸 + 퐼푞푅 + 푗퐼푞푋 (3.6) where 푋 is the synchronous winding reactance. The phasor diagram is given in Fig. 3.6

jXIq

V E

q Iq

Figure 3.6: Phasor diagram with q-axis current for maximum torque per ampere.

As the TFM mainly consists of PM torque, for simplification, the power factor can be defined as:

퐼푋 푃퐹 = cos (arctan ( ) ) (3.7) 퐸

From this equation, it can be observed that the PF of this machine is low due to higher inductance and low back-emf voltage.

The ratio of armature flux to PM flux in this machine is 2.89. That results in a PF of 0.327.

In classical machines, it is less than unity. This is due to the low PM flux linkage results and results in low power factor. A significant amount of loss occurs due to the unused rotor core. A better utilization of the rotor could increase the flux linkage and as a result, the back-emf torque and improve the power factor.

The power factor improvement in the proposed E-Core machine can be substantiated by investigating the magnetic circuit model (MEC) of the two stator cores as shown in Fig.

3.7. The MEC makes the following assumptions for simplification that the permeability of the iron core is infinite.

The flux in one of the windings from the U-TFM MEC shown in Fig. 3.7(c) can be expressed as:

푁퐼 + 퐹푚 휙푈 = (3.8) 2푅푔

where, 휙푈 is the flux in the U-core, 푁 is the number of turns, 퐼 is the current, 퐹푚 is the magnetic field and 푅푔 is the airgap reluctance. The flux in one of the windings from the E-

TFM MEC shown in Fig. 3.7(d) can be expressed as:

3 푁퐼 + 퐹푚 휙퐸 = (3.9) 2 푅푔 where, 휙퐸 is the flux in the E-core.

Magnet Magnet X Core Core Flux Flux path path Winding Winding out out X X Winding x Winding x in in

(a) 2D structure of U-core TFM (b) 2D structure of E-core TFM

NI NI Фu 0.5ФE 0.5ФE

R R g Fm g Rg Fm Rg Rg

Fm Fm Rg Rg Rg Rg Rg

Фu 0.5ФE 0.5ФE NI NI

(c) Simplified MEC of U-TFM (d) Simplified MEC of E-TFM Figure 3.7: Simplified MEC of the two machines. For the same magnet size, core size and material, from (3.8) and (3.9) it can be observed that the flux in the E-core machine is higher. In addition, in the U-core TFM, there is a leakage flux path between the unused rotor core and the stator core as shown in Fig 3.8.

Due to this leakage, the flux in the U-core is represented as (3.16). This leakage path is eliminated in the E-core machine.

휙푈푤𝑖푡ℎ퐿푒푎푘푔푒 = 휙푈 − 휙푙푒푎푘푎푔푒 (3.10)

where, 휙푈푤𝑖푡ℎ퐿푒푎푘푔푒 is the flux in the U-core with leakage flux compensation and 휙푙푒푎푘푎푔푒 is the leakage flux. 58

Magnet NI

Core Фu

R R Rl Flux path g Fm g g Leakage Fm Flux path Rlg Rg Rg

Winding Ф out u X NI x Winding in

(a) 2D structure of U-TFM with leakage (b) Simplified MEC of U-TFM with leakage reluctance Figure 3.8: MEC of U-core with leakage flux. The flux density across the airgap of the two machines in one side is shown in Fig. 3.9.

The 푘푙 in the figure is the percentage of flux lost due to leakage. The leakage flux in the unused core results in lowering the flux linked through the windings for the U-core machine. The flux density on the inner and outer legs is half the airgap flux density in the middle because the flux is divided into two portions before being linked back through the middle core. This results in a higher back-emf in the E-core machine. Thus, the power factor is higher in the E-core due to higher PM flux linkage.

Bg Bg

k B l g Bg/2

(1-kl)Bg

(a) Flux density in airgap for U-core machine (b) Flux density in airgap for E-core machine. Figure 3.9: Airgap flux density of the two machines

The leakage in the unused core is demonstrated further with 2D FEA simulations considering nonlinearities. The flux lines of the machines are shown in Fig. 3.10. It can be observed that there is leakage in the unused rotor core. The corresponding flux density in the airgap is illustrated by the turquoise line as shown in Fig. 3.11. It can be seen that the flux density in the airgap above the unused rotor core is quite high. This is due to the leakage flux that does not link the winding. This phenomenon is more prominent in 3D

FEA due to higher leakage as shown in Fig 3.12. The flux density corresponding to the outer core in Fig 3.11 a) is not torque producing flux whereas the flux density corresponding to both the inner and outer cores in the E-core in Fig. 3.11 b) is torque producing flux.

(a) Flux lines of the U-core machine. (b) Flux lines of E-core machine Figure 3.10: Flux lines of two machines from 2D FEA.

(a) Airgap flux density in U-core machine (b) Airgap flux density in E-core machine Figure 3.11: Airgap flux density from 2D FEA. 60

(a) Airgap flux density in U-core machine (b) Airgap flux density in E-core machine

Figure 3.12: Airgap flux density from 3D FEA. 3.5. Proposed E-Core Transverse Flux Machine Structure

The proposed machine has a dual stator and single rotor with axial airgap on both sides.

The flux linkage between the stator and rotor is in transverse direction with circumferential current in the slots. Thus, this machine can be classified as both an AFM and a TFM. A 2D view of one pole is shown in Fig. 3.13.

Magnet X X X Core Flux path Winding out X X X Winding x in

Figure 3.13: 2D of one pole of the proposed TFM. The magnets are arranged in a flux concentrating manner between the rotor cores. The flux-focusing factor can be adjusted in the axial direction by the height of the rotor core

(Hry) and it is not confined to the diameter of the air gap as in the case of RFM. This 61 facilitates the use of low energy magnets without sacrificing airgap flux. The magnet directions are arranged to have the north poles of the two magnets either pointing towards each other or pointing away from each other.

E-core stators with pole windings envelopes the rotor from two sides in the axial direction as shown in Fig. 3.14. Pole windings facilitate the short flux path shown in Fig

3.13. The individual stator cores are to be supported a by a nonmagnetic endplate at the outer periphery of the machine. The stator cores and the supporting plate at the two ends are shown in the exploded view of the complete motor in Fig. 3.15.

Stator core Rotor core Shaft Leakage reduction magnet Flux focusing magnet Pole Winding

Figure 3.14: Isometric view of one pole-pair.

The magnetic polarities of the magnets are focused towards the middle rotor core as shown in Fig. 3.14. The coils are arranged so that there is clockwise flux flow in the top right window and anti-clockwise in the top left. The flux flow on the other side is mirrored.

Hence, the flux is leaving the middle core and entering through the outer and inner rotor cores. Additional flux-focusing magnets for leakage flux reduction can also be used. They 62 act as flux guides to prevent pole-to-pole leakage and provide additional MMF to the machine.

Outer belt Back Stand Bearing Stator core

Shaft

Stator Rotor Rotor core pieces housing

Figure 3.15: Exploded view of the complete motor assembly.

In rotating machines, the rotor and stator segments are arc-shaped whose circumferential length increases as the radial length increases. However, these shapes with the 2D flux paths of Fig. 3.13 can only be realized with SMC materials to avoid excessive eddy current losses.

The use of laminations in the 2D plane shown in Fig. 3.13 would limit the shapes of the rotor and stator segments to cubes. The cuboid modular rotor cores and magnets make the cutting and stacking simpler. The rotor cores are made of lamination steel stacked together.

The inner and outer rotor core is of the same dimension. Therefore, only two lamination cuts are required for the rotor. The rotor cores are attached to a non-magnetic disk. The rotor cores and the magnets which are sandwiched in between are held together using structural adhesives. A non-magnetic stainless steel belt could also be strapped around the rotor to add further structural integrity.

The E-core is also manufactured by stacking lamination steel. The stator cores are attached to a supporting plate at the two ends as shown in the exploded view of the complete motor in Fig. 3.15.

The windings in the proposed machine are pole windings, which are wound across each leg of the E-core. Therefore, simple modular windings using bobbins can be used making the winding assembly and production automated.

Another possible winding structure for this machine is ring windings with interchanging coils as shown in Fig. 3.16. It consists of two semi-ring windings arranged in an interchanging manner along the stator core slots. One of the windings carries current in the clockwise direction and the other in anti-clockwise direction. This ensures the same flux path in the stator cores as shown in Fig. 3.13. This winding structure is simpler for prototyping, allows for slightly higher fill factor and reduces copper weight.

Semi-ring Winding:- Semi-ring Winding:- clockwise current anti-clockwise current

Figure 3.16: Stator with semi-ring windings.

3.6. Design of E-Core Transverse Flux Machine

The key geometric parameters of the rotor and stator are presented in Fig. 3.17 and tabulated in Table 3.3.

Table 3.3: Parametric l P i w definitions. lm Pp lc lm Parameter Def Pw lo Hst 푃푝 Pole pitch 푃푤 Pole width li 푙𝑖 Inner core length l c 푙푚 Magnet length lo 푙푐 Center core length

푙표 Outer core length Hry H sbi 퐻푟푦 Rotor Height 퐻푠푡 Stator height

퐻푠푏𝑖 Stator back iron length

(a) Rotor (excluding stator) (b) Stator Figure 3.17: Geometric parameters of the proposed machine. The general sizing equation for an electric machine is given by:

휂푚 푇 푃표 = ∫ 푒(푡)푖(푡)푑푡 (3.11) 푇 0 where, 휂 is the efficiency, 푒(푡) is the instantaneous back-emf voltage, 푖(푡) is the instantaneous armature current, 푚 is the number of phases and 푇 is the time period for one electrical cycle. Using the back-emf power waveform factor 푘푝[206], Eqn. (3.11) can be written as:

푃표 = 휂푚푘푝퐸푝푘퐼푝푘 (3.12)

Where, 퐸푝푘 is the peak back-emf voltage and 퐼푝푘 is the peak armature current. The back- emf waveform factor 푘푝 is defined as the average normalized power i.e. the maximum power that can be achieved for a particular signal (back-emf in this case) waveform considering unity power factor. 65

The outer diameter is a crucial parameter in the machine sizing process. If 퐷표 is the rotor outer diameter then a term 휆 which is the ratio of rotor inner diameter (퐷𝑖) to outer diameter is introduced. It is represented by:

퐷 휆 = 𝑖 (3.13) 퐷표

The average airgap diameter, 퐷푔 in terms of 휆 is defined as

(휆 + 1)퐷 퐷 = 표 (3.14) 푔 2

In this machine, the stator line current density or specific electric loading (A) is defined as the number of conductors in all phases times the RMS current (퐼푟푚푠) divided by armature circumference, which can be represented as:

퐼푟푚푠 퐴 = 3푃푁 (3.15) 휋퐷푔 where, 푃 is the number of poles and 푁 is number of conductors per leg per phase and the number 3 is due to the three E-core legs. The relation between the rms and peak current

(퐼푝푘) is:

퐼푝푘 = 푘𝑖퐼푟푚푠 (3.16) where, 푘𝑖 is the current waveform factor. The waveform factors are dependent on the machine pole shape and pole widths. The waveform factor is chosen according to back emf shape as defined in [204-206].

The machines magnetic loading (airgap flux density) is also important as it is a key factor in determining the machine peak emf voltage. In the proposed machine the flux-focusing

66 factor helps determine the air gap flux density (퐵푔) of the machine. The focusing factor

(푘푓) is defined as:

퐵푔 퐴푚 퐻푟푦 푘푓 = = = (3.17) 퐵푚 퐴푝 푙푐 where, 퐵푚 is the working flux of the PMs. The relation between the flux-focusing factor and the air gap flux density is given by:

퐵푔 = 푘푙푘푓퐵푚 (3.18) where 푘푙 is the leakage factor of the machine. The 퐵푚 in this machine is found from a simple magnetic circuit solution of Fig. 3.13. The value of 푘푙 is picked based on differences with FEA. In this study, simple MEC model of the machine is used to determine the leakage factor and working flux of the machine. The airgap flux per side, 휙푔 in the E-core machine considering the central leg to be twice the size of the outer legs can be expressed as

휙푔 = 푃푒푚푏3푃푁퐵푔휏푙푐 (3.19) where, 휏 is the pole pitch and 푃푒푚푏 is the pole embrace. These are defined as:

2휋휆퐷 휏 = 표 (3.20) 푃 푃 푃 = 푊 (3.21) 푒푚푏 휏

The back-emf voltage peak is determined by:

푑휙푔 퐸 = = 6푚 푃 푁퐵 휋휆퐷 푙 휔 (3.22) 푝푘 푑푡 1 푒푚푏 푔 0 푐 푒 where, 푚1 is the number of stator sides per phase and 휔푒 is the electric speed. The sizing equation after inserting (3.21) and (3.15) into (3.12) becomes (3.22)

1 푃 = 휂푚푘 푘 퐴휋퐷 ( )퐸 (3.23) 표 푝 𝑖 푔 3푃푁 푝푘

3.6.1. Initial Machine Design

A design procedure for initially sizing a benchmark design of the E-core machine is outlined in Fig. 3.18. The design process starts with the specifications of the machine for the desired application. Based on the specifications the initial pole number for the machine is selected. It is at this point that a choice is made on the number of phases to use in this machine. In the second stage, an initial machine dimensions are selected. The electrical loading is then selected to meet the desired power specification. The final step in the initial design process involves the design of the stator core (slot width and slot height) to ensure an acceptable current density.

Design specifications

1. Pole number selection

2. Initial radial dimension selection

3. Rotor design

4. Number of turns selection

5. Stator core dimension

First pass design

Figure 3.18: Design flowchart for first pass design.

3.6.2. Specifications

The machine design is dictated by the specifications of the application. The specifications define the power, current, voltage, dimensional and thermal limits of the machine. As a case study, a single-phase machine is designed according to the case study specifications shown in Table 3.4 for a 1 kW direct drive wind turbine application.

Table 3.4: Design Specifications

Rated power 1 kW Max. phase current 52 A (rms) Rated rotor speed 400 rpm Stator Outer diameter 225 mm Rated torque 24 Nm Magnets Ferrite DC bus voltage 48 V Cooling Air cooled

3.6.3. Choice of Pole Numbers

The combination of the stator and rotor poles determines the number of phases in the proposed machine. Single-phase machines could be constructed where the number of the rotor and stator poles is kept the same. Higher pole numbers result in an increased electrical loading as given in Eqn. (3.13). Figure 3.19 shows the effect of changing poles on torque density and power with the same current density and design ratios with respect to pole width (Pw) and pole pitch (Pp). As the number of pole increases, the torque density improves but starts decreasing once the poles saturate which occurred around 42 poles in this machine. The power factor also improves but starts decreasing due to increased inter- pole leakage caused by fringing fluxes at high pole numbers.

Figure 3.19: Effect of pole numbers in a single phase E-core TFM. The rated speed of the machine also dictates the pole numbers. As the pole number increases the flux frequency of the machine increases. This is limited by iron losses and inverter switching capability. Considering the flux level and degree of saturation in the

TFM from FEA simulation, an operating frequency of less than 150 Hz provided acceptable core-loss. In this application the flux frequency is limited to 100 Hz, thus, a pole number of 30 is selected. Initially the pole embrace is selected as 0.5 to have equal space for windings and active core area. The stator and rotor pole widths are also kept the same initially.

3.6.4. Initial Dimensions in Radial Length (Peripheral Length)

The machine is first sized in the radial direction. This constitutes the design of the active length, the core lengths, and magnet length. An important parameter in machines with axial airgap is the choice of 휆. To optimize the machine the 휆 must be chosen diligently. For

AFMs, it has been reported that the optimum value for 휆 is 0.63 to achieve a high value of torque and torque to weight ratio [95]. In the first pass design a 휆 of 0.63 is used with 70 specified outer diameter to determine the shaft length and active airgap length. The maximum diameter is used to fit into the specification

The other important radial dimensions are the core lengths. Key design ratios for sizing these are introduced and defined as:

푙푐 푘푚 = (3.24) 푙푚

푙표 푙𝑖 푘푙푐 = = (3.25) 푙푐 푙푐 where, 푘푚 is ratio between the radial length of the central core 푙푐 and the magnet length

푙푚, 푘푙푐 is the ratio between the central core and the inner (푙𝑖)/outer (푙표) cores. The peripheral length of the magnet using (3.24), (3.25) and (3.14) can be then defined as:

퐷표(1 − 휆) 푙푚 = (3.26) 2퐾푙푐푘푚 + 푘푚 + 2

In the first pass the ratio of 푘푚 is picked as 1. The ratio of 푘푙푐 as 0.5 because the flux in the inner/outer cores will be half that of the central core.

3.6.5. Rotor Design

The initial peripheral core and magnet lengths for the rotor are already designed in step 3.

In this step the height of the rotor core height, 퐻푟푦 is designed. The height of the rotor core determines the flux focusing of the machine. The airgap length is also determined in this stage.

The airgap length for AFMs are typically in the range of 0.8 to 1.4 mm. Higher airgap lengths reduce the working flux density of the magnets and increases leakage. However, setting small airgap lengths are limited due to structural issues.

In this case study, an airgap length of 1 mm is selected. A simple MEC of the machine with the peripheral lengths from step 3 is used to determine the working flux of the magnets.

The machines flux focusing factor is selected such that the airgap attains a peak flux density of 0.9 T. The flux focusing factor from Eqn. (3.17). determines the height of the rotor core.

3.6.6. Turn Number Selection

At this stage, the rotor and stator are dimensionally designed and it is possible to derive the number of turns from the power Eqn (3.20). Equation (3.24) and (3.26) can be used in Eqn

(3.22) and (3.23) to derive the number of turns as

(2푘푙푐푘푚 + 푘푚 + 2)푃표 푁 = 2 (3.27) 6휂푚푚𝑖푘푝푘𝑖푘푚푃퐵푔휔푒푃푒푚푏휋퐷0 (1 − 휆)

In this stage, it is assumed that the machine operates with sinusoidal back-emf voltage.

Thus, 퐾𝑖 is selected as √2 and 퐾푝 as 0.5. For a conservative design, the efficiency is assumed to be 90%.

3.6.7. Stator Design

The slot height in the stator core is selected based on the thermal requirements. In this case, study, the machine will be air-cooled. Therefore, the current density of the coils is limited to <6 A/mm2. With the number of turns, rms current and peripheral length already determined the slot height of the stator is adjusted until the required current density is attainted. The parameters of the first pass design are given in Table 3.5.

Table 3.5: First pass machine design parameters Machine Parameter Value Machine Parameter Value

푃 30 푙𝑖 5.2 mm 퐷표 225 mm 휏 14.84 mm 휆 0.63 푊푟 7.42 mm 퐷𝑖 141.75 mm 푊푠 7.42 mm 푘푚 1 푘푓 2.4 푘푙푐 0.5 퐻푟푦 25 mm 푙푚 10.4 mm 퐻푠푡 22.2 mm 푙푐 10.4 mm 푔 1 mm 푙표 5.2 mm N 3

3.6.8. Effect of Key Design Parameters

After the first pass machine design, the effect of the key design ratios is presented in this section. The design ratios are investigated using 3D FEA in Flux3D software.

1) Effect of 휆: In this machine the outer diameter was fixed. Thus, a change in 휆 resulted in a change in the active airgap of the machine. Increasing 휆 resulted in smaller active airgap. The effect of 휆 on the torque density and power factor of the machine is shown in

Fig. 3.20. It is observed that an increase in 휆 results in a reduction of the power factor and the torque density. However, the use of magnet and current density for a fixed stator height also reduces as shown in Fig 3.20. Therefore, it is important to find an optimum balance between magnet usage, torque density, power factor and current density when selecting 휆.

(a)Effect of torque density and power factor (b)Effect on magnet and current density Figure 3.20: Effect of 휆 on machine performance.

2) Effect of 푘푓: The flux focusing is determined by the height of the rotor. In this analysis, the machine the outer diameter was fixed. Thus, a change in 푘푓 resulted in a change in the air gap flux density. This is illustrated in Fig. 3.21(a). The increased airgap flux density attained with higher 푘푓 results in increasing the weight of the machine as well.

However, the percentage increase in torque is large than the percentage increase in weight.

Thus, an increase in torque density is observed as shown in Fig. 3.21(b). The increased magnetic loading also results in increased power factor. Design optimization for 푘푓 aims at increasing the torque density and power factor within the limit of allowable maximum machine/magnet weight.

(a) Air gap flux density (b) No load voltage and torque

Figure 3.21: Effect of 푘푓 on machine performance.

3) Effect of 풌풎 & 풌풍풄: The design ratios 푘푚 and 푘푙푐 are used to simplify the design procedure by increasing the number of dependent design variables. For a fixed 휆 and 푘푓, as the 푘푚 increases the torque density and power factor of the machine improves as shown in Fig. 3.22. This is due to increased magnet in the machine. The effect of 푘푙푐 on the torque density and power factor is shown in Fig. 3.23. As the 푘푙푐 increases the outer core lengths gets bigger and this results in a reduction in torque density. Smaller 푘푙푐 is preferable as along as the core does not get saturated at rated conditions.

Figure 3.22: Effect of 푘푚. Figure 3.23: Effect of 푘푙푐.

4) Effect of 푷풆풎풃: The 푃푒푚푏 is crucial in the determination of the machines performance. Large 푃푒푚푏 lead to increased magnetic loading (airgap flux density) at the cost of lower electric loading due to smaller winding area as shown in Fig 3.24 (a). The increased magnetic loading results in increased torque density as shown in Fig. 3.24 (b).

The power factor decreases as the leakage between intermediate poles are increased.

(a)Effect on magnet and current density (b)Effect of torque density and power factor

Figure 3.24: Effect of 푃푒푚푏 on machine performance.

As 푃푒푚푏 also effects the shape of the back-emf voltage. The effect of 푃푒푚푏 on the back- emf voltage is shown in Fig. 3.25. If the 푃푒푚푏 is small and below 0.5, the back-emf voltage is lower and has a trapezoidal shape. As the 푃푒푚푏 increases from 0.5 to 0.75 it becomes more triangular. However, beyond 0.75, the back-emf waveform starts becoming more trapezoidal in nature again. The power waveform factor (푘푝) is dependent on the back-emf shape. Thus, the choice of 푃푒푚푏 will dictate the choice of 푘푝 in the design process.

Figure 3.25: Effect of 푃푒푚푏 on back-emf voltage.

Based on these observations an optimized machine was designed in 3D FEA. The machine dimensions are tabulated in Table 3.6.

Table 3.6: Final design of case study machine.

Machine Parameter Value Machine Parameter Value

푃 30 푙𝑖 4.75 mm

퐷표 225 mm 휏 15.289 mm

휆 0.6489 푊푟 8.25 mm

퐷𝑖 146 mm 푊푠 8.25 mm

푘푚 1 푘푓 2.6

푘푙푐 0.475 퐻푟푦 26 mm

푙푚 10 mm 퐻푠푡 21.25 mm

푙푐 10 mm 푔 1 mm

푙표 4.75 mm N 6

3.6.9. Material Considerations

1) Core material: Another important factor in the design of this machine is the selection of materials. The first consideration is whether to use soft magnetic composites (SMC) or

77 laminated steel for the rotor and stator cores. SMC have isotropic magnetic properties and can be molded into complex shapes facilitating 3-D flux paths. However, SMC has a lower magnetic permeability and lower saturation flux density compared to laminated steels as presented in Fig. 3.26(a).

Most laminated cores are made of non-oriented silicon steel sheets where individual steel sheets are stacked together to form the core to help reduce the eddy current losses.

(a) Core material (b) Magnet material

Figure 3.26: (a) BH curve of laminated steel and SMC used in study. (b) Magnetic characteristic of permanent magnets. In rotary electric machines, the stator and rotor segments are arc shaped. An example of the stator core with arc-segments is shown in Fig 3.27(a). The difficulty with the arc segments in the E-core TFM is its fabrication. The arc shape is very difficult to obtain with laminated steels. However, a rectangular segment for the stator and rotor cores is another option where laminated steel can be used. The proposed machine with no arc-elements is shown in Fig. 3.27(b). The case study machine is designed and optimized with arc-shapes and SMC materials, and compared with the machine with rectangles and laminated steel

78 designed in the previous section. The structures for the two machines are shown in Fig.

3.27 and the design parameters and outputs are given in Table 3.7.

(a) Design with arc shapes (b) Design with no arc shape

Figure 3.27: Isometric of view of two design structure of E-core TFM. Table 3.7: Design comparisons with arc and without arc shapes. Parameter Machine with arc shapes Machine without arc shapes Rotor/ Stator material SMC Somaloy-700 Laminated Steel M270_35A Magnet type Ferrite (Br=0.4 T) Ferrite (Br = 0.4 T) Machine Weight 6.81 kg 8.6 kg Magnet weight 1.36 kg 1.46 kg Coil weight 2.57 kg 4.05 kg Torque output 26.425 Nm 28.23 Nm Torque Density 3.88 Nm/kg 3.28 Nm/Kg Power Factor 0.638 0.676

The machine with arc-shapes provides a better magnetic circuit by better utilization of the area. The thinner thickness in the outer pole enables the arc-shaped designs to reduce the copper weight considerably compared to designs with no arcs. Thus, a higher torque density can be achieved. The machine with no-arc still produces a high torque density and

79 has the added benefit of being simpler in construction. The pole-to-pole leakage is also lower in the machine with no-arcs that helps achieve a higher power factor.

2) Permanent magnet material: Generally, three classes of magnets that are used for electric motors: Alnicos, ferrites and rare earth magnets. The characteristics of the three classes of magnets are shown in Fig. 3.26(b). The performance of the case study machine with no-arc and different PM materials are presented in Table 3.8. The tests were conducted with the same number of turns, phase current and zero advance angle.

It is observed that the use of leakage reduction magnets helps improve power factor and torque density when using ferrite and NdFeB magnets. The performances of Alnico magnets are poor due to its low coercive force. The motor needs to be redesigned with higher magnet thickness to have a better performance with Alnico magnets. The use of rare earth magnets improves the performance of the machine significantly. For the same magnet volume, the rare earth magnets would have a higher mass due to higher mass density. The torque with rare earth is 2 times more and the power factor is 34% higher compared to those with ferrites. This would allow a further downscaling of the machine. However, rare earth magnets are considerably more expensive than Alnico or ferrites.

Table 3.8: Performance of E-core machine with different magnets.

Magnet type Leakage Magnet weight Torque Torque density Power factor reduction magnet (kg) (Nm) (Nm/kg) Alnico Yes 2.18 13.78 1.48 0.33 Alnico No 0.93 13.17 1.63 0.35 Ferrite Yes 1.46 27.92 3.25 0.63 Ferrite No 0.63 13.46 1.73 0.39 NdFeB Yes 2.53 55.73 5.78 0.84 NdFeB No 1.08 37.73 4.35 0.76

3.6.10. Multiphase Machine

Multi-phase versions of the proposed TFM can be achieved in two ways. One way is to stack multiple single-phase modules. In this manner, the different phases would be modular in structure and each phase is independent. There will be no magnetic coupling between the two phases.

A two-phase machine can be made on a single stack of the proposed E-Core TFM by mechanically shifting the stators on the two side. In this method, the two phases would be magnetically coupled. A two-phase version of the designed machine on a single stack is shown in Fig. 3.28. A combination of this approach and stacking can also be used to obtain a multi-phase machine.

A third approach is to have an uneven number of rotor and stator poles. The winding will be short-pitched. The numbers of stator and rotor poles can be obtained from:

푁푠 = 2푁푝ℎ푁푟푒푝 (3.28)

푁푟 = 푁푠 − 2푁푟푒푝 (3.29) where, 푁푠 is the number of stator pole, 푁푝ℎ is the number of phases, 푁푟푒푝 is the number of repetitions, and 푁푟 is the number of rotor poles.

Phase A

Phase B

Stator core Rotor core Shaft Leakage reduction magnet Flux focusing magnet Figure 3.28: Two phase E-core TFM by stator shift.

3.7. Cogging Torque Reduction in Proposed Machine

Cogging torque is an important issue in direct drive applications as results in startup difficulties and acoustic noise. PM machines with slotted stators exhibit cogging torque.

Due to the slotted structure, the airgap reluctance varies and causes to a variation in the magnetic energy as rotor rotates. This variation of magnetic energy results in cogging torque. This section of the research investigates different techniques of cogging torque reduction on the E-core machine. The effects of notch or dummy slots in circumferential and transverse direction, skewing of stator cores, stator pole pitch and stator displacement has been investigated in detail. A three level design of experiments based on the Taguchi method is then applied for optimization. The search space and design variable is reduced in each level making the optimization more detailed. This allows for an efficient optimization with a low number of simulations. 3D FEA is used to aid the investigation.

3.7.1. Cogging Torque Minimization Techniques

Several methods exist for minimization of cogging torque. A vast majority of these methods have been applied in RFM. Some techniques have been applied to TFMs as well.

This research examines the feasibility of some the techniques on the proposed E-core TFM. 82

3.7.1.1.Rotor and Stator Pole Numbers

The first step in cogging torque minimization is through the selection of rotor and stator pole numbers. In multiphase machines, the slot/pole ratio is selected to minimize the cogging torque. It is common practice to employ fractional slot windings for reduction of cogging torque in multi-phase machines. However, this study is based on a single-phase double-sided machine where the number of rotor poles is equal to the stator slots. The number of poles though has an effect in the amount of cogging torque. Results of 18, 30 and 42 pole configurations for the machines with the same electrical loading is shown in

Table 3.9. The cogging torque, torque density and power factor increases as the pole number increases in both the machines. The results of the case study single-phase machine indicate a considerable amount of cogging torque that needs to be addressed using different design techniques.

Table 3.9: Performance with different pole numbers

Poles Average full-load Peak cogging Torque density Power factor torque torque ( Nm/Kg) ( Nm) (Nm) 18 28.21 21.17 2.68 0.59 30 30.0 27.5 3.49 0.67 42 28.94 28 3.72 0.66

3.7.1.2.Pole Width

The pole width is another important parameter in cogging torque minimization. In the case study machines, the ratio of rotor pole width to the stator pole width is investigated. FEA results as shown in Fig. 3.29 indicate that a higher width results in lowering the cogging torque amplitude. However, a decrease in average torque is observed. The lowest cogging torque with the highest average torque is achieved when the slot widths the same. This

83 suggests that changing the pole width ratios affect the harmonics of the cogging torque adversely. The effect of the pole width on cogging torque and average torque is shown in

Fig. 3.30. It is possible to increase both the average torque and reduce cogging torque by increasing pole widths. An increase in the pole width results in reducing the air gap reluctance variation and this aids cogging torque reduction. The increase of pole width also affects the power factor and leakage adversely. Thus, it is necessary to keep an optimum balance.

Figure 3.29: Effect on average torque and peak Figure 3.30: Effect on average torque and peak cogging torque. cogging torque. 3.7.1.3.Skewing

Skewing is the most popular method of cogging torque reduction in permanent magnet machines. The stator and rotor side skewing can be applied. It has been shown in the literature that skewing could theoretically reduce the cogging torque to zero. However, there are several manufacturing challenges to skewing in RFMs and AFMs. Traditionally due to these limitations rotor side skewing is more popular in AFMs. The TFMs studied in this research consists of modular stator cores laminated in the radial direction. As a result,

84 stator side skewing shown in Fig. 3.31 can be applied with minimal manufacturing challenges. The effect of skewing on cogging torque and average load torque is presented in Fig. 3.32. It is observed that a significant amount of cogging torque minimization is possible but average torque also decreases.

Figure 3.31: Top view of machine structure with Figure 3.32: Effect of skew angle on average torque stator skewing. (Top view) and peak cogging torque. 3.7.1.4.Stator Displacement

The case study machine has a double-sided stator arrangement thus this enables the application of a stator displacement on the two sides to reduce cogging torque (Fig. 3.33).

The effect of stator displacement is significant and is shown in Fig. 3.34. The average torque remains unaffected if the currents in two stator sides are shifted accordingly. This method is the most effective in reducing cogging torque. This method essentially shifts the harmonics between the top and bottom stator cores such that they add up to a lower cogging torque. However, due to the spatial shift in the two sides a large stator displacement essential converts the machine into a two-phase machine, requiring a higher number of power electronic devices to commutation.

Figure 3.33: Structure for cogging torque reduction Figure 3.34: Effect on average torque and peak with stator displacement on two sides. cogging torque. 3.7.1.5.Dummy Slots in Stator Teeth

Another method of cogging torque reduction is the use of notches or dummy slots in the stator teeth. This method has been applied to surface and interior PM machines. The dummy slots result in increased interactions between the rotor PMs and stator slots that result in a reduction of the peak value of the cogging torque. This is achieved by eliminating some of the cogging torque harmonics. The method can be applied in the proposed machine in two axes as shown in Fig. 3.35. The results of cogging torque reduction with varying slot height and slot width on the x-axis are shown in Fig. 3.36. It is observed that increased slot width and height decreases the cogging torque. However, the average torque is reduced. This method would be easy to apply in the proposed machine. The laminations stack being in the y-axis imposes manufacturing difficulty in dummy slots in the y-axis.

Figure 3.35: Possible slotting structures. Figure 3.36: Effect of slot height and slot width on peak cogging torque for slotting on x-axis. 3.7.2. Design of Experiment Based Optimization

Three-dimensional FEA-based simulations are used in the optimization of the machines to achieve higher accuracy; however, this is computationally intensive. Therefore, it is important to optimize the machine for cogging torque with a lower number of simulations.

The Taguchi method is a form of DOE that allows for an optimization with a small number of simulation runs [198]. The Taguchi method generally involves the following stages:

1.Identification of design variables: In this stage, the key design variables are selected.

2.Development the experimental matrix and experiments: Taguchi’s orthogonal arrays

allow for an investigation of the design search space with a reduced number of

experiments.

3.Analysis: After the experiments, the collected data is analysed. The ratio of average

torque to peak cogging torque is identified as the key response for analysis. It is defined

as:

푇푎푣푔 푦 = (3.30) 푇푝푒푎푘 푐표푔푔𝑖푛푔 푡표푟푞푢푒

4. An analysis of means is performed on the results. It is a statistical technique used to

illustrate variations among groups of data. This method compares the mean of each

group to the mean of the overall process to detect significant differences. Another

statistical tool to aid the design is the signal-to-noise ratio. The signal-to-noise ratio with

the “larger the better” target is used to identify the optimum design levels. It is defined

as:

1 푆푁 = −10 log ( ) (3.31) 푦2 where y represents the performance value. In this study, the statistical tool Minitab is used to aid the analysis.

In the first stage of the optimization, the pole width, stator skewing angle, and stator displacement with four levels of variation are selected for both machines, as shown in

Table 3.10.

Table 3.10: Design variable levels for optimization in Stage 1.

Control Factors Level 1 Level 2 Level 3 Level 4

A Stator displacement 0 0.70 1.40 2.20 B Skew 0 1.10 2.30 3.60 C Pole width 8 8.10 8.25 8.50

This results in the use of an L16 orthogonal array of possible combinations as shown in

Table 3.11. In all cases, the ratio of the average torque to peak cogging torque is selected as the response. This method allows for obtaining a trend of the best design results in only

16 simulations per machine instead of 64 if all combinations were to be simulated. This results in a significant reduction in the optimization time. After the simulations, the results are analysed. The response table of means and signal-to-noise ratios are shown in Table 88

3.12 and Table 3.13 for the proposed machine. The results are graphically represented in

Fig. 3.37.

Table 3.11: L16 orthogonal array and results(Stage 1).

A B C Tcog peak (Nm) Tavg (Nm) Tavg/Cog 0 0 8 27.79 28.02 1.01 0 1.10 8.10 27.15 28.56 1.05 0 2.30 8.25 25.53 29.17 1.14 0 3.60 8.50 23.55 29.93 1.27 0.7 0 8.10 25.79 28.71 1.11 0.7 1.10 8 24.1 28.28 1.17 0.7 2.30 8.50 21.89 29.28 1.34 0.7 3.60 8.25 19.81 28.61 1.44 1.4 0 8.25 20.58 28.09 1.36 1.4 1.10 8.50 18.85 29.15 1.55 1.4 2.30 8 17.46 28.48 1.63 1.4 3.60 8.10 13.17 28.48 2.16 2.2 0 8.50 13.7 29 2.12 2.2 1.10 8.25 10.03 28.2 2.81 2.2 2.30 8.10 5.21 29.38 5.64 2.2 3.60 8 1.77 27.85 15.73

Table 3.12: Analysis of means after Stage 1 of Table 3.13: SN ratio for after Stage 1 of DOE. DOE. Level A B C Level A B C 1 0.94 2.55 7.41 1 1.12 1.4 4.89 2 2.01 3.65 5.77 2 1.27 1.65 2.49 3 4.36 5.74 4.01 3 1.68 2.44 1.69 4 13.6 8.98 3.73 4 6.57 5.15 1.57 Delta 12.68 6.42 3.68 Delta 5.46 3.75 3.32 Rank 1 2 3 Rank 1 2 3

(a) Effect of means (b) Effect of SN ratio Figure 3.37: Analysis after the first stage of DOE.

From the analysis, it can be determined that the design factor A (stator displacement) is the most significant followed by factor B and C. Thus, stator displacement between two sides was selected as 2.2 (level 4).

In the second stage of the optimization procedure, a narrower search space for skew, pole width, and a third and new design variable, the direction of the skew, is used. This design variable is introduced in the second stage because semi-optimum values have already been selected for the skew. The trend for skew is the same on both sides thus including this the first stage would not alter the result of optimization in stage 1. This step verifies the direction of the skew in a small number of simulations. The term opp means that per side the stator cores of intermediate poles are skewed in the opposite direction; this is shown in Fig. 3.38.

Skew angle

Rotor y Rotor x Stator y Stator x

Figure. 3.38:. Top view of machine structure with stator skew in opposite sides.

An L4 array was used in this stage. The orthogonal arrays and the corresponding performance data for the two machines are shown in Table 3.14. The mean on means analysis results in Fig.3.39 indicates that the direction needs to be the same, and a better optimum for factor A and B might be just above this range.

Table 3.14: Orthogonal array and results (Stage 2).

B C A (Pole (Skew Tcog Tavg Tavg/Cog (Skew) width) direction) 2.7 8.05 same 4.83 27.97 5.80 2.7 8.15 opp 12 28.9 2.41 3.25 8.05 opp 11.47 27.37 2.39 3.25 8.15 same 2.84 29.37 10.34

Fig. 3.39: Analysis of means after the second stage of DOE.

In the third stage, the skew angle and pole width are analyzed with a narrower search area.

The array and corresponding results for the third stage are shown in Table 3.15.

Table 3.15: Orthogonal array and results (Stage 3).

A B Tcog Tavg Tavg/Cog 3.25 8.1 2.35 28.46 12.11 3.25 8.25 2.98 29.52 9.92 3.7 8.1 1.84 28.79 15.65 3.7 8.25 1.86 29.27 15.78

The results yielded an optimum skew of 3.7 and stator width of 8.25 mm the proposed machine. Thus, with only 29 simulations it was possible to reduce the cogging torque to a peak of 1.86 Nm from 27.5 Nm while keeping the average torque output at 29.27 Nm. The cogging torque profile of the final machines is shown in Fig 3.40. Note that the cogging torque is slightly higher than it was in the DOE simulations. This difference is due to a better second-order machine in the final simulation. To speed up the optimization, only

92 first-order meshes were considered in the design stage. The machine performance after the optimization process is shown in Table 3.16.

Figure 3.40. Cogging torque of final optimized machine with second-order mesh.

Table 3.16. Key Parameters of reference machine.

Parameter Machine I Winding type Pole No. of poles 30 Speed (rpm) 400 Bus voltage 48 V Power mech. (W) 1173 Initial average torque (Nm) 30.01 Final average torque (Nm) 28 Initial peak cogging torque (Nm) 27.5 Final peak cogging torque (Nm) 2 Air gap (mm) 1 Outer radius (mm) 112.5 Optimized Pole width (mm) 8.25 Optimized Skew angle (degree) 3.7 Optimized Shift (mech. degree) 2.2 Current density (A/mm2 ) 5.416 Total weight (kg) 8.6 Torque density (Nm/kg) 3.255

3.8. Conclusions

The chapter presents the design of a novel E-Core modular TFM. The machine has a double-sided stator configuration with flux concentrating ferrite magnets in the rotor. The flux concentrating principle allows the use of low-cost ferrite magnets while maintaining a high airgap flux density. E-core stators with pole windings are proposed to ensure maximum core and magnet utilization and thus improved power factor. The proposed machine also has a modular structure making it easier to manufacture. An analytical sizing method for the machine is presented using which single-phase, two-phase and three-phase variants of the proposed machine are designed and analyzed using 3D FEA.

This section also presents different designs considerations for cogging torque reduction in transverse flux machines. This paper investigates the effect of pole numbers, pole width, skewing, and stator displacement for cogging torque minimization. Based on the initial analysis, three base factors for cogging torque reduction are selected. A three-level Taguchi method based on DOE is then used to optimize the four factors for reducing cogging torque without considerably sacrificing the average torque output. The 90% reduction in peak cogging torque with a 9% reduction in average torque of the machine.

CHAPTER IV

ANALYSIS AND COMPARISON OF E-CORE MACHINE

4.1. Introduction

In this chapter, the electromagnetic analysis of the E-core machine is presented. The analysis includes no load characteristics, flux leakage analysis, demagnetization characteristics and analysis with load. Multiphase embodiments of the TFM are also presented. The proposed machine is compared with other conventional machine topologies at two different power and speed levels to demonstrate its strengths and weaknesses in comparison to conventional machines.

4.2. Electromagnetic Analysis with 3D FEA

Electromagnetic analysis using 3D finite elements analysis (FEA) on Flux 3D was carried out on a single phase 30-pole E-Core AFM with no arc. The dimensions of the machine are given in Table 3.5. The FEA gives the magnetic flux density and flux paths in different parts of the machine. The flux lines of a single pole using 2D FEA is shown in Fig. 4.1; leakage flux within the slots is observed. The direction of flux paths in one pole pair of the machine is shown in Fig. 4.2. The 2-D flux path of one pole is shown in Fig. 4.2 (b) and matches with the concept presented in Fig. 3.13.

Figure 4.1: Flux lines of one pole with 2D FEA. The flux density distribution at the aligned position with no-load is shown in Fig. 4.3. The edges near the air gap have a higher flux density of around 1.7 T. The flux density in the stator teeth is around 1.3 T. The flux density is higher in the central teeth. The rotor has a relatively low flux density with highest flux density of 1.3 T near the air gap.

(a) Flux path in 1 pole pair. (b) Flux path in one pole. Figure 4.2: Flux path of single phase E-core TFM at aligned position.

Figure 4.3: Flux density at aligned position.

The air gap flux density from the inner airgap to the outer stator is shown in Fig. 4.4 (a).

The density is higher in the central airgap due to leakage and different size of leakage reduction magnets. The airgap flux density from one pole to another along the length of the pole-pitch in the central stator length is shown in Fig. 4.4 (b). It is observed that a high flux density of 0.80 T peak was achieved at the center of middle leg of the E-core stator during the aligned position. This demonstrates that it is possible to have a high airgap flux density through flux concentration when using ferrite magnets.

(a) Flux density from inner to outer stator teeth (b) Flux density from one pole to another Figure 4.4: Airgap flux density at aligned position.

The leakage flux in the machine is analyzed by using cut planes in the middle of the stator and the area between the two adjacent stators. The flux vectors with rated q-axis current at the aligned and unaligned position are shown in Fig. 4.5. The flux leakage at an aligned position between the two poles are in the range of 0.11 T. At the unaligned position with rated q-axis current, there is some leakage between the two poles. The magnitude of the leakage flux vector is low and reaches around 0.12 T near the airgap. This indicates that the proposed machine has low inter-polar leakage. A leakage flux is also present in the radial periphery of the machine. At aligned position, the radial flux leakage from the outside of the rotor is in the range of 0.06 T. At unaligned position, this leakage flux is more prominent and is in the range of 0.07 T to 0.1 T. The extra leakage in the unaligned position results in higher q-axis inductance and as a result lower power factor in TFM machines.

Cut planes (a) Aligned (b) Unaligned

Figure 4.5: Flux vectors in cut planes for with rated current.

The flux linkage of the top stator with no load at 400 rpm is shown in Fig. 4.6 (a). A near sinusoidal flux linkage is observed. The back-emf with no load at 400 rpm is shown in Fig.

4.6 (b), which is near sinusoidal, but with some harmonic components. The spectral content of the flux linkage and the back-emf voltage is shown in Fig. 4.6 (c) and (d) respectively.

(a) Flux linkage of coil (b) Back-emf voltage

Figure 4.6: No load characteristic of top stator.

The demagnetization characteristics of the machine was also tested. The maximum current that in the negative d-axis that would demagnetize the magnets can be expressed as

(퐿푚 + 푔)퐻푑 퐼푑푒푚푎푔 = 2 푧 (4.1) 푃

where, 퐿푚 and 푔 are the magnet thickness and airgap in meters, 푧 is the number of conductors carrying current, 푃 is the number of poles and 퐻푑 is the maximum negative field (A/m) the magnet can handle before demagnetization. The maximum current for the designed machine was found to be theoretically 268 A.

The effect of demagnetization was also studied in 3D FEA. The FEA software had a feature where there remnant flux density of the magnet was adjusted after each time step to accurately predict the demagnetization of the magnets during operation. The proposed machine was tested in six conditions for demagnetizations. The flux density of the magnets with rated q-axis current is shown in Fig 4.7.

(a) Flux density map (b) Flux density with rated 퐼푞 current

100

(e) Flux density with 2x rated −퐼푑 current (f) Flux density after short circuit current Figure 4.7: Flux density surface plots of magnets under different current conditions. The flux density with rated q-axis current shown in Fig 4.7 (b) indicates that there is very little demagnetization and the magnet only drops down to 0.26 T near the edges. The flux density with rated dq axis currents is shown in Fig 4.7 (c). It can be observed that due to the d-axis current there is some flux weakening and the flux density of the transverse magnetized magnets are lower. With rated and 2x rated d-axis currents shown in Fig. 4.7

(d) and (e) indicates much lower flux densities in the magnets. At twice the rated d-axis current the magnet flux density drops down to 0.18 T to 0.2 T. The short circuit current in the proposed machine reaches a maximum of 100 A. The flux density of the magnets after short circuit shown in Fig 4.7 (f) indicates that the machine is designed to withstand

101 demagnetization during short circuits operation. In all of the cases, it was observed that the outer magnet suffers the least amount of demagnetization. This is due to the very little inter pole flux linkage at the outer most periphery of the machine. The other leakage reduction magnets in the inner and center regions should not have been demagnetized ideally.

However, to the inter pole flux leakage there is some degree of demagnetization in these magnets.

The effect of armature MMF applied through the windings on average torque output is shown in Fig. 4.8. The output torque increases as the ampere-turns are increased by increasing the current. The torque and current waveforms for the single phase machine is shown in Fig. 4.9. A torque ripple of nearly 100% percent is observed in the single phase version.

Figure 4.8: Effect of current in windings.

102

a) Torque and current waveforms b) Voltage waveform in one side

Figure 4.9: Torque, current and voltage waveform at rated speed and current of single phase motor.

The efficiency and torque per ampere of the motor was then calculated and shown in Fig

4.10 for the entire speed range. It can be observed that the machine achieves the efficiency at 80% load at rated speed and at higher speeds. The efficiency is lower at the rated condition due to high saturation causing increased coreloss. Copper loss and core loss are the loss terms calculated when evaluating the efficiency. In this machine, the copper loss dominates as the operating speed range is narrow. The torque per ampere of the machine is shown in Fig 4.11. The machine obtains a high torque per ampere below the base speed as the machine is operating in maximum torque per ampere. Above the base speed, flux, weakening is required and this reduces the torque per ampere rating.

103

Figure 4.10: Efficiency plot for the entire speed range.

Figure 4.11: Torque per ampere plot for the entire speed range. A two phase version of the machine with the same design can be obtained by phase shifting two stator cores. The flux linkage and back-emf of the two phase motor are shown in Fig.

4.12. The torque and currents for the two phase machine are shown in Fig. 4.13. A much smoother torque is observed due to the multiphase torque production. The torque per ampere and efficiency is expected to be the same in the two phase embodiment as the sides

(i.e. phases) are independent.

104

(a) Flux linkage of coil (b) Back-emf voltage

Figure 4.12: No load characteristic of two phase motor.

Figure 4.13: Torque and current waveform at rated speed and current of two phase motor.

A three-phase E-core TFM with a 30-20 pole combination with specifications the same as the case study machine is also investigated. A top view of the machine illustrating the windings is shown in Fig. 4.14 (a). An isometric view illustrating the flux density at different parts of the machine is shown in Fig. 4.14 (b).

105

(a) 3D view of the proposed machine

(b) Isometric view of the flux density at max armature current.

Figure 4.14: FEA model and flux density distribution of three phase E-core TFM. The variation of the airgap flux density at no load at the center of one stator pole as the machine rotates is shown in Fig. 4.15 (a). The back-emf of the three-phase machine has higher third and fifth order harmonics as shown in Fig. 4.15 (b). The torque and current waveforms of the single and three phase E-core TFM at the rated speed of 400 rpm is shown in Fig. 4.16. The single-phase machine exhibits a much higher torque ripple compared to the three-phase machine as expected. The three-phase machine also exhibits some torque ripple due to the presence of higher order harmonics in the back-emf voltage.

106

(a) Air gap flux density (b) Back-EMF phase voltage (l-n) at 400 rpm.

Figure 4.15: Air gap flux density and back-emf waveform of three phase E-Core TFM.

(a) Single phase (b) Three phase

Figure 4.16: Torque and current waveforms at rated speed and current for three phase E-core TFM. 4.3. Comparison at High Torque Low Speed Applications

The specifications to be used in the machine designs are provided in Table 3.4 of chapter

The proposed single-phase (M I) and three-phase (M II) E-core TFMs are compared in this section. The design guidelines for the three RFM (Fig. 4.17) in the comparison are:

 All machines have the same outer diameter of 224 mm. This allows for a better

comparison of volume.

 A current density between 5 and 6 A/mm2 is maintained at peak conditions.

107

 The combination of number of turns and currents is set to utilize a maximum DC bus of

48 V at the rated speed of 400 rpm.

 The same lamination material and thickness are used.

 At rated condition, the peak flux density is maintained below 2 T.

 The same magnet material is used.

(a) 6-4 Ferrite surface PMSM with concentrated winding.

(a) 24-4 Ferrite surface PMSM with distributed winding.

108

(a) 24-4 NdFeB surface PMSM with distributed winding.

Figure. 4.17: Cross section and flux density distribution of comparison machines. A 6-4 surface mounted ferrite PM machine with concentrated windings (M III) and a 24-4 surface mounted ferrite PM synchronous machine (SMPMSM) with distributed windings

(M IV) is designed. A SMPMSM with NdFeB magnet (M V) is also compared with the proposed machine. The machines were designed with the mentioned restrictions using particle swarm optimization of an analytical model of the surface PM machine. The machines are compared with respect to efficiency, volume, the active weight of materials, losses and power factor. The cross section and flux density at maximum armature current for the designed RFMs are presented in Fig. 4.17. The U-Core TFM is also designed as a sixth machine (M VI). The key design and performance parameters of the machines are given in Table 4.1.

From the comparison among the four machines, it can be observed that the E-core single- phase machine attains the highest torque density. It is almost 2 to 2.5 times that of ferrite

RFMs. The three-phase E-core machine also achieves a torque density improvement of 2 times compared to ferrite RFMs. The improvement in the torque density is due to a reduction of the active weight of the machine. The active weight of the E-core machines is

109 comparatively smaller due to shorter magnetic flux paths. However, the weight of the coils is higher in the E-core machines, which result in higher copper loss. In addition, the core losses are higher due to a higher fundamental frequency. Thus, the efficiency of the E-core machine is slightly lower. The difference in the rotational frequency is due to the nature of

TFMs and RFMs. TFMs typically have a higher number of poles compared to RFMs. The power factor is lower in the single phase E-core TFM. A slightly higher power factor was observed in the three-phase TFM. The SMPM with distributed windings demonstrates the highest power factor. The TFM also demonstrated a slightly higher torque density compared to NdFeB based SMPM. However, the efficiency is lower by a large margin.

The comparison demonstrates the benefits of the proposed TFM in terms of higher torque density. The power factor and efficiency are also comparable to ferrite SMPMSMs, slightly lower than NdFeB SMPMSMs. In comparison to the U-core TFM, the E-core machine is superior.

110

Table 4.1: Key parameters in comparisons of different machines

Performance M I M II M III M IV M V MVI Speed (rpm) 400 400 400 400 400 400 Remnant Flux density Br (T) 0.4 0.4 0.4 0.4 1.1 0.4 Air gap (mm) 1 1 0.7 0.7 0.7 1 Outer radius (mm) 112.5 112.5 112.5 112.5 112.5 112.5 Stack length (mm) 80 84.8 90 82 45 102 Current density (A/mm2 ) 5.41 5.51 5.34 5.4 5.1 5 Torque (Nm) 28.23 28.2 28.29 29 29.34 24.8 Vrms (V) 17.19 8.66 19.4 19.31 20.32 27.37 Irms (A) 50.91 26.87 31.82 28.28 22.64 107.48 Power mechanical (W) 1182 1181 1185 1214 1229 1039 Core Loss (W) 20 15.9 10.6 8.68 12.48 38.05 Copper loss (W) 135 154 95 120 64 82.48 Efficiency (%) 88.23 87.3 91.75 90.36 94 89.25 Power factor 0.68 0.85 0.64 0.74 0.9 0.18 Weight Magnet (kg) 1.46 1.52 1.66 1.52 0.756 1.60 Weight Coil (kg) 4.05 4.01 3.6 2.4 1.56 1.61 Steel Weight (kg) 3.09 4.16 18.28 12.8 8.256 4.6 Total Weight (kg) 8.6 9.68 23.54 16.72 10.57 8.93 Torque Density (Nm/kg) 3.28 2.91 1.2 1.73 2.78 2.77 Volume (l) 3.18 3.37 3.58 3.26 1.79 4.05 Power density (kW/l) 0.37 0.35 0.33 0.37 0.68 0.26

4.4. Comparison At Medium Torque And Medium Speed Operation

The proposed E-core TFM is also compared with the other axial type machines. The specification for this comparison is given in Table 4.2. The motor is limited in the maximum allowable diameter and axial length. Electrically, the motor is limited to 21 A

RMS and a nominal DC bus voltage of 400 V. The motor will be thermally limited to a current density of 7 A/mm2. To achieve the desired specification rare earth NdFeB magnets with a remnant flux density of 1.21 T will be used. M270_35A lamination based toroidal tape wound cores will be used for the rotor and stator cores. The proposed E-core machine

111 is compared with traditional pancake type axial flux motors in this section. Different stator rotor combinations of axial flux machines are included in the comparison. The different topologies are single stator single rotor (SSSR), single stator double rotor (SSDR), double stator single rotor (DSSR).

Table 4.2: Motor specifications

Magnet NdFeb 35 SH Operation mode Continuous Current density max. 7 A/mm2 Rated Power 5.75 kW Rated Speed 2000 rpm Max Irms used 21 A Nominal Voltage 400 V Lamination M270_35A

The comparison constraints in this comparison are

 All machines have the same outer diameter and axial length. This allows for a better

comparison of volume.

 A current density between 6 and 6.7 A/mm2 is maintained at rated conditions.

 The combination of number of turns and currents is set to utilize a maximum DC bus of

400 V at the rated speed of 2000 rpm.

 The same lamination material and thickness is used.

 The same stator-rotor pole configuration is utilized.

 At rated condition, the peak flux density is maintained below 2 T.

 The same magnet material is used.

 The machines are optimized to obtain the same efficiency of 95%.

The results from 3D FEA of the motors are tabulated in Table 4.3. It is observed that among the different topologies the power factor is significantly different the machines with double 112 stator or double rotor, the magnetic circuit utilizes the available space better. As a result, the leakage flux and armature reactance are lower in those machines resulting in an improved power factor. This improved magnetic circuit of the dual stator or rotor machines due to more active airgap area results in those machines having an improved torque density and power factor. The double stator E-core machine attains a high power factor and torque density compared to the other motors.

Table 4.3: Comparison of the motors for compressor application.

Parameter SSSR SSDR NS SSDR NN DSSR NN DSSR NS E-core Stator poles 18 18 18 18 18 18 Rotor poles 12 12 12 12 12 12 Weight (kg) 7.73 6.90 7.79 7.49 6.72 6.91 Magnet weight (kg) 0.6 0.646 0.646 0.65 0.65 0.697 Average Torque (Nm) 28.35 28.82 31.14 28.12 29.7 28.37 Speed (rpm) 2000 2000 2000 2000 2000 2000 Power (kW) 5.9 6.03 6.5 5.9 6.2 5.94 Torque density (Nm/kg) 3.67 4.18 4 3.75 4.42 4.1 Current density (A/mm2) 6.72 6.45 6.53 6.36 6.7 6.22/6.36 Power factor 0.77 0.96 0.96 0.89 0.91 0.95 Iron loss (W) at 2000 116 118 112 109 123 101 rpm Copper loss (W) 251.5 269 276 256 254 212 Efficiency (%) 94 93.86 94.3 94 94.2 95

The fundamental of the back-emf, rms back-emf voltage, and the peak cogging torque is provided in Table 4.4. The SSSR machine attains the higher rms back-emf voltage and has a more sinusoidal shape. However, the cogging torque is the second highest in this design.

The E core machine has the second highest back-emf voltage but it also has a high cogging torque. The cogging torque is the lowest in the SSDR NS and DSSR NS designs. The airgap flux density is also the highest in the SSSR and E-core machine. However, the active airgap in the E-core is smaller thus, the RMS of airgap flux density is slightly higher. The smaller active airgap also results in higher change in airgap reluctance resulting in higher cogging

113 torque. The back-emf harmonics can be adjusted by changing the magnet-arc, slot-opening and pole shaping. Optimizations of these factors improve torque quality.

Table 4.4: Comparison of the back-emf, cogging torque, and airgap flux densities.

RMS back- Cogging Peak RMS airgap Fundamental emf voltage torque Peak Airgap flux flux density Harmonic (V) (V) (Nm) (T) (T) SSSR 169.81 120.96 1.56 1.05 0.795

SSDR NS 145.41 106.13 1 0.99 0.681

SSDR NN 155.06 112.2 1.11 0.99 0.671

DSSR NN 148.69 107.78 0.7 1.02 0.699

DSSR NS 147.38 106.7 0.75 0.99 0.672

E-core 160.149 115.36 3 1.55 0.824

The electrical properties of the machines are shown in Table 4.5. The inductance is the highest in the SSSR combination due to a higher amount of windings. The NS structures in both the SSDR and DSSSR have higher inductance compared to their NN counterparts due to higher reluctance paths. The saliency in all of the surface magnet designs is nearly

1. The E-core machines with the flux focusing magnets attain a higher saliency. The torque- speed curves of the machines are shown in Fig 4.18.

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Table 4.5: Comparison of electrical parameters of different machines.

Parameter SSSR SSDR NS SSDR NN DSSR NN DSSR NS E-core

Stator poles 18 18 18 18 18 18

Rotor poles 12 12 12 12 12 12

PM flux linkage (V.s) 0.136 0.118 0.124 .119 0.118 0.126 q-axis inductance (mH) 4.13 0.196 2.27 2.13 2.23 3.5 d-axis inductance (mH) 4.01 0.195 2.08 2.11 2.09 2.7

Figure 4.18: Torque-speed characteristics of designed machines.

The torque speed curve is evaluated with maximum torque per ampere operation in the constant torque region until the base speed and flux weakening operation until maximum possible speed. It can be observed that the SSSR combination has a high inductance due to higher number of turns. The higher inductance aids in better flux weakening above the base speed. From the analysis, it is clear that the SSDR and DSSR structure has lower operating range due to lower inductance. The SSSR provides the best option for operation over a wide speed range due to comparatively higher inductance. From the analysis, it is

115 demonstrated that for this application E-core machine offers the best balance of high operating range, torque density, and power factor.

4.5. Conclusions

This chapter presented a detailed electromagnetic analysis demonstrating the electromagnetic characteristics of the proposed TFM topology has also been presented in this chapter. The single phase, two phase with stator displacement and three phase version of the E-core machine was analyzed in 3D FEA. The analysis showed that the proposed machine has a lower flux leakage as all the cores are utilized. The machine was studied under different current conditions to validate the robustness of the design against short circuit current and demagnetization. Simulations with ideal current sources also illustrated the machines load characteristics.

Comparison of the proposed E-core TFM with other topologies of motors in two different specifications is also presented. The first was for a 1 kW 400 rpm direct drive wind turbine.

The comparison showed that the E-core TFM attains a high torque density comparable to rare earth based radial flux PM machines. The benefit of the E-core machine compared to the Z-core has also been demonstrated. A multiphase embodiment of the E-core machine has also been designed and compared with different axial flux machine topologies for a compressor application at 6 kW and 2000 rpm. The E-core machine demonstrated good performance at base speed in terms of power factor, torque density and efficiency. The machine also demonstrated a wide constant power range compared to dual stator AFM.

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CHAPTER V

WINDING CONFIGURATION, MODELING, AND ANALYSIS OF E-CORE TFM

5.1. Introduction

The dissertation in the previous chapters presented the design of the proposed machine.

This chapter will present a new winding configuration with its underlying operating principle and its associated control algorithms. The two-phase embodiment of the proposed

E-core machine is then modeled in the rotating reference frame. The modeled machine is used for controller development, performance analysis and stability analysis of the machine.

5.2. Winding Configuration for Flux Weakening

This dissertation proposes to achieve electrical flux weakening on a dual stator E-core

TFM. Dual stator machines offer a new degree of flexibility in the control in the sense that the two stators can be controlled separately. The winding configurations in stators are an important aspect of this machine. Two winding strategies are proposed and studied for their effectiveness in flux weakening operation. Each set of the winding structure has its own set of advantages and disadvantages and the right winding configuration should be selected based on the desired application.

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5.2.1. Proposed Winding Configurations The case study machine consists of two coils on each stator. This research investigates how the windings are to be connected to the inverter. The top coil and bottom coil of the phase would occupy the slots as shown in Fig. 5.1(a). The standard connection for the coils in a single-phase machine would be to connect them in parallel or series as shown in Fig.

5.2.

Magnet AT AT AT AT AT AT x x x Core Flux path Winding out AB AB AB AB AB AB x x x Winding x in

(a) Magnet AT1 AT1 AT1 AT1 AT1 AT1 x x x AT2 AT2 AT2 AT2 AT2 AT1 Core x x x Flux path Winding AB1 AB1 AB1 out AB1 AB1 AB1 x x x AB2 AB2 AB2 Winding AB2 AB2 AB2 x x x x in

(b) Figure 5.1: a) Coils for standard configuration A, b) Coils for configuration B. Another alternative method is to use two single-phase inverters. Here the top and bottom coils are controlled by two sets of switches as shown in Fig. 5.3. This type of configuration requires another inverter but with half of the original power ratings. The proposed inverter and winding configuration also results in a magnetic and electric isolation between the two 118 sides of the machine. The isolation between the phases provides flexibility in implementing current shaping to achieve torque ripple minimization. However, the lack of coupling between the two sides means that both the coils need to be simultaneously controlled for flux weakening operation. This configuration is referred to as winding configuration A in the rest of the dissertation.

S1 S3 S1 S3 AT

Vdc AB AT AB Vdc

S4 S2 S4 S2

(a) (a) Parallel connection (b) Series connection Figure. 5.2: Standard connection of coils.

S1 S3 S5 S7

Vdc AT AB

S4 S2 S8 S6

Figure. 5.3: Winding configuration A. Winding configuration A has very small interactions between individual winding sets hence a second configuration is proposed. Here through manipulation of the end windings, it would be possible to split individual coils into two as shown in Fig. 5.1(b) and connect the partitioned turns from individual stators in series. Hence, we would still end up with

119 the same number of turns. The proposed structure thus has two coil sets in the same slot increasing the coupling between the two coil sets and two sides of the machine. The corresponding connection with the inverter for this coil configuration is shown in Fig. 5.4.

This winding configuration is referred to as winding configuration B for the rest of the proposal.

S1 S3 S5 S7

Vdc AT-1 AB-2 AT-2 AB-1

S4 S2 S8 S6

Figure. 5.4: Winding configuration B. The mutual interaction through winding configuration B would enable the use one set of windings as torque production winding and the other one as a flux weakening control winding. It is also possible to profile the currents in the two winding sets for torque ripple minimization. In all three winding and inverter configurations, the slot utilization and total terminal resistance of the coils would remain the same.

5.2.2. Machine Models The circuit model of the machine when using the standard configuration can be described by:

푑휆 (5.1) 푉 = 𝑖푅 + 푠 푑푡 120 where, V is the coil voltage, i is the phase current Rs is the phase resistance and 휆 is the flux of the coil. The flux is dependent on the rotor position and phase current which can be described by:

휆 = 휆푠+휆푀+휆푃푀 (5.2) where, 휆푠 is the flux due to self-inductance, 휆푀 is the flux due to mutual inductance and

휆푃푀 is the flux due to the PM. Flux weakening in this configuration is achieved by applying a phase advance between the currents and the PM flux. The torque in this configuration can be described as:

1 푑퐿 1 푑퐿 푑휆 푇푒 = 𝑖2 푠 + 𝑖2 푚 + 𝑖 푀 (5.3) 2 푑휃 2 푑휃 푑휃

As the two coils are separated in sides there would be minimal mutual inductance, and the major torque components would be PM and reluctance torque.

In winding configuration B the top and bottom coil sets are controlled separately. Thus the voltage equation for the top and bottom sets are given by:

푉 = 𝑖 푅 +푑휆1 (5.4) 1 1 푠 푑푡 푉 = 𝑖 푅 +푑휆2 (5.5) 2 2 푠 푑푡 The resulting flux linkages are given as:

휆1 = 휆푠+휆푀+휆푃푀 (5.6) = 𝑖1퐿푠+𝑖2퐿푀+휆푃푀

휆2 = 휆푠+휆푀+휆푃푀 (5.7) = 𝑖2퐿푠+𝑖1퐿푀+휆푃푀

The PM flux per coil is half of that being applied in standard configuration. The torque therefore in this topology can be expressed as:

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1 푑퐿 1 푑퐿 푑휆 푇푒 = (𝑖 + 𝑖 )2 푠 + (𝑖 + 𝑖 )2 푚 + (𝑖 + 𝑖 ) 푀 (5.8) 2 1 2 푑휃 2 1 2 푑휃 1 2 푑휃

Here, the torque production responsibility is shared by the two inverters. This adds an added fault tolerance to the machine as it would still be possible to operate with one winding in case of damage in a particular coil. The switch ratings are also halved as the total current is being processed by two parallel switches.

The fluxes in the two coils are linked through the mutual inductance as:

퐿푚푊푎 = 푘푎√퐿푠푊푎퐿푠푊푎 (5.9) where,푘푎 is the coupling, and 퐿푠푊푎 and 퐿푚푊푎 are the self and mutual inductances of winding configuration A. In this topology due to a large physical separation between the coils, it is assumed that 푘푎~0. The coupling and mutual inductance through the rotor is ignored at this stage. The self-inductance can be calculated as:

푁2 퐿 = (5.10) 푠푊푎 ℝ where, N is the number of turns and ℝ is the reluctance of the coil.

The presence of the mutual inductance would provide a greater flexibility in the control.

This is achieved through the proposed coil configuration discussed in the previous section.

Splitting the coil into two with equal turns results in Eqn. (5.11) for the self-inductance.

푁 푁 ( )2 ( )2 1 퐿 = 2 + 2 = 퐿 (5.11) 푠푊푏 ℝ ℝ 2 푠푊푎

The mutual inductance is now given by

퐿푚푊푏 = 푘푏√퐿푠푊푏퐿푠푊푏 (5.12)

122

In this case the coupling coefficient 푘푏 can be defined as 1, due to the two coils sharing the same slot space in both the top and bottom windings. The value of the self-inductance is halved but it is compensated by the mutual inductance. With the proposed winding configuration, it is possible to apply phase advancing in only one set and keep the other set for the torque production. This results in improving the torque per ampere during flux weakening operation.

5.2.3. Three Phase Machine Drive and Model The proposed winding configuration can also be extended to three-phase machine with dual stators. This section presents the three-phase model of the TFM with proposed winding configuration. The standard inverter to drive three phase TFM is shown in Fig.

5.5.

AH BH CH

Vdc

AL BL CL

AT BT AB BB

CB CT Figure 5.5: Three phase inverter for standard connection of TFM. The corresponding model of the TFM in synchronous dq reference frame is given as:

푑 푉 = 푟 𝑖 + 휆 − 휔 휆 (5.13) 푑 푠−푠푡푑 푑 푑푡 푑 푟 푞

푑 푉 = 푟 𝑖 + 휆 + 휔 휆 (5.14) 푞 푠−푠푡푑 푞 푑푡 푞 푟 푑

휆푑 = 퐿푑−푠푡푑 𝑖푑 + 휆푃푀 (5.15)

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휆푞 = 퐿푞−푠푡푑𝑖푞 (5.16)

3 푃 푇 = [휆 𝑖 + (퐿 − 퐿 )(𝑖 𝑖 )] (5.17) 푒 2 2 푃푀 푞 푑−푠푡푑 푞−푠푡푑 푞 푑 where, V is the phase voltage, 푟푠 is the phase resistance, i is the current, 휆 is the flux linkage,

L is the inductance and 휔푟 is the speed. The subscripts d and q refer to the standard, direct and quadrature axis of the magnet orientation. In this winding and converter topology, flux weakening is achieved by injecting negative d-axis current to reduce the d-axis flux. The inverter configuration when using winding configuration A and B is shown in Fig. 5.6 and

5.7. Here the two full-bridge inverters control the two sets of windings. The two full- bridges in this configuration is rated at half the current in comparison to the full-bridge used in the standard configuration. The three phases in each sets are Y connected to facilitate vector control. The neutrals in the two Y-connected systems are isolated. This independence between the two sets make the drive system more fault tolerant.

S1 S3 S5 S7 S9 S11

Vdc

S4 S6 S2 S10 S12 S8

AT BT AB BB

CT CB

Figure 5.6: Two sets of inverters for winding configuration A.

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S1 S3 S5 S7 S9 S11

Vdc

S4 S6 S2 S10 S12 S8

AT-1 BT-1 AT-2 BT-2 AB-2 BB-2 AB-1 BB-1 CB-2 CB-1 CT-1 CT-2 Figure 5.7: Two sets of inverters for winding configuration B.

The voltage equations of winding configuration A and B for vector control is given in Eqn.

(5.18)-(5.21). The phase resistance, in this case, is half that of the phase resistance in the standard configuration.

푑 푉 = 푟 𝑖 + 휓 − 휔 휓 (5.18) 푑1 푠 푑1 푑푡 푑1 푟 푞1

푑 푉 = 푟 𝑖 + 휓 − 휔 휓 (5.19) 푑2 푠 푑2 푑푡 푑2 푟 푞2

푑 푉 = 푟 𝑖 + 휓 + 휔 휓 (5.20) 푞1 푠 푞1 푑푡 푞1 푟 푑1

푑 푉 = 푟 𝑖 + 휓 + 휔 휓 (5.21) 푞2 푠 푞2 푑푡 푞2 푟 푑2

The difference between configuration A and B arises in flux linkage equations. The PM flux linkage is also divided into the two windings sets. In winding configuration A there is no mutual coupling through the current as demonstrated by Eqn. (5.22)-(5.25).

휓푑1 = 퐿푑푊퐴𝑖푑1 + 휓푃푀 (5.22)

휓푑2 = 퐿푑푊퐴𝑖푑2 + 휓푃푀 (5.23)

휓푞1 = 퐿푞𝑖푞1 (5.24)

휓푞2 = 퐿푞𝑖푞2 (5.25)

125

The flux linkage for winding configuration B is given by Eqn. (5.26)-(5.29). Due to the coils sharing the same slot there is a mutual inductance between the two sets. Thus, the application of a negative d axis current in one phase weakens the flux and reduces the voltage in both of the sets. This would allow greater flexibility in the control where one set could be used for torque control (through the q-axis) and the other handles torque and flux weakening control.

휓푑1 = 퐿푑푊퐵𝑖푑1 + 퐿푚푑푊퐵𝑖푑2 + 휓푃푀 (5.26)

휓푑2 = 퐿푚푑푊퐵𝑖푑1 + 퐿푑푊퐵𝑖푑2 + 휓푃푀 (5.27)

휓푞1 = 퐿푞푊퐵𝑖푞1 + 퐿푚푞푊퐵𝑖푞2 (5.28)

휓푞2 = 퐿푚푞푊퐵𝑖푞1 + 퐿푞푊퐵𝑖푞2 (5.29)

Similar to the model of a single phase machine the following equation illustrates the relationship between the three structures in terms of self and mutual inductances in the dq axis.

퐿푑−푠푡푑 = 2퐿푑푊퐴 = 4퐿푞푊퐵

퐿푞−푠푡푑 = 2퐿푞푊퐴 = 4퐿푞푊퐵 (5.30)

퐿푚푞푊퐵 = 푘푏퐿푞푊퐵 퐿푚푑푊퐵 = 푘푏퐿푑푊퐵

5.2.4. Inductance of E-Core Machine The proposed analytical expressions are verified on the E-core TFM. The unaligned and aligned inductances of the two configurations at different current levels for the case study machine are shown in Table 5.1. The inductances were found through FEA simulations where only the one set of windings are excited and another set was kept at zero.

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Table 5.1: Aligned and unaligned inductances for winding configuration A and B.

Winding Configuration A

Ls (mH) Lm (mH)

Current Aligned Unaligned Aligned Unaligned

20 0.492 0.438 1.48e-4 0.071

40 0.440 0.388 1.47e-4 0.058

80 0.418 0.264 1.43e-4 0.042

Winding Configuration B

Ls (mH) Lm (mH)

Current Aligned Unaligned Aligned Unaligned

20 0.249 0.243 0.196 0.188

40 0.247 0.237 0.192 0.188

80 0.246 1.94 0.191 0.157

From Table 5.1, it is observed that the self-inductance in winding configuration B is lower compared to winding configuration A. However, this is compensated by the increased mutual inductance in winding B compared to winding configuration A. The mutual inductance present in winding configuration A is due to the rotor linking the two sides of the stator. At higher currents with high saturations, it can be observed that the difference between the self-inductances for the two windings is lower. This is due to a lower saturation of the core in winding configuration B since the current is passed through two stator slots.

5.2.5. Simulation Results

The effectiveness of the proposed method was observed in two conditions using FEA analysis. In this first condition, only one of the two sides was current controlled with rated current and the other phase was kept open. The current advance angle was swept and the 127 effect of voltages was observed. The results are plotted in Fig. 5.8 a) and Fig. 5.8 b).With winding configuration B, the back emf voltage can be reduced in both the controlled and open terminals proportionately due to mutual inductances. In winding configuration A, the advance angle affects the controlled phase greatly. Furthermore, since only one side is utilized in the machine stator the voltages are also higher due to increased armature reaction. The open terminal voltage in this case increases slowly because it offers an alternate flux path for the additional field weakening flux. The effect of advancing one set of coils and keeping the other one at a constant advance angle is also illustrated in Fig. 5.8 c) and 5.8 d) in terms of maximum and rms terminal voltages respectively. It can be observed that in winding configuration A, when A1 is advanced the voltage of A2 (non advanced coil) remains constant or slightly increases as there is no mutual interaction between A1 and A2. However, in winding configuration B, when B1 is advanced the voltage of B2 (non advanced coil) also gets reduced. This illustrated the possibility of using one set for flux weakening when using configuration B. The presented analysis is performed at the rated speed of 400 rpm.

(a) Effect of first coil’s advance angle on the (b) Effect of first coil’s advance angle on the rms maximum open circuit voltage of the second coil. open circuit voltage of the second coil.

128

(c) Effect of advance angle on one set of coil with (d) Effect of advance angle on one set of coil with second having no advance angle, on maximum second having no advance angle, on rms terminal terminal voltage voltage Figure 5.8: Effect of current advance angle of first coil on terminal voltage on second coil. The effect of this winding topology on the dynamic characteristics of the machine is shown in Fig. 5.9 to 5.11. In winding configuration A, the same advance angle is applied to both the sets as their respective terminal voltages are independent. In winding configuration B, one set of coils is used for flux weakening and the other for torque production. At higher speeds, both sets are used for flux weakening but at different ratios in winding configuration B. Due to the presence of mutual inductance and greater control flexibility, winding configuration achieves a better torque-speed characteristic as shown Fig 5.9. The torque per ampere above base speed is also better in winding configuration B as shown in

Fig 5.10. The proposed machine with winding configuration B achieves a high constant power speed range (CPSR) of 4 despite a low saliency ratio as shown in Fig 5.11.

129

Figure 5.9: Effect of winding configuration on Figure 5.10: Effect of winding configuration on torque-speed curve. torque per ampere at rated current.

Figure 5.11: Power-speed curve at rated configuration for different winding configuration.

5.3.Rotating Reference Frame Model of Two Phase E-Core Machine

The space vectors of a two phase E-core machine is shown in Fig. 5.12. These space vectors represent the orientation of the winding fluxes. The winding fluxes with time varying currents synchronized in the proper phase create the rotating magnetic field required for torque production. The two winding fluxes of phases a and b are placed so that there exists a 90-degree electrical phase shift between them. The orthogonal currents phase moves

130 around the physical a-b axis of with the rotor position defined by 휔푡, where 휔 is the rotor speed in rad/s and 푡 is the time.

b axis

q axis d axis d q b wt

a a axis

Figure 5.12: Space vector representation of two phase machine. The winding flux in the proposed machine varies in a sinusoidal manner. As a result, a sinusoidal winding current is necessary. The sinusoidal variation of the current complicates the current control of the machine. A simpler strategy is to develop a rotating reference with respect to the physical reference frame. The speed of the rotation of the rotating reference frame is synchronized with the rotating magnetic field such that AC variation can be decoupled. An example of the rotating dq axis reference frame is illustrated in Fig. 5.12.

The rotating reference frame facilitates analysis of the of dynamics other than the fundamental due to the machines rotation and greatly simplifies control. The transformation matrix between the two co-ordinate systems can be defined for an array of

X as:

푋 cos (휃) − sin(휃) 푋 [ 푎] = [ ] [ 푑] (5.31) 푋푏 sin(휃) cos(휃) 푋푞

Where the 휃 = 휔푡

Similarly,

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푋 cos (휃) sin(휃) 푋 [ 푑] = [ ] [ 푎] (5.32) 푋푞 − sin(휃) cos(휃) 푋푏

Thus, the transformation matrix can be defined as

cos (휃) − sin(휃) 0 1 푇 = [ ] = 푒퐽휃 where 퐽 = [ ] (5.33) sin(휃) cos(휃) −1 0

The flux linkage of proposed machine can be represented as

휆푎푏(휃) = 퐿푎푏(휃)𝑖푎푏 + 휆푃푀(휃) (5.34)

퐿푠 −퐿푚 퐿푎푏(휃) = [ ] (5.35) −퐿푚 퐿푠

Applying the transformation matrix

−퐽휃 −퐽휃 푒 휆푑푞 = 퐿푎푏(휃)푒 𝑖푑푞 + 휆푃푀(휃) (5.36)

퐽휃 −퐽휃 퐽휃 휆푑푞 = 푒 퐿푎푏(휃)푒 𝑖푑푞 + 푒 휆푃푀(휃) (5.37)

휆푑푞 = 퐿푑푞𝑖푑푞 + 휆푃푀푑 (5.38)

The voltage equations

푑휆 푣 = 푎푏 + 푟 𝑖 (5.39) 푎푏 푑푡 푎푏 푎푏

Therefore applying transformation and chain rule,

푑휆 푒−퐽휃푣 = 푒퐽휃 푎푏 + 푟 푒−퐽휃𝑖 + 퐽휔 휆 (5.40) 푑푞 푑푡 푎푏 푑푞 푟 푑푞

After simplification the voltage equations in the rotating reference frame are

푑 푉 = 푟 𝑖 + 휆 − 휔 휆 (5.41) 푑 푠 푑 푑푡 푑 푟 푞

푑 푉 = 푟 𝑖 + 휆 + 휔 휆 (5.42) 푞 푠 푞 푑푡 푞 푟 푑

132 where,

휆푑 = 퐿푑𝑖푑 + 휆푃푀 (5.43)

휆푞 = 퐿푞𝑖푞 (5.44)

Thus, the voltage equations can also be expressed as:

푑 푉 = 푟 𝑖 + 퐿 𝑖 − 휔 퐿 𝑖 (5.45) 푑 푠 푑 푞 푑푡 푞 푟 푞 푞

푑 푉 = 푟 𝑖 + 퐿 𝑖 + 휔 퐿 𝑖 + 휔 휆 (5.46) 푞 푠 푞 푑 푑푡 푑 푟 푑 푑 푟 푃푀

The power equation can be given by

푝푒 = 푣푑𝑖푑 + 푣푞𝑖푞 (5.47)

퐿 푑 퐿 푑 푝 = 푟 𝑖2 + 푟 𝑖2 + 푑 𝑖2 + 푞 𝑖2 + 휔 휆 𝑖 − 휔 휆 𝑖 (5.48) 푒 푠 푑 푠 푞 2 푑푡 푑 2 푑푡 푞 푟 푑 푞 푟 푞 푑

The electromagnetic torque is due to the last two terms and can be given by

푝푒푚 = 휔푚푇푒 = 휔푟휆푑𝑖푞 − 휔푟휆푞𝑖푑 (5.49) where 휔 = 푃 휔 , 푟 2 푚

푃 푇 = (휆 𝑖 − 휆 𝑖 ) (5.50) 푒 2 푑 푞 푞 푑

푃 푇 = (휆 𝑖 + (퐿 − 퐿 )𝑖 𝑖 ) (5.51) 푒 2 푝푚 푞 푑 푞 푞 푑

The relationship between the electromagnetic torque and the mechanical system can be defined by

2 푑휔 2 푇 = 퐽 푟 + 퐵 휔 + 푇 (5.52) 푒 푚 푃 푑푡 푚 푃 푟 푙

133 where, 푇푙 is the load torque, 퐽푚 is the inertia of the rotor and the connected load, 퐵푚 is the viscous friction coefficient. In steady state, the current dynamics disappear and the voltage equations can be defined by

푉푑 = 푟푠𝑖푑 − 휔푟퐿푞𝑖푞 (5.53)

푉푞 = 푟푠𝑖푞 + 휔푟퐿푑𝑖푑 + 휔푟휆푃푀 (5.54)

The steady state vector diagram is given in Fig 5.13.

q-axis va RsIs Ldid Is l0 iq V0 b Lqiq d

id lPM d-axis

Figure 5.13: Steady-state vector diagram of machine in dq reference frame. 5.4. Control of E-core Machine

The E-core machine can operate in 4 different control trajectories. They are defined as:

1. Field oriented control where 𝑖푑 = 0

2. Maximum torque per ampere control (MTPA).

3. Flux weakening control.

4. Maximum torque per voltage control.

5. Unity power factor control.

5.4.1. Id=0 Control

In this control method, only the q-axis current is commanded and regulated. The machine in this control method would only produce PM torque. 134

5.4.2. Maximum Torque Per Ampere Control (MTPA)

In machines with reluctance and PM torque, an optimum level of current between the dq- axis needs to be employed to obtain the maximum torque per ampere. The MTPA equation can be derived by differentiating the torque equation with respect to the maximum possible current. To aid this process the current can be expressed in terms of vectors as

𝑖푑푠 = −𝑖푠푠𝑖푛훽 (5.55)

𝑖푞푠 = 𝑖푠푐표푠훽 (5.56)

The torque equation can then be expressed as

푃 푇 = (휆 𝑖 푐표푠훽 + 0.5(퐿 − 퐿 )𝑖2푠𝑖푛2훽) (5.57) 푒 2 푝푚 푠 푞 푑 푠

The angle 훽 with the maximum torque per ampere can then be expressed by

푑푇 푃 푒 = (휆 𝑖 (−푠𝑖푛훽) + (퐿 − 퐿 )𝑖2푐표푠2훽) = 0 (5.58) 푑훽 2 푝푚 푠 푞 푑 푠 which can be written as

2 2 2 −(휆푝푚𝑖푠(푠𝑖푛훽) + (퐿푞 − 퐿푑)𝑖푠 (cos 훽 − sin 훽)) = 0 (5.59)

2 2 (휆푝푚𝑖푑푠 + (퐿푞 − 퐿푑)(𝑖푞푠 + 𝑖푑푠)) = 0 (5.60)

2 2 (퐿푞 − 퐿푑)𝑖푑푠 + 휆푝푚𝑖푑푠 + (퐿푞 − 퐿푑)𝑖푞푠 = 0 (5.61)

(5.62) 휆 1 2 푃푀 2 2 𝑖푑푠 = + √휆푃푀 + 4(퐿푞 − 퐿푑) 𝑖푞푠 2(퐿푞 − 퐿푑) 2(퐿푞 − 퐿푑)

135

휆 휆2 푃푀 푃푀 2 𝑖푑푠 = + √ + 𝑖푞푠 2(퐿 − 퐿 ) 2 푞 푑 4(퐿푞 − 퐿푑) (5.63)

The torque from the corresponding q-axis current can be determined from

2 2 2 2 (4휆푃푀 − 4(퐿푑 − 퐿푞) 𝑖푞 + 4(휆푃푀 − 4푇푒)휆푃푀𝑖푞 + (휆푃푀 − 4푇푒) (5.64) 2 − 3푃휆푃푀 = 0

5.4.3. Flux Weakening Control

Flux weakening control: In this control strategy, the d-axis flux linkage is controlled via the d-axis armature current, which allows the flux to be weakened. The flux weakening control strategy is typically employed above the base speed where the applied phase voltage is limited by the available DC bus voltage. The voltage can be expressed as

2 2 푉 = √푣푞푠 + 푣푑푠 (5.65)

If the resistive losses are neglected the voltage can be expressed as

2 2 푉 = √(휔푟퐿푑𝑖푑 + 휔푟휆푃푀) + (−휔푟퐿푞𝑖푞) (5.66)

If the maximum allowable voltage is 푉표푚 the equation can be expressed as

2 푉표푚 2 2 ( ) = (퐿푑𝑖푑 + 휆푃푀) + (퐿푞𝑖푞) (5.67) 휔푟

From this relation the d-axis current can be given by

2 2 (휔푟퐿푑𝑖푑 + 휔푟휆푃푀) + (−휔푟퐿푞𝑖푞) (5.68)

136

2 휆푃푀 1 푉표푚 2 𝑖푑 = − + √(( ) + (퐿푞𝑖푞) ) (5.69) 퐿푑 퐿푑 휔푟

5.4.4. Maximum Torque Per Voltage Control (MTPV)

Maximum torque per voltage control: This control method tracks the optimal current vector for maximum torque per voltage. This can be expressed as follows from [243]

휆푃푀 + Δ휆푑 𝑖푑 = − (5.70) 퐿푑

2 √휆0 + Δ휆푑 𝑖푞 = (5.71) 퐿푞

2 2 −퐿 휆 + √(퐿 휆 ) + 8(퐿 − 퐿 ) 휆 푞 푃푀 푞 푃푀 푞 푑 0 (5.72) Δ휆푑 = 4(퐿푞 − 퐿푑)

5.4.5. Unity Power Factor Control

Unity power factor control: In this control, the power factor is desired to be unity.

Therefore, the angle between phase current vector and the voltage vector is zero as:

푣푞푠 𝑖푞푠 = = 푐표푠휙 (5.73) 푣푑푠 𝑖푑푠

From this using the previous notations and considering power factor as unity, the d-axis current can be expressed as

2 2 −휆푃푀 ± √(휆푃푀) − 4퐿푞퐿푑𝑖푞 𝑖푑 = (5.74) 2퐿푑

5.5.Characteristic Curves and Dynamic Simulation of E-Core Machine

The electrical parameters of the machine were calculated from FEA and used to model the machine in the dq reference frame. The machine parameters are tabulated in Table 5.2. 137

Table 5.2: Key electrical parameters of the machine.

Power 1.2 kW

Torque 28 Nm

Speed 400 rpm

Max Speed 1600 rpm

No. of poles 30

No. of slots 30

Flux linkage (휆푃푀) 0.0270 Vs/rad

q-axis inductance 0.514 (mH)

d-axis inductance 0.5 (mH)

The phase plane plot of the machine with the MTPA trajectory is shown in Fig 5.14. Due to very little saliency, the MTPA almost always tracks the Id=0 curve. The torque curve along the phase plane is also not highly elliptical because of low saliency. The characteristic current is defined as

휆 퐼푐ℎ = 푃푀 (5.75) 퐿푑

In the proposed motor, the characteristic current is lower than the current limit. Hence, the machine would operate at maximum torque per volt trajectories (MTPV). The machine would transition into MTPV at 800 rpm when the MTPV intersects the current limit.

138

Figure 5.14: Phase plane characteristics of the E-core machine. The torque speed curves at different rated currents are illustrated in Fig. 5.15. The corresponding torque per ampere is shown in Fig. 5.16. The machine operates at MTPA upto 600 rpm. After that, the machine operates in FW and MTPV operating modes where extra current is required to weaken the flux. The machine does not demonstrate any saturation as the characteristics are attained from a linear model.

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Figure 5.15: Torque-speed curve of proposed machine at different current levels.

Figure 5.16: Torque per ampere curve of proposed machine for entire operating range.

140

A Simulink model based on the linearized dq model is developed for dynamic simulation and verification of the proposed machine. The currents in the abc and dq reference frame is given in Fig. 5.17 and 5.18. The torque waveform is illustrated in Fig. 5.19. The back- emf and flux linkage profile in the dq model does not include space harmonics associated with machine. As a result, torque ripple is not evident from this simulation. However, this model is fast and provides a good reference for the controller development.

Figure 5.17: Phase current in abc domain in Figure 5.18: Phase current in dq domain in dynamic simulation with dq model. dynamic simulation with dq model.

Figure 5.19: Torque in dynamic simulation with dq model.

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A detailed model of the machine is developed using flux maps from FEA (lookup table

(LUT) model). The controller for this simulation is developed using dq model of the machine. A transient performance of the machine is shown in Fig. 5.20 where the machine is ramped upto 400 rpm with a 10 Nm constant load torque.

Figure 5.20: Torque, speed currents from transient simulation. A closer look at the torque waveform illustrates that the motor torque has a ripple content.

This due to the presence of space harmonic effects on the flux linkage maps. The torque and current waveforms at rated conditions is illustrated in Fig 5.21 – 5.23. The torque is

142 slightly lower at the rated current as the models were built from 1st order FEA simulation data which underestimates the torque.

Figure 5.21: Phase current in abc domain in Figure 5.22: Phase current in dq domain in dynamic dynamic simulation with LUT model. simulation with LUT model.

Figure 5.23: Torque waveform in dynamic simulation with LUT model. 5.6.Stability analysis of E-core machine

The PM machine in the dq reference frame voltage equations, torque equations and mechanical equations can be linearized to perform small signal stability analysis. The

143 stability analysis indicates the operating points at which the system is vulnerable to get disturbances that would cause the machine to become unstable in open loop control. To linearize the machine a new parameter defined as the load angle is introduced. It is expressed as

훿 = 휃푒 − 휃푟 (5.76) where, 휃푒 and 휃푟 are the electrical angular position of the stator voltage vector and the rotor position respectively. This was demonstrated in the vector diagram in Fig. 5.13. The derivative of the new parameter results in a new state equation expressed as

푝훿 = 휔푒 − 휔푟 (5.77)

The new notation of 훿 is also used to express the dq voltages as

푣푞 = 푣표푐표푠훿 (5.78)

푣푑 = −푣표푠𝑖푛훿 (5.79)

Substituting the new voltage equations into the main voltage equations results in

푑 푣 푐표푠훿 = 푟 𝑖 + 퐿 𝑖 + 휔 퐿 𝑖 + 휔 휆 (5.80) 표 푠 푞 푑 푑푡 푑 푟 푑 푑 푟 푃푀

푑 −푣 푠𝑖푛훿 = 푟 𝑖 + 퐿 𝑖 − 휔 퐿 𝑖 (5.81) 표 푠 푑 푞 푑푡 푞 푟 푞 푞

The torque equation also can be expressed as

푃 2 푑휔 2 (휆 𝑖 + (퐿 − 퐿 )𝑖 𝑖 ) = 퐽 푟 + 퐵 휔 + 푇 (5.82) 2 푝푚 푞 푑 푞 푞 푑 푃 푑푡 푚 푃 푟 푙

The four differential equations can be expressed in state variable form as

𝑖푞 휔푟 휆푃푀 푣표푐표푠훿 푝𝑖푞 = − − ( + 𝑖푑) + (5.83) 휎휏푠 휎 퐿푑 휎퐿푑

144

𝑖푑 푣표푠𝑖푛훿 푝𝑖푑 = − + 휎휔푟𝑖푞 − (5.84) 휏푠 퐿푑

1 푃 2 1 푃 푝휔 = ( ) (휆 𝑖 + 퐿 (1 − 휎)𝑖 𝑖 ) − 퐵 휔 − 푇 (5.85) 푟 퐽 2 푃푀 푞 푑 푞 푑 퐽 푚 푟 2퐽 푙

푝훿 = 휔푒 − 휔푟 (5.86) where, the saliency ratio and the electrical time constant is defined as

퐿푞 휎 = (5.87) 퐿푑

퐿푑 휏푠 = (5.88) 푟푠

The state variable equations are in the form of

푥̇ = 푓(푥, 푢) (5.89)

The equations are then linearized to result in

Δ푥 = 퐴(푋)Δ푥̇ + 퐵(푋)Δ푢 (5.90)

Where, Δ푥 and Δ푢 is the perturbation for the state variable 푥 and system inputs, 퐴(푋) and

퐵(푋) is the transition matrix and input matrix.

The state equations are linearized using the small perturbation as

푥푖 = 푋 + Δ푥푖 (5.91)

The resulting linearized model of the machine can be expressed as:

145

Δ𝑖푞 Δ𝑖 푝 [ 푑 ] Δ휔푟 Δ훿

1 휔표 1 휆푃푀 푣표 − − − ( + 퐼푑푠) − sin (훿표) 휎휏푠 휎 휎 퐿푑 휎퐿푑 Δ𝑖푞 1 푉푠 휎휔 − 휎퐼 − 푐표푠훿 Δ𝑖 = 표 휏 푞푠 퐿 0 [ 푑 ] 푠 푑 Δ휔 1 푃 2 1 푃 2 퐵 푟 ( ) (휆 + 퐿 (1 − 휎)퐼 ) ( ) (퐿 (1 − 휎)퐼 ) − 푚 0 Δ훿 퐽 2 푃푀 푑 푑 퐽 2 푑 푞 퐽 (5.92) [ 0 0 −1 0 ]

cos(훿 ) 0 0 표 푠𝑖푛훿표 − 0 0 Δ푣표 퐿푑 + [Δ휔푒] 푃 0 0 − Δ푇푙 2퐽 [ 0 1 0 ]

where the state transition matrix is

1 휔표 1 휆푃푀 푣표 − − − ( + 퐼푑푠) − sin (훿표) 휎휏푠 휎 휎 퐿푑 휎퐿푑 1 푉푠 휎휔 − 휎퐼 − 푐표푠훿 퐴(푋) = 표 휏 푞푠 퐿 0 푠 푑 1 푃 2 1 푃 2 퐵 (5.93) ( ) (휆 + 퐿 (1 − 휎)퐼 ) ( ) (퐿 (1 − 휎)퐼 ) − 푚 0 퐽 2 푃푀 푑 푑 퐽 2 푑 푞 퐽 [ 0 0 −1 0 ]

The eigen values of the transition matrix represent the system poles. The location of the poles in the s-plane indicates the system’s stability characteristics. The eigen values of the poles are determined from the solution of the determinant given by:

det (푠퐼 − 퐴(푥)) = 0 (5.96)

The eigen value plot of the machine at different excitation frequency at no load is shown in Fig 5.24. The eigenvalues corresponding to the stator poles (electrical system poles) lie in the far left half plane of the machine. The eigenvalues corresponding to the rotor and mechanical dynamics lie near right half plane of the s-plane, with the eigenvalues in going

146 into instability at certain frequencies. The zoom in plot of the rotor poles is shown in Fig

5.25.

Figure 5.24: Eigen value plot with different frequency at no load.

Figure 5.25: Zoom into the rotor poles at no load.

147

The eigen value plot of the machine at different excitation frequency and at different load is shown in Fig 5.26. The current trajectory at different loads and frequency is determined from the optimum control region at that point (MTPA,FW or MTPV). The eigenvalues corresponding to the stator dynamics move towards the right half plane of the of motor as the load increases. The eigenvalues of the rotor is shown in Fig 5.27. It can be observed that as the load increases the system becomes more damped and moves to the left half plane of the machine.

Figure 5.26: Eigen value plot with different frequency at different loading conditions.

148

Figure 5.27: Zoom into the rotor poles at different loads. 5.7. Conclusion

This chapter presents the study of different winding configurations for double stator TFM.

A new winding configuration is proposed which increases the constant power range of the machine. The new winding structure maintains the same winding resistance and simplicity while offering the flexibility of torque profiling and a greater flux-weakening region. At low speeds and low torque, only one winding set is utilized for torque production. As the torque, increases both of the winding sets can be utilized. At higher speeds, one set is dedicated only for torque production and the other one has additional responsibility of flux weakening control, thereby extending the flux-weakening region. This also results in the machine requiring a lower rms current compared to standard winding schemes where both 149 sets are advanced. The configuration also proposes the use of parallel power semiconductor devices for increasing the overall drive efficiency.

The chapter also presented a rotating reference frame model of the E-core machine in its two-phase embodiment. The dq model of the drive system enabled the use of conventional

3-phase PM motor control techniques in the proposed motor. The performance of the machine with the model throughout the operating conditions was presented.

The dq model was linearized to perform small signal stability analysis on the proposed motor. A new parameter, which is the difference between the excitation and rotating frequency, was introduced for the linearization. The analysis was used to identify the operating points at which the motor is susceptible to position error. It also demonstrated whether the machine could operate in volt/hertz control. The analysis showed that there is not enough damping for the machine to operate in volt/hertz control.

150

CHAPTER VI

EXPERIMENTAL PROTOTYPING AND RESULTS

6.1. Introduction

The E-core machine presented in this dissertation has been prototyped in house for proof of concept. This chapter presents the process for building the prototype machine. The machine is then tested on a load cell for verification of simulation results. The prototype could be configured to operate at different air gaps and with multiple phase shifts between the two sides. The winding was also made such that the winding configurations proposed in chapter IV could be tested experimentally.

6.2. Mechanical Prototype Development

The exploded view of proposed machine with the mechanical structure is shown in Fig.

6.1. The cut view of the machine is shown in Fig 6.2. The back stands support the stator pieces and rotor housing supports the rotor pieces, which are glued in using epoxy (Epoxy

ET538) from Permabond Company. An outer ring shown in Fig 6.2 provides further rigidity from centrifugal force.

151

Outer belt Back Stand Bearing Stator core

Shaft

Stator Rotor Rotor core pieces housing Figure 6.1: Exploded view of the machine with mechanical supports.

Backstand

Outer ring Rotor Housing Bearing Lamination and magnet Shaft pieces

Figure 6.2: Cut view of the machine with mechanical supports. The modular rotor cores and magnets are cubes, which makes the cutting and stacking simpler. The rotor cores are made of lamination steel (M19) stacked together. The inner and outer rotor cores’ have the same dimensions. Therefore, only two lamination cuts are required for the rotor. Individial lamination sheets of M270_35A at 29 gauge (0.35 mm) were cut according to the required dimensions and welded to required width. The final

152 rotor blocks are shown in Fig. 6.3. Similarly, Y30 grade ferrite magnets for flux concentration and leakage reduction in the required dimensions was procured. The magnets for the protoype are shown in Fig 6.4.

Figure. 6.3: Rotor cores of the prototype. Figure. 6.4: Ferrite magnets of the prototype.

Figure. 6.5: Rotor housing with shaft and bearing. The rotor cores are attached to a non-magnetic disk. Aluminum 6061 plates were machined into the required dimension to act as the non-magnetic disk for holding the rotor pieces.

Carbon steel 14L was used for the shaft. The machined rotor housing with the shaft is

153 shown in Fig. 6.5. Radial ball bearings are to be used in this prototype. A single layer of the rotor core with the magnets is already glued together and as shown in Fig. 6.6. Once all the rotor core pieces were glued a holding gig was used for the assembly with the rotor housing. The holding gig is shown in Fig 6.7. The holding gig is made from Delrin material which does not react with epoxy and does not stick with it. The rotor housing, shaft and the rotor core pieces for assembly are shown in Fig 6.8.

Figure 6.6: Single stack of rotor with three rotor cores Figure 6.7: Rotor assembly gig machine from a and two magnets. block of Delrin.

154

Figure 6.8: Process of assembling rotor stacks to rotor housing with rotor gig.

Once the epoxy solidifies the connection between the active materials and the rotor housing the holding gig is removed. The reverse side of the holding gig is then used to provide the flat surface and the middle rotor pieces are inserted as shown in Fig. 6.9. In both the cases, rubber bands are used to provide the compression necessary during the curing process.

After the epoxy settles, an aluminum ring is inserted for counteracting centrifugal forces.

The epoxied rotor is shown in Fig. 6.10. It can be observed that at this stage the epoxy resulted in uneven airgap at the rotor surface. This airgap was smoothed using a precision sanding setup by turning the machine on a lathe and controlling the distance of the rotating sandpaper on a roll. A vacuum was also used to collect the dust from the sanding process.

A picture of the setup is shown in Fig. 6.11. The complete rotor after sanding is shown in

Fig 6.12.

155

Figure 6.9: Leakage flux reduction magnets and plastic Figure 6.10: Complete rotor after epoxying. spacers inserted to complete rotor.

Figure 6.11: Setup for smoothing rotor surface. Figure 6.12: Complete rotor after sanding.

The E-core is also manufactured by stacking lamination steel (M19). The stator cores are attached to a supporting plate at the two ends. The back stands were also machined out from Aluminium 6061. The machined out back stand is shown in Fig. 6.13. The stator cores were connected to the endplates via structural epoxy. The final back stands with the stator cores are shown in Fig 6.14. The back stands also have supporting holes around the stator core slots. These holes are machined so that the shift between the top and bottom stator

156 plates can be realized. This would aid the verification of the cogging torque reduction technique.

Figure 6.13: Stator back stand. Figure 6.14: Back stand with the stator cores epoxied in.

Semi-ring windings were used to ease the manufacturing. The edges of the stators were not beveled thus a thick coat of insulation was required to prevent the windings from scratching and shorting. Heat shrinks were used to aid this process. In this design, this step was carried out after the assembly of the stator with the housing. In hindsight, it would be better to insulate the stator cores before assembly with the back-stands. The stators after insulation are shown in Fig 6.15. The windings were made using AWG 15 gauge magnet wire. The forms were initially made and then inserted into the stator housing. The form-wound windings are shown in Fig. 6.16. The windings were then inserted into the slots and varnished. The combination of varnish and elasticity of the winding helped secure it to the stator. The final stator core is shown in Fig 6.17, The sides of the stator core were also covered with slot liner. The entire process was hand wound thus the slot fill factor was lower than initially envisioned. This resulted in a prototype with higher than expected resistance and current density. The edges of the stator core were also covered with slot liner for added insulation. Thus, the prototyped machine had degraded thermal capability than 157 expected. This would lower the efficiency of the experimental machine. The completed stator and rotors were then assembled as shown in Fig. 6.18.

Figure 6.15: Stator after insulating E-core. Figure 6.16: Form wound coils by hand winding.

Figure 6.17: Final Stator core with windings Figure 6.18: Complete prototyped machine. and insulation.

6.3. Development of TFM Drive The TFM drive for evaluating the experimental prototyped was developed using a commercial inverter and a dSpace controller. The drive consists of two APS IAP300T

(300A 850V) inverters connected in a back to back configuration to attain the desired 6-

158

Phase Bridge inverter. In each case, only 4 bridges will be used. The other two bridges would not be utilized. The drive can operate with switching frequencies up to 10 kHz upto

600 A peak currents. An interface board for communication between the drive and the controller has been developed. The interface board provides the buffers and necessary voltage shifts needed for the PWM gate signals. The interface boards also condition the current for input by the ADC of the controller. A DSpace MicroAutobox is used as the controller. The inverter, interface boards, control boards and the complete drive systems are shown Figs 6.19-6.22 respectively.

Figure 6.19: Drive for testing TFM.

159

Figure 6.20: Interface board for testing TFM. Figure 6.21 dSpace controller for testing TFM.

Figure. 6.22: Complete drive and controller setup for testing TFM. The TFM motor was coupled with Parker servomotor through a torque transducer as shown in Fig 6.23. The parker motor was used as a motor/generator for no-load and load testing of the prototyped machine. The setup is shown in Fig 6.23. An external fan was used for cooling the stators of the prototyped machine.

160

Figure 6.23: Mechanical setup of TFM coupled with servomotor through torque transducer. 6.4. Motor Controller

The prototyped machine was operated as motor for experimental verification. A simple dual band hysteresis based controller was used to regulate the current and a PI controller to regulate the speed. The block diagram of the controller in single phase is shown in Fig.

6.24. The inverter setup and the hysteresis controller is shown in Fig. 6.25 and 6.26 respectively. The dual band hysteresis current control allows the inverter to apply magnetization (+VDC), Freewheeling (0V) and demagnetization (–VDC). The small band controls one switch and regulates the current between magnetization and freewheeling as only S1 switches and S2 is the opposite of S1. When there is a large current error, the second S2 switch also switches with the same command as S1applying magnetization or 161 demagnetization voltage. The polarity of the current determines whether the small band control S1 or S2 and vice versa.

A Current ref I Speed ref reference Error calculation Controller generation Bref

Er Er wref a b +- w w Hysteresis Speed q Controller Estimator Gate signals dSpace controller Interface Board and I I a b Inverter

PMSM TFM LOAD

Figure 6.24: Block diagram of a single phase TFM controller.

Small band

S1 S3 S5 S7 S1 Hysteresis Controller Error Vdc AT AB

S2 S4 S2 S8 S6 Hysteresis Controller Large band

Figure 6.25: Inverter configuration for a single phase Figure 6.26: Dual band hysteresis current TFM. regulator for single phase TFM. A dq based controller was used for the two phase embodiment of the proposed machine.

The block diagram of the controller is shown in Fig. 7.27. The controller diagram of the

162 current regulator is shown in Fig 6.28. In this case, the regulation is in the dq domain facilitating a narrower current regulation band.

Vq Va Gate S1 S3 S5 S7 w Speed Iq Current Sine ref + dq-ab signalsVdc AT AB Controller Regulator V - Vd b PWM S4 S2 S8 S6 w Id Inverter MTPA Id Ia w And FW Ib controller Iq ab-dq Ic q q Speed Estimator w LOAD TFM From encoder Figure 6.27: dq based field oriented controller (FOC) for two phase TFM.

lpm Ldwr

+ I Vqref qref + PI + + - + Rs Iqact

Ldwr

Lqwr

Idact Rs - + - I Vdref dref + PI +

Figure 6.28: Current regulator for two phase machine in dq domain. 6.5. Experimental results This section presents the experimental results of the experimental prototype. Initially the discrepancies between the designed and actual machine is highlighted. The results of the experiments are presented to validate the proposed concept.

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6.5.1. Discrepancies in Construction The prototype is developed as a proof of concept motor to demonstrate the fundamental operation of the novel TFM structure. The rotor structure in the concept involved trapezoidal magnets in leakage reduction magnets. However, to minimize cost all of the magnets were made to be rectangular. Figure 6.29 demonstrates the original rotor structure and the further simplified rotor structure. Due to modification, the total airgap flux decreased slightly which would result in lower airgap flux density.

Rotor core Leakage reduction magnet Flux focusing magnet

a) Proposed b) Simplified design design for cost reduction Figure 6.29: Rotor structure of proposed machine and built prototype. The total lamination stack were in the experimental prototype was desired to be 8.25 mm in peripheral direction. However, the lamination thickness of 0.343 mm resulted in achieving only 8.1788 mm with a stacking factor of a 92%. Furthermore, the same stacking factor could not be achieved in all of the stator cores and a tolerance of ±0.02mm was observed. The laminations in the prototype were stacked together through spot welding.

This resulted in a shorts across the laminations that would increase the core loss and would degrade the magnetic properties of the material.

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The setup shown in Fig. 6.30 was used to measure the BH curve of the stator cores after welding. The schematic of the set is shown in Fig 6.31. The magnetic field strength was calculated from the measured input current using the following Eqn.

푁 퐼 (7.1) 퐻 = 푝 푝 푙푒푓푓

Where, 푁푝 is the number of turns in the primary, 퐼푝 is primary current and 푙푒푓푓 is the effective length of the core. The voltage in the second from Faraday’s law can be expressed as

푑휙 (7.2) 푉 = 푁 푠 푠 푑푡

Where, 푉푆 is the secondary voltage, 푁푠 is the number of turns in the secondary, 휙 is the flux in the core.

The Opamp in the circuit given in Fig. 6.31 operates as an integrator as,

푑푉 푉 (7.3) 표푢푡 = − 푠 푑푡 푅1퐶1 Using this in Faraday’s law, the flux density can be calculated as

푉 퐶 푅 (7.4) 퐵 = − 표푢푡 1 1 푁푠퐴푒푓푓 where, 퐴푒푓푓 is the effective core area.

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Figure 6.30: Setup for measuring BH curve.

Oscilloscope

Current sensor

AC C1 Primary

R1 + Secondary -

GND1 Integrator Figure 6.31: Schematic of setup for measuring BH curve. Figure 6.32 presents the measured hysteresis curve of the magnetic core. The corner points of the hysteresis curve are obtained by changing the excitation voltage from the AC source.

The corner points are then used to obtain the static magnetization curve of the material.

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Figure 6.32: BH curve from experiment. The static BH curve from the experiment and the expected curve is shown in Fig. 6.33. It can be observed that there was a 5% discrepancy. The difference could be attributed to degradation of the magnetic properties during the stacking process. The magnet grade was also different in the experiment compared to the initial design. In the initial design, the magnet had a remnant flux density of 0.4 T. However, in the experiment the magnets had a remnant flux density of 0.32 T.

Figure 6.33: Static magnetic characteristics of expected and experimentally evaluated material.

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6.5.2. Experimental Verification The machine was tested in different scenarios to demonstrate the correlation between the theoretical development and experimental proof of concept machine. The scenarios are

 Case 1: Single phase machine at 2.80 mm airgap.

 Case 2: Single phase machine at 1.80 mm airgap.

 Case 3: Single phase machine at 1.35 mm airgap.

 Case 4: Single phase machine at 1.28 mm airgap with 4 degree shift between two

sides.

 Case 5: Two phase machine at 1.28 mm airgap.

No-load back emf voltages at different speeds were obtained for all the different airgaps.

The machine was operated at under load in Case 1 and 2. Due to high cogging torque and limitations of the torque transducer load testing could not be performed on the single phase machine at lower airgaps. Case 1 was also used to verify the effectiveness of the winding configuration A and configuration B. The experimental verification section first presents the complete results at Case 1, followed by the results in Case 5. The results from Case 2 to 4 is then used to verify some of the design aspects of the machine such as cogging torque.

6.5.2.1. Case 1: Single Phase Machine at 2.8 mm Airgap

The no-load back-emf voltage waveform from the experiment at 400 rpm is shown in Fig.

6.34. The back-emf from FEA is plotted using markers on top of experimental data. A close correlation was observed between the experimental results and FEA simulation.

Table 6.1 details the difference in RMS back-emf voltages between the experiment and the

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FEA simulations. The FEA in this case underestimates the back-emf voltage but overestimates the cogging torque due to meshing issues. It was observed in simulations that the exact location of the coils affected the back-emf voltage but did not affect the cogging torque.

Figure 6.34: Back-emf voltage from experiment and FEA.

Table 6.1: No-load voltages at different speeds.

Speed Back-emf voltage from Back-emf voltage from FEA % difference experiments (V) (V) (Br=0.32T)

200 2.323 2.318 0.2%

400 4.586 4.65 1.386%

600 6.798 6.954 2.26%

800 9.119 9.271 1.65%

The machine was tested under the load by connecting the machine output to a programmable dc load through a diode rectifier. The average torque at different reference current peaks for the simulation and experiment is shown in Fig. 6.35. The average torque

169 at different rms currents is shown in Fig 6.36. It is observed that there is a good correlation at higher currents but a poor one at low currents. The difference is starker when comparing torque per rms current. This difference can be attributed down to the difference in the current harmonics in the FEA simulations and in experiments. In FEA, only the fundamental harmonic is present. However, switching frequency harmonics are present.

The effect of the switching harmonics on the currents is more profound at low current levels. Thus, the difference between FEA and experiment is largest at low current levels.

The current at a load of 4.65 Nm is shown in Fig 6.37. and at 1.18 Nm in Fig 6.38. The current shape could have been improved by increasing the switching frequency. In the experiments, it was limited to a maximum of 10 kHz.

Figure 6.35: Average torque vs peak reference Figure 6.36: Average torque vs rms current. current.

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Figure 6.37: Phase current at a 4.65 Nm average Figure 6.38: Phase current at 1.18 Nm average torque. torque. 6.5.2.2. No-Load Back-emf Voltage At Different Airgap

The developed prototyped incorporated a manufacturing design that allowed for varying the airgap. Table 6.2 illustrates the back emf voltage at different airgaps and the finite element results. The waveform of the back-emf voltage and the FEA is shown in Fig. 6.39.

It can be observed that as the airgap is reduced the experimental machine experiences slightly larger flux leakage than previously predicted and thus the difference is higher.

However, the % difference is still acceptable.

Table 6.2 No load voltage at different airgap.

Speed Airgap =2.8 mm Airgap 1.8 mm Airgap 1.25 mm

(rpm) Experiment FEA Experiment FEA Experiment FEA Back-emf Back-emf Back-emf Back-emf Back-emf Back-emf voltage (V) voltage (V) voltage (V) voltage (V) voltage (V) voltage (V) 200 2.32 2.32 3.05 3.11 3.62 3.76

400 4.59 4.65 6.05 6.14 7.11 7.19

600 6.79 6.95 9.04 9.20 10.65 10.80

800 9.12 9.27 12.09 12.27 14.4 14.70

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Figure 6.39: Comparison of back-emf voltage in experiment with FEA results at different airgap at 400 rpm.

6.5.2.3. Cogging Torque at Different Airgap And Stator Displacement

The cogging torque in the prototyped machine has been evaluated at different airgaps and different stator displacements. The results from experiments and FEA are tabulated in

Table 6.3. There is a good correlation between the expected and actual cogging torque with a maximum of 15% error with the 2.2-degree shift between the two-stator sides. This can be attributed to differences between measured airgap and actual airgap. Another cause for discrepancies is the mesh accuracy at high airgap. The experiments indicate that as airgap increases the cogging torque increases. It also proves that as a shift between the bottom and top stator cores result in cogging torque reduction as proposed in Chapter III.

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Table 6.3: Cogging torque at different airgap and stator displacement.

Experiment FEA Condition Cogging torque Cogging torque % Difference (Nm) (Nm) Airgap = 2.8 mm 5.5 5.2 4.6 No shift Airgap = 1.8 mm 8.6 9.2 6.7 No shift Airgap = 1.25 mm 13 12.7 2.5 No shift Airgap = 1.25 mm 6.8 7.9 14.6 2.2 degree shift Airgap = 1.25 mm 1.9 1.9 2.1 3 degree shift

6.5.2.4. Winding Inductance and Flux Weakening

The winding inductances of the machine at different air gaps was measured using an RCL meter at 100 Hz frequency. The inductances at different air gaps are tabulated in Table 6.4.

It can be observed that the mutual inductance is very low in winding configuration A. The mutual inductance is higher in winding configuration B. As the airgap decreases the inductance also increases for both the winding configurations as the reluctance decreases with reducing airgap.

Table 6.4: Measured winding inductance with different winding configuration.

Total Self- Self- Mutual series Winding Air gap inductance inductance inductance inductance configuration coil A1 (H) coil A2 (H) (H) (H) 2.54 4.69E-04 4.57E-04 9.04E-04 -1.08E-05 A 1.60 4.84E-04 4.83E-04 9.28E-04 -1.92E-05 A 1.25 5.06E-04 4.90E-04 9.43E-04 -2.66E-05 A 2.54 2.72E-04 2.79E-04 9.18E-04 1.84E-04 B 1.60 2.75E-04 2.82E-04 9.30E-04 1.86E-04 B 1.25 2.77E-04 2.84E-04 9.44E-04 1.92E-04 B 173

The winding configurations in Chapter V was also verified during the dynamic operation of the machine. The flux weakening action of winding configuration A and B was tested by controlling the machine through one coil and keeping the other one open. The fundamental of the back-emf voltage on the open coil was calculated for different advance angles. The results are shown in Fig. 6.40. It can be observed that the voltage trends in the open coils are similar to that found in FEA simulations. The data experimentally verified the flux weakening capability of winding configuration B by just advancing one coil.

Figure 6.40: Fundamental of the back-emf voltage in open coil when coil 1 is advanced. 6.5.2.5. Case 5: Two phase machine at 1.28 mm airgap

The stator of the prototype machine was shifted by 30 mechanical degrees to affect an electrical phase shift of 90 degrees between the top and bottom stator sides. This resulted in the two phase embodiment of the proposed E-core machine. The two phase machine has

174 lower cogging torque at smaller airgaps and facilitates the control of the machine in the rotating reference frame.

The no-load voltages of the two phase machine is shown in Fig. 6.41. The back-emf voltage contains 3rd and 7th harmonics. The frequency spectrum of the back emf is shown in Fig 6.42. The back-emf voltage rms from the simulation is 7.85 V and it is 7.54 V in the experiment. i.e. 4 % difference.

Figure 6.41: Back-emf voltage of two phase machine at 400 rpm.

Figure 6.42: Frequency spectrum of back-emf voltage of two phase machine at 400 rpm. 175

The machine in the two phase configuration could now be controlled with a dq current regulator. The current wave shapes from hysteresis and dq current regulators are shown in

Fig 6.43. It can be observed that the switching ripple is higher in the hysteresis controller resulting in a larger current envelope. The currents with the dq current regulators has a higher switching frequency and track the current better.

(a) Current with hysteresis controller at 3 Nm, 400 (b) Current with dq controller at 3 Nm, 400 rpm. rpm.

(d) Current with dq controller at 4 Nm, 400 rpm. (c) Current with hysteresis controller at 4 Nm, 400 rpm.

Figure 6.43: Current waveforms with different current regulators at two sample load points.

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The current and torque waveforms of the machine operating at 400 rpm and 9.4 Nm torque is shown in Fig. 6.44 and 6.45. The torque is measured by the torque transducer. It can be observed that the torque has a high torque ripple and harmonic content. This can be attributed to the spatial harmonics of the back emf waveform.

Figure 6.44: Phase current at 400 rpm and 9.4 Nm torque.

Figure 6.45: Torque at 400 rpm with peak current reference of 44 A. The load as a function of the rms current at rms currents at 400 rpm is shown in Fig. 6.46.

The current regulation is poor at low currents due to low inductance and switching

177 frequency. As a result, the torque per ampere is lower. At higher currents, the torque per ampere improves. The torque per ampere of the machine at 400 rpm is shown in Fig. 6.47.

The power factor of the proposed machine at 400 rpm is shown in Fig. 6.48. It can be observed that as the current increases the power factor presents a good correlation with the

FEA simulations. The results at 600 rpm are shown in Fig 6.49-6.51. The data was captured using a WT 3000 power analyzer

Figure 6.46: Average torque vs rms current at 400 rpm.

Figure 6.47: Torque per ampere vs rms current at Figure 6.48: Power factor vs rms current at 400 400 rpm. rpm.

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Figure 6.49: Average torque vs rms current at 600 rpm.

Figure 6.50: Torque per ampere vs rms current at Figure 6.51: Power factor vs rms current at 600 600 rpm. rpm. The maximum tested torque at 600 rpm as the machine required a higher voltage or flux weakening to operate. The power factor at both the speeds was found to be greater than

0.72 at higher. This is closely correlated with the simulated power factor calculations.

6.6. Conclusion

In this chapter, the experimental prototyping procedure and results of the proof of principle machine are presented. The prototype was developed in-house with the laminations and magnets procured from outside vendors. The procedure for prototyping the proof of principle machine was presented. An experimental setup using a commercial inverter drive 179 and dSpace controller were setup for testing the prototype. The machine was coupled to a commercial servomotor for load tests through a torque transducer. The machine was tested in different air gaps and stator displacements between the two sides. A good correlation between the experimental results and FEA simulation was observed. The experimental results validated the working principle of the prototype machine, the design procedure, cogging torque reduction techniques, flux weakening through different winding topologies and a high power factor.

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CHAPTER VIII

CONCLUSION AND FUTURE WORK

7.1. Conclusions

This dissertation presented the design, analysis, prototyping and experimental evaluation of a novel dual stator flux concentrated transverse flux machine (TFM) with an axial airgap. The proposed machine provides higher torque densities compared to conventional machine types and is very effective in direct drive applications where machines are operated at high torque and low speed.

The machine consisted of two E-core shaped stators with pole or semi-ring windings for guiding the flux to/from the middle leg of the E-core from/to the inner and outer legs of the E-core. A rotor with flux concentrated ferrite magnets was sandwiched between the two stators. The flux was concentered to the rotor core corresponding to the middle leg of the stator core with transverse and longitudinally oriented magnets. The flux concentration allowed the use of ferrite magnets to attain high airgap flux densities.

The novel machine topology increased the magnet and core utilization to achieve a high torque density and power factor. The dissertation focused on the design, winding configurations, control and experimental implementation of the novel machine.

Chapter II presented a literature review of the state of the art in radial flux machine (RFM), axial flux machine (AFM) and TFM. The review primarily focused on

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machines designed for direct drive applications and machines with 3D flux paths (AFM and TFM). The review on TFM outlined the benefits and drawbacks of different TFM machine topologies. This chapter also included a review of modeling, cogging torque reduction, and wide speed operation of AFMs and TFMs.

Chapter III presented the design of the novel E-core TFM. The machine was developed based on the power factor analysis of the U-core machine. It was found that the power factor could be improved by utilizing all three-rotor cores. An E-core shaped stator facilitated better use of the rotor core. To achieve this pole or semi-ring windings need to be used. Analytical sizing equations for the E-core machine and a design methodology based on the sizing equations were developed. A 1 kW 400 rpm machine is designed based on the sizing equations and then fine-tuned using 3D FEA. This chapter also presented different design considerations for cogging torque minimization in TFMs.

A three-stage design of experiment (DOE) based optimization method was used for cogging torque minimization.

Chapter IV presented the electromagnetic analysis of the proposed machine topology using 3D FEA. The electromagnetic performance of the machine at no-load and rated load conditions was evaluated. The machines robustness against demagnetization in short circuit conditions were also evaluated. It was found that the designed machine was robust against demagnetization up to twice the rated d-axis current. Also in this chapter, the proposed E-core machine was compared with other machine topologies in two applications. The first application was a 1 kW 400 rpm direct drive application. The machine was compared with other RFMs and the U-core TFM. It was found that the proposed E-core machine achieved a high torque density and power factor. The machine's 182

performance was comparable to rare-earth based RFMs in terms of power density. The second application was for driving a compressor load. A 5.75 kW 2000 rpm motor was required for the specifications. In this application, the proposed E-core machine was compared with different AFMs. It was found that the proposed machine achieved an ideal balance of high torque density, power factor and operating speed range. The other topologies had deficiencies in either one of these characteristics to meet the required specification.

Chapter V presented different winding strategies for controlling the dual sided

TFM. A split winding topology where one winding consists of the bottom and top sides are connected in series is proposed. This topology results in larger mutual inductance between the two coils at the cost of lowering self-inductance. The mutual inductance allows one side to control only the torque and the other to control the flux weakening.

Thereby, allowing greater control flexibility. The two-phase embodiment of the machine was then modeled in the rotating dq reference frame. The dq model was used to develop a dynamic simulation and current controllers for the machine. A lookup table based simulation was also established to include space harmonic effects of the machine. The last section of Chapter V presented the small signal analysis of the proposed machine.

The analysis indicated the machines robustness to position sensor error at different operating points.

Chapter VI presented prototyping and experimental validation of the proposed machine topology and winding configurations. The proof of principle machine was prototyped in-house using simplified magnet shapes for cost reduction. The prototyping led to further insights on steps to follow to make the proposed machine. An experimental 183

test platform, based on a commercial inverter and a dSPACE controller was setup for verifying the machine’s performance.

The main contributions of this thesis can be summarized as:

 A literature review was conducted on existing RFM direct drive machines.

 A literature review was conducted on AFM and TFM topologies, modeling and sizing

of machines with 3D flux paths

 A novel double-sided E-core TFM with flux concentrating magnets is proposed.

 Analytical sizing equations, design methodology and cogging torque reduction

techniques for the proposed machine topology is developed.

 A novel winding configuration for dual stator machines is developed and applied to

the proposed E-core machine. The winding configuration enables better flux

weakening, and a larger constant power speed range.

 A rotating reference frame based model of the two-phase embodiment of the

proposed E-core transverse flux machine developed. The model is used to derive

different controllers, evaluate dynamic performance of the machine.

 A small signal stability analysis of the E-core machine for its entire operating range is

presented. The analysis demonstrated the points at which the proposed machine is

most susceptible to position sensing noise.

 A comparison of the proposed E-core machine with radial and axial flux machines is

presented for two different applications.

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 A prototype of the proposed E-core machine is fabricated in the Alternative Energy

Laboratory of the University of Akron as a proof of principle machine and

experimental validation.

 An experimental platform was established for rapid controller implementation and

testing.

7.2. Future Work

This dissertation presented a novel TFM topology capable of achieving a high torque density with non-rare earth magnets and a high power factor. The research presents a host of different options for future work. They are listed as:

 Develop a procedure for more accurate and automated manufacturing of the proposed

machine topology.

 Develop a wide bandgap based drive for the machine to switch at higher frequencies

to improve current control.

 Prototype and validate the performance of the three phase version of the proposed

TFM.

 Investigate the parameter sensitivity due to the tolerance of manufacturing on the

proposed machine with respect to performance.

 Investigate slot-pole combinations of the proposed three phase E-core TFM.

 Investigate the avenues for incorporating torque ripple minimization and sensorless

control algorithms used in synchronous machines as the machine.

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APPENDIX I: Matlab Scripts

A1: Script for generator torque-speed and performance curve from electrical parameters clear all close all clc lambdaPM=0.0270; n=30; Lq=0.5147e-3; Ld=0.5e-3; wmax = 1600; wstep=50; i=1; IImax= 72; Istep = 6; Vdc = 48; Rs = 0.02656; sq =2/pi; sp = 1/sqrt(3); Si = 0.5;

Vam = 1*Vdc;

Ich= -lambdaPM/Ld; k=1; for Imax=1:Istep:IImax+1; for w=0:wstep:wmax; wr=0.5*n*w*pi/30; id1= lambdaPM/(4*(Lq-Ld)) - sqrt(((lambdaPM^2)/(16*(Lq- Ld)^2))+0.5*Imax^2); iq1= sqrt(Imax^2-id1^2);

id2=(lambdaPM*Ld-sqrt((lambdaPM*Lq)^2+(Lq^2-Ld^2)*((Lq*Imax)^2- (Vam/wr)^2)))/(Lq^2-Ld^2); iq2= sqrt(Imax^2-id2^2); if (id2^2>Imax^2) id2=0; iq2=0; end

wr=0.5*n*w*pi/30; Dl=(-Lq*lambdaPM+sqrt((Lq*lambdaPM)^2+8*((Lq- Ld)^2)*(Vam/wr)^2))/(4*(Lq-Ld)); id3= -(lambdaPM+Dl)/Ld; iq3 = sqrt((Vam/wr)^2-Dl^2)/Lq; Im3 =sqrt(id3^2+iq3^2); V3 = wr*sqrt((Ld*id3+lambdaPM)^2+(Lq*iq3)^2);

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idy(i)=id3; iqy(i)=iq3;

V1 = wr*sqrt((Ld*id1+lambdaPM)^2+(Lq*iq1)^2); if V1<=Vam; id(i)=id1; iq(i)=iq1; Te(i)=(n/2)*(lambdaPM*iq1+(Ld-Lq)*iq1*id1); vq(i)=-wr*Lq*iq1; vd(i)= wr*(Ld*id1+lambdaPM); end if V1>Vam id(i)=id2; iq(i)=iq2; Te(i)=(n/2)*(lambdaPM*iq2+(Ld-Lq)*iq2*id2); vq(i)=-wr*Lq*iq2; vd(i)= wr*(Ld*id2+lambdaPM); end

if (Im3

i=i+1; end w=0:wstep:wmax; we=w*pi/30; %plot(w,Te); %plot(w,Te.*we); hold on; IDD(:,k)=id; IQQ(:,k)=iq; TEE(:,k)=Te; XX(:,k)=w; k=k+1; i=1; end %% Torque speed curve at diff. levels figure(1) plot(w,TEE) xlabel('Speed (rpm)') ylabel('Torque (Nm)') title('Torque v Speed Characteristics')

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figure(2) plot(w,IDD) xlabel('Speed (rpm)') ylabel('d axis current (A)') title('d axis current v Speed Characteristics') figure(3) plot(w,IQQ) xlabel('Speed (rpm)') ylabel('q axis current (A)') title('q-axis current v Speed Characteristics')

TpA=TEE./sqrt(IDD.^2+IQQ.^2); figure(6) contourf(XX,TEE,TpA) xlabel('Speed (rpm)') ylabel('Torque per ampere (Nm/A)') title('Torque per ampere v Speed Characteristics') figure(5) plot(w,TpA(:,end)) xlabel('Speed (rpm)') ylabel('Torque per ampere (Nm/A)') title('Torque per ampere v Speed Characteristics')

Pw=400; i=1; for w=0:wstep:wmax; i=i+1; if Pw==w break; end end figure(4) plot(sqrt(IDD(i,:).^2+IQQ(i,:).^2),TEE(i,:)) xlabel('Current') ylabel('Torque (Nm)') title('Torque vs current')

A2: Script for stability analysis of E-core TFM

% clear all % close all % clc P=30; Bm=0.04; 208

J=0.033; Rs = 0.02656; Lq=0.5147e-3; Ld=0.5e-3; lambdaPM=0.0270; Ts=Ld/Rs; sigma = Lq/Ld; RatedI = 72; Is=1*RatedI; wmax = 200; wstep=1; Vdc = 48; sq =2/pi; sp = 1/sqrt(3); Si = 0.5; Vam = 1*Vdc; i=1; for w=0:wstep:wmax; wr=w*2*pi; if Is>0

id1= lambdaPM/(4*(Lq-Ld)) - sqrt(((lambdaPM^2)/(16*(Lq- Ld)^2))+0.5*Is^2); iq1= sqrt(Is^2-id1^2);

id2=(lambdaPM*Ld-sqrt((lambdaPM*Lq)^2+(Lq^2-Ld^2)*((Lq*Is)^2- (Vam/wr)^2)))/(Lq^2-Ld^2); iq2= sqrt(Is^2-id2^2);

Dl=(-Lq*lambdaPM+sqrt((Lq*lambdaPM)^2+8*((Lq- Ld)^2)*(Vam/wr)^2))/(4*(Lq-Ld)); id3= -(lambdaPM+Dl)/Ld; iq3 = sqrt((Vam/wr)^2-Dl^2)/Lq; Im3 =sqrt(id3^2+iq3^2); V3 = wr*sqrt((Ld*id3+lambdaPM)^2+(Lq*iq3)^2); idy(i)=id3; iqy(i)=iq3;

V1 = wr*sqrt((Ld*id1+lambdaPM)^2+(Lq*iq1)^2); if V1<=Vam; Id(i)=id1; Iq(i)=iq1; Te(i)=(P/2)*(lambdaPM*iq1+(Ld-Lq)*iq1*id1); Vd(i)=Rs*iq1-wr*Lq*iq1; Vq(i)= Rs*id1+wr*(Ld*id1+lambdaPM);

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end if V1>Vam Id(i)=id2; Iq(i)=iq2; Te(i)=(P/2)*(lambdaPM*iq2+(Ld-Lq)*iq2*id2); Vd(i)=Rs*iq2-wr*Lq*iq2; Vq(i)= Rs*id2+wr*(Ld*id2+lambdaPM); end

if (Im3

else Ids=0; Iqs=0; Vds=0; Vqs=wr*lambdaPM; end % alpha=acos(-1/(Is*Ld*(1-sigma^2))-sqrt((1/(Is*Ld*(1- sigma^2)))^2-sigma^2/(1-sigma^2))); % Iqs=Is*sin(alpha); % Ids=Is*cos(alpha); % Vds=Rs*Iqs-wr*Lq*Iqs; % Vqs= Rs*Ids+wr*(Ld*Ids+lambdaPM); i=i+1; A=[ -1/(sigma*Ts) -wr/sigma -(1/sigma)*(lambdaPM/Ld + Ids) Vds/(sigma*Ld); sigma*wr -1/Ts sigma*Iqs -Vqs/Ld ; (1/J)*((P/2)^2)*(lambdaPM+Ld*(1-sigma)*Ids) (1/J)*((P/2)^2)*(Ld*(1-sigma)*Iqs) -Bm/J 0; 0 0 -1 0]; E=eig(A);

figure(1)

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plot(E,'X','markersize',2,... 'MarkerEdgeColor','green') grid on; xlabel('Real part (rad/s)') ylabel('Imaginary part (rad/s)') hold on; end x=[1 30 60 120 200] i=1; for h=1:1:5; w=x(i); wr=w*2*pi; if Is>0

id1= lambdaPM/(4*(Lq-Ld)) - sqrt(((lambdaPM^2)/(16*(Lq- Ld)^2))+0.5*Is^2); iq1= sqrt(Is^2-id1^2);

id2=(lambdaPM*Ld-sqrt((lambdaPM*Lq)^2+(Lq^2-Ld^2)*((Lq*Is)^2- (Vam/wr)^2)))/(Lq^2-Ld^2); iq2= sqrt(Is^2-id2^2);

V1 = wr*sqrt((Ld*id1+lambdaPM)^2+(Lq*iq1)^2); if V1<=Vam; Id(i)=id1; Iq(i)=iq1; Te(i)=(P/2)*(lambdaPM*iq1+(Ld-Lq)*iq1*id1); Vd(i)=Rs*iq1-wr*Lq*iq1; Vq(i)= Rs*id1+wr*(Ld*id1+lambdaPM); end if V1>Vam Id(i)=id2; Iq(i)=iq2; Te(i)=(P/2)*(lambdaPM*iq2+(Ld-Lq)*iq2*id2); Vd(i)=Rs*iq2-wr*Lq*iq2;

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Vq(i)= Rs*id2+wr*(Ld*id2+lambdaPM); end

if (Im3

A=[ -1/(sigma*Ts) -wr/sigma -(1/sigma)*(lambdaPM/Ld + Ids) Vds/(sigma*Ld); sigma*wr -1/Ts sigma*Iqs -Vqs/Ld ; (1/J)*((P/2)^2)*(lambdaPM+Ld*(1-sigma)*Ids) (1/J)*((P/2)^2)*(Ld*(1-sigma)*Iqs) -Bm/J 0; 0 0 -1 0]; E=eig(A);

figure(1) plot(E,'X','markersize',12,... 'MarkerEdgeColor','magenta',... 'LineWidth',2) strfrq =['\omega=' num2str(x(i)),'Hz'] text(real(E),imag(E),strfrq,'FontSize',10) grid on;

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xlabel('Real part (rad/s)') ylabel('Imaginary part (rad/s)') hold on; i=i+1; end

A3: Script for dq phase plane plot of machine characteristics clear all clc lambdaPM=0.0270 n=30; Lq=0.5147e-3; Ld = 0.5e-3; Vdc = 48; Rs = 0.02656; sq =2/pi; sp = 1/sqrt(3); Si = 0.5; Vs = sq*Vdc; Vam=Vs; rs=0.02656; freq=[40 80 100 200 300]; w0=2*pi*freq; iq=0:1:85; id=-85:1:0; [id, iq]= meshgrid(id,iq); lambdaq=Lq*iq; lambdad=Ld*id+lambdaPM*ones(size(id)); lambda = sqrt(lambdaq.^2+lambdad.^2); contour(id,iq,lambda,'DisplayName','Flux linkage (Wb)'); hold on;

Te=(n/2)*(lambdaPM*iq+(Ld-Lq)*iq.*id); contour(id,iq,Te,'DisplayName','Torque (Nm)'); iq=0:1:85; IdMtpa=lambdaPM*ones(size(iq))/(2*(Lq-Ld))- 1*sqrt((lambdaPM*ones(size(iq))/(2*(Lq-Ld))).^2+iq.^2); plot(IdMtpa,iq,'DisplayName','MTPA trajectory')

TeMtpa=(n/2)*(lambdaPM*iq+(Ld-Lq)*iq.*IdMtpa);

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id=-85:1:0;

Is=72; theta=0:0.01:pi; Idcir=Is*cos(theta); Iqcir=Is*sin(theta); plot(Idcir,Iqcir,'DisplayName','current limit circle')

i=1 for i=1:1:5 iq=sqrt(((ones(size(id)).*Vs)/w0(i)).^2- (Ld*ones(size(id)).*id+lambdaPM*ones(size(id))).^2)/(Lq); Iqmat(i,:)=iq; end i=1; for w=0:50:25000; wr=0.5*n*w*pi/30; Dl=(-Lq*lambdaPM+sqrt((Lq*lambdaPM)^2+8*((Lq- Ld)^2)*(Vam/wr)^2))/(4*(Lq-Ld)); id3= -(lambdaPM+Dl)/Ld; iq3 = sqrt((Vam/wr)^2-Dl^2)/Lq; Im3 =sqrt(id3^2+iq3^2); V3 = wr*sqrt((Ld*id3+lambdaPM)^2+(Lq*iq3)^2); idx(i)=id3; iqx(i)=iq3; i=i+1; end Ich= -lambdaPM/Ld; plot(Ich,0,'x','markersize',20) plot([idx Ich'],[iqx 0']) plot(id,Iqmat,'linewidth',3,'DisplayName','Speed voltage limit circles') ylim([0 85]) xlim([-85 0])

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