design of an interior permanent

Design of an Interior Permanent Magnet Machine with Concentrated

Windings for Field WeakeningApplications

By

Lester Chong

A thesis submitted to

THE UNIVERSITY OF NEW SOUTH WALES

in partial fulfilment of the

requirements for the degree of

Doctor of Philosophy

(Electrical Engineering)

August, 2011

i

ACKNOWLEDGEMENTS

I am extremely grateful to my two supervisors Professor Faz Rahman and Dr Rukmi Dutta for

all their time, guidance and invaluable advice given to me over the duration of my PhD. I

thankfully acknowledge the inputs from my examiners and Associate Professor John Fletcher. I

would also like to thank the Australian Government and the University of New South Wales for

sponsoring my studies.

I am very grateful to the wonderful staff and at School of Electrical Engineering and

Telecommunications, especially Dr Baburaj Karnayil, Richard Tuck and Gamini Liyadipitiya. I

am also grateful for the advice given by Subash and Seetha from the school of mechanical

engineering. I would like to thank Dr Howard Lovatt and Colin Bilson at CSIRO for their help

and advice.

A special thank you to my family, especially my mother Jenny Ong who has selflessly worked

so hard to raise and support us; my fiancé Janice and the Liao family for their support from the

start to the final stages of my PhD. Last but not least I would like to thank my wonderful friends

and colleagues for making my time in Sydney so special and unforgettable.

ii

ABSTRACT

This thesis presents the design of an interior permanent magnet (IPM) machine with

concentrated windings (CW) for field-weakening applications. The initial phase of this

work involved a feasibility study and comparison with the CW surface permanent

magnet machine. Subsequently a CW-IPM machine was designed and constructed with

the aim of achieving a wide constant power speed range (CPSR). Lastly, based on the

constructed design, scalability and efficiency studies were performed.

The work done in this thesis has led to the successful construction of a prototype

machine achieving a very wide 7.2:1 CPSR. At the time of writing, there is no available

literature that clams such a wide CPSR in a concentrated wound permanent magnet

machine. Distributed winding machines capable of achieving such a CPSR have

complex rotors and hence manufacturing issues. The proposed design was subjected to

the same size constraint as two previously constructed 550W distributed winding IPM

machines. With this constraint, the advantage of shorter end winding length was

exploited and the effective length of the machine was increased. This resulted in a

significant increase in output power to 800W throughout the CPSR. A detailed study on

losses performed in this work showed that despite the increased harmonic content

generated by CW, frequency related losses can be minimized through design methods,

and over an 80% efficiency can be achieved throughout the CPSR. Mechanical stress

analysis of the rotor indicated that iron bridges were required between poles to prevent

excessive stress inflicted on the inter-pole link sections during high speed operation.

Based on confidence gained from the experimental verification of the CW-IPM machine

design, a scalability study was performed and designs up to 30kW were proposed. A

iii

study on efficiency optimization was also carried out and the prototype machine was

redesigned to produce up to 93% efficiency.

The work done in this thesis has setup a strong basis for future work on CW-IPM

machines for automotive traction drives and has also proven that this machine type is

suitable for high performance industrial applications requiring high efficiency over a

very wide CPSR.

iv

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .................................................................................. i

ABSTRACT ............................................................................................................ ii

TABLE OF CONTENTS ...................................................................................... iv

LIST OF FIGURES ............................................................................................... x

LIST OF TABLES ................................................................................................. xix

NOMENCLATURE .............................................................................................. xx

CHAPTER 1 ........................................................................................................... 1

1. INTRODUCTION ........................................................................................... 1

1.1 GENERAL BACKGROUND ............................................................................... 1

1.2 LITERATURE REVIEW .................................................................................... 9

1.2.1 IPM Machine Technology .......................................................................... 9

1.2.2 Concentrated Non-overlapping Windings in AC Machines ...................... 16

1.3 SCOPE AND ORGANISATION OF THESIS .......................................................... 25

CHAPTER 2 ........................................................................................................... 28

2. NUMERICAL METHODS FOR THE ANALYSIS AND PREDICTION OF

MACHINE PARAMETERS ............................................................................. 28

2.1 INTRODUCTION .............................................................................................. 28

2.2 THE FINITE ELEMENT METHOD ............................................................................. 30

2.2.1 Brief Background of Finite Element Analysis ........................................... 31

2.2.2 Mathematical Formulations for the Physical Model ................................. 31

2.2.3 Discretisation of the Study Domain ........................................................... 34

2.2.4 Defining Boundary Conditions .................................................................. 37

2.2.5 Galerkin’s Method for Deriving Finite Element Equations ...................... 39

2.2.6 Solving Finite Element Equations with Newton Raphson Method ............ 41

2.2.7 Process of a Time Stepping Finite Element Model ...................................... 43

v

2.3 FINITE ELEMENT METHOD FOR DETERMINING MACHINE PARAMETERS AND PERFORMANCE CHARACTERISTICS .................................................................. 45

2.3.1 Construction of Geometry and Assignment of Mesh ................................. 45

2.3.2 Defining Material Properties ..................................................................... 47

2.3.3 Coupling of Electrical Circuits .................................................................. 48

2.3.4 Performance Calculation .......................................................................... 49

2.4 CONCLUSION ................................................................................................ 53

CHAPTER 3 ........................................................................................................... 54

3. INVESTIGATION OF THE CONCENTRATED WINDING IPM FOR WIDE FIELD WEAKENING APPLICATIONS ..................................................... 54

3.1 INTRODUCTION ............................................................................................. 54

3.2 CHOICE OF SLOT AND POLE COMBINATION .................................................. 55

3.2.1 Winding Factor and EMF ........................................................................... 57

3.2.2 Cogging Torque ......................................................................................... 62

3.3 PERFORMANCE IN COMPARISON TO DISTRIBUTED WINDING IPM MACHINE 65

3.3.1 Airgap Flux Harmonics ............................................................................. 65

3.3.2 Saliency Ratio and Constant Power Capability ........................................ 68

3.3.3 End Winding Length .................................................................................. 73

3.3.4 Slot-fill Factor ........................................................................................... 74

3.4 COMPARING THE IPM AND SPM MACHINES WITH CONCENTRATED WINDINGS ..................................................................................................... 75

3.4.1 Airgap Flux Produced by the Magnets ...................................................... 76

3.4.2 Constant Power Speed Range .................................................................... 79

3.5 CONCLUSION ................................................................................................. 81

CHAPTER 4 ........................................................................................................... 82

4. DESIGN OF A 1KW IPM MACHINE WITH CONCNETRATED WINDINGS

FOR ACHIEVING A VERY WIDE CPSR ................................................... 82

4.1 INTRODUCTION ............................................................................................. 82

4.2 CONDITIONS FOR MAXIMISING THE CPSR .................................................... 83

4.3 CHOICE OF WINDING ARRANGEMENT ........................................................... 88

4.4 MATERIAL CONSIDERATIONS ........................................................................ 90

4.4.1 Permanent Magnet Material ..................................................................... 90

vi

4.4.2 Core Material ............................................................................................ 92

4.4.3 Stator Coil and Insulating Material .......................................................... 94

4.5 OPTIMISATION OF MACHINE GEOMETRY .................................................... 96

4.5.1 Stack Length ............................................................................................ 96

4.5.2 Rotor Outer Diameter and Airgap Length .............................................. 99

4.5.3 Stator Geometry ...................................................................................... 100

4.6 ROTOR DESIGN AND STRUCTURAL CONSIDERATIONS ................................. 104

4.6.1 Structural Considerations ....................................................................... 106

4.7 FINAL MANUFACTURED DESIGN ................................................................. 112

4.7.1 Back EMF from the Finite Element Model ............................................. 114

4.7.2 Cogging Torque from the Finite Element Model .................................... 116

4.7.3 Inductance and Saliency Ratio from the Finite Element Model ............. 116

4.7.4 Torque Performance from the Finite Element Model ............................. 118

4.8 CONCLUSION ............................................................................................... 119

CHAPTER 5 ........................................................................................................ 120

5. ANALYSIS OF LOSSES IN AN IPM MACHINE WITH CONCENTRATED

WINDINGS FOR FIELD WEAKENING APPLICATIONS ...................... 120

5.1 INTRODUCTION ............................................................................................ 120

5.2 MMF HARMONICS AND LOSSES IN MACHINES WITH CONCENTRATED WINDINGS ................................................................................................... 121

5.3 CORE LOSS .................................................................................................. 127

5.3.1 Comparison of Steel Grades ................................................................... 129

5.3.2 Core Loss of the Final Design ................................................................ 131

5.4 MAGNET LOSS ............................................................................................. 132

5.4.1 Comparison SPM and IPM Magnet Losses ............................................ 134

5.4.2 Effects of Magnet Segmentation .............................................................. 136

5.4.3 Magnet Loss of the Final Design ............................................................ 139

5.5 STATOR WINDING LOSS .............................................................................. 140

5.6 MECHANICAL LOSSES ................................................................................. 143

5.7 FIELD-WEAKENING PERFORMANCE WITH THE INCLUSION OF LOSSES FROM THE FINITE ELEMENT MODEL ............................................................................. 147

5.8 CONCLUSION .............................................................................................. 148

vii

CHAPTER 6 ........................................................................................................ 149

6. VECTOR CONTROL OF THE IPM MACHINE WITH CONCENTRATED

WINDINGS .................................................................................................... 149

6.1 INTRODUCTION ............................................................................................ 149

6.2 CONTROL METHODOLOGY .......................................................................... 152

6.2.1 Basic Equations Describing the PM Machine ........................................ 153

6.2.2 Variation of Current Phase Angle .......................................................... 154

6.2.3 Current and Voltage Limits ..................................................................... 157

6.2.4 Maximum Torque per unit Current and Field-weakening Trajectories .. 161

6.3 CONTROLLER ARCHITECTURE ..................................................................... 164

6.3.1 Three phase Inversion Technique ........................................................... 165

CHAPTER 7 ........................................................................................................ 170

7. CONSTRUCTION AND PERFORMANCE ANALYSIS OF THE

CONCENTRATED WOUND IPM MACHINE PROTOTYPE ............... 170

7.1 INTRODUCTION ............................................................................................ 170

7.2 CONSTRUCTION PROCESS ............................................................................ 171

7.2.1 Manufacturing Duration ......................................................................... 171

7.2.2 Rotor Assembly ....................................................................................... 173

7.2.3 Stator Core Assembly and Stator Winding ............................................. 175

7.3 OPEN CIRCUIT PARAMETERS ....................................................................... 178

7.3.1 Back EMF ............................................................................................... 178

7.3.2 Cogging Torque ...................................................................................... 179

7.3.3 Inductance and Saliency Ratio ................................................................ 182

7.4 STEADY STATE ANALYSIS ........................................................................... 185

7.4.1 Torque and Power Characteristics ......................................................... 185

7.4.2 Steady State Voltage and Current Characteristics ................................. 189

7.5 TRANSIENT RESPONSE UNDER MTPA OPERATION ..................................... 192

7.5.1 Transient Voltage and Current Characteristics ...................................... 192

7.5.2 Torque Transients ................................................................................... 194

7.6 PERFORMANCE COMPARED TO DISTRIBUTED WINDING IPM MACHINES ..... 196

7.6.1 Power and Torque versus Frequency Comparison ................................. 198

7.6.2 Cogging Torque Comparison .................................................................. 199

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7.6.3 Efficiency Comparison ............................................................................ 201

7.6.4 Magnet Volume Comparison .................................................................. 202

7.7 CONCLUSION ............................................................................................... 203

CHAPTER 8 ........................................................................................................ 204

8. EFFICIENCY OPTIMISATION AND SCALABILITY OF THE

CONCENTRATED WINDING IPM MACHINE ........................................ 204

8.1 INTRODUCTION ............................................................................................ 204

8.2 EFFICIENCY OPTIMISATION ......................................................................... 205

8.2.1 Proposed Designs for Efficiency Optimisation ....................................... 206

8.3 SCALABILITY OF THE CONCENTRATED WINDING IPM MACHINE ................ 210

8.3.1 Airgap Length Variation ......................................................................... 210

8.3.2 Magnet Strength and Armature Current Variation ................................. 211

8.3.3 Effect of Scaling the Machine Size .......................................................... 214

8.4 CONCLUSION ............................................................................................... 220

CHAPTER 9 ........................................................................................................ 221

9. CONCLUSION AND SUGGESTION FOR FUTURE WORK ................ 221

9.1 CONCLUSION OF THIS THESIS ...................................................................... 221

9.2 SUGGESTIONS FOR FUTURE WORK ............................................................. 225

REFERENCES .................................................................................................... 227

APPENDIX A ...................................................................................................... 243

A. AC STANDSTILL TEST APPLIED TO THE FINITE ELEMENT MODEL OF THE SEGMENTED IPM MACHINE .......................................................................... 243

A.1 Results of AC Standstill Test Implemented on the Segmented IPM Machine 243

APPENDIX B ....................................................................................................... 245

B. SALIENCY RATIO OPTIMISATION .................................................................. 245

B.1 Optimisation of Saliency Ratio by Variation of Rotor Magnet Shape ........... 245

ix

APPENDIX C ...................................................................................................... 249

C. INDUCTANCE WAVEFORMS AND SALIENCY RATIO FOR VARIOUS SLOT/POLE COMBINATION AND FOR DOUBLE-LAYER WINDINGS .................................. 249

C.1 Inductance Waveform and Saliency Ratio – Comparison of Various Slot/pole Combinations ............................................................................................. 249

C.2 Inductance Waveform and Saliency Ratio – Comparison with Double-Layer Windings .................................................................................................... 251

APPENDIX D ...................................................................................................... 253

D. THERMAL MODEL ......................................................................................... 253

D.1 Thermal Model Approximating Temperature at Various Parts of the Machine ...................................................................................................... 253

APPENDIX E ....................................................................................................... 255

E. FINAL MACHINE DRAWINGS ........................................................................ 255

E.1 ABB Casing used (with Original Induction Motor) ..................................... 255E.2 Stator of the CW-IPM Prototype ................................................................. 256E.3 Rotor of the CW-IPM Prototype .................................................................. 257E.4 Shaft of the CW-IPM Prototype ................................................................... 259E.5 Key (shaft) of the CW-IPM Prototype ......................................................... 260E.6 End-plates of the CW-IPM Prototype .......................................................... 261

APPENDIX F ....................................................................................................... 262

F. EXPERIMENTAL SETUP ................................................................................. 262

F.1 The Experimental Setup ............................................................................... 262F.2 Control Algorithm ......................................................................................... 264F.3 3-phase IGBT Inverter .................................................................................. 267F.4 Kollmorgen PM Machine Specifications ...................................................... 270

APPENDIX G ...................................................................................................... 271

G. PUBLICATION LIST ....................................................................................... 271

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LIST OF FIGURES

Fig. 1.1 Classification of AC machine types used for traction applications 2

Fig. 1.2 Various IPM motor geometries 4

Fig. 1.3 Various stator winding layouts 6

Fig. 1.4 Typical PMSM drive system block diagram 7

Fig. 1.5 Ideal field-weakening characteristics of a drive system 8

Fig. 2.1 Various methods to solve Maxwell equations and predict machine performance

28

Fig. 2.2 Typical finite elements 35

Fig. 2.3 Two dimensional triangular element 36

Fig. 2.4 Dirichelet boundaries 38

Fig. 2.5 Machine with quarter cyclic-symmetry 39

Fig. 2.6 Newton Raphson method 43

Fig. 2.7 Flow chart for the time-stepping finite element process 44

Fig. 2.8 Prototype machine geometry – showing regions 45

Fig. 2.9 DW-IPM showing the repletion of phase coils every quarter 46

Fig. 2.10 Mesh structure of the CW-IPM machine 47

Fig. 2.11 B-H Curve for hard and soft magnetic materials 48

Fig. 2.12 Representation of core material characteristics in terms of an analytic solution

49

Fig.2.13 Representation of permanent magnet material demagnetisation characteristics

49

Fig. 2.14 Three-phase star conneted circuit with current excitation 50

Fig. 2.15 Meshing of a three-layer airgap 52

Fig. 3.1 14-pole IPM machine with various slot and pole combinations 56

Fig. 3.2 EMF phasor diagram 59

xi

Fig. 3.3 3-phase EMF waveforms and corresponding frequency spectrum over 1 electrical cycle for 14-pole IPM machinewith different slot and pole combinations

61

Fig. 3.4 Cogging torque waveforms for various slot and pole combination

63

Fig. 3.5 Flux waveform and corresponding frequency spectrum of a 14-pole, double-layer, DW machine model

66

Fig. 3.6 Flux waveform due to armature reaction for single- and double-layer CW

67

Fig. 3.7 14-pole DW IPM with flux being channeled to the d- and q-axis

68

Fig. 3.8 14-pole, 18-slot, CW-IPM flux plot showing no obvious d or q-axis flux paths

69

Fig. 3.9 Inductance waveform measured from UNSW Segmented IPM machine

71

Fig. 3.10 Inductance waveform of an 18-slot, 14-pole CW-IPM machine

71

Fig. 3.11 d- and q-axis inductance comparison 72

Fig. 3.12 Estimated reduction in end winding length 73

Fig. 3.13 Advanced winding methods to achieve a high saliency ratio 74

Fig. 3.14 Performance comparison of different magnet shapes 75

Fig. 3.15 Flux density plot of the v-shaped IPM model showing saturation regions

77

Fig. 3.16 Airgap flux produced by the different rotor configurations 78

Fig. 3.17 Peak power and CPSR comparison between three rotor types 79

Fig. 4.1 Rotor types used for increasing saliency ratio 83

Fig. 4.2 Contour plot showing the variation of magnet remanent fluxdensity versus rated current

87

Fig. 4.3 Permanent magnet demagnetisation curve 90

Fig. 4.4 Magnetisation curve of 35RM300 93

Fig. 4.5 Core loss curve of 35RM300 94

xii

Fig. 4.6 Resistance and copper loss per phase as temperature increases 95

Fig. 4.7 ABB casing with inserted 18-slot stator core 96

Fig. 4.8 End winding length comparison between UNSW DW stator with windings done on a plastic model

97

Fig. 4.9 Hand winding methods 98

Fig. 4.10 Airgap length variation with output power and CPSR 99

Fig. 4.11 Key parameters defining the stator geometry 100

Fig. 4.12 Flux density plots showing peak flux density in the yoke and tooth

102

Fig. 4.13 Plastic stator made with three different slot opening widths 103

Fig. 4.14 IPM rotors showing inter-pole link sections 104

Fig. 4.15 V-angle variation 105

Fig. 4.16 Normalised power versus speed characteristics with variation of v-angle

105

Fig. 4.17 Various types of SPM rotors 106

Fig. 4.18 IPM rotor with buried single-piece/pole magnets 107

Fig. 4.19 Modelled solenoid-magnet model 108

Fig. 4.20 Sections for centrifugal force calculation 109

Fig. 4.21 Model showing outward normal pressure on each section of the rotor

109

Fig. 4.22 Mechanical stress analysis of rotor 110

Fig. 4.23 Final 18-slot, double-layer winding layout 112

Fig. 4.24 Three-phase induced line to neutral back EMF voltage from the FE model (at 50Hz)

114

Fig. 4.25 Induced line to line voltage versus speed 114

Fig. 4.26 Comparison of EMF waveform between the CW-IPM and DW-IPM

115

Fig. 4.27 Comparison of EMF waveform between the CW-IPM and DW-IPM – frequency spectrum

115

xiii

Fig. 4.28 Cogging torque of final design comapred to an equivaent integral-slot DW model

116

Fig. 4.29 Self- and mutual-inductance waveform of final model with 3Arms current excitation

117

Fig. 4.30 Torque ripple of final model at base speed 118

Fig. 4.31 CPSR of final design with base frequency of 50Hz 118

Fig. 5.1 Comparison of flux distribution in a CW and DW machine 121

Fig. 5.2 Ref. to fig. 3.5 122

Fig. 5.3 Ref. to fig. 3.6 122

Fig. 5.4 Contribution of eddy current and hysteresis loss 124

Fig. 5.5 Ref. to fig. 4.5 128

Fig. 5.6 Annular steel model to determine eddy current and hysteresis loss constants

128

Fig. 5.7 Core loss comparison at 50 and 500Hz with different steel grades

130

Fig. 5.8 Core loss with chosen steel grade at various frequencies 131

Fig. 5.9 Extrapolated values of measured hysteresis and eddy current loss for sintered neodymium magnets at 50Hz

133

Fig. 5.10 3D model of a single-pole and single-phase excitation – v-shaped IPM

134

Fig. 5.11 3D model of a single-pole and single-phase excitation – SPM 134

Fig. 5.13 Comparison of magnet losses between IPM and SPM machine 135

Fig. 5.14 Variation of magnet eddy current loss with number of magnet segments due to slot and carrier harmonics – Comparison between IPM, inset and SPM rotors

137

Fig. 5.15 Circulating eddy currents in a non-segmented a) SPM magnet pole, b) V-shaped IPM magnet pole

137

Fig. 5.16 Circulating eddy currents in a segmented magnet poles 138

Fig. 5.17 Magnet losses in an SPM machine with variation of segment number

138

xiv

Fig. 5.18 Magnet losses in an IPM machine with variation of segment number

139

Fig. 5.19 Magnet losses versus frequency in the final design withsintered NdFeB magnets

140

Fig. 5.20 Inner-diameter view of stator teeth showing estimated winding length

142

Fig. 5.21 Drawing of rotor indicating key components to calculate bearing friction loss

143

Fig. 5.22 Power loss due to bearing friction at various speeds 144

Fig. 5.23 Power loss due to windage at various speeds 146

Fig. 5.24 Modelled power versus speed performance with inclusion of losses

147

Fig. 6.1 2-pole IPM machine showing d-q axis reference frames 150

Fig. 6.2 Space vector dq-axis phasor diagram 151

Fig. 6.3 Calculated torque comprising of alignment and reluctance torque

154

Fig. 6.4 Current phasor under MTPA and Field-weakening operation 155

Fig. 6.5 Back EMF, induced current and induced voltage waveforms under MTPA and maximum field-weakening operation

156

Fig. 6.6 Circle diagram for IPM and SPM machine showing current and voltage limits of the system

157

Fig 6.7 Classification of machine type by characteristic current 160

Fig. 6.8 id and iq field-weakening current trajectory for the CW-IPM model

161

Fig. 6.9 Comparison of d-axis current trajectories by Morimoto’s equations and through repetitive testings

163

Fig. 6.10 Vector control system block diagram 164

Fig. 6.11 Rectifier – Inverter for producing three-phase outputs to the machine

165

Fig. 6.12 Switching vectors of the space vector modulation method 166

Fig. 6.13 Switching pattern for sector 1 168

xv

Fig. 7.1 Duration breakdown and steps of construction process 172

Fig. 7.2 Laser-cut rotor lamination 173

Fig. 7.3 Complete rotor stack with magnets inserted 174

Fig. 7.4 Completed dynamically-balanced rotor 174

Fig. 7.5 Completed stator stack 175

Fig. 7.6 Measurement of end winding length in UNSW CW-IPM stator

176

Fig. 7.7 Comparison of UNSW CW-IPM machine assembly and DW S-IPM machine

177

Fig. 7.8 Measured line to line and line to neutral back EMF waveforms compared against modelled values

178

Fig. 7.9 Measured line to line back EMF versus speed compared against modelled values

179

Fig. 7.10 Cogging torque measurement setup 179

Fig. 7.11 Measured cogging torque points compared against results obtained from FE model

180

Fig. 7.12 Curve fitted cogging torque waveform 181

Fig. 7.13 Ref. to fig. 4.29 182

Fig. 7.14 Measured self and mutual-inductance waveform from the prototype with 3Arms current excitation

183

Fig. 7.15 Variation of dq-axis inductances with current 184

Fig. 7.16 Experimental setup to measure back EMF and torque/power versus speed performance

185

Fig. 7.17 Measured dq-axis current points under field weakening operation

186

Fig. 7.18 Measured line to line voltage versus speed 187

Fig. 7.19 Measured torque versus speed characteristics of the CW-IPM machine prototype

187

Fig. 7.20 Measured efficiency versus speed 188

Fig. 7.21 Steady-state speed waveforms 189

xvi

Fig. 7.22 Steady state id current waveforms 190

Fig. 7.23 Steady state iq current waveforms 190

Fig. 7.24 Steady state current and voltage inputs to the machine in abcreference frame

191

Fig. 7.25 Speed step from standstill to base speed 192

Fig. 7.26 id current waveforms with speed step from standstill to base speed

192

Fig. 7.27 iq current waveforms with speed step from standstill to base speed

193

Fig. 7.28 Current and voltage inputs to the machine in abc reference frame with step change in speed

193

Fig. 7.29 Torque transient when CW-IPM machine accelerates from standstill to base speed at full load

194

Fig. 7.30 Measured torque ripple at steady state 195

Fig. 7.31 Comparison of three UNSW IPM machines 197

Fig. 7.32 CPSR comparison between the three UNSW IPM machines 198

Fig. 7.33 Normalised output torque comparison between the three UNSW IPM machines

199

Fig. 7.34 Cogging torque comparison between the three UNSW IPM machines

200

Fig. 7.35 Cogging torque as a percentage of output torque at base speed – comparison between the three UNSW IPM machines

200

Fig. 7.36 Efficiency comparison between the CW-IPM and S-IPM machine up to 200Hz

201

Fig. 7.37 Comparison of magnet volume per kW the three UNSW IPM machines

202

Fig. 8.1 Axial length comparison between two different slot-fill methods

206

Fig. 8.2 Designs used for efficiency optimization indicating outer dimensions

207

xvii

Fig. 8.3 Efficiency and power versus speed performance of the two efficiency optimised model

208

Fig. 8.4 Airgap length versus CPSR and input power – scalability study

210

Fig. 8.5 Airgap length versus efficiency and core loss – scalability study

211

Fig. 8.6 Magnet remanent flux density versus input current and input power – scalability study

212

Fig. 8.7 Flux density plot of CW-IPM machine under saturated and unsaturated conditions

213

Fig. 8.8 Magnet remanent flux density versus total machine losses and efficiency – scalability study

213

Fig. 8.9 Comparison between the three machine sizes used in scalability study

215

Fig. 8.10 Input power, output power and efficiency versus speed characteristics of the 5kW design

217


218

Fig. 8.12 Losses in the three machine sizes as a percentage of total loss – scalability study

219

Fig. A.1 Segmented IPM machine 243

Fig. A.2 AC standstill test on the S-IPM machine using FE analysis compared to other methods

244

Fig. C.1 Three 14-pole layouts used in the saliency ratio comparison 249

Fig. C.2 Self- and mutual-inductance for the 6-slot, 14-pole, single-layer model

254


250


250

Fig. C.5 Single- and double-layer layout used in the saliency ratio comparison

251

xviii

Fig. C.6 Self- and mutual-inductance for the 6-slot, 14-pole, double-layer model

251

Fig. D.1 Approximate model used in thermal analysis 254

Fig. F.1 Complete experimental Setup 262

Fig. F.2 d-space control desk, real-time graphical user interface 263

Fig. F.3 3-phse IGBT inverter (casing off) 267

Fig. F.4 IGBT inverter schematic 268

Fig. F.5 Connections between the IGBT inverter and control boards 269

xix

LIST OF TABLES

Table 3.1 Winding factor and LCM for different Spp values 60

Table 3.2 Key specifications of Models with Different Magnet Shapes 76

Table 4.1 Advantages and disadvantages of different magnet types 91

Table 4.2 Power and CPSR with variation of v-angle 105

Table 4.3 Mechanical data for silicon steel grade (JFE-35JN210) 110

Table 4.4 Specifications of the final design 113

Table 5.1 Properties of compared core grades 129

Table 5.2 Comparison of magnet losses between IPM and SPM machine 135

Table 5.3 Suitable conductor sizes and properties 141

Table 5.4 Bearing friction loss on each bearing at various speeds 144

Table 5.5 Reynolds number, torque coefficient and winding loss at various speeds

146

Table 6.1 Space vector modulation look-up table 167

Table 8.1 Key specifications of the two Optimised CW-IPM Machine Designs

208

Table 8.2 Key specifications of the three CW-IPM Machine Designs 217

Table C.1 Saliency ratios for various layouts 252

Table D.1 Key machine parameters used in thermal model 253

Table D.2 Estimated temperature at various parts of the machine 254

Table F.1 Kollmorgen PM machine specifications – Loading machine 270

xx

NOMENCLATURE A

Airgap area [m2]

Magnet pole area [m2]

Area of slot [m2]

Cross sectional area of a wire [m2]

Magnetic vector potential

Z-axis scalar potential

AC Alternating current

BAirgap flux density due to the magnets [T]

Magnet remanent flux density [T] Flux density normal to the pole surface [T]

Magnetic flux density vector [T]

CCircumference [m]

CPSR Constant power speed range

CW Concentrated non-overlapping winding

DD Diameter [m]

Dos Stator outer diameter [m]

d-axis Direct axis

d Number of nodal degrees of freedom

DC Direct current

DTC Direct torque control

DW Distributed winding

xxi

EEMF Electromotive force [V]

e Electromotive force (instantaneous) [V]

EMF reference phasor of winding element [V]

Electromagnetic field vector

Ff Frequency [Hz]

fs Sampling frequency [Hz]

FE Finite element

FOC Field oriented control

FFT Fast Fourier transform

HMagnetic field vector [Hz]

IPhase A current [A]

Phase B current [A]

Phase C current [A]

Characteristic current [A]

Rated current [A]

IM Induction machine

IMA Integrated motor assist

IPM Interior permanent magnet

ISA Integrated starter-alternator

JElectric current density [A/m2]

Equivalent electric current density from armature coils [A/m2]

Equivalent electric current density from magnets [A/m2]

xxii

KEddy current loss constant

Hysteresis loss constant

Torque constant

Winding factor

Pitch factor

Distribution factor

Skew factor

LStack length of machine [m]

Airgap length [m]

Rotor length [m] Stator inductance [H] d-axis inductance [H]

q-axis inductance [H]

Self-inductance of phase A winding [H]

LCM Lowest common multiple

M Mutual inductance between phase A and B winding [H]

MMF Magneto motive force [AT]

Mass of object [kg]

Magnetization vector

MTPC Maximum torque per current

NNumber of turns per phase [Turns]

Number of turns per coil [Turns]

Winding function of phase A [Turns]

xxiii

Winding function of phase B [Turns]

Rotational speed [RPM]

P Magnetic pressure [Pa]

Eddy Current Loss [W]

Hysteresis Loss [W]

Total core loss [W]

Magnetic polarisation at saturation [C/m2]

Pole pairs

PM Permanent magnet

PMSM Permanent magnet synchronous machine

PWM Pulse width modulated

Qq-axis Quadrature axis

RRadius [m]

Airgap radius [m]

Resistance

Reluctance [AT/Wb]

Reluctance in the airgap [AT/Wb]

Residual

SDisplacement [m]SSppp Slots per pole per phaseSSfff Slot fill factor

Slots

xxiv

SEG Segmented

SPM Surface permanent magnet

SVM Space vector modulation

TT Torque [Nm]

t Time [s]

Electro-magnet/alignment torque [Nm] Reluctance torque [Nm]

Cogging torque [Nm]

VV Voltage [V]

Velocity [m/s]

WWeight function

W Virtual work

Speed in radians per second

ref Speed reference signal

Greek Letters and SymbolsTemperature coefficient of resistivity [1/k]

Magnet internal permeance [Wb/A]

Flux [Wb]

Airgap flux [Wb]

Permanent magnet flux [Wb]

Flux linkage [Wb]

Permanent magnet flux linkage [Wb]

Mechanical speed [rad/s]

Rotor position [degrees]

Rotor mechanical position [degrees]

xxv

Permeability [H/m]

Permeability of free space [H/m]( ) Magnet relative permeability [H/m]

Resistivity

Conductivity [S/m]

Current displacement angle rads

Electric scalar potential

Electric scalar potential

Boundary

Numbers2D Two-dimensional

3D Three-dimensional

1

CHAPTER 11. Introduction

Chapter 1 will give an introduction to the permanent magnet synchronous machine, with

the main focus on the interior permanent magnet (IPM) type for field-weakening

applications. A general overview of the drive system architecture with different modes

of operation will be examined. Two major research areas which are relevant to this

thesis will be reviewed, namely, the IPM machine technology, and the concentrated

non-overlapping windings (CW) used in permanent magnet alternating current (AC)

machines. This chapter will also summarise research in various literatures relevant to

this work. Lastly, this chapter will provide an overall outline of this thesis.

1.1 GENERAL BACKGROUND

Over the years, the application of electric motors has replaced vast numbers of

mechanical rotating devices. From tiny motors used in wristwatches, to very large

motors used for ship propulsion and wind turbines. There are numerous types of electric

motors available for present-day applications, of which the AC type are most commonly

used in high performance applications due to its increased efficiency and excellent

dynamic performance. The classifications of common types of AC motors are shown in

fig. 1.1 [1-4].

Chapter 1: Introduction

2

Fig. 1.1 Classification of AC machine types used for traction applications

Machine types described in fig. 1.1, are suitable for traction/field-weakening

applications. While work on Halbach machines is still in the research phase, the

induction, SPM, inset, and IPM machine types have already been applied to present day

traction drive systems. Some of the examples include [2]:

Induction machine: GM Chevrolet Silverado hybrid and GMC Sierra hybrid

SPM/Inset PM machine: Honda Insight and Civic hybrids

IPM machine: Toyota Prius and Ford Escape hybrid

Induction, SPM and inset PM machines usually have a lower power rating compared to

the IPM machine and are most commonly applied as an integrated motor assist (IMA)

system, where the main driver of the vehicle is the internal combustion engine while the

electric motor assists. On the other hand, the IPM machine itself produces up to 73kW

of power (for the case of the 3rd Generation Prius) and can be driven in full electric

mode, producing zero emissions.

AC Machines

Synchronous

Induction machine

SPM machine

Inset PM machine

IPM machine

Asynchronous

Halbach machine

Distributed windings

Concentrated windings

Electrically excited machine


3

This thesis will focus on the IPM machine type, which is generally preferred due to

three main reasons: Firstly, the buried magnets make the rotor structurally stronger,

which make it more capable of withstanding higher speeds. Secondly, the additional

useful reluctance torque, resulting from the salient pole structure, thus giving the motor

greater field-weakening capabilities. Additionally this saliency allows sensorless control,

properties which the SPM does not offer. Lastly, the possibility of changing the

geometry of buried magnets in the rotor makes it possible to employ flux concentration,

and provides the possibility of saliency ratio optimisation [3, 5].

With the availability of high energy permanent magnet materials and advanced power

electronics, the fields in which IPM machines can be applied to are rapidly broadening.

They include aerospace, nautical, automobile, rail transportation, medical, generation

and industrial process automation [6-11].

Common magnet geometries include single-piece/pole, rectangular shaped magnet

design (fig. 1.2a), segmented magnet design (fig. 1.2b), v-shaped magnet design (fig.

1.2c), and the multi-barrier design (fig. 1.2d) [12-14].


4

(a) rectangular, single-piece/pole magnets (b) segmented magnets

(c) v-shaped magnets (d) multi-barrier magnets

Fig. 1.2 Various IPM rotor geometries

Each of these designs has its advantages and disadvantages: The single-piece/pole

magnet design, for example, is the easiest to manufacture, but has larger magnet losses

compared to the other designs due to the larger magnet pole surface [15]. The

segmented magnet design has lower magnet losses and better field-weakening capability

but requires more magnet pieces. It also results in decreased magnet flux density due to

the leakage flux in the iron bridges [13]. For further explanation of the segmented

machine design, one could refer to [174]. The v-shaped magnet design provides flux

concentration but also requires more magnet pieces compared to the single-piece/pole


5

design. The multi-barrier magnet design creates a very high saliency ratio, but

consequently results in an increased amount of structural stress on the rotor steel [12].

In practice, there is no single rotor that can satisfy all applications. The pros and cons of

each design as well as more specific magnet type and shape have to be altered to meet

desired specifications. As magnets are very brittle, there are also practical limits to the

manufacturability of the magnets.

Before the 21st century, the majority of IPM machines were designed with distributed

stator windings (DW). The use of CW was not popular due to a poor torque to

magnetomotive force (MMF) ratio. However in the early 21st century, Cros and

Viarouge [16], Magnussen and Sadarangani [17] proved that by an appropriate choice

of slot and pole combination, the winding factor can be significantly increased, thus

increasing output torque. Additionally it was also shown that with appropriate slot and

pole combination, cogging torque can also be reduced.

In CW, the opposite polarity of the corresponding phase coil is located in the next slot,

therefore end windings do not overlap. This results in a much shorter end winding

length compared to DW, which is beneficial for applications with space constraints.

Stator windings can either be single- or double-layer. The choice depends on the desired

machine performance characteristics. Single-layer CW creates high self-inductance and

low mutual-inductance which leads to better fault-tollerant capability. On the other hand,

double-layer CW has lower airgap MMF harmonic components, thereby resulting in

smaller torque ripples and lower magnet eddy current losses [18-20]. The winding

layouts for single- and double-layer DW are shown in fig.1.3a and 1.3b, while the

layouts for single- and double-layer CW are shown in fig.1.3c and 1.3d respectively.


6

(a) Single-layer distributed winidngs (b) Double-layer distributed windings

(c) Single-layer concnetrated winidngs (d) Double-layer concentrated widnings

(e) Double-layer modular concentrated widnings

Fig. 1.3 Various stator winding layouts


7

Occasionally, double-layer CW is further classified into subcategories: traditional CW

and modular CW [21-23]. Traditional CW does not have the same phase windings

around consecutive teeth (fig.1.3d), whereas modular CW (fig.1.3e) does. Modular CW

has the advantage of reduced torque ripple; however, it generates increased harmonic

content compared to traditional CW. In this thesis, CW would be only classified as

single- or double-layer and would not be further divided into traditional and modular.

The standard method used to determine the phase coil arrangements is as shown in [16].

Drives for present day applications require fast response and precise control of position,

speed and torque, hence control loops with constantly improving controller algorithms

are required. A commonly used drive system block diagram for a permanent magnet

synchronous machine (PMSM) is shown in fig. 1.4.

Most drive systems in the past made use of rotor position sensors to achieve precise

control. Recently, there has been keen interest in sensorless control schemes, such as

sensorless direct torque control (DTC), which eliminates the need for a physical sensor.

Fig. 1.4 Typical PMSM drive system block diagram

ControllerPower

Converter Load

Input Power

PMSM,PWM

Signal


8

The operation of the drive can be classified into two parts: the constant torque

(maximum torque per unit current (MTPC) region), and the constant power (field-

weakening region). The width of the field-weakening region is also known as the

constant power speed range (CPSR) of the machine. With the current kept at rated

value throughout the entire speed range, voltage increases with speed till its rated value

is reached. This point is the limit of the MTPC region. After which, in order to increase

the speed further, the field of the machine has to be weakened to keep voltages within

operating limits. Field weakening is achieved by splitting the current into two

components – namely the d-axis (magnet pole axis) and the q-axis (inter-pole axis)

components. By the decoupling these two currents, each of them could be made to

control the torque and flux independently. In order to maintain a constant power speed

range, the magnitude of negative d-axis current Id increased to weaken the magnet field

and maintain constant voltage, inevitably the q-axis current Iq has to be decreased to

maintain a constant armature current Ia. The limit to which the field of the machine can

be weakening to achieve a wide constant power speed range depends on two key factors:

the saliency ratio and the characteristic current. In an ideal case, a drive system would

be able to reach infinite speeds as shown in Fig 1.5.


9

Fig. 1.5 Ideal field-weakening characteristics of a drive system

1.2 LITERATURE REVIEW

DW-IPM machines have been widely used in high performance industrial applications

over decades. CW-IPM machines on the other hand have only more recently found their

way into industrial markets. This section reviews well established work in IPM machine

technology as well as recent research in CW for AC machines.

1.2.1 IPM Machine Technology

The IPM machine has been a popular choice for field-weakening applications. Global

research on the IPM machine dates back to the late 1970s and early 1980s when the first

few papers were published; there is still very significant research interest in this area

today. The popularity of the IPM machine is due to the embedded structure of its

Torque

Input Voltage

Flux

Speed

Armature Current

Output Power

Speed

Speed

Speed

tSpeed

Constant torque (MTPC region)

Constant power(Field-weakening region)


10

magnets, which lowers the risk of demagnetisation, increases the mechanical robustness

of the rotor and provides additional reluctance torque. The small airgap design in most

IPM machines makes it excellent for flux weakening, as the negative armature reaction

can effectively reduce airgap flux. The IPM machine also gives the machine designer

the freedom to vary the magnet pole geometry, thereby broadening the machine’s area

of application.

Leading studies in IPM machine technology has included patents and several papers

setting the basis for research in this area. Steen [24] filed a patent on synchronous

motors with buried permanent magnets having several geometrical configurations. He

stated that the buried magnets produced additional direct-axis (d-axis) flux in aid of the

flux generated by the inductive copper bars during no-load operation. Honsinger [25]

illustrated a detailed mathematical representation of the IPM machine which included

its magnetic fields and parameters. Rahman et al. [26] presented the equivalent circuit

model to determine the d-axis and quadrature-axis (q-axis) reactance. Consoli and

Renna [27] illustrated a detailed representation of the IPM machine in the rotor

reference frame, and demonstrated an equivalent circuit model to determine iron losses.

Chalmers et al. [28] presented a study of the IPM machine through extensive

experiments with frequency variations. They explained how the q-axis reactance can be

more accurately obtained with the consideration of saturation. One of the first papers to

illustrate the use of finite element (FE) analysis in IPM machine design was by Schiferl

and Lipo [29]. They showed how FE analysis is used to increase the prediction accuracy

of losses at low voltage levels by considering harmonics caused by armature excitation.

Noticing the IPM machine’s superiority when used in flux weakening applications,

Jahns et al. [30] first addressed the IPM machine’s characteristics when used as a high-


11

performance variable speed drive. Jahns [31] then performed a novel study on the flux

weakening of the IPM machine, thereby successfully extending its constant power

speed range. Since then, the use of IPM machines for flux weakening operations has

soared. Soong et al. [12, 32] introduced the optimal field-weakening conditions for IPM

machines using the parameter plane concept. They constructed and compared several

rotor types and proved that the multi-barrier IPM rotor produced the most promising

field-weakening performance. Soong et al. [33, 34] also developed a new axially

laminated IPM motor capable of achieving an extremely wide CPSR. Honda et al. [35,

36] did a study on the effects of various winding types and rotor configuration on the

field-weakening performance of the IPM machine. Jolly et al. [37] used genetic

algorithms to determine the optimal CPSR of an IPM machine confirming their results

with FE analysis.

The IPM machine’s characteristics were constantly compared to those of other AC

machines. Fratta et al. [38] compared the torque density and flux weakening ability of

the IPM machine with the induction machine, and highlighted that the IPM would have

better electromagnetic performance if mechanical issues were resolved. A

controllability comparison between the IPM and SPM machines under various operating

requirements of the current vector control scheme was done by Morimoto et al. [39].

They concluded that the IPM machine offered better flux-weakening capability. Zhu et

al. [40] compared the iron loss between the IPM and SPM machines. They indicated

that the iron loss of the IPM machine would be lower under open-circuit conditions but

significantly higher in the field-weakening region compared to the SPM machine, due to

the increased harmonic content in the armature field. Kyung-Tae et al. [41] compared

the effects of rotor eccentricity on the IPM and SPM rotor, in which they concluded that


12

the IPM is more prone to the effects of rotor eccentricity. Jung Ho et al. [42] studied the

inductance variation of a hybrid synchronous reluctance/IPM motor and found out that

the addition of buried magnets increased the saliency ratio, thus increasing output

torque and power factor.

A substantial amount of research efforts was focused on the control of the IPM machine.

Morimoto et al. [43] very clearly illustrated the control algorithm for an IPM motor with

a high performance current regulator over the entire speed range. Uddin et al. [44]

compared various current controllers for a voltage source-driven IPM drive and

proposed a hybrid type converter to exploit the best characteristics of the different

controllers.

The desire to completely eliminate position sensors and to increase the reliability of

drive systems sparked keen research interest in sensorless control of IPM machines.

Rahman et al. [45] as well as Ogasawara and Akagi [46, 47] were among to first authors

to implement sensorless control on IPM machine. At the same time, Corley and Lorenz

[48] achieved sensorless control over a wide speed range including zero speed. Haque et

al. [49] used the high frequency injection method to estimate the initial rotor position in

an attempt to completely eliminate sensors from IPM drives from start up. Sergeant et al.

[50] studied the effects of rotor geometry on sensorless control. Gyu-Hong et al. [51]

highlighted the effects on machine control performance due to varying Ld and Lq under

various load conditions, and proposed a control method with the addition of inductance

estimation.

Cross-coupling between the d- and q-axis fluxes affects machine parameter prediction,

thus studies were made to minimise its effects. Bianchi et al. [52-54] studied the effects

of various rotor structures on cross-coupling and sensorless control, including the high


13

frequency signal injections technique to determine the rotor initial position. They noted

that the multi-flux barrier motor produced the lowest cross-coupling effects and hence

lower saturation. The multi-flux barrier motor with sensorless control was later studied

by Wu at al. [55].

The end of the 20th century saw drastic improvements in computational resources and

techniques. This allowed machine designers to efficiently determine parameters and

perform optimisation strategies. Novel attempts to reduce cogging torque with the aid of

two-dimensional (2D) FE analysis by rotor pole or stator tooth shaping was done by

Filho et al. [56]. Fujishima et al. [57] as well as Kano and Matsui [58] adopted the FE

and genetic algorithm search method to derive optimal multi-objective designs.

Yamazaki [59] illustrated a method to calculate IPM machine parameters, including

rotor and stator iron losses, with FE analysis. Efficiency optimisation by geometric

variation was carried out by Sim et al. [60] using finite element models. Dong-Hun et

al. [61] attempted to reduce cogging torque by producing the rotor stack with unequal

lamination in the outer diameters. Ki-Chan et al. [62] studied the effects on machine

parameters and torque performance by varying the shape of rotor link sections. They

showed by FE analysis that small variations of the link sections could significantly

affect cogging torque and saliency ratio. Parsa and Lei [63] studied the effects of torque

ripple and performance characteristics when key machine parameters were varied.

Kioumarsi et al. [64] attempted to reduce torque ripple and increase field-weakening

performance by drilling additional holes in the rotor. Kang et al. [65] also attempted to

reduce cogging torque by rotor surface shaping and by adding notches in the steel. They

showed that the EMF harmonics and cogging torque amplitude could be effectively

reduced. Han et al. [66] attempted to reduce torque ripple by varying the number of


14

slots and number of rotor barriers. They showed that multi-barrier rotors with an odd

number of slots per pole pair resulted in low torque ripple. Sanada et al. [67]

experimented with several designs and proved that the use of asymmetric flux barriers

was beneficial in reducing torque ripple in multi-barrier IPM machines. Fang at al. [68]

showed that torque ripple and cogging torque can be reduced with a double-layer rotor.

Kim at al. [69] studied the effects of geometric variations of magnets in the IPM

machine to reduce torque ripple.

Computational methods also made the calculation of losses more accurate and realisable.

Loss minimisation was also made less costly and more effective. Kawase [70] analysed

permanent magnet eddy current losses in the IPM machine with three-dimensional finite

element (FE) analysis, and showed the effectiveness of reducing eddy current losses by

axially dividing the magnets. Zivotic-Kukolj [71] proposed geometric variations to the

multi-barrier IPM machine to reduce iron losses. Ionel et al. [72] improved the accuracy

of modelling core losses by allowing hysteresis loss to vary with both flux density and

frequency, but leaving the eddy current and excess losses to vary only with flux density.

Yamazaki and Seto [73] studied iron loss of the IPM machine at various operating

speeds, and concluded that at low speeds PWM inverters contribute the most to iron

losses, whereas losses from PM MMF harmonics are more significant during field-

weakening operation. Wang et al. [74] studied the effects of temperature on the torque

performance and machine losses in an IPM machine using FE analysis. Yamazaki and

Kanou [75] as well as Okitsu et al. [76] proposed more efficient yet equally accurate

alternatives to the full three-dimensional (3D) FE method for IPM rotor loss calculation.

Seo et al. [77] studied iron loss on machines with integral and fractional slot DW. They

showed that the with fractional-slot configuration, iron loss in the stator is reduced


15

slightly, but iron loss in the rotor is increased significantly, especially at high speeds.

Yamazaki and Ishigami [78] attempted to reduce iron loss by altering the rotor core

structure by having slits or air-pockets at various parts of the magnet surface. Yamazaki

and Abe [79] further investigated the effects of magnet segmentation in IPM motors,

and concluded that the axial length of each magnet segment should not be more than

twice the skin depth of the eddy currents produced by the dominant harmonics. Han et

al. [80] attempted to minimize eddy current loss in the stator teeth of IPM rotors under

field-weakening conditions and highlighted that double-layer rotor magnets resulted in

lower losses compared to single-layer rotor magnets. Tseng and Wee [81] investigated

various methods to determine core loss in the IPM machine, in which they stated the

relationship between flux and core loss as well as appropriate core loss calculation

methods to use at different stages of the machine design to save resources. Stumberger

et al. [82] studied the iron losses under field-weakening operation and stated that the

rotor iron losses is substantial, despite there being a very small portion of iron is present

above the magnets. Ma et al. [83] proposed a method to increase the accuracy of

calculating iron loss with FE analysis using rotational fields and flux density harmonics.

Barcaro et al. [84] also studied how the design of rotor flux barriers and the amount of

PM material affected the losses in an IPM machine.

Equivalent circuit and analytical models were also continuously improved and used as

an alternative or together with FE models for quicker calculations. Fernandez-Bernal et

al. [85] attempted to establish parameters for any kind of PM synchronous machine. Lee

et al. [86] improved the equivalent circuit model of the IPM machine taking into

account the effects of saturation. Zhu et al. [87] proposed an analytical model for the

multi-barrier and segmented IPM airgap flux without armature excitation.


16

Structural and thermal issues are closely related to durability, acoustic noise and

efficiency that can be addressed in the design stages of the drive system. Lovelace et al.

[88] addressed mechanical issues regarding the structural stresses inflicted on the multi-

barrier IPM rotor during high-speed operation. The effects of rotor eccentricity of IPM

machines structures were further investigated by Hwang et al. [89]. El-Refaie et al. [90]

modelled the thermal properties of a multi-barrier IPM machine by the use of the

lumped-parameter and FE methods, showing that these two methods were in good

agreement.

An important factor increasing the reliability of the drive system is its inherent ability to

tolerate faults. Welchko et al. [91] studied the effects of single-phase faults on IPM

machines, and highlighted some useful points in the design of the drive control strategy

to minimise the effects of faults. Bianchi et al. [92] proposed a method to compensate

unbalanced faults in the three phases to maintain smooth torque production.

1.2.2 Concentrated Non-overlapping Windings in AC machines

Up to the early 21st century, CW were mostly applied to DC machines. Earlier

published papers on the application of CW in PM AC machines recognised increased

EMF harmonics, lower torque density and narrower CPSR compared to machines with

DW [36]. Later studies by Cros et al. [16, 93], as well as Magnussen and Sadarangani

[16, 17, 93] proved that a winding factor very close to unity and low cogging torque are

achievable if an appropriate slot and pole combination is chosen. These studies sparked

global research interests in fractional slot CW for use in 3-phase PM AC machines.

There were numerous attempts to find the most ideal slot and pole combination to

achieve desired performance characteristics. Nakano et al. [94] illustrated the increases


17

eddy current loss in SPM machines with CW due to asynchronous rotating components

in the MMF waveform. They demonstrated how various slot and pole combinations

resulted in lower losses. The results indicate that eddy current loss decreases inversely

with the number of slots. Reddy et al. [95] carried out a detailed study on losses in SPM

machines with CW and graphed losses with FE analysis for various slot and pole

combinations as well as magnet types. Jussila et al. [96, 97] explained and modelled the

losses in low speed CW machines with several possible slot and pole combinations.

They also proposed a set of guidelines in designing machines with CW. El-Refaie and

Jahns [98] studied the scalability of SPM machines with CW in achieving wide CPSR.

In this study they concluded that a high number of slots and poles is beneficial in

achieving a wide CPSR. Xu and Sun [99] as well as Salminen et al. [100, 101]

presented pull out torque and percentage torque ripple comparisons of various slot and

pole configurations for CW-PM machines. Their results show that torque increases as

the number of slots per pole per phase (Spp) increases. Gerada et al. [102] compared

CW-SPM generators with various slot and pole combinations for achieving high

efficiencies and high torque densities.

The key favourable characteristic of CW is its non-overlapping coils, which reduce the

overall amount of copper required and shortens end winding length. Murakami et al.

[103] exploited CW’s advantage of non-overlapping coils in the design of high-speed

constant torque IPM machines with reduced size and increased efficiency. Using

different prototypes, they showed that flat, rectangular shaped windings resulted in

shorter end winding length and higher slot-fill factor.

Non-overlapping coils also simplify the stator winding process and permit pre-wound

stator assemblies, thus increasing the slot-fill/packing factor. Jack et al. [104] used


18

compressed copper conductors on separable tooth pieces to achieve a 78% slot-fill

factor. They also showed the significant increase in efficiency and torque density in a

machine constructed by this method. Akita et al. [105, 106] showed performance

characteristics of a machine produced by the joint lapped-core method, which achieved

a 75% fill factor. This was one of the pioneering methods which achieved such a high

slot-fill factor on laminated cores. There were also several patents regarding the

manufacturing of CW stators with the aim of simplifying the winding process and

achieving a high slot-fill factor [107-111].

CW is often contrasted with the more commonly applied DW structure. Asano et al.

[112] showed that CW produced larger radial forces acting on each stator tooth,

resulting in increased vibrations compared to DW. They addressed this issue by

enlarging the airgap size. Magnussen et al. [113] compared parameters, torque and

speed characteristics of an SPM machine having distributed and CW with different

Spp combinations. They concluded that the DW model produced larger torque up to

base speed while the CW model achieved a wider CPSR. Kwon et al. [114] presented

a comparative study on the IPM machine with CW and DW for field-weakening

applications. In this study they showed that the saliency ratio in CW was lower

compared to DW, leading to lower reluctance torque and hence lower overall torque

produced. However, it was also noted that lower current was required for weakening the

field, making the CW machine more efficient in the field-weakening region.

CW are usually classified as single-layer, (alternate teeth wound), or double-layer, (all

teeth wound). Both the single and double-layer windings have advantageous

characteristics in different applications. Ishak et al. [115] compared machine parameters

and performance characteristics of a single and double-layer CW SPM machine. They


19

concluded that the latter resulted in significantly lower torque ripple, but also had

reduced torque density. El-Refaie et al. [18, 116] emphasised the importance of

winding inductance on operating performance and presented an analytical model to

calculate inductance. They compared the self and mutual-inductances of single and

double-layer fractional slot CW, and showed that both inductance values were higher

with single-layer windings due to higher slot leakage and MMF harmonics. El-Refaie

and Jahns also compared the efficiencies of single and double-layer CW in an SPM

machine. They highlighted that double-layer windings result in higher efficiency due to

lower harmonic content compared to single-layer windings, but result in lower overload

torque capability. Wrobel et al. [23] studied the thermal performance of a CW outer

rotor PM machine and indicated the significant increase in temperature of the double-

layer wound machine compared to single-layer one.

The inherent fault tolerance capability of CW makes it an excellent choice for high

reliability applications. Abolhassani and Toliyat [117] exploited the fault tolerant

behaviour of CW and designed a five phase machine, which was proven to have little

performance de-rating under single phase and switch faults. Bianchi et al. [20] presented

design considerations including the fault resistant capability of a fractional slot CW.

They pointed out that while single-layer windings present higher fault resistant

capability, they are more suited for machines with larger airgaps due to the increase in

airgap harmonics. Shah et al. [118] analysed faults in double-layer, vertical and

horizontal concentric wound stators. Fault currents measured from these two

configurations had almost exactly the same magnitudes.

There was also a significant amount of research interest in optimising the performance

of CW machines with various rotor types and structures. Lindh et al. [119] presented


20

detailed comparisons on CW-IPM and CW-SPM motors having open and semi-closed

stator slots. They concluded that the choice of IPM rotors resulted in higher overall

efficiencies compared to SPM rotors with open slots. Salminen et al. [120] also

compared the performance of CW machines between the SPM and IPM rotor types with

CW. Their results indicated that machines with surface magnets produced larger pull

out torque, whereas machines with embedded magnets resulted in lower copper loss.

Han et al. [121] compared losses between a single- and double-layer magnet barrier

rotors with DW and CW. Experiments carried out showed a trade-off between the rotor

and stator losses in the two rotor types. Kawaguchi et al. [122] proposed a cogging

torque reduction technique in an IPM machine with CW by rotor flux barrier shaping.

Kano et al. [123, 124] also attempted to reduce torque ripple in a CW-IPM machine by

varying the rotor flux barrier angle. Kim et al. [125] also produced a design to reduce

torque ripple and cogging torque by simple variations to both the stator and rotor core

geometry. Lee et al. [126, 127] compared the performance of a CW IPM machine with

various rotor shapes, and concluded that C-shaped magnets had the most potential in

reducing torque ripple and improving torque density. Kim et al. [128] studied the

demagnetisation characteristics of various buried rotor types with CW, and stated that

the multi-barrier design was the least susceptible to demagnetisation compared to the

single-layer and v-shaped designs.

The application of CW resulted in an increase in inductance values which helped in

achieving optimal field-weakening conditions. This created significant research interest

in the application of CW to machines used for field-weakening applications. El-Refaie

and Jahns [129] first performed a comparison of different machine types including: IPM

and SPM machines with DW and an SPM machine with CW. The comparison proved


21

that SPM machines with CW had excellent field-weakening potential. Later, El-Refaie

and Jahns [130, 131] exploited the field-weakening potential of CW in SPM machines

and performed an in-depth study in this area of application. They successfully designed

and built a prototype which managed to achieve very good efficiency with an extremely

wide 6:1 experimental CPSR. Soong et al. [132] demonstrated the use of parameter

planes on SPM machines with CW to narrow down the design region, adhering to

freedom car specifications. Munoz et al. [133] presented a comparison of PM machines

with CW and DW. They noted that the benefits of having shorter end turns with CW is

lost as stack length is increased. In terms of field-weakening ability, CW reduces the

saliency ratio thereby limiting the field-weakening ability of the machines. Deak et al.

[134] measured the field-weakening performance of two different machines: one having

double-layer CW with semi-closed slots and the other having single-layer CW with

open slots and unequal tooth-widths. It was shown that overall losses for the single-

layer winding machine were lower in the constant torque region but became larger

compared to the double-layer machine in the wider constant power speed regions.

Although the increase in harmonic content created by CW aids in achieving optimal

field-weakening conditions, it also introduces additional harmonics, thus increasing core

and magnet losses especially at higher frequencies. A significant amount of research has

been conducted to model and reduce these additional losses. Mellor et al. [135]

illustrated a computationally efficient FE method used to calculate losses and power

output from SPM machines with CW. Meier and Soulard [136] attempted to estimate

iron loss from measured magnetic flux densities of an SPM machine with CW. They

illustrated the difficulties in calculating losses in tooth-tips and yoke due to non-uniform

flux distribution. Nuscheler [137] also presented a method to calculate the rotor eddy


22

current losses of PM machines with CW, in which he discussed how losses can be kept

to a minimum. Bottauscio et al. [138] measured losses of a SPM machine with CW at

various operating speeds, considering both solid and laminated rotor cores. They

showed that while PM losses remained relatively constant, there was a huge difference

in rotor core losses (rotor core loss was almost negligible with the laminated core).

Nakano et al. [139] modelled the eddy current losses in a SPM machine with CW and

emphasised the importance of choosing an appropriate slot and pole combination in

achieving low losses. Yamazaki et al. [140] performed a rotor loss comparison between

the IPM, inset and SPM rotors, in which he showed that the IPM had lowest magnet

losses followed by the inset. The SPM produced the greatest amount of losses but could

be effectively reduced by increasing the number of segments. It was also confirmed that

magnet losses in CW are higher compared to DW [141]. Polinder et al. [142], although

not successful in modelling the losses of machines with CW, indicated useful pointers

to consider before loss modelling.

The increased harmonic content produced by CW also resulted in increased vibrations

and acoustic noise during operation. Wang et al. [143] presented a study of resultant

vibrations caused by a modular CW machine. Lee et al. [144, 145] presented a study of

acoustic noise on IPM machines with CW. It was shown that with the optimal slot

opening width, barrier and pole angle, normal forces can be reduced and hence acoustic

noises will lessen. Araki et al. [146] addressed the effects of vibrations in a CW-PM

machine and attempted to reduce its effects by the inclusion of slits on the rotor surface.

Some configurations of CW had asymmetrical structures which resulted in unbalanced

radial forces acting on the rotor. Xu and Li [147] pointed out the effects of radial

unbalanced pull forces caused especially by CW, and charted the unbalanced forces for


23

two different 9-slot motors with CW. It was observed that the choice of slot and pole

combination had a very large effect on unbalanced radial pull force.

Often accurate 3D FE modelling requires large amounts of time and computational

resources. Therefore there have always been attempts at deriving a more

computationally efficient and accurate mathematical representation of the CW model.

Jingai at al. [148] illustrated mathematical models of brushless motors with CW under

various operating conditions. Qu and Lipo [149] presented a general closed-form

analytical method which could be used to model single and double-layer CW.

Abdennadher et al. [150] presented an analytical derivation of inductances of PM

machine with CW and DW. Tangudu et al. [151, 152] presented a lumped parameter

circuit model for an IPM machine with fractional slot CW. They also proposed an

economical and accurate method to separate the reluctance and magnet torque terms.

Meier and Soulard [153] attempted to validify the d-q axis theory on SPM machines

with CW. They showed that steady state operating characteristics such as torque can

still be calculated despite the increase in MMF harmonics. Duan et al. [154] proposed a

particle swarm optimisation method to optimise designs of SPM machines with CW.

This proposed method had a faster computation time compared to FE analysis and was

proven to agree with analytical methods.

Currently there are keen research interests in the sensorless control of PM AC machines

with CW. Reigosa et al. [155] presented a comparative study on the self-sensing

capability of various machine types, including the IPM machine with fractional slot CW.

In this study they made useful non-subjective pointers in which preferred attributes for

both CW and DW were stated. Eilenberger el al. [156, 157] implemented sensorless

control on two different PM machines with single- and double-layer CW. It was shown


24

that the estimated rotor position was almost identical to the actual rotor position with

only slight deviations in both machines. They also tested the overload, short circuit and

field-weakening capability of the single-layer machine, and commended on this

performance for future traction applications. Imai et al. [158] studied the effects of

sensorless control of a CW machine with two different rotor configurations. They

showed that the rotor without flux flowing through the inter-pole link sections achieved

better sensorless performance. Sensorless control strategies have also been successfully

implemented in an IPM machine with CW by Kojima et al. [159].

From 2007 onwards, the use of CW-PM machines began to gain popularity for

industrial applications. Wang et al. [160] studied the CW-IPM machine for undersea

propulsion with the requirement of a high power factor. They indicated with the aid of

the parameter plane the trade-off between CPSR and power factor. Ionel [161]

highlighted the increased use of electrical motors for household appliances in the US,

including the use of CW. Cistelecan and Popescu [162] exploited the advantage CW’s

simplified winding structure to design a 10kW synchronous wind generator, in which

they also highlighted the need to use double-layer windings because of the lower MMF

harmonics produced. Kazmin et al. [163] presented a comparative study on various

winding configurations and machine geometries to design an in wheel traction motor.

They found the CW-SPM machine most suitable for this particular application. Alberti

et al. [164] designed, manufactured and successfully tested a 1kW integrated starter

alternator, achieving the desired high starting torque and wide CPSR characteristics.

Germishuizen and Kamper [165, 166] designed a large 150kW railway traction machine,

clearly illustrating the design process and considerations; performance results obtained

from the manufactured machine were also documented. In a recent paper, El-Refaie


25

[167] presented a detailed overview of fractional-slot CW PM machine technology and

its applications, highlighting the large number of major research contributions to this

area. He also stated the challenges faced and proposed future work in this area of

research.

1.3 SCOPE AND ORGANISATION OF THESIS

The general objective of this thesis is firstly to present a feasibility study on the IPM

machine with CW used for field-weakening applications. Subsequently to design,

optimise and construct a CW-IPM machine to achieve a wide field-wakening range with

specific design targets. Finally, with the successful design and experimental verification

of the prototype machine, modifications will be proposed to increase its efficiency, as

well as to scale up the machine. The study, design and experimental verification will

help clarify the advantages and disadvantages of implementing CW in IPM machines,

as well as to demonstrate its prospects in industrial applications requiring high

efficiency over a very wide field-weakening range.

This thesis is organised as follows:

This chapter covers the general background of relevant technology. It also provides an

in-depth review of relevant work for this thesis and highlights the scope and

organisation of this thesis.

Chapter 2 will present numerical techniques in solving electromagnetic field problems.

Of the various numerical methods, the most commonly used method – the FE method –

will be explained in greater detail. The chapter will show how the mathematical

formulation of the physical model is derived; also how approximations are formulated


26

and solved using Galerkin’s method and Newton Raphson’s iteration. Lastly, chapter 2

will give a basic overview of a 2D FE design process with the use of Magsoft-Flux2D.

Chapter 3 will state advantages and disadvantages of implementing CW on the IPM

machine. It will study various parameter optimisation methods that are used with the

CW-SPM machine; the suitability of these methods will be determined for

implementation on the CW-IPM machine. With the aid of FE models, a suitable slot

and pole combination as well as suitable rotor magnet geometry will be determined.

Chapter 4 will clearly state goals for the design of a CW-IPM machine prototype. The

chosen base layout in chapter 3 will be optimised to achieve a wide field-weakening

range and desired torque/power characteristics. The electromagnetic as well as

structural properties of materials, which affect the performance of the machine will also

be studied. Lastly, chapter 4 will give detailed specifications of the optimal model

which will be constructed for verification purposes. The overall machine parameters and

performance characteristics will be predicted using FE analysis and output

characteristics will be shown.

Chapter 5 will show how CW machines are more susceptible to frequency related losses

compared to DW. Losses in various parts of the final machine model will be determined

with the use of 2D and 3D FE analysis. With the material properties available,

mechanical losses will be calculated. The chapter will also show how losses vary with

material type, as well as with different rotor configurations. Finally the overall predicted

losses at various operating speeds will be used to predict the overall efficiency of the

machine.


27

Chapter 6 will illustrate the control methodology, controller architecture and inversion

technique used to produce the final three-phase inputs to the prototype CW-IPM

machine. It will also compare how the d-axis current trajectory calculated by a widely

used vector control technique for DW-IPM differs from the ‘ideal’ trajectory obtained

through repetitive testing.

Chapter 7 will conclude and verify the entire design process of the CW-IPM machine in

this work. The manufacturing process of the prototype CW-IPM machine will be stated

and detailed performance characteristics of the prototype will be shown. Lastly the

machine’s performance characteristics will also be compared to two other equally sized

DW-IPM machines.

Based on the confidence gained from the verification of FE results and lessons learnt

from the design of the first CW-IPM prototype, chapter 8 will propose two different

models, (derived from the prototype with geometrical alterations), to optimise efficiency.

Also the scalability of prototype CW-IPM will be studied and scaled up versions will be

presented.

Chapter 9 will conclude the work presented in this thesis and provide suggestions for

future work to be done on the CW-IPM machine.

28

CHAPTER 2NUMERICAL METHODS FOR THE ANALYSIS AND PREDICTION OF MACHINE PARAMETERS

2.1 INTRODUCTION

Present day numerical methods provide a high degree of accuracy in the design of

electrical machines. They allow the designer to predict and optimise machine

parameters and operating characteristics before committing to build the physical

structure, reducing the resources and time required to complete the machine with

desired specifications.

In electrical machines, behaviour is governed by the interaction of electromagnetic

fields created by armature reaction and permanent magnets. These electromagnetic

fields can be expressed in terms of Maxwell equations and the machine’s performance

can be predicted by solving these equations by various methods, some of which are

shown in Fig. 2.1.

Fig. 2.1 Various methods to solve Maxwell equations and predict machine performance

Numerical methods

Finite element method

Electromagnetic analysis

(Maxwell equations)

Analytical methods

Lumped-parameter model

Equivalent circuit model

Finite difference method 2D

3D

Chapter 2: Numerical Methods for the Analysis and Prediction of Machine Parameters

29

The path indicated in bold in Fig. 2.1, shows the preferred method for solving most

modern-day, complex magnetic field problems. Although analytical methods have much

faster solving times compared to numerical methods, they are limited to relatively

simple problems. Compared to other numerical techniques, the FE method has the

following advantages [168]:

Applicable to any field problem (Some of which are: electromagnetic, heat

transfer and stress analysis).

No restriction on geometrical shape.

No restriction on boundary conditions and loading.

No restriction on material properties.

Accuracy versus time can be varied according to the choice of mesh size.

The FE solution closely resembles the actual field distribution in the region.

Chapter 2 will give a general overview of the FE method, leading up the FE design

methods used in to this work. It shows how mathematical formulations of the physical

model are derived, as well as how approximations are formulated and solved using the

Galerkin’s method and Newton Raphson iteration.


30

2.2 THE FINITE ELEMENT METHOD

The FE method is a numerical technique used to solve field problems of structures with

complex geometries and non-linear material properties. This is done by dividing the

entire region of analysis into smaller finite elements which are connected to the

neighbouring elements by two or more nodes. By applying field equations in each of the

elements and ensuring continuity at each node, equations for the entire structure can be

solved. FE analysis of a physical event can be typically expressed in the following steps:

Pre-processing

Construction of geometry

Subdividing study area into finite elements (Meshing)

Assigning material properties

Assigning excitation sources

Assigning boundary conditions

SolvingDeriving and assembling element matrix equations

Solving the equations for unknown variables

Post-processing Analysis of results obtained

There are numerous forms of finite element applications, some of which are: structural,

magnetic and thermal. These applications can be classified into different types of field

problems, such as:

StaticInput sources are time invariant

Used for steady state DC/fixed load analysis

TransientInput sources are time-variant

Used for transient AC/load-variant analysis

Steady State Field sources are time-variant but periodic

Used for steady state AC/constant load-variation analysis


31

2.2.1 Brief Background of Finite Element Analysis

The first use of FE analysis for solving magnetic field problems involving rotating

electrical machinery dates back to the 1960s. Ahamed and Erdelyi [169] introduced a

mathematical model for the salient pole machine in terms of partial differential

equations. Erdelyi et al. [170] then implemented the theory based on this method to

create an FE model to model the transient behaviour of a DC motor. Silvester and Chari

[171, 172] were among the first to introduce solutions to non-linear electromagnetic

field problems for electrical machines. Since then, there has been ongoing research in

FE analysis of electrical machines. Although the FE method, (like all other modelling

methods), cannot be a hundred precent accurate, its ability to solve complex problems

with high degrees of accuracy has made it an essential part in the design of almost all

high performance electrical machines.

2.2.2 Mathematical Formulations of the Physical Model

Maxwell’s equations are used to describe the non-linear magnetic fields within the

electrical machine and how they relate to their sources. In differential form Maxwell

equations can be expressed as: = 0 (2.1)× = (2.2)× = (2.3)

The zero divergence of magnetic flux ( ) in (2.1) indicates that no source is present.

(2.2) describes how magnetic field ( ) reacts to the electric current density ( ). (2.3)

represents the induction of electric field ( ) due to the negative rate of change of

magnetic flux.


32

Mathematical formulations for the physical model involve solving the electromagnetic

problem. This is done by solving for the magnetic field distribution given an input

source – that is, solving (2.2). For simplicity, only the current source excitation is

considered first. In this case, the magnetic field is proportional to the flux density as

expressed in (2.4): = (2.4)

where,

= Permeability of the material

By substituting (2.4) into (2.2), we get:

The electromagnetic problem can simplified by introducing the magnetic vector

potential ( ) and electric scalar potential ( ). The relationship between these two

potential values and field variables is shown in (2.6) and (2.7) respectively.= × (2.6)

+ = (2.7)

Substituting (2.6) into (2.5): 1 × × = (2.8)

Simplifying this problem further with the Laplacian of , (2.8) can be expressed as:1 × = (2.9)

and subsequently simplified by the use of Coulomb gauge = 0 to give:1 = (2.10)

× 1 = (2.5)


33

Current density can be expressed in terms of field values shown in (2.11) and the field

values can then be replaced by potentials from (2.6) and (2.7).= + × (2.11)

= + + × × (2.12)

where,

= Conductivity of the material

= Velocity of a material with respect to a given reference frame

From (2.10) and (2.12): 1 + × × = (2.13)

(2.13) is the governing equation physical model without permanent magnet excitation.

To create a model involving permanent magnet excitation, the permanent magnet

material can be modelled by a magnetisation vector model based on the B-H curve.

Considering permanent magnet excitation, (2.4) becomes:

= + (2.14)

where,

= Magnetisation vector

By substituting (2.14) into (2.2) the equation can be modified to include permanent

magnet excitation in addition to the current only excitation:1 + × × = + × (2.15)

The term describes the input resulting from armature current and × describes

input resulting from permanent magnets. For the sake of simplification these two terms

will be written as J and J respectively. To eliminate the velocity term, the moving


34

frame is taken as the reference frame and the relative velocity becomes zero. (2.15) is

then reduced to: 1 + = J + J (2.16)

(2.16) is the general governing equation for the physical model with time varying fields

with the consideration of both current and permanent magnet excitation.

In two dimensions, the magnetic vector potential has only z-axis components, thus it

can be reduced to the z-axis potential ( ). The governing equation for a two

dimensional analysis is therefore given by:1 + = J + J (2.17)

The partial differential equation in (2.17) can be regarded as the system equation. With

the magnetic vector potential used as a key variable, the entire study domain can be

discretised by a mesh of finite elements.

2.2.3 Discretisation of the Study Domain

The FE method solves the partial differential equation (2.17) by looking for an

approximate function which describes the behaviour of each element. The elements are

held together by nodes. The accuracy of the solution would depend on the size of the

elements. A smaller mesh results in higher accuracy, but requires more elements to

make up the study domain, leading to a longer computing time. In general, the mesh

should be most dense where field-change gradients are the largest and least dense where

the field change is relatively constant. Fig. 2.2 shows some typical elements for one-,

two- and three-dimensional problems. For one-dimensional domains, shorter

interconnected line segments make up the original linear structure. For two-dimensional


35

domains, common elements would be rectangles for discretising rectangular regions or

triangles for more irregular-shaped regions. For three-dimensional domains,

tetrahedrons and hexahedrons are the more commonly used element shapes.

One dimensional (line) elements

Two dimensional (surface) elements

Three dimensional (brick) elements

Fig. 2.2 Typical finite elements

Each of these elements can be represented by a polynomial in terms of the potential A.

For example the basic three node triangle with nodal degrees of freedom can be

represented by: = + + y (2.18)

For a six node triangle, the expression would be represented by a quadratic equation

(2.19) with six nodal degrees of freedom. = + + y + + xy + (2.19)


36

For a three-dimensional brick element, the field can be expressed as:= + + y + + xy + + + (2.20)

Solving these polynomials requires the constants to be solved in terms of the

interpolated field variables An.

Using the basic three node triangle as an example, unknown constants , and

have to be solved. The three node triangle is represented by x and y-axis coordinates

with x1 = y1 = y2 = 0 as shown in Fig. 2.3.

Fig. 2.3 Two dimensional triangular element

Evaluating the expression at the nodes:

= 1 0 01 01 (2.21)

Solving for :

= = = ( ) + (2.22)

Thus the interpolated field expression for the three node triangle is given by:

= [ ][ ] { } (2.23)

A1(x1, y1)

A2(x2, y2)

A3(x3, y3)

)

x-axis

y-axis


37

where,

[ ] = [ ][ ] [ ] = 1 0 01 1 01 { } = (2.24)

The discretised magnetic vector potential in each element can be generally expressed as:

where,

= Number of nodal degrees of freedom

Unknown field quantities in (2.17) can then be replaced by (2.25). These replaced

quantities however, contain errors. These errors or residuals can be reduced if error

minimisation techniques are used to derive the equations. Of the many error

minimisation methods available, Galerkin’s method is most commonly used for solving

boundary value problems in electromagnetics [173]. Before applying Galerkin’s method,

certain boundary conditions have to be stated. These boundary conditions will be shown

in the next section.

2.2.4 Definition of Boundary Conditions

Imposed boundary conditions affect the accuracy and efficiency of the FE solution

[174]. There are three main groups of boundary conditions:

Dirichlet’s condition

Neumann’s condition

Periodicity condition

= ( , ) (2.25)


38

Dirichlet’s Boundary Condition

In Dirichlet’s boundary condition, a value is assigned on the boundary

conditions are most commonly imposed on the surface of the rotor inner diameter C-D

and stator outer diameter A-B as shown in Fig 2.4.

Fig. 2.4 Dirichelet boundaries

It is common to assign the condition of = 0, as long as the leakage flux beyond these

boundaries is negligible. The high magnetic permeability of the core materials normally

ensures that the majority of the flux is contained within the boundaries, hence making

the assumptions valid.

Neumann’s Boundary Condition

Neumann’s boundary condition is satisfied when the derivative of is assigned to be

normal to the boundary Neumann’s boundary condition is normally imposed to a

region that has symmetry.

A

B

C

D


39

Periodic Boundary Condition

Periodic boundary condition is assigned between two or more boundary lines using

symmetries in the geometry or magnetic field distribution. Among these lines, a

principal line is selected and the other line(s) is (are) expressed as a function of the

potential of the principal line. This boundary can significantly reduce the size of the

numerical model. Fig. 2.5 shows a 4-pole machine with quarter symmetry..

Fig. 2.5 Machine with quarter cyclic-symmetry

It is advisable to solve boundary value problems analytically whenever possible.

However, most practical problems do not have an analytical solution, so popular

approximate methods such as Galerkin’s method are used to derive the FE equations.

2.2.5 Galerkin’s Method for Deriving Finite Element Equations

Weighted residual and variational methods are the more commonly used methods in

deriving FE equations. Galerkin’s method is a particular form of the weighted residual

method and is the most popular method due to its accuracy and simplicity of

C

ABD


40

implementation. Galerkin’s method deals with the differential equation directly and

solves the field problem by residual reduction [175-177].

To describe Galerkin’s method, a domain is declared, in which the physical problem

is defined, letting ( , ) be a differential operator containing the trial solution ( , ) and ( , ) be a given forcing function of and .

The trial solution ( , ) will contain an error and there remains a residual ( ( )).

The mathematical statement to the physical problem can be expressed as:

In domain : ( , ) ( , ) = ( , ) (2.26)

By the use of a weight function ( ), the integral of the residuals is forced to zero over

the domain . This can generally be expressed as:

( , ) = 0 (2.27)

In terms of the machine model equation in (2.17), the expression would be:

1 + + J J = 0 (2.28)

For Galerkin’s method, in each element is chosen to be equal to an interpolating

function ( ) [178]: = for i = 1, 2 , 3, …, E (2.29)

where E is the total number of elements.

The general expression in computational matrix form is given by:[ ]{ } = { } (2.30)

where [ ] is the global coefficient matrix which is dependent on interpolating functions

and its elements in the column and row – are given by:


41

= (2.31)

As before { } is the column vector of unknown coefficients:

{ } = (2.32)

and { } is the column vector whose elements are dependent on the forcing functions ( ).

= ( ) (2.33)

In electromagnetics, (2.30) describes a deterministic system where there exists an input

source or excitation.

2.2.6 Solving Finite Element Equations with the Newton Raphson Method

Solving electric machine problems involves dealing with non-linearities in both

electromagnetic and structural material characteristics. For this thesis, an example of a

problem involving non-linearity is calculating mechanical stress inflicted on the inter-

pole link sections under high speed operations, where the stress on the core material is

not directly proportional to the strain. These non-linear equations can be solved using

iterative methods such as the Newton Raphson method [179, 180] – a common method

used for solving FE problems.

To formulate the Newton iteration, a general 2D energy functional ( ) will first be

defined. From (2.9), where the magnetic potential is expressed in terms of the input

current density, the following expression can be obtained: 1 + 1 = (2.34)


42

and a suitable functional for (2.34) would be:

( ) = ( ) (2.35)

where ( ) is the energy density associated with the trial solution.

With the determined functional ( ) and the trial solution , the gradient of ( ) is

first found by Taylor series expansion:

= + + (2.36)

The iteration process can now be set up, letting be the correct solution to . The trial

solution can be expressed as:

= + (2.37)

With an initial assumption of the estimated potential , the iterative process can begin

and the step difference from the correct potential can be calculated. This step

difference is added to to achieve a better estimate and the entire process is repeated

until the correct potential is found. Fig. 2.6 gives a basic procedure for Newton

Raphson’s method of achieving convergence:


43

Fig. 2.6 Newton Raphson method

This iterative process can be generally expressed as:

( ) = ( ) ( ) ( ) (2.38)

2.2.7 Process of a Time Stepping Finite Element Model

When solving a time-dependent problem, the solution to the whole problem consists of

solving the problem at discrete time intervals (time steps). The solutions at each time

interval are dependent on the solution of the previous time step. Of the various

application types, transient or time stepping analysis is most commonly used for the

analysis of electrical machines, due to many time-dependent aspects such as: movement

of the rotor, time-variant excitation of individual phases and the developed torque. The

flowchart for the time stepping solving process is shown in Fig. 2.7:

( )

( )

( )Slope Slope

( )


44

Fig. 2.7 Flow chart for the time-stepping finite element process

Yes

Terminate time stepping

End

NoYes

Yes

Time Step(Tstep = Tstep + 1)

Rotation of rotor mesh

Generation of coefficient matrix

Start

Error(solution)<

Error(tolerance)

Post Process

Recalculate in next iteration

Solve for approximate solution


45

2.3 FINITE ELEMENT METHOD FOR DETERMINING MACHINE

PARAMETERS AND PERFORMANCE CHARACTERISTICS

In this work, a number of machine models were created, compared and optimised FE

analysis. The final design chosen for prototype construction is a concentrated wound,

double-layer, 18-slot, 14-pole, IPM machine with v-shaped magnets, as shown in Fig.

2.8. Here, the design process of the model using Magsoft-Flux2D will be discussed in

detail.

Fig. 2.8. Prototype machine geometry – showing regions

The stages in a basic design process are as follows:

Construction of geometry and assignment of mesh (discretisation)

Definition of material properties

Performance analysis

2.3.1 Construction of Geometry and Assignment of Mesh

During the construction of geometry, it is important for the designer to recognise

symmetry in the design. When used together with the appropriate boundary condition,

the computational time can be significantly reduced due to a reduced size of the study

Statorcore

Stator windings

Rotor magnets

Rotor core

Shaft

AirgapStator slot opening

Air sections in magnet slots


46

domain. Common types of symmetry include axis symmetry and plane symmetry. For

rotational machines, axis symmetry can be applied if the revolutionary axis passes

through the origin of the coordinate system. For the models created in this work, axis

symmetry (quarter symmetry in particular) could only be used on the integral-slot DW

machines, where the phase coils are equally distributed around the stator (fig. 2.9 shows

a model of UNSW segmented DW-IPM with phase coils repeating every quarter).

Fig. 2.9. DW-IPM showing the repletion of phase coils every quarter

After geometrical construction of the principal portion, a mesh has to be created. In FE

analysis, the accuracy of the approximate solution depends to a great extent on the

quality of the mesh. Some general rules for meshing include:

The mesh should be well proportioned.

Ideal elements for a surface mesh should equilateral triangles or squares.

The mesh should not be unnecessarily fine.

A typical mesh structure for the prototype machine with consideration of the

abovementioned rules is shown in Fig. 2.10.


47

Fig. 2.10 Mesh structure of the CW-IPM machine

After the mesh is created, the quality of mesh can be further validated by observations

such as:

The field lines should be continuous within a specified region.

The action force should be equal to the reaction force in a rotating machine.

Current and voltage through a coil should be the same when computed by

different methods.

2.3.2 Defining Material Properties

Before defining the desired regions to parts of the created machine geometry, material

properties have to be defined – for example, properties for the permanent magnets, rotor

and stator core, as well as windings. Material properties are made up of various

behavioural laws such as:

Material Type Constitutive Equations Material property

Magnetic = (2.4) = Magnetic permeability

Dielectric = (2.39) = Electric permeability

Conductive = (2.40) = Electric conductivity


48

Additionally, materials may be anisotropic and non-linear; material properties may also

vary with temperature and frequency. Thus, the behavioural laws can get very complex

if an accurate representation of materials is required.

Magnetic materials are generally characterised by the hysteresis cycle, otherwise known

as the B-H curve. B-H curves for soft and hard magnetic materials are shown in Fig.

2.11a and 2.11b respectively.

Soft Magnetic Materials(Core)

Hard Magnetic Materials(Permanent magnets)

(a) Soft magnetic materials (b) Hard magnetic materialsFig. 2.11 B-H Curve for hard and soft magnetic materials

Isotropic electrical steel laminations are chosen as the core material for this prototype

and an analytic solution is used to model its properties. The solution consists of a

straight line representing the linear region (2.39) and an arctangent curve (2.40)

representing the saturated region shown in Fig. 2.12. This solution is used instead on

tabulated B-H curve as specific material properties were not available at the beginning

of this work. Furthermore, having an exact material match was not crucial to the

outcome of this thesis.

B

H

1st

Quadrant

3rd

Quadrant

B

H

2nd

Quadrant


49

Fig. 2.12 Representation of core material characteristics in terms of an analytic solution( ) = (2.39)

( ) = + 2 ( 1)2 (2.40)

where,

= magnetic permeability of free space

= initial relative permeability

= magnetic polarisation at saturation

Permanent magnets are chosen as the rotor field source. The performance of magnets is

most commonly described in the second quadrant of the B-H curve [181]. The magnet

temperature rating is chosen such that the knee of the demagnetisation curve doesn’t

enter the second quadrant, and the B-H curve can be represented by a linear function, as

shown in Fig. 2.13. This unidirectional linear function can be represented by (2.41).

Fig. 2.13 Representation of permanent magnet material demagnetisation characteristics

B [T]

H [A/m]

Linear representation of

unsaturated region

Asymptote line passing through = +Saturated region represented

by an arctangent curve

B [T]

H [A/m]t

Demagnetisation line


50

//( ) = // // + (2.41)

After declaration of B-H characteristics, the magnet orientation has to be defined.

Common choices of orientation include positive radial, negative radial, positive

orthoradial and negative orthoradial. The prototype, however, has v-shaped magnets,

thus making the abovementioned orientation choices invalid. The magnets shown in Fig.

2.8 have to be individually orientated.

2.3.3 Coupling of Electrical Circuits

An external electric circuit can be coupled to the magnetic model via solid or stranded

conductors. While solid conductors reduce losses at low frequencies, this form of

conductors result in high eddy current loss at higher frequencies, thus stranded

conductors are more suitable for AC machine designs. A typical circuit with three-phase

current excitation is shown below, (noting that a two phase current excitation is used to

represent the actual three phase model in the mesh current method [182]):

Fig. 2.14 Three-phase star conneted circuit with current excitation

End winding inductances

Current sources

Positive and negative phase coils


51

Current sources are defined, and coils of the three different phases are assigned to their

respective regions in the FE model. The terminal voltage ( ) comprises the voltage

generated due to the winding resistance ( ), end turn inductance ( ) and generated back

EMF due to flux ( ) as show below:

= + + (2.42)

2.3.4 Performance Calculation

Back EMF

To determine the induced voltage in the machine, a prime mover is required. In

Magsoft-Flux2D this can simply be done by assigning a fixed rotor speed. A similar

circuit to Fig. 2.14 can be used, except that in this case the current sources would be

replaced by infinite resistance assigned to all three phases. Without excitation, the

induced voltage in the conductors (2.43) would only be from the instantaneous induced

back EMF ( ) given by: = (2.43)

Cogging Torque

The interaction between the rotor magnets and the stator teeth results in a variation of

reluctance in the airgap. This amount of variation, as well as the magnitude of magnet

flux linked across the airgap, determines the magnitude of cogging torque produced. In

Magsoft-Flux2D, cogging torque ( ) is found by rotating the rotor slowly with an

imposed speed and finding the rotational force ( ) using the virtual works method, as

expressed in (2.44).


52

= (2.44)

where,

= Mechanical virtual work done

( ) = Mechanical displacement

For the calculation of cogging torque, the airgap mesh should be made up of very good

quality elements. Thus it is advisable to use a three layer airgap as shown in Fig. 2.15:

Fig. 2.15. Meshing of a three-layer airgap

Output Torque

In Magsoft-Flux2D, generated torque can also be calculated by the virtual work method

as described earlier. The circuit in Fig. 2.14 can be used and excitation current values

can be defined as: = 2( 2 + ) (2.45)= 2 2 + 23 + (2.46)

where,

= frequency of excitation

= time at each iteration

= the current angle

Compressible airgap

Stationary airgapRotating

airgap


53

2.4 CONCLUSION

This chapter introduced the FE method used for modelling machine characteristics and

performance. It presented the different stages and types of field problems of FE analysis

relevant to this work. The derivation of the system equations in terms of partial

differential equations and subsequent discretisation of the study domain were shown.

This chapter showed various element types and how elements were connected through

expressions evaluated at nodes. Galerkin’s method for deriving the FE equations and

Newton Raphson’s method of achieving an error-free solution were shown. Lastly, this

chapter also stated the FE design process of the prototype machine, indicating how key

machine, parameters and performance characteristics were calculated in Flux2D.

FE methods shown in this chapter will be used in this thesis to compare, design and

optimise permanent magnet machine models. Other than Flux2D, other FE methods

used include: ANSOFT-Maxwel13 – used to model 3D FE electromagnetic analysis and

ANSYS – used to model mechanical stresses in the rotor.

54

CHAPTER 3INVESTIGATION OF THE CONCENTRATED WINDING IPMMACHINE FOR WIDE FIELD WEAKENING APPLICATIONS

3.1 INTRODUCTION

The principal cause of developed torque in PM machines is the interaction of the fields

from the permanent magnet and rotating stator electromagnetic field. Therefore the

quality of torque produced is largely dependent on the winding design and the

configuration of the magnet poles.

In three-phase synchronous AC machines, windings which result in sinusoidal back

EMF waveforms are desirable for achieving high efficiency and low torque ripple [183].

Before the 21st century, the means of achieving sinusoidal back EMF was primarily to

design windings so that MMF waveforms were close to sinusoidal. This made

distributed windings (DW) the winding of choice until recently when Cros and

Viarouge [16]; Magnussen and Sadarangani [17] proved that sinusoidal EMF in SPM

machines could be generated by the use of fractional-slot CW.

This chapter studies the suitability of applying fractional-slot CW in IPM machines to

achieve the desired performance characteristics. With the help of FE analysis, several

CW models will be created and compared to an integral-slot DW model. Subsequently,

the field-weakening performance of two CW-IPM with different magnet geometry will

be compared to the CW-SPM machine. This chapter is a preliminary study to ensure

that the benefits of applying CW outweigh the disadvantages, so that further research

does not lead to futile designs. It will also set the basis for the design and optimisation

of the final model in the next chapter.

Chapter 3: Investigation of the Concentrated Winding IPM Machine for Wide Field-weakening Applications

55

3.2 CHOICE OF SLOT AND POLE COMBINATION

Despite numerous advantages over DW, such as a higher slot-fill factor, shorter end-

windings and decreased manufacturing complexity, CW has been unpopular for use in

AC machines due to its characteristic of producing MMF and EMF waveforms which

are rich in harmonics. However, in recent years it has been verified that CW has the

capability of producing sinusoidal EMF waveforms with appropriate slot and pole

combinations [16, 17], sparking global research interest in this winding type for AC

synchronous machines.

Slot and pole combinations are commonly referred to by the number of slots per pole

per phase (Spp). For example, a 3-phase machine with 6-slots and 2-poles would have an

integral-slot distribution of Spp=1, whereas 6-slots, 4-poles would have a fractional

distribution of Spp = 1/2. This fractional distribution is often termed fractional-slot

windings. Unlike in integral slot windings, the phase coils are not periodic over a pole

pitch, (as seen in fig. 3.1a). Thus, an appropriate selection of phase coil arrangement is

essential in producing a sinusoidal EMF waveform of the desired magnitude. If the Spp

is too small (as in the case where Spp = 1/7, shown in fig. 3.1b), a large portion of a rotor

pole of opposite polarity will be under the same stator pole, thus supressing the total

EMF generated in that phase. Fig. 3.1 compares the integral-slot DW machine with

fractional-slot CW machines having 1/7, 2/7 and 3/7 Spp.


56

(a) 2Spp DW (b) 1/7Spp CW

(c) 2/7Spp (d) 3/7Spp CW

Fig. 3.1 14-pole IPM machine with various slot and pole combinations

While selecting the appropriate the Spp to get the desired EMF waveform, the periodicity

between the stator teeth and rotor magnets also changes. Consequently, this changes the

peak cogging torque value. The following sub-sections illustrate the effects of these two

parameters (EMF and cogging torque) and how they can be estimated by simple

analytical methods.


57

3.2.1 Winding Factor and EMF

In an IPM motor, torque is generated by the interaction between the permanent magnet

field and the stator electromagnetic field caused by the armature reaction. The

developed torque for a single phase excitation can generally be expressed as follows:

, , = 12 12 + (3.1)

where,

= Flux from permanent magnets

= Supply current (to the stator coils)

The first term in the torque equation, extracted to (3.2), is known as the reluctance

torque ( ), and is related to the variation of stator inductance ( ) with rotor position

( ). This variation of stator inductances is caused by pole saliencies or flux barriers.

Reluctance torque is contributes to the total torque generated by the IPM machine.

( , ) = 12 (3.2)

The second term, shown in (3.3) is known as cogging torque ( ). It caused by the

interaction of magnet flux and stator slots, resulting in the variation of reluctance ( ).

, = 12 (3.3)

The last term, shown in (3.4), is known as electro-dynamic torque or alignment torque

( ). This is the main contributor to the useful torque produced by the machine. is

related to the variation of mutual inductances between the stator and rotor. In particular,

it is the interaction between the back EMF and stator current.

, , = k N d d (3.4)


58

The winding factor ( ) affects the shape and magnitude of flux linkage across the air

gap, and affects how harmonics of individual coil back EMF phasor are summed

together to form the overall phase EMF. A low winding factor means that the harmonic

components of the EMF are relatively high as compared to the fundamental component

resulting in lower magnitude of useful EMF. A lower winding factor can be treated as a

reduction in the effective number of turns per phase in stator windings as shown in the

electro-dynamic torque equation (3.4). The EMF in turn affects the efficiency and

torque density of the machine. It is therefore important to obtain a high winding factor

in the initial design stages with an appropriate choice of Spp.

Generally, the winding factor is made up of three parts:

= (3.5)

where,

= Pitch factor,

= Distribution factor

= Skew factor

Concentrated windings are usually not skewed, as it will significantly increase the

complexity and cost of constructing the machine. Therefore the third term can be

omitted. Although the pitch factor can be easily calculated, calculating the distribution

factor can be quite complex. An alternative method that can be used to determine both

the pitch and distribution factor together is the EMF phasor method [17]. A simple

example of this method is shown below. Each EMF phasor is represented by:

= (3.6)where,

= Reference EMF phasor element,

= winding element number,

= number of pole pairs

= number of slots.


59

A 6-slot, 4-pole machine layout (shown in fig. 3.2) is used in this example.

(a) 6-slot, 4-pole design showing phase coils and winding element numbers

(b) Phasor diagram showing how each element phasor make up for each phase

Fig. 3.2 EMF phasor diagram

By substituting element numbers ( = 0,1,2,..5) into (3.6), and by Euler’s equations we

get:

For = 0: = = (0) + (0) = For = 1: = = ( 0.5) + (0) = and so on (till = no. of slots – 1).

Vectors / / are achieved when all the winding elements corresponding to a

particular phasor are in phase. The winding factor of each phase can then be calculated

by dividing vectors / / by / / respectively.

Although a unity winding factor is not achievable for fractional-slot windings, a value

very close to unity can be achieved with certain combinations. Table 3.1 shows the


60

winding factors of single- and double-layer windings with several slot and pole

combinations.

Table 3.1Winding factor and LCM for different Spp values

Poles 4 6 8 10 12 14 16Slots

6

Spp 1/2 1/4 1/5 1/7 1/8kw (Single layer) 0.866 0.866 0.866 0.866 0.866kw (Double layer) 0.866 0.866 0.500 - -

LCM 12 24 30 42 48

9

Spp 1/2 3/8 3/10 3/12 3/14 3/16kw (Single layer) 0.866 0.945 0.945 0.866 0.945 0.945kw (Double layer) 0.866 0.945 0.946 0.764 0.473 0.175

LCM 18 72 90 36 126 144

12

Spp 1/2 2/5 2/7 1/4kw (Single layer) 0.866 0.966 0.966 0.966kw (Double layer) 0.866 0.933 0.933 0.866

LCM 24 60 84 48

15

Spp 1/2 5/12 5/14 5/16kw (Single layer) 0.866 0.808 0.866 0.866kw (Double layer) 0.866 0.906 0.951 0.951

LCM 30 60 210 240

18

Spp 1/2 3/7 3/8kw (Single layer) 0.866 0.945 0.945kw (Double layer) 0.866 0.902 0.931

LCM 36 126 144

21

Spp 1/2 7/16kw (Single layer) 0.866 0.932kw (Double layer) 0.866 0.851

LCM 42 336

24

Spp 1/2kw (Single layer) 0.866kw (Double layer) 0.866

LCM 48

3-phase CW machines with double-layer windings require slots in multiples of 6 in

order for the phase coils to be equally distributed. Thus 6, 12 and 18 slots are chosen

and the same 14-pole rotor will be used.


61

Here the back EMF from the four designs shown earlier in fig. 3.1 is compared.

(a) 2Spp DW

(b) 1/7Spp CW

(c) 2/7Spp CW

(d) 3/7Spp CW

Fig. 3.3 3-phase EMF waveforms and corresponding frequency spectrum over 1 electrical cycle for 14-pole IPM machine with different slot and pole combinations

0

10

20

30

0 5 10 15

Volt

0

10

20

30

0 5 10 15

Volt

0

10

20

30

0 5 10 15

Volt

0

10

20

30

0 5 10 15

Volt

28.4V

21V

27.6V

14.5V

( )Time (s) Frequency components (n-order)

Time (s) Frequency components (n-order)

Time (s)0 5 10 15Frequency components (n-order)

Time (s)0 5 10 15

Frequency components (n-order)


62

By comparing the back EMF waveforms from fig. 3.3, it can be seen that all, except the

6-slot model, produced near-perfectly sinusoidal (line to neutral) back EMF waveforms.

The 84-slot, DW-IPM machine, (with a calculated winding factor of 0.933), generated

an EMF waveform with the highest magnitude of 28.4Vrms. From the values shown in

table 3.1, the 12-slot, 14-pole model also has a winding factor of 0.933. Therefore it

should produce the same back EMF magnitude. However, due to the rotor magnet pole

pitch being smaller than the stator pole pitch, the flux from the opposing magnet pole

cancels the total amount of flux that is linked to a phase coil, resulting in a lower than

expected winding factor. The same condition was seen in the 6-slot, 14-pole model.

This indicates that having a larger number of slots than poles are required.

Based on back EMF obtained by the DW-IPM machine, the 18-slot design, which has a

winding factor of 0.902 (from table 3.1), the calculated back EMF should by 27.5Vrms.

From the 18-slot FE model, it is shown that the back EMF magnitude achieved

(27.6Vrms) agrees with the calculated value.

3.2.2 Cogging Torque

Cogging torque is a result of the variation of stator inductances due to the interaction of

rotor and stator poles. It contributes to vibrations and noise, leading to severe

restrictions in the machine performance. The cogging torque equation was stated in

earlier in (3.3).

There are several methods by which cogging torque can be reduced, some of which are

rotor flux barrier shaping [122], stator chamfer angle shaping [125] and shaping of the

rotor outer radius [61]. These methods, are however, heavily based on trial and error

techniques to achieve the optimal geometry. Another common method to reduce


63

cogging torque in machines with integral slot windings is by skewing. However, in

fractional-slot windings skewing would lead to a significant decrease in induced EMF,

as well as increase the complexity and cost of constructing the machine. In actuality, the

use of fractional-slot windings itself aids in the reduction of cogging torque as it

eliminates periodicity between slots and poles.

To quantify the amount of reduction with different slot and pole combinations, the

lowest common multiple (LCM) method is used, which is basically the LCM of the

number of slots and poles. A higher LCM would yield a lower peak value in the

cogging torque waveform but result in higher frequency fluctuation. The LCM of

various combinations is stated in table 3.1. Fig. 3.4. gives an example of cogging torque

waveforms for three different Spp values. The 1, 2/7 and 3/7 Spp combinations have

LCMs of 42, 84 and 126 respectively. Results verify the reduction in cogging torque

magnitude as the LCM increases.

Fig. 3.4 Cogging torque waveforms for various slot and pole combination

From the FE results shown in this section, it can be seen that the choice of slot and pole

configurations directly affect both the winding factor and the cogging torque

magnitudes. In the abovementioned comparison, the 18-slot, 14-pole model seems to be

-1.3%

-0.8%

-0.3%

0.3%

0.8%

1.3%

0 0.2 0.4 0.6 0.8 1

Torq

ue (%

Rat

ed)

Normalized Time (P.U.)

42-slots, 14-polesmachine (1 Spp)

12-slots, 14-polesmachine (2/7 Spp)

18-slots, 14-polesmechine (3/7 Spp)


64

the most appropriate choice as it produces a high winding factor (0.902) and very low

cogging torque magnitude (as it has a high LCM of 126). Thus this combination will be

used as the basis for the prototype design in this thesis.

Other suitable candidates for this study would be the 12-slot, 10-pole model as well as

the 18-slot, 16-pole model. The 18-slot, 14-pole model was chosen over the 12-slot, 10-

pole model as a lower cogging torque is desired. (The LCM produced by the 12-slot,

10-pole model – the LCM was 60 as opposed to the 126 in the chosen configuration).

The 18-slot, 14-pole model was chosen over the 18-slot, 16-pole model because a

higher base speed was required. (An approximate base speed with 16-poles would be

375RPM as opposed to 429RPM in the 14-pole model).


65

3.3 PERFORMANCE IN COMPARISON TO DISTRIBUTED WINDING IPMMACHINE

The growing popularity of CW is due to factors such as:

Shorter end-windings due to non-overlapping coils.

Less amount of copper used.

Simplified and possible automation of manufacturing process [105].

Higher slot-fill factor [104, 105].

Lower stator copper loss.

Higher tolerance to phase faults [20].

Additional leakage inductance increases CPSR in SPM machines [130].

There are, however, also advantageous factors which still make DW a preferred choice

over CW. Some of these are:

DW generates less MMF harmonics leading to lower core and magnet losses.

Higher saliency ratio leading to higher reluctance torque.

Unity winding factor can be achieved resulting in larger electro-dynamic torque.

High performance control techniques including sensorless control are readily

available.

In this section, the key differences between CW and DW will be discussed.

3.3.1 Airgap Flux Harmonics

The popularity of DW is due to its ability to produce MMF waveforms which are close

to sinusoidal. On the contrary, CW produces MMF waveforms which are rich in

harmonics. The MMF produced by stator coils can be expressed follows:

= (3.7)

where,

= Flux density from the stator poles

= Airgap surface area

= Airgap reluctance


66

If the airgap length and overall slot opening widths are kept constant, the MMF is

directly proportional to the airgap flux density produced by the stator current. The

airgap flux density of a typical 14-pole, double-layer, DW machine with magnets

removed is shown in fig. 3.5:

Fig. 3.5 Flux waveform and corresponding frequency spectrum of a 14-pole, double-layer, DW machine model

The only term that contributes to electro-dynamic torque production is the fundamental

component. The other terms contribute to increased core and magnet eddy current losses,

as well as additional leakage inductance. A detailed mathematical explanation of how

the additional harmonic components lead to increased frequency-related losses will be

shown in chapter 5.

Due to CW being non-sinusoidal in nature, it is expected that significant harmonic

components will be present in the airgap flux waveform. Airgap flux waveforms in

single- and double-layer, 18-slot, 14-pole CW models with magnets removed are shown

in fig. 3.6a and 3.6b respectively:

-0.25

0

0.25

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

Fundamental component (torque-producing term)

00 00Airgap circumference (mm)

25Frequency components (n-order)


67

(a) 14-pole, 18-slot, single-layer CW machine model

(b) 14-pole, 18-slot, double-layer CW machine model

Fig. 3.6 Flux waveform due to armature reaction for single- and double-layer CW

Comparatively, the double-layer model produces much lower MMF harmonic

components than the single-layer model. Due to the nature of the machine designed for

this work, (where operating frequency can exceed several times the base frequency –

making the machine more susceptible to frequency related losses), the double-layer CW

was selected as the base layout in this work.

-1

-0.5

0

0.5

1

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

-0.5

-0.25

0

0.25

0.5

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

Fundamental component (torque-producingterm)

Fundamental component (torque-producing term)

00 00Airgap circumference (mm) Frequency components (n-order)

Airgap circumference (mm) Frequency components (n-order)


68

3.3.2 Saliency Ratio and Constant Power Capability

The two main factors contributing to the field-weakening performance of IPM machines

are saliency ratio and characteristic current. Saliency ratio ( ) given by (3.8),

contributes to the additional reluctance torque as shown in (3.1), which is additive to the

total IPM machine torque.

= (3.8)

where,

= d-axis inductance

= q-axis inductance

In an IPM machine < , resulting in > 1.

Measuring the saliency in integral-slot windings is less time consuming as the rotor can

be positioned according to the d- and q-axis flux paths (fig. 3.7) and the d- and q-axis

inductances can be measured accordingly. Fig. 3.7a shows the flux path across the pole

axis, while 3.7b shows the flux path over the inter-pole axis.

(a) Flux being channeled to the d-axis (pole axis)

(b) Flux being channeled to the q-axis (inter-pole axis)

Fig. 3.7 14-pole DW IPM with flux being channeled to the d- and q-axis

In fractional-slot CW, the d- and q-axis flux paths are not obvious due to the

aperiodicity between slots and poles as shown in fig. 3.8.

q-axis

d-axis

q-axis

d-axis


69

Fig. 3.8 14-pole, 18-slot, CW-IPM flux plot showing no obvious d or q-axis flux paths

To measure d- and q-axis inductances in CW-IPM machines, the AC standstill test is

deemed most suitable [184]. The AC standstill test was implemented in FE analysis and

its accuracy was verified against the UNSW 4-pole segmented DW-IPM machine

(shown in Appendix A). With the FE results agreeing with the range of measured values,

this method was then used to measure the saliency ratio of the CW-IPM machine. To

account for saturation, measurements were taken at different current values. It should

also be noted that the effect of cross coupling was not studied as it would not

significantly affect the results.

With this method, inductances in the d and q-axes are determined from the self-

inductance ( ( )) and mutual-inductance ( ( )) waveforms expressed by:


70

( ) = 2 (3.9)

( ) = 2 (3.10)

where,

= Voltage drop across the excited phase A,

= Voltage induced in the phase B due to excitation in phase A,

= Stator resistance

= frequency of excitation.

= Rotor position

= Input current

By plotting , versus rotor position and using curve fitting or FFT, the DC and

second harmonic terms of the respective waveforms can be determined. Subsequently,

the d- and q-axis inductances ( and ) can be determined by (3.11) and (3.12). The

derivation of these equations can be found in [184].

= 32 ( ) 2 + (3.11)

= 32 ( ) + 2 + (3.12)

where,

= DC term of the self-inductance

= Second harmonic term of the self-inductance (3 times base frequency for this 3-phase machine)

= DC term of the mutual-inductance

= Second harmonic term of the mutual-inductance (3 times base frequency for this 3-phase machine)


71

As a comparison, and , for the UNSW Segmented DW-IPM is shown in fig. 3.9

below. This machine produced a saliency ratio of over 1.7.

Fig. 3.9 Inductance waveform measured from UNSW Segmented IPM machine [174]

and for CW-IPM machines generally have a lower second harmonic term and a

larger DC term, indicating lower saliencies. The inductance waveforms for an 18-slot,

14-pole model shown in fig. 3.10, resulted in a very small saliency ratio of 1.04.

Fig. 3.10 Inductance waveform of an 18-slot, 14-pole CW-IPM machine

2.0E-032.2E-032.4E-032.6E-032.8E-033.0E-03

0 10 20 30 40 50

Henr

y

Deg

Self inductance (La)

-8.0E-04

-7.0E-04

-6.0E-04

-5.0E-04

-4.0E-04

0 10 20 30 40 50

Henr

y

Deg

Mutual inductance (Mab)


72

A comparison of CW and DW with the same IPM rotor was done in [114]. The results

show that CW resulted in a lower saliency ratio. This was due to a significant increase

in the d-axis inductance, but with q-axis inductance remained almost the same as shown

in fig. 3.11:

(a) D-axis inductance comparison (b) Q-axis inductance comparison

Fig. 3.11 d- and q-axis inductance comparison [114]

As a consequence of a decrease in , the saliency ratio is decreased. Hence additional

reluctance torque contributions from IPM machines with CW are not as significant as

compared to DW-IPM machines. This implies that for CW-IPM machines, the CPSR

should be optimised by satisfying characteristic current equilibrium conditions rather

than achieving a high saliency ratio.


73

3.3.3 End Winding Length

The key advantage of CW is the reduction in end-winding length due to non-

overlapping coils. This enables the effective stack length of the machine to be increased

in a given amount of space. Fig.3.12 compares end-winding lengths of DW and CW:

(a) Single-layer distributed winding

(b) Single-layer concentrated winding

(c) Double-layer concentrated winding

Fig. 3.12 Estimated reduction in end winding length

Compared to single-layer DW (Fig. 3.12a), the end-winding length of a single-layer CW

(Fig. 3.12b) is nearly half, and for a double-layer CW (Fig. 3.12c), a quarter. For CW,

the end-winding length is also largely dependent on factors such as the quality as well

as the format of the winding.

2 4


74

3.3.4 Slot-fill Factor

The slot-fill factor otherwise known as the packing factor is inversely proportional to

the copper loss in the machine. Therefore, having the highest possible slot-fill factor is

essential for achieving optimal efficiency in the machine.

The advantage that CW has over DW is that coils are wound around individual stator

teeth. This allows the use of more advanced winding methods such as the joint lapped

core method [105, 106], and prepressed windings in separable tooth pieces [104]. Fig

3.13a and 3.13b show the abovementioned processes respectively:

(a) Joint-lapped core windings [106] (b) Prepressed windings in a welded powered-iron core stator [104]

Fig. 3.13 Advanced winding methods to achieve a high saliency ratio

Typical slot-fill factors of up to 35% can be achieved for DW and up to 45% can be

achieved for CW by traditional hand winding methods (based on our constructed IPM

machines). With the joint-lapped core and prepressed winding CW methods, a slot-fill

factor of up to a 78% can be achieved. Thus, these methods can effectively reduce

copper loss and end-winding length. Furthermore, with the joint-lapped core method,

the winding process can be automated, making the production process quicker.


75

3.4 COMPARING IPM AND SPM MACHINES WITH CONCENTRATED WINDINGS

As shown in section 3.2, the saliency ratio of IPM machines with CW falls significantly,

compared to IPM machines with DW. This makes the electromagnetic performance of

the CW-IPM machine closer to that of a CW-SPM machine. Extensive studies on CW-

SPM machines have been carried out by El-Refaie and Jahns, with some of the key

contributions shown in [18, 90, 98, 116, 130, 131, 167, 185]. They managed to prove

that with fractional-slot CW, a very wide CPSR could be achieved in the SPM machine

– a machine that was known to have very little or no field-weakening capabilities. Fig.

3.14 shows common forms of SPM and IPM rotors:

(a) Surface mounted permanent magnets

(b) Interior single-piece/pole permanent magnets

(c) Interior v-shapedpermanent magnets

Fig. 3.14 Performance comparison of different magnet shapes

Compared to the SPM machine, the IPM machine has the following advantages:

Buried magnets increase the mechanical robustness of the rotor

Magnets are not directly exposed to the airgap flux making them less prone to

large eddy current losses and risk of demagnetisation.

Greater flexibility in rotor variations, allowing flux concentrations and saliency

ratio alterations.


76

3.4.1 Airgap Flux Produced by the Magnets

This sub-section will compare airgap flux produced by the rotor permanent magnets

from fig. 3.14.

A general relation between magnet pole and airgap area can be described in (3.15).

= 1 + (3.15)

where,

= Total airgap flux density due to the magnets

= Magnet pole area

= Airgap area

= Magnet internal permeance

= Airgap reluctance

= Magnet remanent flux density

The equation above tells us that a larger magnet pole surface and smaller airgap length

would result in greater airgap flux density. In the comparison done here, airgap length is

kept constant. Key model parameters are shown in table 3.3. This equation holds when

comparing two SPM machines with different pole surface areas. But when comparing

the SPM rotors with IPM rotors, (especially for IPM with v-shaped magnets), saturation

in the rotor core significantly affects the airgap flux. Fig. 3.15 shows saturation of the

inter-pole and pole areas of the rotor core:

Table 3.3Key Specifications of Models with Different Magnet Shapes

Rated stator current 15Arms

Total number of series turns per phase 133turnsAir gap length (IPM) 1mmAir gap length (SPM) 1mm + Magnet depth

Magnet volume per pole 2870mm3

Magnet remanent flux density 1.3TBase speed 428.571rpm (50Hz)


77

Fig. 3.15 Flux density plot of the v-shaped IPM model showing saturation regions

Saturation in the core can be separated into two portions, the first being the saturation of

the inter-pole area, and the other, the saturation of the pole area. The saturation effects

in the inter-pole area are much stronger, thus the actual magnet span of the magnet is

reduced. The saturation effects in the pole sections are mild; this only slightly increases

the permeance of the magnet flux path through the rotor core to the airgap. (3.15) can be

modified by adding two constants to take saturation into account as follows:

= ,1 + , (3.16)

where,

, = permeability constant affecting actual span of the magnet pole

, = permeability constant reducing the flux density (from )

, limits the peak airgap flux while , reduces the peak width (causing it to

fall off faster) as shown in fig. 3.16 below.

Saturation of inter-pole area

Saturation of pole axis


78

(a) Airgap flux produced by SPM rotor (b) Airgap flux produced by IPM rotor withsingle-piece/pole magnets

(c) Airgap flux produced by IPM rotorwith v-shaped magnets

Fig. 3.16 Airgap flux produced by the different rotor configurations

The SPM machine has a pole surface area of 1418mm2 per pole, whereas the IPM with

single-piece magnets has a pole surface area of 1327mm2 per pole. Naturally, due to a

smaller pole surface and the inclusion of saturation effects in the latter design, the

overall airgap flux density is lower. The magnet surface area per pole for the v-shaped

IPM rotor is 2165mm2, significantly larger than the other two designs. However, due to

saturation effects, the flux density waveform (shown in 3.16c) is narrower and of

slightly lower magnitude compared to the SPM machine. When compared to the single-

piece IPM, the v-shaped IPM produced a larger peak value of flux density. But, due to


79

having higher saturation in the inter-pole area, the waveform is narrower – resulting

only in a slightly higher RMS airgap flux density.

3.4.2 Constant Power Speed Range Comparison

Here, the CPSR and peak power performance of the three rotors in fig. 3.14 are

compared. These three rotors are modelled with the same CW stator with equal

excitation current. The rotor field is weakened by the variation of the current angle ( )

to maintain a constant power after base speed. In particular, the current angle is

increased as greater negative d-axis current is required to weaken the permanent magnet

field. This supresses the back EMF induced in the phase coils- hence helping to

maintain constant power over an increased speed range. It is assumed that the initial

rotor position is 0 (the rotor EMF axis is in line with the stator current axis).

= (2 + ) (3.17)

= 2 23 + (3.18)

= 2 + 23 + (3.19)

Fig. 3.17 Peak power and CPSR comparison between three rotor types

0

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000 2500 3000 3500

Surface Magnets (1mm+AG) Flat-Shaped Magnets (1mmAG)V-Shaped Magnets (1mmAG)

Speed (RPM)

Pow

er (W

)

base4.3:1CPSR

5.6:1CPSR

7.2:1CPSR


80

Fig. 3.17 shows that the SPM machine had the highest power density from base speed

up to the 4:1 CPSR point. The IPM machine with v-shaped magnets, on the other hand

produced slightly less power but a wider CPSR. The IPM machine with rectangular

single-piece/pole magnets was not able to outperform the other two designs in terms of

both power density and CPSR. The results indicate that the IPM machine with v-shaped

magnets would be the most suitable candidate to achieve good field-weakening

characteristics.


81

3.5 CONCLUSION

Chapter 3 has investigated the suitability of implementing CW on the IPM machine. It

was shown that due to the fractional-slot distribution used in CW, sinusoidal back EMF

and low cogging torque can be achieved at a small expense of a lower winding factor

compared to equivalent integral-slot machines. By comparing several 14-pole layouts, it

was seen that the 18-slot model produced a sinusoidal back EMF waveform with the

highest magnitude of induced voltage of the models.

In a comparison of MMF waveforms, it was shown that the MMF waveforms produced

by CW contain much higher harmonics compared to DW models. Additionally, it was

shown that single-layer CW contains significantly higher harmonic content compared to

double-layer CW.

Different winding methods were investigated and it was shown that by advanced

winding methods, a slot-fill factor of up to 78% can be achieved.

Lastly, this chapter showed that the CW-IPM machine with rectangular single-

piece/pole magnets is inferior to the CW-SPM machine in terms of torque density and

field weakening capability. The CW-IPM with v-shaped magnets, on the other hand,

produced improved field weakening capability, but with slightly lower peak torque

density as the CW-SPM machine due to saturation effects. It should also be noted that

since fractional-slot windings result in reduced saliency ratio in IPM machines, the

same results will be expected if fractional-slot DW are used – that is, lower torque

density is expected in IPM compared to SPM machines.

The next chapter will build upon the findings in this chapter to arrive at a final

optimised design.

82

CHAPTER 4DESIGN OF AN IPM MACHINE WITH CONCENTRATED WINDINGS FOR FIELD WEAKENING APPLICATIONS

4.1 INTRODUCTION

General design goals for PM machines used for field-weakening applications include:

Achieving a very wide CPSR

High efficiency in the constant power region

High torque densities with low torque ripple

In this work, the CW-IPM will be compared with two equally-sized DW-IPM machines.

To demonstrate that the CW-IPM is a suitable candidate for field-weakening

applications the following specific goals are set:

Achieving sinusoidal back EMF waveform with high winding factor

Low cogging torque

High torque density – With a shorter end-winding length, the effective stack

length of the machine can be increased. The output power of this design should

exceed 580W, which has been achieved by both UNSW IPM machines.

A very wide CPSR – greater than 4:1

High efficiency – exceeding 85% in the constant power region.

In this chapter, the CW-IPM is designed and optimised in order to achieve these design

goals. The method to optimise the CPSR by achieving characteristic current equilibrium

is shown; rotor geometry and airgap length are also varied to further increase the CPSR.

Material considerations and manufacturing methods are looked into. Mechanical

stresses on the inter-pole link sections of the rotor are also investigated. Lastly, full

specifications of the final FE design will be stated and predicted performance

characteristics will be presented.

Chapter 4: Design of an IPM Machine with Concentrated Windings for Field Weakening Applications

83

4.2 CONDITIONS FOR MAXIMISING THE CPSR

As mentioned in chapter 3 the saliency ratio in a CW-IPM machine is reduced due to

the significant increase in d-axis inductance and with q-axis inductance remaining

relatively constant.

In order to achieve a high saliency ratio, the inter-pole or q-axis flux paths should have

as little resistance as possible, while the pole or d-axis should have barriers to create

resistance. Based on these principles, axially laminated (fig.4.1a) and multi-barrier

(fig.4.1b) designs are often used to achieve high saliency ratios [12, 186].

(a) 4-pole axially laminated rotor (b) 4-pole multi-barrier rotor

Fig. 4.1 Rotor types used for increasing saliency ratio [12, 186]

Flux paths in integral-slot DW machines are periodic, thus the rotor pole geometry can

be shaped to channel d- and q-axis flux. However in CW machines these flux paths are

not obvious, (as shown in fig. 3.8). Attempts to increase the saliency ratio by rotor

magnet geometry variations (appendix B), showed that saliency ratio increments with

optimised designs were small – the maximum saliency ratio achieved was 1.14. Most of

the designs achieving higher saliencies were also impractical as it required very thin

inter-pole link sections, which would be subjected to high mechanical stresses during

high speed operation.

q-axis flux path

d-axis flux path

q-axis flux path

d-axis flux path


84

Additionally, in [187, 188], the saliency ratios for double-layer CW as well as for

different Spp combinations were also investigated, (this comparison is shown in

appendix C). In this comparison, it was also shown that the saliency ratio remained

relatively low, (between 1.06 and 1.11).

Thus the rotor magnet geometry was selected based on its ability to produce the

required magnet flux-linkage and to maintain mechanical robustness of the rotor, rather

than to achieve the optimal saliency ratio.

With a low saliency ratio achieved in the CW-IPM machine, the key condition for

optimising CPSR is achieved by satisfying the characteristic current equilibrium

conditions as shown in (4.1).

= = ( ) = (4.1)

where,

= Rated current

= Permanent magnet flux linkage

The following shows a breakdown and the relationship between these two terms (

and ).

is affected by both the self-and mutual inductance in the following relationship:

= 32 ( ) 2 + (4.2)

where,

= 1st harmonic component of self-inductance

= 1st harmonic component of mutual-inductance

= 2nd harmonic component of self-inductance and

= 2nd harmonic component of mutual-inductance


85

Self-inductance and mutual-inductances vary as a function of the armature

windings as well as effective airgap. They can be expressed in terms of machine

parameters, shown in (4.3) and (4.4) respectively [130]. ( ) = ( ) ( ) (4.3)

( ) = ( ) ( ) ( ) (4.4)

where,

= Permeability of free space

= Airgap radius

= Stack length of the machine

= Airgap length

= Phase A winding function

= Phase B winding function

In CW machines, the magnitude of self-inductance is high, while the magnitude of

mutual-inductance is relatively low compared to DW machines [20]. Therefore the

magnitude of varies essentially with self-inductance, and the following conditions

can be assumed:

2The variation of these parameters may also affect , which can be generally

described in terms of the number of series turns under a pole ( ) exposed to airgap

flux ( ) as follows [3, 174, 189]: = (4.5)


86

where, is made up of two terms: the flux density normal to the pole surface ( ) and

the pole area ( ). (4.5) can be expanded further as follows:

= = (4.6)

where,

= Rotor outer radius (proportional to airgap radius in (4.3))

= Pole span

can further broken down to give:

= 1 + ( ) (4.7)

where,

( ) = Magnet relative permeability

= Magnet thickness

Substituting (4.7) into (4.6), we get:

= 1 + ( ) (4.8)

and the following relation can be attained:


87

The relation between the abovementioned variables relating to and indicate that,

in order to effectively change the characteristic current, three parameters, (independent

of ), can be varied. They are: , and .

Taking as example to see how it can be used to satisfy characteristic current

equilibrium conditions, we shall assume the machine geometry and number of turns are

kept constant (thus Ld is constant). Then, with a range of rated current values, can be

chosen to satisfy characteristic current equilibrium conditions and achieve optimal

CPSR, as shown in the contour plot (fig. 4.2):

Fig. 4.2 Contour plot showing the variation of magnet remanent flux density versus rated current

Fig. 4.2 shows that with an almost linear relation between the rated current and magnet

remanent flux density (Green region), the CPSR up to a range of 10 to 15:1 can be

achieved if equilibrium conditions are met. The steep variations in contours indicate the

importance on achieving characteristic equilibrium conditions in the optimisation of

CPSR. The plot also shows that the optimal region narrows towards the end as the steel

gets saturated with higher currents.

1.09T

1.13T

1.18T

1.24T

1.29T

3A 3.25A 3.5A 3.75A 4A 4.25A 4.5A 4.75A 5A 5.25A 5.5A

10-15 5-10 0-5

(Rated Current)(M

agne

t Rem

anen

tFlu

x D

ensi

ty)

CPSR (X : 1)


88

4.3 CHOICE OF WINDING ARRANGEMENT

The choice of winding arrangement affects the winding factor, which in turn affects the

efficiency, output power and field-weakening performance of the machine. Unlike

integral-slot DW, the arrangement of phase coils in fractional-slot CW to achieve the

desired winding factor is not as straight forward and is often hard to visualise. Generally

the windings should be arranged such that maximum flux is linked from the magnets to

the stator coils. A method for obtaining the optimal phase coils arrangement in CW to

achieve the highest possible flux linkage was illustrated by J. Cros and P. Viarouge in

[16].

The following example briefly explains this method by the use of an arbitrary 12-slot,

14-pole, double-layer model (with Spp = 2/7).

Step 1: Using the number of slots per pole per phase (Spp), a sequence of ‘1’s and ‘0’s

can be obtained. The numerator represents the number of ‘1’s and the denominator

represents the total number of integers in the sequence.

For = , there are two ‘1’s for a sequence of seven integers with the rest being ‘0’s.

1 1 0 0 0 0 0

Step 2: The sequence is re-written such that the ‘1’s and ‘0’s alternate with the ones

being the first integer.

1 0 1 0 0 0 0

Step 3: Repeat this sequence until the total number of ‘1’s equal to the number of slots

(in this case with twelve slots, the sequence repeats six times).


89

Step 4: Under each integer the winding sequence A C’ B A’ C B’ A C’B A’ C B’ . . . . .

is written out:

Step 5: The integers under ‘1’s will be used as one layer of the winding

Step 6: The other layer will be filled with the opposite polarity in the neighbouring slot.

With this winding method, flux-linkage will be maximised and the winding factors for

various Spp values as shown in table 3.1 can be achieved.


90

4.4 MATERIAL CONSIDERATIONS

Selection of materials depends on the requirements of torque density, weight, cost,

operating temperature range and external demagnetisation fields. The three key

materials to consider are: permanent magnets, core and coil material [190]. This section

explains how the materials were selected for this design, covering key properties such as

saturation, energy density and thermal considerations. Losses of these materials will be

discussed in greater detail in chapter 5.

4.4.1 Permanent Magnet Material

Permanent magnet characteristics can be described by the demagnetisation curve shown

in fig. 4.3. From this curve desired magnet parameters such as - remanent flux density

(Br), coercivity (Hc), and recoil permeability (μr) can be determined.

0

Fig. 4.3. Permanent magnet Demagnetisation curve

There are several types of permanent magnet materials in the market. Ferrite (FeO),

Alnico (AlNiFeCo), Samarium-cobalt (SmCo) and Neodymium-iron-boron (NdFeB)

are more commonly used. The advantages and disadvantages of these materials are

stated in table 4.1 below [191-194].

0

NormalCurve

H H

B

HIncr

easi

ng T

empe

ratu

reBr

iHc

μr=Fig 4 3

HHcHH Hc

B

IntrinsicCurve Demag.

Paths


91

Table 4.1Advantages and disadvantages of different magnet types

Magnet type Advantages Disadvantages

Ferrite Least expensive magnet material

High operating temperature up to

300 ºC

Hard and brittle

Lowest remanent flux

density of up to 0.42T

Alnico High operating temperature up to

520 ºC

Lowest temperature coefficient

(0.02%/ºC)

Extremely hard and brittle

Can be easily

demagnetised

Samarium-cobalt High remanent flux density of up to

1.16T

Extremely resistant to corrosion

High resistance to demagnetisation

High operating temperature of up

to 350ºC

Low temperature coefficient

(0.04%/ºC)

High coercivity

Extremely hard and brittle

Most expensive magnetic

material

Neodymium-

iron-boron

Highest remanent flux density of

up to 1.48T

High resistance to demagnetisation

Least brittle

Lower cost compared to SmCo

High coercivity

Low operating temperature

up to 200ºC

High temperature

coefficient (0.12%/ºC)

Susceptible to corrosion

NdFeB magnets are the preferred choice in present day applications due to its

reasonable cost, high coercivity and high remanent flux density [195].

However, NdFeB magnets have comparatively low operating temperatures, which cause

the knee from the third quadrant to enter the second quadrant if the temperature gets too

high (fig. 4.5). When the knee enters the second quadrant, (the coercivity of the material

decreasing), and with armature flux opposing the flux from the magnets, the risk of


92

irreversible demagnetisation is increased dramatically [3]. Therefore, the thermal

aspects of the magnets have to be considered in the design stage. To estimate

temperatures within the machine a basic 1kW CW-IPM model was created in Motor-

CAD (as shown in appendix D). The model showed that under ‘worst-case scenario’

conditions, the magnets would operate to under 110°C. NdFeB magnets have maximum

operating temperatures of between 80°C to 220°C and curie temperatures of between

310°C and 380°C for different grades. The maximum energy product of the magnetic

grade is inversely proportional to the temperature rating of the magnet. For example, a

magnet grade with 80°C operating temperature has remanent flux density of up to 1.48T,

whereas a grade with 220°C operating temperature has a flux density of only up to 1.2T

[196]. The chosen grade of NdFeB magnet is N28UH with remanent flux density of

1.04 to 1.09T and operating temperature of 200°C. Each magnet piece has a dimension

of 2mm x 13.5mm x 79mm and had nickel and copper coating (Ni-Cu-Ni) to prevent

corrosion.

4.4.2 Core Material

Silicon sheet steel is widely used in stator and rotor cores of electric machines. This is

due to properties such as: high saturation magnetisation, low cost and relatively low

losses [197, 198].

The silicon steel grade was selected based on the torque required and the tolerance to

losses. Saturation and loss are inversely proportional to each other. For example, grade

35JN210 has a saturation point (B50) at 1.65T and core loss of 2.05W/kg at 1.5T/50Hz,

whereas grade 50JN1300 has a saturation point (B50) at 1.76T and core loss of 8.1W/kg

at 1.5T/50Hz.


93

For machines designed for field-weakening applications, cores with low losses are

preferred, as excitation frequency could exceed several times the base frequency.

Furthermore with CW, the additional high frequency leakage harmonics would result in

additional core losses. These issues will be studied in greater detail in chapter 5.

The chosen rotor and stator core material, (grade 35RM300 – from Australian supplier

Sankey), is non-oriented silicon sheet steel with a thickness of 0.35mm. It has a

saturation point (B50) at 1.68T, and core losses of 2.6W/kg at 1.5T/50Hz. The

magnetisation and core loss curves provided by the supplier are shown in fig. 4.4 and

4.5 respectively. For the model, the declaration of material properties was based on a

saturation point (B50), at 1.65T with a 10% safety factor.

Fig. 4.4 Magnetisation curve of 35RM300 (provided by Sankey)


94

Fig. 4.5 Core loss curve of 35RM300 (provided by Sankey)

4.4.3 Stator Coil and Insulating Material

The ideal coil material is one with infinite conductivity and the lowest temperature

coefficient of resistance [199]. Copper is a common choice for coil material due to its

relatively lower price, high conductivity, good mechanical strength and a relatively low

temperature coefficient of resistance. The amount of I2R loss per coil can be calculated

by (4.10).

= 2 (4.10)

where,

= Number of turns per coil = Conductor resistivity

= Cross-sectional area of a wire

= Machine stack length


95

The available cross-sectional area per wire is found based on the available stator slot

area ( ), slot-fill factor Sff and the number of turns per coil, as shown in (4.11). The

factor of 2 in the denominator is due to the chosen double-layer windings layout.

= 2 (4.11)

Excessive amounts of I2R losses may increase the operating temperature causing

insulation degradation or even breakdown. This can be prevented by predicting losses

with temperature increases. Resistance of a conductor due to temperature rise can be

estimated by (4.12). The resistance and copper loss per phase in the final model as

temperature increases is shown in fig. 4.6 below.

= [1 + ( )] (4.12)

where,

= Current operating temperature

= Initial operating temperature

= Resistance of conductor at current operating temperature

= Resistance of conductor at initiation operating temperature

= Temperature coefficient of resistivity (0.004041 for copper)

Fig. 4.6 Resistance and copper loss per phase as temperature increases

Present-day winding insulation materials such as Nomex® have operating temperatures

of up to 220°C, and are able to withstand temperatures of up to 400°C for several hours

based on Arrhenius law [200].


96

4.5 OPTIMISATION OF MACHINE GEOMETRY

One of the aims of this design was to achieve a high torque density with a specific size.

More specifically- the prototype machine must fit into the same ABB casing shown in

fig. 4.7 which was originally used to house a 550W induction machine.

Fig. 4.7. ABB casing inserted 18-slot stator core

4.5.1 Stack Length

The stack length of the machine was determined based on the axial length of the

original ABB machine – 55mm stack length and 27mm end-winding length per side, (fig.

4.8a). A plastic stator was built to estimate the end-winding length of a double-layer

CW stator. The “horizontal-fill” method (fig. 4.9a) was used and the end-winding length

was measured to be 14.5mm for a 40% Sff (fig. 4.8b).


97

(a) End-windings for double-layer DW stator (b) End-windings for plastic double-layer CW stator

Fig. 4.8 End winding length comparison between UNSW DW stator with windings done on a plastic model

Slots in double-layer CW can also be wound using the vertical-fill method, (fig 4.9b).

The advantage of the vertical-fill method is that the end-winding length will be

approximately half the end-winding length when wound with the horizontal method.

This results in lower copper loss, and also allows space for a longer stack. However,

this method is extremely time-consuming, (approximately 45 to 60 minutes for 90 coils).

Furthermore, this method increases the chances of having unequal number of turns per

phase as a former and counter can be used to pre-wind coils.

Although the horizontal-fill method results in a thicker end-winding length and higher

copper loss, this method is a lot less time consuming (20 minutes per coil – with a

minimum slot opening with of 1.2mm) and a slot-fill factor of up to 44% can be

achieved. The likelihood of having unequal turns per coil is also lower, as a machine

can be used to aid the winding process.


98

(a) Horizontal-fill method

(b) Vertical-fill method

Fig. 4.9 Hand winding methods

Despite the expected decrease in efficiency and power density, the horizontal method

was chosen to reduce the production hours, cost of production, and possibility of error

in this initial prototype.

Compared to the end-winding length of the DW machine (25.5mm per side), the end-

winding length of the prototype machine was 12.5mm per side, (shown in fig. 4.9).

Therefore, with an additional 26mm of axial space in the casing, the effective stack

length can be increased from 55mm to 80mm. This will allow the original power

density of the DW-machine (550W) to be increased to (550 X 80/55 = 800W).

2Side viewFront view

Side viewFront view


99

4.5.2 Rotor Outer Diameter and Airgap Length

The rotor outer diameter was chosen to be 80mm, 1mm smaller than the two other

comparison DW-IPM machines. This was done to make space for a larger airgap.

Typically, motors of this size, (under 1kW), have airgap lengths between 0.3mm to

0.5mm. In CW motors, the additional leakage harmonic terms created result in localised

saturation and unbalanced pull forces [20]. This would cause increased core losses and

significantly reduce the field-weakening performance of the machine. To reduce the

effects of the leakage harmonic terms caused by armature reaction, the airgap length of

the IPM machine can be increased. It was shown in [201] that a larger airgap resulted in

a significant increase in CPSR. Conversely, it would also result in larger reluctance for

the permanent magnet flux linked with the stator coils. This would cause the output

power to decrease. Fig. 4.10 shows the effects of airgap length variation with output

power and CPSR.

(a) Airgap length variation with output power (b) Airgap length variation with CPSR

Fig. 4.10 Airgap length variation with output power and CPSR

The final airgap length chosen is was 1.2mm. This helps in achieving a wide CPSR

(>7:1) and an output power of approximately 800W. In order to sustain such high power

with such a large airgap, high energy magnets with maximised surface area per pole

500700900

11001300150017001900

0 0.5 1 1.5

Pow

er (W

)

Airgap Length (mm)

4

5

6

7

8

9

10

0 0.5 1 1.5

CPS

R (X

: 1)

Airgap Length (mm)


100

must be used. The maximisation of magnet surface resulted in rotor structural issues

with single-piece/pole, rectangular-shaped magnet designs, thus v-shaped magnets with

iron bridges were preferred. This will be discussed later in section 4.6 of this chapter.

4.5.3 Stator Geometry

The stator inner diameter of 82.4mm was obtained from the rotor outer diameter and

airgap length. The basic stator geometry can be defined by four main parameters: tooth

width, yoke length, shoe thickness, and slot opening width, as shown in fig. 4.11.

Ideally, small tooth width, yoke length and shoe thickness are desired. As such, a larger

slot area can be achieved to contain larger conductors, which in turn lowers copper loss.

A wide slot opening width ( ) is also desired for simplifying the winding process.

However, smaller areas in the teeth and yoke mean a higher saturation level in these

areas if large currents are used.

Fig. 4.11. Key parameters defining the stator geometry

Slot opening width ( )

Tooth width ( )

Yoke length ( )Slot area ( )

Shoe thickness ( )


101

Manually calculating the exact stator geometry to control saturation levels can be

complex. Thus a simple two-step process is used here – Firstly, a linear relationship

between the flux and stator geometries is used as an initial estimation [202].

Subsequently FE analysis will be used to ‘fine-tune’ the geometry to ensure that

equivalent flux is achieved in the tooth and back iron as well as to prevent saturation

from occurring at key portions of the stator.

From [202], the estimated yoke length and tooth width is given as follows:

The yoke length or back iron ( ) is given by:

= 2 (4.13)

and the tooth width ( ) is given by:

= (4.14)

where,

= Stator inner diameter

= Peak airgap flux density

= Number of pole pairs

= Yoke flux density

= Tooth flux density

= Number of stator slots

The desired core material has a saturation magnetisation of 1.68T, hence, allowing for a

10% safety margin, peak flux density of of the yoke and tooth was chosen to be 1.5T.

With the chosen peak flux density in the yoke and tooth, the estimated yoke length and

tooth width from (4.13) and (4.14) are 5.3mm and 6.8mm respectively. As a first step of

optimisation, the stator was designed with these values. The design was then further

optimised by the use of FE analysis where non-linearities in the core material were

taken into account.


102

Fig. 4.12 Flux density plots showing peak flux density in the yoke and tooth

The final yoke length and tooth width were 5.1mm and 7.4mm respectively. These

dimensions produced peak flux of 1.48T in the yoke and 1.47T in the tooth as shown in

fig. 4.12.

Slot Opening Width

The FE results show that wider slot openings and smaller shoe thickness result in a

lower CPSR. However, smaller slot openings would lead to increased difficulty in

inserting the stator coils, and thicker shoes would lead to smaller slot areas. For this

design, the ideal shoe thickness was found 1.4mm (as small as possible to allow larger

slots, but big enough to prevent oversaturation of the shoe region) and a suitable slot-

opening width was determined as follows:

Color Shade ResultsQuantity : |Flux density| Tesla

Time (s.) : 0.001 Pos (deg): 2.571Scale / Color13.07917E-6 / 187.43178E-3187.43178E-3 / 374.85045E-3374.85045E-3 / 562.26915E-3562.26915E-3 / 749.68785E-3749.68785E-3 / 937.10661E-3937.10661E-3 / 1.124531.12453 / 1.311941.31194 / 1.499361.49936 / 1.686781.68678 / 1.87421.8742 / 2.061622.06162 / 2.249042.24904 / 2.436462.43646 / 2.623872.62387 / 2.811292.81129 / 2.99871

B = 1.47T

B = 1.48T


103

With the main considerations being the ease and time taken to wind the stator; at the

same time investigating the possible slot-fill factor, plastic stator portions were made

with three different slot opening widths: 1.2mm, 1.6mm and 2mm as shown in fig. 4.13.

Fig. 4.13 Plastic stator made with three different slot opening widths

60 turns of winding, diameter 0.80mm, were fitted into the respective slots. The

duration taken to fit the conductors into the slots with respective slot openings were: 1.2

mm – 15 mins; 1.6mm – 12mins, and 2mm – 5mins. The ideal (lossless) CPSR obtained

for the various slot opening widths from FE analysis was: 1.2mm – 14:1; 1.6mm – 12:1

and 2mm – 9:1. Although more time was required to wind the stator as the slot-opening

widths decrease, the slot-fill factor was the same with all three widths. Since the same

slot-fill factor could be achieved and with the preference of achieving a wider CPSR,

the 1.2mm was selected in the final prototype.


104

4.6 ROTOR DESIGN AND STRUCTURAL CONSIDERATIONS

Compared to the SPM machine, the IPM machine has buried magnets. The

disadvantage of having buried magnets is that the width and thickness of the magnets

are limited by the inter-pole link sections, especially if single piece/pole magnets are

used, (fig. 4.14a).

(a) single-piece/pole magnet design (a) v-shaped magnet design

Fig. 4.14 IPM rotors showing inter-pole link sections

One way to increase the torque density of the machine is to use v-shaped magnets, (fig.

4.14b), which increase the surface area of the magnets and provides flux concentration.

It was shown in chapter 3 that v-shaped magnets produced higher torque density

compared to rectangular, single piece/pole magnets with the same volume. Additionally

v-shaped magnets provide additional flexibility of v-angle variation to achieve desired

airgap flux density. Figure 4.15 shows the variation of magnet surface area and

corresponding airgap flux density when the v-angle is varied:

Inter-pole link

sectionsInter-pole

link sections


105

(a) 120º v-angle (b) 60º v-angleFig. 4.15. V-angle variation

In order to maintain the characteristic current equilibrium, rated current had to vary with

changes to the v-angle. The power ratings and optimised CPSR with various v-angles

are shown in Table 4.2 below [201]. Magnet volume is not constant for this set of

results. The per unit power versus speed curves for the various designs are shown in fig.

4.16.

Table 4.2Power and CPSR with variation of v-angle

v-angle Power at base speed CPSR120º 600W 4.2:1

90º 725W 6:1

60º 1050W 10:1

30º 1835W 8:1

Fig. 4.16 Normalised power versus speed characteristics with variation of v-angle

00.20.40.60.8

11.21.4

0 1000 2000 3000 4000

120 degrees 90 degrees 60 degrees 30 degrees

Speed (RPM)

Pow

er (P

.U.)

Bair = 0.70T

Am = 587mm2

v-angle = 120°

Bair = 0.97T

Am = 951mm2

v-angle = 60°

6:1CPSR

8:1CPSRbase

4.2:1CPSR

10:1CPSR


106

The above figure and table show that power increases as v-angle is reduced; however

CPSR starts to decrease past 60º. Thus, an angle of 60º is chosen as the optimal value

for this particular design.

4.6.1 Structural Considerations

In an SPM rotor, the permanent magnets (which are inherently brittle), attached on the

outside of the rotor are structurally vulnerable [203]. Various methods are used to

maintain the mechanical robustness, but each presents its own problem. Glued magnet

pieces, (fig 4.17a), are the easiest to manufacture but, are not suitable for high speed

operations due to the possibility of magnets detaching from the rotor. Full-cylindrical

rotor magnets, (fig 4.17b), are more secure but are vulnerable to vibration and

expansion of the rotor core. Retaining sleeves, (fig 4.17c), are suitable for high speed

operations but present additional rotor losses.

(a) SPM rotor with Glued magent pieces [204]

(b) SPM rotor with full-cylindrical rotor magnets

[205]

(b) SPM rotor with magnets enclosed in a retaining sleeve

[206]

Fig.4.17 Various types of SPM rotors

IPM rotors on the other hand, have the advantage of magnets being contained inside the

rotor. (Fig. 4.18 shows an IPM rotor with buried single-piece/pole magnets). This

simplifies the rotor manufacturing process, reduces rotor magnet losses, and enhances

the mechanical robustness of the rotor.


107

Fig. 4.18 IPM rotor with buried single-piece/pole magnets

The key disadvantages of IPM rotors are: rotor core losses will be higher and the

magnet pole span and thickness are limited by the inter-pole link sections. The inter-

pole link section has to be made thinner and longer as the required magnet volume

increases, thereby subjecting them to large mechanical stresses, especially at high

speeds.

During operation, two types of forces are inflicted upon the rotor poles – magnetic

forces from the stator coils, and centrifugal forces during high rotational speeds. The

surface force or magnetic pressure ( ) is expressed in (4.15) where the centrifugal

force ( ) is calculated based on (4.16), both of which are acting in an outward normal

direction to the rotor surface [207].

= 2 (4.15)

= ( ) (4.16)

where, = Permeability of free space = Mass of object subjected to force = Radius of cylinder

Buried magnets


108

To obtain a general estimate of the magnetic pressure created by stator and rotor pole

interaction, a basic solenoid-magnet model, (as shown in fig. 4.19), was created. It

simulates the ‘worst-case’ over-current scenario, where the airgap flux density was

modelled to be 1.5T. The airgap length was modelled as 0.6mm to account for any rotor

eccentricities.

Fig. 4.19 Modelled solenoid-magnet model

The resultant attractive force acting in the direction normal to the magnet surface is

1075N. This would be equivalent to approximately 1MPa of pressure acting normal to

the magnet surface.

-1

-0.5

0

0.5

1

1.5

0 5 10 15

mm

Tesla

Region vectors resultsQuantity :Flux density TeslaColour scale26.35732E-3 / 309.69441E-3309.69441E-3 / 593.03149E-3593.03149E-3 / 876.36858E-3876.36858E-3 / 1.159711.15971 / 1.443041.44304 / 1.726381.72638 / 2.009722.00972 / 2.293052.29305 / 2.576392.57639 / 2.859732.85973 / 3.143073.14307 / 3.42643.4264 / 3.709743.70974 / 3.993083.99308 / 4.276414.27641 / 4.55975

ToothCoil Coil

Magnet0.6mm Airgap

AirgapFlux


109

To calculate centrifugal force, the v-shaped magnet model was used. It included the

mass of the magnets as well as the rotor steel.

Fig. 4.20 Sections for centrifugal force calculation

Due to a relatively small rotor radius (40mm), the calculated centrifugal pressure at

6000rpm (maximum speed) was small (174kPa). Adding the centrifugal pressure to the

pressure resulting from the magnetic forces, total outward normal pressure of 1.174MPa,

acting on each pole section, was attained. In order to analyze the effects of these forces

on the inter-pole link sections, an FE model as shown in fig. 4.21, was created.

Figure 4.21 Model showing outward normal pressure on each section of the rotor

The mechanical data for the selected steel grade is given in table 4.3.

Silicon steel sectionDensity = 7600 kg/m3

Volume = 7.73X10-6 m3

Mass = 58.71g

Magnet sectionsDensity = 7500 kg/m3

Volume 2.025 X 10-6 m3

Mass = 15.19 g/piece


110

Table 4.3Mechanical data for silicon steel grade (JFE-35JN210) [198]Young’s modulus 1.7e5 [MPa]Poisson ratio 0.28Density 7.6e-6 [kg/mm2]Thermal expansion 1.2e-5 [1/°C]Tensile yield strength 400 [MPa]Compressive yield strength# 400 [MPa]Ultimate tensile strength 515 [MPa]

# Estimated quantity – Data not found

Three different models with 0.7mm inter-pole link sections were compared-

Rectangular single-piece/pole magnet model, v-shaped magnet model (60º v-angle), v-

shaped magnet model with 0.7mm iron bridge. Maximum principal stress points of

these three models were shown in Fig. 4.22a to 4.22c, respectively.

(a) single-piece/pole magnets (b) v-shaped magnets no bridges

(c) v-shaped magnets with bridges

Fig. 4.22 Mechanical stress analysis of rotor

15.3MPa

12.5MPa

25.1MPa

133.5MPa

103.6MPa

154.6MPa

130.3MPa


111

The mechanical model shows that the maximum stress imposed on all the three models

was within the mechanical limits of the chosen silicon steel grade. However, the model

with v-shaped magnet and bridges was preferred, as it allowed greater flexibility in

minor alterations to the magnet slot size and v-angle to eliminate any unforseen errors.


112

4.7 FINAL MANUFACTURED DESIGN

The final CW-IPM design was a 14-pole, 18-slot, double-layer winding layout with v-

shaped magnets. The final design was chosen based on the appropriate selection of

slot/pole combination and magnet shape (shown in chapter 3); as well as the

optimisation and material selection process shown earlier in this chapter. Here, key

machine parameters and torque performance characteristics of the final FE design will

be illustrated. Full specifications of the final design are shown in Table 4.4, and

technical drawings are shown in Appendix C.

The final winding layout is shown in fig. 4.23 (PA, PB and PC represents positive

terminals for each phase coil while MA, MB and MC represent negative terminals).

Fig. 4.23 Final 18-slot, double-layer winding layout


113

Table 4.4Specifications of the final design

Stator outer diameter 130mmRotor outer diameter 80mmAirgap length 1.2mmStator inner diameter 82.4mmShaft outer diameter 24mmStack length (stator) 80mmStack length (rotor) 79mmArea per half slot 86.3mm2

Stator and Rotor lamination thickness 0.35mmSlot-opening width 1.2mm

Number of slots 18slots / double-layerWinding type Double-layer concentratedPacking (slot-fill) factor 41.5%Number of turns per coil (around each tooth) 115turnsDiameter of each conductor strandConductor insulating material max. temp.Slot insulating material max. temp.Cooling arrangements Natural convection (Fin cooled)Area per half slot 86.3mm2

Number of poles 14polesNo. of magnet pieces 28pieces (2 X 14poles)Magnet dimensions 13.5mm X 2mm X 79mm Desired remnant flux density (Grade) 1.04 – 1.09T (Raremag - N24EH)Magnet temperature rating 200°CMagnet coating Ni-Cu-NiCore material Non-oriented silicon steelSaturation mag. of laminations 1.68T @5000A/mPredicted core loss at 50Hz/1.5T 2.60W/KgYield strength of laminations 2

Resistivity of lamination -cm

Rated voltage (RMS) 240V/phaseRated current (RMS) 2.55A/phaseMaximum rated torque at base speed 18NmMaximum operating speed 6857rpm d-axis inductance (at rated current) 81.16mHq-axis inductance (at rated current) 84.45mHStator resistance at ambient temperatureMagnet flux linkage 0.48Wb


114

4.7.1 Back EMF from the Finite Element Model

The predicted back EMF from the final FE model is shown below:

Fig. 4.24 Three-phase induced line to neutral back EMF voltage from the FE model (at 50Hz)

It can be observed that the modelled phase back EMF is near-perfectly sinusoidal, all

three phases are balanced and 120º apart. The induced voltage per phase when the

machine is ran at 428.6RPM (50Hz) is 91.6Vrms. The modelled line to line induced

voltage at the same speed is sinusoidal, and has a value of 158.6Vrms. The linear

relationship between induced line to line voltages versus rotor speed is shown in fig.

4.25:

Fig. 4.25 Induced line to line voltage versus speed

-150

-100

-50

0

50

100

150

0 0.005 0.01 0.015 0.02

Va(L-N)

Vb(L-N)

Vc(L-N)

0200400600800

1000120014001600

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Indu

ced

Volta

ge (V

)

Time (s)

Indu

ced

Vol

tage

(Vrm

s)

Speed (RPM)


115

To determine the winding factor, the final design was compared to an equivalent

integral-slot, double-layer, DW machine with the same rotor. This comparison is shown

in fig. 4.26 below. The corresponding harmonic spectrums of these waveforms are

shown in fig. 4.27.

Fig. 4.26 Comparison of EMF waveform between the CW-IPM and DW-IPM

Fig. 4.27 Comparison of EMF waveform between the CW-IPM and DW-IPM – frequency spectrum

It can be seen that both these winding types produce equally sinusoidal back EMF

waveforms. However, due to a higher winding factor, the DW-IPM machine produced a

higher fundamental term, (233.2Vrms), compared to the CW-IPM machine,

-250-200-150-100

-500

50100150200250

0 0.005 0.01 0.015 0.02

CW-IPM DW-IPM

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CW-IPM DW-IPM

4 5 6 11 12 13

Indu

ced

Vol

tage

(V)

Time (s)

Indu

ced

Volta

ge (V

)

Harmonic number

224.3Vrms 233.2Vrms

Near-zero harmonics


116

(224.3Vrms). The DW-IPM machine has a distribution factor of 0.9659, and a pitch

factor of 0.9695; this results in a winding factor of 0.933. Based on these values,

fundamental magnitude achieved for a unity winding factor should be 249.9Vrms and

the expected magnitude of the 18-slot, 14-pole model should be (249.9Vrms x 0.902 =

225.45Vrms). With a value of 224.3Vrms achieved, the result agrees with the tabulated

values in table 3.1.

4.7.2 Cogging Torque from the Finite Element Model

The cogging torque magnitude of the final design, (3/7Spp), compared to an integral-

slot (2Spp) DW model, is shown in fig. 4.28. It is shown that the final design produces

2.5 times lower peak to peak cogging torque magnitude compared to the DW model.

This is due to the elimination of periodicity of slots and poles, which lowers the

magnitude of the cogging torque but increases its fluctuating frequency.

Fig. 4.28 Cogging torque of final design comapred to an equivaent integral-slot DW model

4.7.3 Inductance and Saliency Ratio from the Finite Element Model

Since, the calculation of inductances by aligning the winding axes to the d- and q-axis

of the rotor is not accurate in CW machines, d- and q-axis inductances are calculated by

applying AC standstill test conditions to the FE model. The self- and mutual inductance


117

waveforms of the final design from the FE model are shown in Fig. 4.29 (for single-

phase, 50Hz, 3Arms current excitation).

Fig. 4.29 Self- and mutual-inductance waveform of final model with 3Arms current excitationLd, Lq and saliency ratio obtained from the DC and second harmonic terms of these

waveforms are as follows.

= ( ) 2 += 81.16mH

= ( ) + 2 += 84.45mH= = 1.04


118

4.7.4 Torque Performance from the Finite Element Model

In order to account for small fluctuations, steps/electrical cycle had to be small (200

steps per cycle). The characteristic current of the machine was found to be 2.55Arms (at

which the widest CPSR could be achieved). With the peak voltage set to 240V(1-l), the

rated torque at a base speed of 428.6rpm is 15.14Nm (equivalent to 679W of power).

The torque ripple at this speed is 2% of the torque produced as shown in fig. 4.30.

Fig. 4.30 Torque ripple of final model at base speed

With the abovementioned rated values, a > 10:1 CPSR can be achieved. The peak

power achieved was 880W (at 300Hz).

Fig. 4.31 CPSR of final design with base frequency of 50Hz

The power versus speed characteristic shown in fig. 4.31 is for the ideal case where

losses are ignored. Due to frequency-related losses, the output power and CPSR may be

affected. The performance with the inclusion of losses will be discussed in chapter 5.

14.714.814.9

1515.115.215.315.415.5

0 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Pow

er (W

)

Speed (RPM)

Torq

ue (N

m)

Time (s)

>10:1 CPSR

0.31Nm(p-p)


119

4.8 CONCLUSION

This chapter showed the optimisation process of the 14-pole, 18-slot, double-layer CW-

IPM machine to achieve a wide CPSR and desired torque performance. The key steps in

this design were:

Positioning of phase windings to achieve highest winding factor

Material considerations

Rotor magnet design and structural considerations

Optimising the CPSR with by satisfying characteristic current equilibrium

conditions

Further extend the speed range by airgap length and rotor geometry variations

FE analysis showed that the final design can achieve over 10:1 (lossless) CPSR with the

capability of producing over 880W of peak power for a voltage limit of 240V(l-l). By

comparing FE models of the final CW-IPM machine with the integral-slot DW-IPM

machine, it was shown that the expected winding factor (0.902) and significantly lower

cogging torque can be achieved. It was also shown that high inductance values were

achieved with Ld being similar to Lq – resulting in a saliency ratio is almost unity (1.04).

In this chapter, the design process only considered the ideal scenario where both

electrical and mechanical losses were omitted. Losses will be considered separately in

the chapter 5. The test results from the constructed design will be shown in chapter 7,

where the FE results will be verified.

120

CHAPTER 5ANALYSIS OF LOSSES IN AN IPM MACHINE WITH CONCENTRATED WINDINGS FOR FIELD WEAKENING APPLICATIONS

5.1 INTRODUCTION

A key aim in almost all high performance PM machine design is to minimise losses. In

machines used for field weakening applications, frequency related losses in particular

have to be carefully considered.

Losses in PM machines are separated into two main areas – electrical losses and

mechanical losses.

Electrical Losses:

Core losses – Eddy current and hysteresis losses

Permanent magnet losses

Copper loss

Mechanical losses:

Bearing losses

Windage losses

Chapter 5 will highlight the causes of increased frequency-related losses in an IPM

machine with CW in comparison to DW. The effects of varying material type and

geometry will be investigated. The abovementioned electrical and mechanical losses

will be studied and quantified in terms of the final FE design presented in chapter 4.

Losses would be found at various frequencies and used to provide a more realistic field

weakening performance of the machine.

Chapter 5: Analysis of Losses in an IPM Machine With Concentrated Windings for Field Weakening Applications

121

5.2 MMF HARMONICS AND LOSSES IN MACHINES WITH

CONCENTRATED WINDINGS

Compared to DW, the MMF waveform produced by CW contains additional MMF

harmonics and sub-harmonics not rotating in sync with the synchronous frequency. Fig.

5.1 show the magnetic flux distribution in a CW and DW machine. (The flux

distribution shown is by armature excitation only).

(a) Flux distribution of 14-IPM rotor with a fractional-slot CW stator

(b) Flux distribution of 14-IPM rotor with an integral-slot DW stator

Fig. 5.1 Comparison of flux distribution in a CW and DW machine

MMF ( ) produced by the stator coils is basically expressed as flux density produced by

the stator (Bs) linked across an airgap of surface area (Arot) with reluctance ( ).= (5.1)

If the machine geometry, including airgap length and slot opening width, is kept

constant, the only parameter that will affect MMF across the airgap is the flux density

produced by the armature reaction. The airgap flux waveforms generated by the DW

model (fig. 5.2), has a fundamental component at 7 times the base frequency, which is

the torque producing term in this 14-pole machine model. On the other hand, CW


122

produces a dominant fundamental in addition to several other significant harmonic and

sub-harmonic components. Fig. 5.3, gives a comparison of MMF waveforms produced

by single-layer and double-layer CW.

Fig. 5.2 Airgap flux waveform and harmonic spectrum produced from a DW model

(a) (b)Fig. 5.3 Airgap flux generated by 18-slot (a) single-layer CW, (b) double-layer CW

-0.25

0

0.25

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

-1

-0.5

0

0.5

1

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

-0.5

-0.25

0

0.25

0.5

0 100 200

Tesla

0

0.1

0.2

0.3

0 25 50

Tesla

Fundamental Term

Fundamental TermFundamental

Term

nth order leakage harmonic terms

nth order leakage harmonic terms


123

The total loss in the core depends on two main terms hysteresis loss and eddy current

loss as shown in (5.2). = + (5.2)

where, = Eddy current loss constant = Hysteresis loss constant = Maximum flux density = Material dependent Steinmetz loss constant (in the range of 1.6 to 2.0) While hysteresis loss depend largely on material and flux density, eddy current loss is

proportional to the frequency squared, making it much more susceptible to leakage

harmonic components which are several times higher than the operating frequency

[208]. In the field-weakening region, an additional CPSR factor is further multiplied to

the fundamental and leakage components. For example: in operation at 10 times the

base frequency of 50Hz, a leakage harmonic component n=42 would be fluctuating at

3000Hz.

To better visualise the proportion of losses, it is common to divide the total loss by

frequency to keep hysteresis term constant; with the assigned as 2, (5.2) can be

simplified [192, 197, 209].

= + (5.3)

A graphical representation of this equation is shown in fig. 5.4.


124

Fig. 5.4 Contribution of eddy current and hysteresis loss

As the hysteresis loss is largely material dependent and little can be done to minimise it,

emphasis will be placed on eddy current loss, in which the choice of lamination

thickness can help in minimising losses.

For a general concept on how the increase in airgap harmonics affects eddy current loss,

Faraday and Maxwell equations can be used.

Equating the electric field ( ) in a closed path c along the surface to the induced voltage( ) and flux linkage we get:

= = = (5.4)

Equating current density ( ) to the electric field, we have: = (5.5)

Say a fluctuating magnetic flux density (B) acts on a thin piece of material with

conductivity thickness width (w). Eddy current (Peddy) induced in this

conductor can be expressed as follows:

esis lossFrequency (Hz)

t and hf1

Contribution of eddy current loss

Contribution of hysteresis loss


125

= 1 (5.6)

Assuming that flux density is uniform across the surface, flux linkage will be:

= (5.7)

The induced voltage in (5.4) can be expressed as:

= = (5.8)

If is reduced to infinitely thin sections (x), the electric field along the closed path in

(5.4) can be described by:

= 2 = (5.9)

From (5.5) the induced current density at the surface of the material is given by:

= = (5.10)

The eddy current loss shown in (5.6) in terms of the induced current density can be

described as follows:

= 1 1 (5.11)

= 12 (5.12)

For integral-slot DW, a sinusoidal airgap flux density (fig. 5.2) is assumed, then (5.12)

can be solved to obtain:

= 12 (5.13)

= 6 (1 + 2 ) (5.14)


126

where the terms in the square brackets are usually absorbed in the eddy current constant

(Ke).

In CW, the function would not only depend on the fundamental but other leakage

harmonic components as well. The eddy current loss for CW can thus be generally

expressed in (5.15) where Bn is the nth harmonic component of the waveform as shown

fig. 5.3.

= 12 1 ( ) (5.15)

From (5.15) it can be seen that the most effective way to reduce eddy current loss is by

minimising flux density harmonics. Although the introduction of additional harmonic

components is unavoidable with CW, double-layer CW windings substantially reduce

these components. For this particular reason, double-layer was chosen over single-layer

CW windings in the final design.

In the PM machine, eddy current loss occurs mainly in the core and magnets. As

mentioned in the chapter 4, non-oriented silicon steel is chosen as the core material due

to its price and performance characteristics. Within the range of silicon steel grades,

conductivity may vary up to 35% [198, 210], resulting in different core losses. The

thickness of the material also affects core loss. This chapter will study the effects of

core loss as the steel grade/thickness is varied.

For the magnet material, there is a huge variation of conductivity between the two

different methods by which NdFeB magnets are made. Sintered magnets have a typical

conductivity of 625X103 -m)-1 whereas bonded magnets have a conductivity of

7.14X103 -m)-1. Thus, in areas such as in an SPM machine used for FW applications

where magnet losses are high, bonded magnets are commonly used at the expense of


127

lower magnet remanent flux densities. In cases where high torque density and low

magnet losses are required, sintered-segmented magnets can be used [140, 211].

The comparison of SPM and IPM magnet losses, as well as the effects of magnet

segmentation and variation of magnet type will be quantified this chapter.

5.3 CORE LOSS

In machines used for field-weakening applications, frequency-related losses have to be

carefully considered and minimised due to constant operation at high frequencies.

Furthermore the increase in leakage harmonic terms as a result of applying CW makes

the machine more susceptible to increased core and rotor losses.

One method of separating the hysteresis and eddy current losses is derived from the

relationship mentioned by Yeadon [212]; the book states that in typical steel

laminations (grades M19 through to M45), hysteresis loss at 60Hz make up

approximately 67% of the total core loss and eddy current loss makes up the other 33%.

The material chosen (35RM300) has core loss 3.25W/kg at 60Hz/1.5T (shown in fig

5.5), which is similar to grade M19. Thus, this approximation is valid for the breakdown

of hysteresis and eddy current loss at 60Hz and the total core loss can be expressed as:= + (5.16)

where, = 13 (5.17)

= 23 (5.18)

This estimation gives us an eddy current loss of 1.08W/kg and hysteresis loss of

2.17W/kg. In order to determine core losses due to harmonics components, various


128

operating frequencies as well as saturation levels, the hysteresis ( ) and eddy current

loss constants ( ) must first be found.

Fig. 5.5 Core loss curve of 35RM300 provided by Sankey showing core loss at 60Hz/1.5T

To ensure consistency between FE models in Magsoft-Flux2D, a narrow annular-core

specimen consisting of thin laminations is created (as shown in fig. 5.6):

Fig. 5.6 Annular steel model to determine eddy current and hysteresis loss constants

The surface area of the core was chosen such that the flux distribution throughout the

core is at a relatively constant flux density – in this case 1.5T. Frequency of excitation

Constant flux density throughout surface area (3.3% difference margin)

Is (60Hz)

Annular laminated-core structure

Coils with number of turns producing 1.5T flux density in core


129

was set to be 60Hz. The volume of the core was chosen to be equivalent to 100g of

silicon steel.

From this model, the values of and was found by trial and error, to achieve eddy

current loss of 1.08W/kg and hysteresis loss of 2.17W/kg. The values were 0.29 and

151 respectively. These loss constants can then be used to obtain the core loss in the

machine model at various excitation frequencies. ( and is found in this way for

each steel grade).

5.3.1 Comparison of Steel Grades

Here the chosen steel grade (35RM300) will be compared with two other steel grades

with different thicknesses- 50JN350 and 65JN800 [198, 213]. Key features of the

specific grades are shown in table 5.1.

Table 5.1Properties of compared core grades

Material Type

Lamination Thickness

Saturation Mag. (B50)

Stacking Factor

Total Core Loss @60Hz/1.5T

35RM300 0.35mm 1.68T 95% 3.25W/kg 151 0.29

50JNE350 0.50mm 1.68T 96% 4.45W/kg 263 0.39

65JNE800 0.65mm 1.72T 97% 10.15W/kg 495 0.89

With and found using the annular model, the losses at 50 and 500Hz are shown in

fig. 5.7. Stacking factor in the above table was stated as a reference (being proportional

to output torque) – it should be noted that in the loss calculations, stacking factor was

not included as differences would not be very significant.

mailto:@60Hz/1.5T


130

Fig. 5.7 Core loss comparison at 50 and 500Hz with different steel grades

As a percentage of output power, core loss in the constant torque region (50Hz) is low

(<2.5%), therefore a maximum difference in total core losses among the steel grades (of

10.6W) does not significantly affect the efficiency. However, in the higher field-

weakening region (500Hz), the core loss as a percentage of output power becomes

significant (>13%), and the maximum difference in total core losses (of 74.1W) would

result in almost a 10% difference in efficiency.

The results emphasise the importance of using thin laminations with low losses when

designing machines for field-weakening applications. Thicker laminations, (like the

65JN800), are more suitable for machines operating at lower frequencies, (within the

constant torque region), where torque density is of higher priority. As a percentage of

total loss, it is expected that core loss would be low. Hence this rough estimation

indicated above would suffice for the study of this preliminary prototype. A more

detailed measurement of losses would be required for future prototypes where core

losses significantly impact the overall efficiency of the machine.

1.4 4.7 6.0 14.3

19.1

33.4

2.4 8.0 10.3

24.2 29.5

53.7

4.5 15.3

19.7

46.6

60.9

107.5

0

20

40

60

80

100

120

Rotor coreloss @50Hz

Stator coreloss @50Hz

Total coreloss @50Hz

Rotor coreloss @500Hz

Stator coreloss @500Hz

Total coreloss @500Hz

35RM300 50JN350 65JN800Po

wer

loss

(W)


131

5.3.2 Core Loss of Final Design

The core loss in the final design with the chosen material (35RM300) at various

frequencies is shown in fig. 5.8.

Fig. 5.8 Core loss with chosen steel grade at various frequencies

As expected, core loss increases exponentially with frequency. The percentage of stator

to rotor core loss is several times higher (77% from the stator, compared to 23% from

the rotor, at 50Hz) in the constant torque region where the d-axis current is zero. In the

field-weakening region, rotor core losses become substantial, contributing to a large part

(43% at 500Hz) of the total core loss in the machine.

0

5

10

15

20

25

30

35

40

45

50

50 100 200 300 400 500

Rotor CoreLoss

Stator CoreLoss

Ploss(rotor) = 2.57WPloss(stator)= 3.73W





Pow

er lo

ss (W

)

Frequency (Hz)



132

5.4 MAGNET LOSS

With the core loss substantially reduced by the choice of thin silicon steel laminations,

the time varying fields may still create substantial losses in the magnets, especially in

SPM machines. A great deal of research interest is focused on the study and

minimisation of magnet losses in CW-PM machines. Commonly used strategies to

reduce magnet losses are by the use of bonded instead of sintered magnets at the

expense of lower magnet strength, or the use of sintered-segmented magnets [141, 208,

214, 215].

While the magnet eddy current loss constant can be easily calculated by conductivity

and thickness of the magnets, the hysteresis loss data is not being readily available.

Here, the hysteresis loss constant was estimated by extrapolating measured data from

Fukuma et al. [216] and Shinichi et al. [208]. In their work, hysteresis and eddy current

losses in sintered neodymium were measured when exposed to low flux densities up to

0.1T. The results show that while the hysteresis loss increase was relatively linear; there

was a slight exponential increase to eddy current loss. Extrapolated polynomial trend

lines were fitted into measured results obtained from the abovementioned papers, as

shown in fig. 5.9. More accurate loss measurements will be left for future work – when

the equipment becomes available to test magnet losses. For this work, this estimate

would suffice as it will be shown later that magnet losses in the CW-IPM machine make

up only a very small percentage (0.5%) of total losses.


133

Fig. 5.9 Extrapolated values of measured hysteresis and eddy current loss for sintered neodymium magnets at 50Hz [208, 216]

The typical operating point of the PMs in the final design is 0.6T. Values obtained from

the extrapolation at that flux density are 10.1W/kg for hysteresis and 4.6W/kg for eddy

current loss. There are several FE methods for calculating magnet losses. The purpose

of using this method (declaration of eddy and hysteresis loss constants) is due to the

advantage of being able to study the effect of each loss separately.

For neodymium magnets, conductivity of magnets is readily available from

manufacturers’ datasheets. Thus eddy current loss constant can be calculated by the

following formula [209]:

= 6 (5.19)

With each magnet piece being 79mm long, for sintered and bonded neodymium

magnets are calculated to be 6416 and 73 respectively.

With the relation between and obtained from the extrapolated values shown in fig.

5.9, can be estimated. The magnet loss constants can then be used to study magnet

losses with 3D FE model using ANSOFT-Maxwell13.

0

2

4

6

8

10

12

14

0 0.1 0.2 0.3 0.4 0.5 0.6

Hystesis Loss [W/kg] Eddy Current loss [W/kg]

Poly. (Hystesis Loss [W/kg]) Poly. (Eddy Current loss [W/kg])

10.1W

4.6W

Pow

er lo

ss (W

/kg)

Flux Density (T)


134

5.4.1 Comparison of SPM and IPM Magnet Losses

Compared to the IPM machine, (shown in fig 5.10), the SPM machine has permanent

magnets that are directly exposed to airgap flux, (shown in fig, 5.11), thus higher

magnet losses are expected [217]. Here, PM losses in SPM machines are quantified and

compared against the IPM machine.

Fig. 5.10 3D model of a single-pole and single-phase excitation – v-shaped IPM

Fig. 5.11 3D model of a single-pole and single-phase excitation – SPM

In these two models, airgap between the magnet outer surface and stator inner radius is

1.2mm, (the same airgap as in the IPM model). The volume and grade of magnet are

kept constant. A magnet loss comparison between these two machine types at 50Hz and

500Hz are tabulated in table 5.2 and graphed in fig. 5.13 below. The magnet losses

quantified in this section refers to total magnet losses in a 14-pole machine.


135

Table 5.2Comparison of magnet losses between IPM and SPM machine

50Hz 500HZPeddy Phys Pmag(total) Peddy Phys Pmag(total)

IPM(sintered mag.) 0.018W 0.034W 0.052W 0.560W 0.340W 0.900WSPM(sintered mag.) 2.133W 4.140W 6.273W 67.320W 37.900W 105.220WSPM(bonded mag.) 0.024W 1.110W 1.134W 0.771W 11.094W 11.865W

Fig. 5.13a Magnet losses in an IPM machine with sintered magnets

Fig. 5.13b Magnet losses in an SPM machine with sintered magnets

Fig. 5.13c Magnet losses in an SPM machine with bonded magnets

0.02 0.03 0.05

0.56

0.34

0.90

0

0.2

0.4

0.6

0.8

1

Eddy currentloss @50Hz

Hysteresisloss @50Hz

Total magnetloss @50Hz




Pow

er lo

ss (W

)

2.1 4.1 6.3

67.3

37.9

105.2

0

20

40

60

80

100

120







Pow

er lo

ss (W

)

0.0 1.1 1.1 0.8

11.1 11.9

0

2

4

6

8

10

12

14


Hysteresis loss@50Hz



Hysteresis loss@500Hz


Pow

er lo

ss (W

)


136

Because the magnets are being exposed to the airgap flux containing high leakage

harmonic content, (and with no protecting sleeves around the magnets), total magnet

losses in the SPM models are very much higher than that of the IPM model. In [216,

208], the measurement of magnet losses in an SPM machine show that at frequencies

lower than 1kHz, hysteresis loss is higher compared to eddy current loss. Results in

table 5.2 is consistent with the measured losses, in the sense that hysteresis loss is

higher compared to Eddy current loss at 50Hz but lower at 500Hz.

It should also be mentioned that the inverse is true for rotor core losses (that is: the rotor

core loss in the SPM machine is negligible as compared to the IPM rotor core loss due

to the magnets damping most of the varying harmonic terms from armature reaction).

Fig. 5.13 also shows that the total magnet losses with SPM bonded magnets are about

10 times lower than that of the SPM model with sintered magnets.

While the use of bonded magnets is highly favourable in SPM machines, in IPM

machines the use of bonded magnets at the expense of a reduction in torque density is

clearly not, since sintered PM losses make up less than 0.1% of the power produced.

5.4.1 Effects of Magnet Segmentation

Despite the very low magnet loss obtained in the IPM model, it would be useful to study

the effects of magnet segmentation in the SPM and IPM models. The work done in this

section takes reference to well-established work in various literature, some of which are

[140, 214, 215, 218, 219].

In work done by Yamazaki et al. in [140], magnet losses due to carrier and slot

harmonics in different rotor types were compared. With the variation of the number of

segments, SPM machines show a gradual decrease in manget eddy current loss as the


137

number of segments is increased, whereas IPM machines exhibit peaks (shown in fig.

5.14).

Fig. 5.14 Variation of magnet eddy current loss with number of magnet segments due to slotand carrier harmonics – Comparison between IPM, inset and SPM rotors [140]

In this section, the effects of segmenting magnets in the IPM and SPM models are

compared. The same models shown in fig. 5.10 and 5.12 are used. Fig. 5.15 shows the

circulating eddy currents in the single SPM magnet pole piece, as well as in the IPM

magnet pole consisting of two magnet pole pieces.

(a) SPM magnet pole (b) V-shaped IPM magnet pole

Fig. 5.15 Circulating eddy currents in a non-segmented poles


138

Fig. 5.16 shows the circulating eddy currents same magnet poles when the magnets are

segmented.

(a) SPM magnet pole (b) V-shaped IPM magnet pole

Fig. 5.16 Circulating eddy currents in a segmented magnet poles

The total magnet losses in all 14-poles obtained at 50 and 500 Hz for the SPM and IPM

machine models are shown in fig. 5.17 and fig. 5.18 respectively.

Fig. 5.17 Magnet losses in an SPM machine with variation of segment number

0

20

40

60

80

100

120

No Segments 3 Segments 6 Segments 9 Segments 12 Segments

SPM @50Hz SPM @ 500Hz

Tota

l mag

net l

oss (

W)

100%

44.4% 41.8% 39.7% 39.6%


139

Fig. 5.18 Magnet losses in an IPM machine with variation of segment number

Fig. 5.17 and 5.18 show that, while there is a gradual decrease in PM losses for the SPM

model, the decrease in PM losses for the IPM model was not constant, exhibiting a peak

with 9 segments. These results comply with the results obtained by Yamazaki shown in

fig. 5.14. It can be seen that segmentation has greater effect on losses in the SPM

machine as compared to the IPM machine, where more segments are required to achieve

the same percentage of losses.

With a difference of a mere 49.3% (at 500Hz) with 12 magnet segments compared to a

single pole-piece, the cost of increased complexity and duration of manufacturing the

IPM rotor is not worthwhile for this design.

5.4.2 Magnet Losses in the Final Design

In the final sintered non-segmented magnets were used. The total magnet losses for the

final model us shown in fig. 5.19:

0

0.2

0.4

0.6

0.8

1

No Segments 3 Segments 6 Segments 9 Segments 12 Segments

IPM @50Hz IPM @ 500Hz

Tota

l mag

net l

oss (

W)

100%

70.9%59.2%

78.8%

50.7%


140

Fig. 5.19 Magnet losses versus frequency in the final design with sintered NdFeB magnets

The above figure shows that the total magnet loss for the final design is very low

(making of for less than 1.5% of total output power of the machine). The breakdown of

losses show that hysteresis loss increases linearly, and is the dominant loss in the

magnet for frequencies <200Hz, whereas the eddy current loss increases exponentially

with frequency due to its frequency squared dependence, and begins to dominate at

higher frequencies. Compared to total core loss in the rotor, magnet losses in the IPM is

very small. Majority of the losses occurs in the rotor iron.

5.5 STATOR WINDING LOSS

Stator winding loss – also known as I2R, copper or joule loss – occurs when the

armature windings are excited by an external source. Of the total loss in PM machines,

the largest portion is usually due to I2R loss [220]. I2R is not frequency dependent and is

constant throughout the speed range, so the CPSR is not affected by this loss. This is

due to the copper conductors being thin enough to have 100% skin-depth throughout the

operating region. I2R loss is described in the following formula:

= 2 (5.20)

where, = Number of turns per coil

= Conductor resistivity (1.68X10-8 for copper)

= Cross-sectional area of wire

00.20.40.60.8

11.21.41.6

0 50 100 200 300 400 500 600

Eddy currentloss

HysteresislossPo

wer

loss

(W)

00 300 40Frequency (Hz)

Peddy = 34%Phys = 66%





141

A common standard for wire sizes is the American wire gauge (AWG) standard. Some

wire sizes for typical machines in the range of 1kW are shown in table 5.3 below [221,

222]. Values indicated are for a 25°C ambient temperature and for frequencies below

60Hz.

Table 5.3Suitable conductor sizes properties

AWG Diameter(mm)

Area(mm2)

Copper Resistance(

17 1.150 1.04 16.6118 1.024 0.823 20.9519 0.912 0.653 26.4220 0.812 0.518 33.3121 0.723 0.410 42.0022 0.644 0.326 52.9623 0.573 0.258 66.7924 0.511 0.205 84.2225 0.455 0.162 106.226 0.405 0.129 133.9

In machines with high torque densities, I2R losses are greater due to the larger amount

of current and number of turns (ampere-turns AT) required. One way of reducing this

loss is by the use of thicker conductors, which would in turn require a larger slot area.

The slot area in the stator is maximised by optimising tooth and yoke area, such that the

flux densities in these areas are kept just under the saturating limit of the core material,

as shown in chapter 4.

With a fixed slot area, the only way to increase conductor size and lower I2R losses is

by increasing the slot-fill factor given by the following equation:= (5.21)


142

In the final CW-IPM design, a slot-fill factor of 41.5% was assumed.

The estimated average winding length is shown in fig. 5.20. The average length of each

end potion of the winding is 10mm. By adding these to the 80mm stator stack length,

the estimated axial length of each strand is 100mm. The span of the slot measured from

the inner diameter of the stator yoke is approximately 21mm. Therefore the total

estimated length per turn is 242mm.

Fig. 5.20 Inner-diameter view of stator teeth showing estimated winding length

Each coil consists of 115turns, and each phase consists of 6 coils. Therefore the total

number of turns per phase is 690. The total length of wire required for 690 turns is

167m. With a 41.5% slot-fill factor, a suitable wire size would AWG22, (which is a

e for

167m of

operating frequency.

100mm Estimated winding axial length

80mm Stator stack length

21mm Estimated slot span

(measured from yoke)


143

5.6 MECHANICAL LOSSES

Mechanical losses consist of mainly bearing and windage losses [197, 220, 223].

Bearing loss is dependent on factors such as the bearing type, bearing diameter, rotor

speed, load and lubricant used. Windage loss occurs when friction is created with the

rotating parts of the machine and the surrounding air.

Bearing losses can be calculated with the following formula [220]:= 0.5 (5.22)

where,

= Mechanical speed of the rotor

= Bearing loss constant

= Force acting on the bearing

= Bearing inner diameter

The following figure shows the final drawing of the entire rotor. Its mass is calculated

based on the known volume and density of the various materials used. Bearing friction

loss occurs in two bearings.

Fig. 5.21 Drawing of rotor indicating key components to calculate bearing friction loss

Bearing 1Inner Diameter = 20mmBearing constant = 0.0015

Bearing 2Inner Diameter = 17mmBearing constant = 0.0015

Rotor coreDensity = 7650kg/m3

Total Mass = 2.182kg

MagnetsDensity = 7500kg/m3

Total Mass = 0.448kg End platesDensity = 8000kg/m3

Total Mass = 0.30kg

ShaftDensity = 8000kg/m3

Total Mass = 0.650kg

Downward force acting on bearing


144

From the estimated weight of the rotor, the downward force acting on the bearings is

calculated by: = (5.23)

where,

= mass of the rotor

= gravity (9.81m/s2)

The power loss due to friction in each bearing is shown in table 5.4 and the total loss is

plotted in fig. 5.22. The calculated force F and bearing loss constant are 35.12Nm

and 0.0015 respectively.

Table 5.4Bearing friction loss on each bearing at various speeds

Frequency 50 100 200 300 400 500 600 700

Speed (rpm) 429 857 1714 2571 3429 4286 5143 6000

P(bearing1) (W) 0.020 0.040 0.080 0.121 0.161 0.201 0.241 0.281

P(bearing2) (W) 0.024 0.047 0.095 0.142 0.189 0.236 0.284 0.331

P(total) (W) 0.044 0.087 0.175 0.262 0.350 0.437 0.525 0.612

Fig. 5.22 Power loss due to bearing friction at various speeds

The results show that bearing loss increases linearly with speed. This loss is small

compared to other electrical losses.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1000 2000 3000 4000 5000 6000

Speed VsBearing loss

Tota

lBea

ring

loss

(W)

Speed (rpm)


145

Windage loss ( ) is another form of mechanical loss; however, unlike frictional

loss, it has a non-linear increase in magnitude as speed increases. The rotor can be

modelled as a rotating cylinder in an enclosure, and power loss is due to the resisting

drag torque on the cylinder. This can be expressed as follows [220]:= 0.03125 (5.24)

where,

= Torque coefficient which has to be separately determined

= Roughness coefficient (Between 1-1.4)

= Density of air (1.184 kg/m3)

= Rotor diameter

= Rotor length

To determine the torque coefficient ( ), the Couette Reynolds number first has to be

determined. The Reynolds number ( ) is given by:

= 2 ( ) (5.25)

where,

= Airgap length( ) = Dynamic viscosity of air (18.6 μPa)

and for between 64 and 500, the torque coefficient is given by:

= 2 2 / .( ) . (5.26)

And for between 500 and 50000, the torque coefficient is given by:

= 1.03 2 / .( ) . (5.27)

These calculated values are shown in table 5.5, and power loss due to windage versus

speed is plotted in fig. 5.23.


146

Table 5.5Reynolds number, torque coefficient and winding loss at various speeds

Frequency 50 100 200 300 400 500 600 700Speed (rpm) 429 857 1714 2571 3429 4286 5143 6000

137 274 548 822 1096 1371 1645 19190.036 0.024 0.015 0.013 0.011 0.010 0.009 0.008

Pwindage (W) 0.001 0.007 0.037 0.101 0.208 0.363 0.572 0.842

Fig. 5.23 Power loss due to windage at various speeds

Fig. 5.23 shows that although windage loss is almost negligible at low speeds, it

increases exponentially and becomes more significant at speeds in the wider field

weakening region.

00.10.20.30.40.50.60.70.80.9

0 1000 2000 3000 4000 5000 6000

Speed VsWindage loss

Win

dage

loss

(W)

Speed (rpm)


147

5.7 MODELLED FIELD-WEAKENING PERFORMANCE WITH INCLUSION

OF LOSSES

The lossless field-weakening performance of the final CW-IPM machine model shown

in chapter 4 (fig. 4.27), achieved a 10:1 CPSR with peak power of 880W. Fig. 5.24.

shows the abovementioned field-weakening performance, with the inclusion of total

losses highlighted in this chapter.

Fig. 5.24 Modelled power versus speed performance with inclusion of losses

With the inclusion of losses, an efficiency of between 78.9% and 73.8% was achieved.

The low efficiency was due to the structure of the machine (long axial length) for the

purpose of fitting into the same casing as comparison machines. It should be noted that

a machine of the same volume but with a wider outer diameter and a shorter axial length

would lead to a high efficiency. This will be shown later in chapter 8.

The 10:1 CPSR was maintained but peak power dropped to 700W.

At base speed 50Hz (429rpm), almost all the losses are I2R loss (96.6%) and the

remaining 3.4% is due to core loss. Magnet and mechanical losses at lower frequencies

are negligible. At 500Hz (4285rpm) the percentage of core loss is increased to 16.1%.

Magnet and total mechanical losses were still very small (0.4% altogether). A large

percentage of losses (83%) is still due to I2R losses.

0

200

400

600

800

1000

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Pow

er (W

)

Speed (rpm)

Input Power Output PowerCPSR = 10:1

73.8% 78.8% 78.9% 78.4% 76.7% 74.8%


148

5.8 CONCLUSION

This chapter showed how the increase in harmonics resulting from CW affected

frequency-related losses. The two main categories of losses were studied and quantified

based on known material properties as well as theory and experimental results obtained

from available literature. The losses that were covered were:

Electromagnetic losses

Core loss (varies exponentially with frequency)

Magnet loss (varies exponentially with frequency)

I2R Loss (constant)

Mechanical losses

Bearing friction loss (varies linearly with speed)

Windage loss (varies exponentially with speed)

With appropriate selection of steel thickness/grade, frequency related losses in this

model remained low, resulting in total core loss of < 4.5% of total power at the

maximum operating speed.

In a comparison of magnet losses, it was shown that the magnet losses in the CW-IPM

machine was almost negligible magnet losses as compared to the magnet losses in the

CW-SPM machine. It was confirmed that for the CW machine, the segmentation of

magnets was more effective in reducing SPM as compared to IPM magnet losses.

The overall losses were combined and applied to the lossless FE model, (shown in

chapter 4). It was shown that a 10:1 CPSR was achieved and efficiencies between

78.9% and 73.8% were obtained throughout the speed range.

In chapter 7, the loss prediction methods in this chapter will be experimentally verified

by the efficiency measured from the constructed CW-IPM prototype.

149

CHAPTER 6VECTOR CONTROL OF THE IPM MACHINE WITH CONCENTRATED WINDINGS

6.1 INTRODUCTION

Prior to the change of variables proposed by Park [224] in 1929, complex differential

equations were used to describe a machine’s performance with sinusoidally varying

quantities – currents, voltages, and flux linkages.

Park introduced a method (Park’s transformation) to refer the time-varying quantities

from the stator to the rotor reference frame, thus allowing these time-varying quantities

to be expressed in terms of DC quantities – the direct-axis (d-axis) and quadrature-axis

(q-axis) as shown in fig 6.1. The d-axis, otherwise known as the pole or flux axis, and

has to be aligned with the magnetic axis of phase A. The q-axis, otherwise known as the

inter-pole axis has a 90 electrical degrees displacement from the d-axis.

Chapter 6: Vector Control of the IPM Machine with Concentrated Windings

150

Fig. 6.1 2-pole IPM machine showing d-q axis reference frames

In the d- and q-axis reference frame, the voltage and currents are represented by space

vectors as shown in fig. 6.2. Control of the amplitude and phase of these vectors

determines the performance of the machine, thus the term ‘vector control’. As vector

control affects the spatial orientation of the rotor and stator fields, it is also commonly

referred to as field-oriented control (FOC) [174, 225, 226]. FOC is a well-known and

simple algorithm which can be easily implemented on a fixed point digital signal

processor.

Phase A axis ( r ) (Stator ref. frame) ((Direct axis

(Rotor ref. fame)

Phase C axis (Stator ref. frame)

Phase B axis (Stator ref. frame)

Quadrature axis (Rotor ref. frame)

r


151

Fig. 6.2 Space vector dq-axis phasor diagram

With vector control, current is decoupled into torque- (iq) and flux- (id) producing

components. This results in transient response characteristics similar to those of a

separately excited DC machine [227].

The aim of this work is to run the machine over a wide CPSR, as well as to achieve

error-free speed responses under steady state condition. To do so, the vector control

method is employed. A well-known field-weakening method proposed by Morimoto in

[43] was successfully implemented in available DW-IPM machines, however these

methods resulted in a slight ‘over-suppression’ of the permanent magnet flux in the

CW-IPM machine.

This chapter will state the vector control method, controller architecture and inversion

technique used to produce the final three-phase inputs to the prototype CW-IPM

machine. The id trajectories during field-weakening operation calculated by equations proposed by Morimoto will be compared with trajectories obtained by repetitive testings.

d-axis (flux axis)

q-axis (EMF axis)

Iq Ef IqR jIqXs

jIdXs IdR

V I Id

(fm


152

6.2 CONTROL METHODOLOGY

6.2.1 Basic Equations describing the PM Machine

The 3-phase voltage equation used for describing a PM machine involves stator currents,

flux linkages and reactance values expressed as follows [227-229]:

= + = + + ( ) (6.1)

= + = + + ( ) (6.2)

= + = + + ( ) (6.3)

where, , , = Phase voltages, , = Phase currents, , = Total flux linkage in each phase windings

= Synchronous inductance( , , ) = Flux linkage in each phase windings due to rotor field

= Stator winding resistance per phase

Park’s transformation which transforms the three phase quantities to two axis quantities

can be expressed by matrix A:

= 2323 4323 4312 12 12

(6.4)

Applying Park’s transformation matrix to the three phase voltage, flux and current gives

us the following voltage equations in the dq reference frame.

= + (6.5)


153

= + + + (6.6)

= + = 0 for the case where 3-phases are balanced (6.7)

and expressed in matrix form is given by:

= + + 0 (6.8)

where, , = d and q axes phase inductances

, = d and q axes phase currents

= Speed in electrical radians per second

= Peak permanent magnet flux linkage

For an IPM machine, the well-known torque equation derived in [39, 230], in the dq

reference frame is given by:

= 32 + (6.9)

It should be noted that saturation casues variation in and temperature causes

variation in . However within the operating range of the CW-IPM machine in this

thesis, the rotor and stator steel are operated below the saturation region; hence these

issues would not be studied here.

The parameters of the modelled CW-IPM machine required for torque calculation are:

= ( )/ = 0.41 Wb= 84.45 mH= 81.16 mH


154

Here torque will be split into two terms – the alignment term and the saliency term as

shown in fig. 6.3, where the variation of torque versus Id will be shown. Iq will not be

shown but will follow the relationship = .

Fig. 6.3 Calculated torque comprising of alignment and reluctance torque from (6.9)

From fig. 6.3 it can be seen that in the CW-IPM model, the contribution of the

alignment torque makes up most of the total torque produced by the machine. Since the

reluctance term is almost negligible, the torque equation may be simplified to that of an

SPM machine:

= 32 (6.10)

6.2.2 Variation of Current Phase Angle

The current phase angle ( ) is the angle between the current phasor and the back EMF

axis as shown previously in Fig. 6.2. Variation of this angle affects the values of the d-

and q-axis current, which in turn affects the flux and torque produced by the machine.

For control of the prototype CW-IPM machine, the current angle will be varied to

achieve maximum torque per unit current (MTPC) control, where the current angle is


155

in-phase or almost in-phase with the back EMF phasor (fig. 6.4a), and field-weakening

(FW) control, where the current angle is made to lead the back EMF phasor (fig. 6.4b).

(a) Current phase angle under maximum torque per unit current operation

(b) Current phase angle under field-weakening operation

Fig. 6.4 Current phasor under MTPC and Field-weakening operation

In 3-phase quantities, the current angle is simply a time delay added into the current

equations as follows: = (2 + ) (6.11)

= 2 23 + (6.12)

time

V Ef I

Ef IqR jIqXs V I

pm

Ef V I

time

Iq Ef IqR jIqXs

jIdXs IdR V I

Id pm


156

= 2 + 23 + (6.13)

With variation of this current angle, the machine can be controlled to operate with

optimal efficiency, maximised torque and a wider CPSR above base speed under the

constraints of current and voltage limits.

For the CW-IPM machine model, the variations of EMF, current and voltage with time

at base speed, (MTPC operation), as well as maximum speed, (FW operation), is shown

in fig. 6.5a and 6.5b respectively.

(a) Respective waveforms at base speed under MTPC operation

(b) Respective waveforms at maximum speed under field-weakening operation

Fig. 6.5 Back EMF, induced current and induced voltage waveforms under MTPC and maximum field-weakening operation

= 79

I Ef V

I Ef V


157

Fig 6.5a shows the current in phase with the emf waveform. While in fig. 6.5b current

leads. This leading current waveform suppresses the back emf induced in the coils.

This suppression also causes distortion in the voltage waveform as shown in the figure.

6.2.3 Current and Voltage Limits

The maximum torque produced by the machine depends on the imposed armature

current limits, the maximum speed is limited by the maximum output voltage of the

inverter. In order for the CW-IPM machine to achieve a wide constant power speed

range and optimal torque density, the operating limits of the drive should be determined

by the circle diagram [31, 230]. The circle diagram consists of current-limiting circles

and voltage-limiting ellipses as shown in fig 6.6. Fig. 6.6a and 6.6b show limiting

values and trajectories for the IPM machine and SPM machines respectively.

(a) Circle diagram for an IPM machine

(b) Circle diagram for a SPM machine

Fig. 6.6 Circle diagram for IPM and SPM machine showing current and voltage limits of the system

Current limiting circlesMTPC trajectory ybase

12Voltage limiting ellipses

MTField-weakening trajectory

, 0Is(max)

Current limiting circles CMTPC trajectory base1

2Voltage limiting ellipses

Field-weakening trajectory

, 0 Is(max)


158

Since the saliency ratio of the CW-IPM machine is so low, the id and iq current

trajectories would be similar to that of the SPM machine in fig 6.5b.

In the circle diagrams, the outer most limit of the current-limiting circle is expressed

simply as:

( ) = + (6.14)

and the voltage-limiting ellipse at various speeds is given by:

( ) = + (6.15)

where under ideal and steady state operations and derived earlier in (6.5) and

(6.6) is given by: = (6.16)= + (6.17)

Thus, in terms of current values, the voltage limiting ellipse is given by:

( ) = + + (6.18)

The centre of the voltage limiting ellipses lies at the point:

, 0 (6.19)

From standstill to base speed, the machine operates within the current limit along the

MTPC trajectory. When base speed is reached, the operating point follows anti-

clockwise along the current limiting circles. This results in an increase in - at the

expense of . An increase in - creates a larger opposing flux to the rotor pole axis,

which temporarily ‘weakens the field’ of the magnets. Field-weakening of the magnets

helps to limit the amount of flux that is linked to the stator windings, thus limiting the


159

back EMF generated. This helps to maintain voltage under operating limits as speed

continues to increase past base speed.

The control limits on the field-weakening range of the machine depend on the

characteristic current. Practical IPM machines can be classified in two categories:

Type 1: ( ) <Type 2: ( ) >In terms of field-weakening control, type 1 machines have a finite field-weakening

range, whereas type 2 have an infinite range. This is due to the centre of the voltage

limiting ellipse lying outside the current limiting circle for type 1 machines and inside

for type 2 as shown in 6.7a and 6.7b respectively. With the centre of the voltage limiting

ellipse lying outside of the current limiting circle, there exists a maximum speed beyond

which both the current limits and voltage limits can no longer be satisfied. Whereas if

the centre of the voltage limiting ellipse lies inside the current limits, both these limits

would always be satisfied with the application of the voltage-limited maximum output

trajectory, thus theoretically resulting in an infinite speed range.

(a) Type 1 machine with centre of voltage limiting ellipse lying outside of the current limiting circle

Field-weakening trajectory max

base MTPC trajectory

, 0


160

(b) Type 2 machine with centre of voltage limiting ellipse lying inside of the current limiting circle

Fig 6.7 Classification of machine type by characteristic current

The CW IPM machine falls under the category of a type 1 machine as the rated current

is lower than the characteristic current. Thus the voltage-limited maximum output

trajectory cannot be applied to this machine. For this work the machine would operate

only with the two trajectories- the MTPC trajectory and the field-weakening trajectory.

The id and iq current trajectory plotted for the final CW-IPM FE model is shown in fig.

6.8.

Fig. 6.8 id and iq field-weakening current trajectory for the CW-IPM model

max Voltage-limited trajectory

Field-weakening trajectory MTPC trajectory base


161

Fig. 6.8 shows the very large requirement of negative d-axis current for initial field-

weakening up to 200Hz. The requirement of additional negative d-axis current

decreases exponentially as speed increases. In the FE model, the limit on this field-

weakening trajectory as speed increases is where the armature field can no longer

maintain constant power, (higher than power produced at base speed), at a specific

voltage limit.

6.2.4 Maximum Torque Per unit Current and Field-Weakening Trajectories

Here two trajectories will be compared: firstly, the trajectory calculated by widely used

Morimoto’s equations in [43]; secondly, values obtained when the machine is regarded

as an SPM machine during MTPC operation and subsequently by repeated testing in the

field-weakening region.

Under MTPC operation, calculated by [43] is shown in (6.20), and the remaining

to produce torque at full load is shown in (6.21).

= 4 16 + 2 (6.20)

( ) = (6.21)

When regarded as an SPM machine, the maximum torque point will intersect with the

current limit circle along the q-axis. Thus will be equal to zero and at full load, will

be equal to the supply current. = 0 (6.22)

( ) = (6.23)


162

For both these trajectories, the speed at the maximum torque point is determined by

( ) as well as the voltage limit of the inverter ( ). = ( )+ ( ) (6.24)

In the field-weakening region, cross-coupling effects will be omitted, and will be

regarded as an independent quantity of . While is largely determined by the speed

controller to produce sufficient torque to achieve the desired speed, will be used to

supress flux produced by the magnets and maintain constant power.

From [43], for field-weakening is calculated by (6.25).

= + 1 (6.25)

Through repetitive testings, the values of required to weaken the magnet field are

lower as compared to (6.25). The trajectories comparing these two methods applied to

the CW-IPM FE model are shown in fig. 6.9.


163

Fig. 6.9 Comparison of d-axis current trajectories by Morimoto’s equations and through repetitive testings

From the fig. 6.9 it is shown that the CW-IPM model requires a lower amount of d-axis

current to maintain constant voltage/power, as speed is increased. Chapter 7 will show

that a similar characteristic is seen in the constructed prototype machine.


164

6.3 CONTROLLER ARCHITECTURE

The input to the controller is a speed reference signal ref), and the outputs of the

controller are the desired three-phase voltages and currents with desired magnitudes and

phase displacements. To obtain the desired magnitudes and phase displacements, a 3-

phase fully-controlled inverter is used. The controller block diagram is shown below:

Fig. 6.10 Vector control system block diagram

This system requires a position sensor, which is mounted to the shaft of the machine.

The position feedback is used to convert 3-phase quantities to dq-axis quantities; it is

also differentiated with respect to time to provide a speed feedback. Simple high-gain PI

controllers are implemented to achieve the desired speed and dq-axis current dynamics,

as well as to remove any tracking or following error. The compensated errors must be

first converted back to three-phase references to be fed into the inverter.

Speed controller Current ref. Generatoriq current controllerid current controller

dq -1

dq

Inverter

refCTref

ag

iq(ref)

id(ref)iq

id

Vref(a,b,c)

ia,b,c

mCW IPM


165

6.3.1 Three-phase Inversion Technique

For traction applications, the only available energy source is usually the battery

producing DC voltages. This DC supply is then inverted to desired 3-phase supply

currents and voltages with desired magnitudes and phase displacements. Fig. 6.11 gives

an example of the inverter architecture for the drive system used in this work. (A more

detailed schematic, as well as its connections to the controller board can be seen in

appendix F).

Fig. 6.11 Rectifier – Inverter for producing three-phase outputs to the machine

In the experimental set up, a 3-phase AC source is rectified using an uncontrolled full-

bridge rectifier to produce a desired DC bus input voltage to the inverter. This DC bus

voltage will then be converted to desired AC signals by modulating techniques. Two

common modulating techniques include the sinusoidal pulse width modulation (SPWM)

scheme, and the space vector modulation (SVM) scheme. Here, SVM is preferred due

Controlleria,b,c

m

S1

S2

S3

S4

S5

S6VDC

+

-Switching signals S1 – S6

CW IPMUncontrolled full-bridge rectifierThree-phase input from source


166

to its lower hardware requirements and a higher modulation ratio of 0.907 compared to

0.785 in the SPWM scheme.

In the SVM scheme, the desired three phase quantities Van, Vbn and Vcn are sampled in

time at a specified sampling frequency (fs) and are represented in terms of space vectors

as shown in fig. 6.12.

There are eight possible switching states (V0 to V7), six of which are termed switching

vectors (V1 to V6) and the other two (V0 and V7) are termed zero vectors.

Fig 6.12 Switching vectors of the space vector modulation method

The SVM method uses a look-up table (table 6.1) to determine the switching states.

This look-up table contains a set of switching rules which enable the voltage vector Vx to

rotate continuously with smooth transition from one sector to the next.

V1 (1,0,0)

V2 (1,1,0)V3 (0,1,0)

V4 (0,1,1)

V5 (0,0,1) V6 (1,0,1)

Sector 1Sector 2

Sector 3

Sector 4Sector 5

Sector 6v1

v2 SeVx

V0 (0,0,0) V7 (1,1,1)

Vref(max)


167

Table 6.1Space vector modulation look-up table

State S1 S2 S3 S4 S5 S6 Van Vbn Vcn Space Vector

0 OFF ON OFF ON OFF ON 0 0 0 V0 = 0,0,0

1 ON OFF OFF ON OFF ON V1 = 1,0,0

2 ON OFF ON OFF OFF ON V2 = 1,1,0

3 OFF ON ON OFF OFF ON V3 = 0,1,0

4 OFF ON ON OFF ON OFF V4 = 0,1,1

5 OFF ON OFF ON ON OFF V5 = 0,0,1

6 ON OFF OFF ON ON OFF V6 = 1,0,1

7 ON OFF ON OFF ON OFF 0 0 0 V7 = 1,1,1

Taking sector 1 as an example, the relationship between Vx and the two vectors V1 and

V2 is given by: (3 ) = 3 (6.26)

= 3 (6.27)

In terms of v1 and v2,

= 23 (3 ) (6.28)

= 23 (6.29)

Vectors v1 and v2, which are subsidiary vectors of vectors V1 and V2 respectively,

determines the position of the rotating vector Vx. The desired magnitude of the voltage

Vx is controlled by activating vectors V1 and V2 for durations t1 and t2 respectively over

half a period Ts/2. The expression of Vx in terms of activations times is given as:


168

= + = / + / + ( ) / (6.30)

where, = / (6.31)

= / (6.32)

= / (1 ) (6.33)

The switching pattern for sector 1 is shown in fig. 6.13:

Fig. 6.13 Switching pattern for sector 1

This process is repeated for the other five sectors. In this way, the magnitude, frequency

and phase of the voltage can be varied according to the desired output voltage signal as

specified by the controller.

V0 V1 V2 V7 V7 V2 V1 V0

t0/2 t1 t2 t0/2

Ts/2 Ts = 1/fs

Phase APhase BPhase C


169

6.4 CONCLUSION

This chapter has illustrated the control methodology of the CW-IPM machine. It

showed the voltage and current limits that the drive is subjected to by use of the circle

diagrams. Due to the centre of the voltage limiting ellipses lying outside of the current

limiting circle, the voltage limited trajectory is not applicable for the CW-IPM model.

The model was subjected to two different current trajectories: one being the widely-

used trajectory calculated by Morimoto’s equations and the other through repetitive

testings. It was shown that the actual current required to weakening the magnet field

and maintain constant voltage is lower than that calculated by available equations.

Lastly this chapter also showed the general controller architecture and the SVM

technique used to generate the three phase input quantities.

170

CHAPTER 7CONSTRUCTION AND PERFORMANCE ANALYSIS OF THE CONCENTRATED WINDING IPM MACHINE PROTOTYPE

7.1 INTRODUCTION

The work done in previous chapters provided a study of the CW-IPM machine for use

in field-weakening applications. From this study, a final 14-pole, 18-slot model was

designed and optimised using FE analysis. The final FE model was built to verify

studies and predicted performance characteristics.

This chapter will first give an overview of the construction process of the CW-IPM

prototype (which was the final FE design shown towards the end of chapter 4).

Problems encountered and lessons learnt during the construction process will be stated

in order to facilitate quicker and less problematic manufacturing for future designs.

Subsequently, the open circuit parameters of the prototype machine will be measured,

and compared with results achieved by the FE model. Control techniques shown in

chapter 6 will be used to run the machine in constant torque and field-weakening

regions. A steady state analysis will be performed and the torque performance of the

CW-IPM machine in both operating regions will be shown. Transient characteristics of

the machine in the MTPC region will also be briefly covered. Lastly, the performance of

the CW-IPM machine will be compared with two other similar-sized DW-IPM

machines.

Chapter 7: Construction and Performance Analysis of the Concentrated Winding IPM Machine Prototype

171

7.2 CONSTRUCTION PROCESS

The construction process of the CW-IPM machine can be broken down into three steps:

the rotor and stator assembly; stator winding; and finally the total machine assembly.

The total manufacturing time of the final CW-IPM prototype was twelve months. This

section illustrates the abovementioned three steps of constructing the motor, as well as

the manufacturing timeline of the construction process.

7.2.1 Manufacturing Duration

The flow-chart in fig. 7.1 shows the entire construction process from the date when

designs were submitted to the manufacturers to the date the experimental setup was

completed. The reason for describing this process is to give future PhD

students/researchers a clearer picture of what has to be done if a prototype is to be

constructed. Key delays in the manufacturing process will be stated and suggestions to

speed up the process will be made.

Key delays for the manufacturing process and suggestions to avoid them include:

Delay: Redesigning of unmanufacturable portions of the initial model.

- Suggestion: Regular meetings with manufacturer during the design stage

Delay: Duration taken for the desired steel grade to be shipped.

- Suggestion: Choose and order desired core material before the design

Delay: Manufacturing errors in cutting of laminations.

- Suggestion: Not applicable.

Delay: Windings not being wound according to a specified layout.

- Suggestion: Commercial winders are not always adaptable to new winding

types. Coils can be fitted by the winders but phase connections can be done in

our labs.


172

Fig. 7.1 Duration breakdown and steps of construction process

Meeting with CSIRO:Discussion of design

Correction of unmanufacturable portions

Choice of alternate steel grade

Ordering of magnets from China (RareMag)

Correction of slot opening size, magnet slot size

Modelling performance with available steel grade

Odering of steel (Sankey) and lazer cutting (LazerXperts)

Rotor assembly (CSIRO):Stacking laminations; insertion of magnets; dynamic balancing

Stator assembly (CSIRO):Stacking laminations; heat shrinking into casing

Removal of original stator and rotor from ABB casing

Winding of stator (Atom Electrical)

Assembly of machine and experimental setup (UNSW)

Start of manufacturing process

Month 1 to Month 3

Month 4 to Month 8

Month 9 to Month 11

Month 12


173

7.2.2 Rotor Assembly

As mentioned in chapter 4, the material used for both the rotor and stator laminations

was 0.35mm thick (35RM300). A laser-cut rotor lamination of the prototype is shown in

fig. 7.2. The 79mm rotor stack was assembled by pressing one lamination at a time

down a shaft; tapered ends of the shaft simplify this process.

On completion of the stack, magnets are then inserted. Inserting the magnets is a fairly

easy task, as all the magnet pieces get drawn into the rotor stack. The completed rotor

stack with magnets inserted is shown in fig. 7.3.

Fig. 7.2 Laser-cut rotor lamination

It should also be noted that axially segmented magnets, (for the purpose of eddy current

loss reduction), can also be easily inserted piece by piece into the rotor. The segments

making up a magnet pole would not be repelled out of the slot as initially expected.

Magnet slots4mm d holes for bolts to holding end-plates and laminations together

6mm key hole


174

Fig. 7.3 Complete rotor stack with magnets inserted

Lastly the end plates are bolted on, bearings mounted and the rotor is dynamically

balanced. Dynamic balancing is done by drilling holes into the endplates to achieve

rotational weight balance.

Fig. 7.4 Completed dynamically-balanced rotor

Shaft

Magnets

Endplate

Bolts

Bearing mounted

Holes drilled in endplate to achieve dynamic balance


175

7.2.3 Stator Core Assembly and Stator Windings

The same rotor steel grade (35RM300) is used in the stator. The completed 80mm stator

stack is shown in fig. 7.5. Six equally spaced, w-shaped groves were cut into the outer

periphery of the stator for welding and alignment purposes. It should be noted that these

groves should be situated in the inter-slot section, so as not to hinder flux paths in the

stator yoke section.

Fig. 7.5 Completed stator stack

The stator was wound with the horizontal-fill method, as discussed previously in

chapter 4. The windings done by Atom Electrical are of acceptable quality, with 42%

slot-fill factor achieved. The initially achieved 14.5mm end winding length with the

plastic stator could not be achieved in the winding of the prototype stator; the actual end

winding length measured 18.5mm (shown in fig. 7.6).

Groves situated in the inter-slot sections


176

Fig. 7.6 Measurement of end winding length in UNSW CW-IPM stator

7.2.4 Overall Machine Assembly

Due to the high remanent flux density of the magnets, inserting the rotor into the stator

required the use of an aluminium sleeve. This method is tedious and causes damage to

both the stator and rotor laminations. An alternative method of assembling the machine

is to first remove the magnets from the rotor; insert the rotor; then re-insert the magnets.

For this machine, the time taken to assemble it using the latter method was slightly less

compared to the use of an aluminium sleeve. Fig. 7.7 shows the completed CW-IPM

machine assembly in comparison to the DW S-IPM machine.


177

Fig. 7.7 Comparison of UNSW CW-IPM machine assembly (right) and DW S-IPM machine (left)


178

7.3 OPEN CIRCUIT PARAMETERS

In chapter 4, it was shown that with an 18-slot, 14-pole FE model, a high winding factor

and sinusoidal back EMF could be achieved. Due to the elimination of slot and pole

periodicity achieved by fractional-slot distribution, very low cogging torque can also be

achieved.

7.3.1 Back EMF

For back EMF measurements, the CW-IPM machine terminals were left open-circuited

and the machine was ran at various speeds by a prime mover (1kW Kollmorgen

machine). The measured line to line- and line to neutral- induced voltages were 154Vrms

and 89Vrms respectively. These values were very similar to the modelled values, albeit

slightly lower (157Vrms and 92Vrms). The near-sinusoidal shape of the measured

waveforms also followed very closely to the modelled ones as shown in fig. 7.8.

Fig. 7.8 Measured line to line and line to neutral back EMF waveforms compared against modelled values

-250-200-150-100

-500

50100150200250

0.005 0.01 0.015 0.02 0.025

ModelledVab @50Hz

MeasuredVab @50Hz

ModelledVan @50Hz

MeasuredVan @50Hz

Indu

ced

Vol

tage

(V)

Time (s)

VL-N(Measured) = 89Vrms

VL-N(Modelled) = 92Vrms

VL-L(Modelled) = 157Vrms

VL-L(Measured) = 154Vrms


179

Fig. 7.9 shows the linear increase in back EMF and speed.

Fig. 7.9 Measured line to line back EMF versus speed compared against modelled values

7.3.2 Cogging Torque

Cogging torque in the CW-IPM machine is expected to have a high frequency carrier

signal with a low frequency modulating signal. The experimental setup shown in fig.

7.10 consists of a 0.6m beam, balanced on both sides, weights, and a position sensor. By

gradually adding weights at each position, the amount of torque required to rotate the

machine at various angles can be calculated. The cogging torque measurements made in

the clockwise direction make up the positive half of each fluctuation, and vice versa.

Fig. 7.10 Cogging torque measurement setup

0100200300400500600700800

0 500 1000 1500 2000

ModelledVab Vs.Speed

MeasuredVab Vs.Speed

Speed (rpm)

Indu

ced

Vol

tage

(Vrm

s)

0.6m Beam (Balanced on both sides)

Position Sensor(Connected to DS1104 Board)

Weights (1g to 500g)


180

Fig 7.11a (measurements from 3°-10°) and 7.11b (measurements from 12°-18.5°)

compares the cogging torque points measured over 1 cogging torque period (20

mechanical degrees), with the results obtained from the FE model.

(a) Measurement range – 3 to 10 degrees

(b) Measurement range – 12 to 18.5 degrees

Fig. 7.11 Measured cogging torque points compared against results obtained from FE model


181

From fig. 7.11, it is shown that the measured points agrees with values from the FE

model, with slight deviations in the rotor angle. The peak magnitude of the measured

points were higher (approximately 2x higher) than the peaks of the waveform obtained

by the FE model. Considering that the cogging torque values are extremely small (<

±0.018Nm(p-p)), effects on bearing striction and/or rotor eccentricity/balance (which

were not considered in the FE model), would contribute significantly to the magnitude

of measured torque points. Due to the high frequency fluctuations created by fractional

slot distribution, measured cogging torque points had to be taken in 0.2 degree intervals.

This contributed to the errors in the rotor positions where torque was measured.

From the measured cogging torque points, a curve achieved from FE analysis was fitted.

This curve termed as ‘expected cogging torque waveform’ (shown in fig. 7.12), would

be used in place of the actual measured cogging torque waveform in the subsequent

sections as a comparison to the DW-IPM models.

Fig. 7.12 Curve fitted cogging torque waveform

It can be seen that the modulation of the cogging torque waveform is proportional to the

width of the slot (i.e. 2 cycles per slot), similar to that of regular integral slot machines.

Envelope for peak cogging torque values


182

The only difference is the high frequency ripples, which are caused by the aperiodic

flux linkage in other slots and phases (a characteristic of fractional slot windings),

which has been reported in several recent papers as well.

7.3.3 Inductance and Saliency Ratio

The inductance waveform was measured using the AC standstill test method with

single-phase excitation, (stated in chapter 3). Static measurements were performed in

two degree increments throughout one electrical revolution, with the position being read

from a mounted encoder. The variation of voltage in self and mutual-phases was then

used to calculate the self- and mutual-inductance values at each position. The self and

mutual-inductance values (measured at 3A) from the finite element model, as shown in

chapter 4 are re-illustrated here as a comparison to the measured values. Fig. 7.13 shows

the inductance values from the FE model and fig. 7.14 shows the values measured from

the prototype.

Fig. 7.13 Modelled self- and mutual-inductance waveform from the FE model with 3Armscurrent excitation


183

Fig. 7.14 Measured self and mutual-inductance waveform from the prototype with 3Arms current excitation

From fig. 7.13 and 7.14, it is seen that the average and peak to peak magnitude of the

self-inductance obtained in both the FE model and prototype machine are relatively

similar. While the mean value mutual-inductances are also relatively similar, the

variations in the prototype machine are much higher compared to the FE model. This

larger variation in mutual–inductance leads to a higher saliency ratio of 1.12, compared

to an almost negligible saliency ratio of 1.04 in the FE model. Ld and Lq for the FE

model are 81.16mH and 84.45mH, whereas Ld and Lq for the actual machine are

82.52mH and 92.48mH respectively. The most probable reason for this difference is,

that 2D FE model was not able to account for some of the flux leakage occurring toward

the end of the windings. We can also conclude here that end-turn winding of the q-axis

inductance is more than the d-axis inductance. This is in fact advantageous for the

machine because it can be a tool to optimize the saliency ratio.


184

With different excitations, saturation of the core also causes the inductance to change

slightly. Fig. 7.15 compares the measured and modelled dq-axis inductance values

between 1Arms to 3Arms.

Fig. 7.15 Variation of dq-axis inductances with current

Fig. 7.15 shows that overall inductance values fall as the current increases. For the

measured inductance, the increase in current has a greater effect on the q-axis

inductance compared to the d-axis inductance, thus leading to a slight decrease in the

saliency ratio with higher currents.

0

20

40

60

80

100

1 1.5 2 2.5 3

Indu

ctan

ce (m

H)

Current (A)

d-axis inductance(modelled)

q-axis inductance(modelled)

d-axis inductance(measured)

q-axis inductance(measured)


185

7.4 STEADY STATE ANALYSIS

The steady state analysis of the machine includes the torque/power versus speed curves

as well as the id and iq trajectory required to achieve the curves; the voltage trajectory

from zero to maximum speed; and efficiency over the CPSR. Steady state waveforms of

the input currents and voltages as well as id and iq values will also be shown.

7.4.1 Torque and Power Characteristics

In Chapter 4, it is shown that a 10:1 CPSR can be achieved for the FE model with an

input line to line voltage of 240Vrms and a base speed of 429rpm. Due to loading and

equipment constraints – torque transducer, gearbox and loading generator are rated for a

shaft torque of approximately 10Nm – as well as the desire to achieve a higher

efficiency, the voltage limit on the constructed CW-IPM prototype was increased:

Input line to line voltage: 340Vrms

Rated current: 2.2Arms

Base speed with rated voltage: 573rpm

The main components of the experimental setup are shown in fig. 7.16. (the full setup is

shown in appendix F)

Fig. 7.16 Experimental setup to measure back EMF and torque/power versus speed performance

CW-IPM motor(connected to inverter)

Torque transducer

Loading generatorWith external resistor bank (not shown)

Gearbox(4:1)

Encoder


186

The three-phase supply to the CW-IPM machine is from an inverter (diagram shown in

chapter 6, fig 6.7). The three-phase space vector modulation (SVM) generated supply

voltage and currents were derived based on controller outputs. The controller

implemented in C code, ran together with dSPACE control desk which provided the

graphical user interface on a Windows-based PC. Input and output signals of the

controller were handled by a DS1104 ADC/DAC control board.

From zero to base speed, the machine ran under MTPC conditions. For the CW-IPM

machine, it is assumed that under MTPC operation, id is zero and iq is equal to the

supply current is. This is due to the fact that the saliency ratio is close to unity. After

base speed, when the rated voltage is reached, id is then made to oppose the flux

produced by the rotor magnets. This is done to maintain constant voltage by suppressing

the induced back EMF as speed increases. The required id and iq current trajectory to

maintain constant voltage with increasing speed is shown in fig. 7.17:

Fig. 7.17 Measured dq-axis current points under field weakening operation

Maximum FW point

MTPC point

FW Region

Unstable region


187

The voltage measured throughout the speed range from operation in the MTPC region

to the maximum achievable speed in the field weakening region is shown in fig. 7.18:

Fig. 7.18 Measured line to line voltage versus speed

From the above figure, it can be seen that a constant voltage can be maintained after

base speed when the FW trajectory in fig. 7.17 is followed. Here the field-weakening

range/CPSR is taken from base speed (the point where the rated voltage is reached) to

the point where power drops below the value achieved at base speed. The torque and

power versus speed characteristics based on the current and voltage points from the

abovementioned figures are shown in fig. 7.19:

Fig. 7.19 Measured torque versus speed characteristics of the CW-IPM machine prototype

050

100150200250300350400

0 1000 2000 3000 4000 5000

Line to line voltage versus speed

Inpu

t vol

tage

(VL-

L)

2000 3000Speed (rpm)

MTPC Region

FW Region


188

With a voltage limit of 340VL-L, greater than 7:1 CPSR (7.2:1 max) can be achieved.

Output power at base speed is 762W; over 800W of power is achieved just slightly

above base speed all the way to the 7:1 FW point. The maximum power of 905W was

achieved at 1290rpm. Over 80.8% efficiency was achieved from base speed till the 6.2:1

FW point. The efficiency of the machine versus speed is plotted in fig. 7.20:

Fig. 7.20 Measured efficiency versus speed

Within the 6.2:1 range (indicated in fig. 7.20) the efficiency varied from 80.8% to 83%.

Measured efficiency before and after this range dropped rapidly to 61.4% at the lowest

measured speed of 191rpm, and to 65.1% at the highest achieved speed of 4889rpm,

(which was the maximum speed where constant voltage can be maintained, 8.5:1 point).

Therefore, the optimal operating range in terms of efficiency would be between 573rpm

(base speed) and 3562rpm, resulting in a 6.2:1 CPSR. Comparison between the

experimental results and the predicted efficiency (by calculations and FE analysis)

showed result were very close (with 0.2 – 3% error). This justifies the loss predictions

shown in chapter 5.

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Measured Efficiency vs. SpeedPredicted Efficiency vs. Speed

> 80% Efficiency over a 6.2:1 CPSR

Effic

ienc

y (%

)

Speed (rpm)


189

7.4.2 Steady State Voltage and Current Characteristics

This section illustrates the steady state speed, currents and voltages in the dq-axis

reference frame, as well as the three phase current and voltage input to the machine.

These readings were taken at base and maximum FW speed. The speed waveforms

under full load conditions are shown in fig. 7.21. The signals in red (#1:2) are the

desired controller references, and the signals in green (#1:1) are the following/actual

output signals.

(a) Base Speed (b) Maximum Speed

Fig. 7.21 Steady-state speed waveforms

The steady state speed output follows the reference with zero error at base and

maximum field-weakening speed. The following speed signal at maximum speed is

constant, but at base speed the signal has low magnitude perturbations. At these two

speeds current and voltage signals in their corresponding reference frames are shown in

fig 7.22.

Time (s)

(RPM

)

Time (s)

(RPM

)


190

(a) Base Speed (b) Maximum Speed

Fig. 7.22 Steady state id current waveforms

Reference id values are user inputs to the program and are therefore constant. The

following id signals contain high frequency fluctuations of substantial magnitude. These

fluctuations, which are also present in the in the iq actual signal, lead to vibrations and

additional acoustic noise in the very low speed and near the maximum speed of the

machine.

(a) Base Speed (b) Maximum SpeedFig. 7.23 Steady state iq current waveforms

The slight fluctuations in the reference iq current waveform were more pronounced at

higher speeds. The actual iq current waveforms follow the reference waveforms as long

as the required voltage does not exceed limited values. After the maximum speed of

Time (s)

(A)

Time (s)

(A)

Time (s)

(A)

Time (s)

(A)


191

4889rpm, iq becomes uncontrollable and develops following errors, thus the CW-IPM

drive is limited to this speed.

The corresponding current waveforms and voltage pulses in the abc reference frame for

steady state operation is shown in fig. 7.24 below: (Switching frequency used here is

10kHz).

(a) Current and voltage waveforms at base speed of 60rad/s

(b) Signals at maximum FW speed of 426rad/s

Fig. 7.24 Steady state current and voltage inputs to the machine in abc reference frame

Time (s)

Curr

ent (

A)

Volta

ge (V

)Vo

ltage

(V)

Time (s)

Curr

ent (

A)


192

7.5 TRANSIENT RESPONSE UNDER MTPC OPERATION

In this work, the steady state performances would be sufficient to verify the CPSR,

power density and efficiency of the prototype CW-IPM machine. Thus, only the basic

dynamic responses in the MTPC region (standstill to base speed) will be shown. Control

strategies to improve the dynamic performance of the CW-IPM machine are currently

being studied.

7.5.1 Transient Voltage and Current Characteristics

Fig. 7.26 shows the speed step response of the CW-IPM drive:

(a) No load (b) Full load

Fig. 7.25 Speed step from standstill to base speed


Fig. 7.26 id current waveforms with speed step from standstill to base speed

Time (s) Time (s)

(RPM

)

(RPM

)

Time (s) Time (s)

(RPM

)

(RPM

)


193

The id current waveforms show large negative spikes during the speed transition,

getting more pronounced with a higher load, despite the reference being zero.


Fig. 7.27 iq current waveforms with speed step from standstill to base speed

The actual iq current waveforms follow the reference well, however, high frequency

fluctuations are present in the reference signal.

The corresponding current waveform and voltage pulses for the speed step at no load

and full load in the abc reference frame is shown in fig. 7.28 below:

(a) No load

Vol

tage

(V) C

urrent (A)

Time (s)

Time (s) Time (s)

(RPM

)

(RPM

)


194

(b) Full loadFig. 7.28 Current and voltage inputs to the machine in abc reference frame with step change in

speed

7.5.2 Torque Transients

The output torque of the machine is determined from a torque transducer mounted

between the drive and the loading machine. Fig. 7.29 shows the torque transient at full

load when the machine accelerates from standstill to base speed. Fig. 7.30 shows the

corresponding torque ripple when steady state is reached.

Fig. 7.29 Torque transient when CW-IPM machine accelerates from standstill to base speed at full load

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2

Current (A

)Vol

tage

(V)

Time (s)

Torq

ue (N

m)

Time (s)

Section of torque ripple shown in fig. 7.31


195

Fig. 7.30 Measured torque ripple at steady state

The output torque ripple was 2.1Nm(peak to peak), which amounts to 16.5% of the total

torque produced at base speed. The magnitude of torque ripple is higher than predicted.

This could be due three main reasons:

i) The noisy gearbox (in terms of vibrations) at the load – resulting in relative

fluctuations at the torque transducer.

ii) The second reason being the controller design. More detailed parameter

identification and control strategies which are currently being implemented

fall beyond the scope of this thesis. This strategies, implemented on the

CW-IPM machine will be shown in future publications.

iii) Lastly, increased torque ripple could be caused by the load machine and

misalignment in coupling.

0

2

4

6

8

10

12

14

1.8 1.85 1.9 1.95 2

Torque ripple magnitude = 2.1Nm(peak to peak) To

rque

(Nm

)

Time (s)


196

7.6 PERFORMANCE COMPARED TO DISTRIBUTED WINDING IPM

MACHINES

The main aim of this thesis was to design and build a CW-IPM machine to achieve

higher torque/power density, wider CPSR, lower cogging torque, and of equivalent

efficiency as two other available DW-IPM machines of equal size [13]. As a

comparison, two other previously constructed, equally sized DW-IPM machines will be

used. All three machines were designed to fit in the same 550W ABB casing. The two

DW machines have 4-poles, while the CW machine has 14-poles. This is due to the

required 14-pole, 18-slot layout to achieve low cogging torque and an appropriate back

EMF waveform, as mentioned in earlier chapters. Since pole numbers are not equal, a

comparison of output torque would not be appropriate. Most other quantities such as

CPSR, output power, cogging torque and efficiency can still be compared.

The first DW IPM machine (shown in fig. 7.31a) has regular single-pieced, flat shaped

poles. It uses sintered magnets with Br = 1.05T. This machine will be named IPM-I.

The second DW-IPM machine, (shown in fig. 7.31b), has segmented magnets. It uses

bonded magnets with Br = 0.78T. This machine will be named S-IPM.

It should be pointed out that the IPM-I was designed based on prior knowledge and

experience. No optimisation strategy was implemented. The S-IPM machine was

designed and optimised in a similar fashion to the CW-IPM machinewith FE analysis

as shown in this work. Additional details on its optimisation can be seen in [174].

The final CW-IPM machine model is shown in fig. 7.31c. It uses a similar magnet grade

as IPM-I with Br = 1.04T.


197

(a) Single piece per pole IPM with DW (DW IPM-I)

(b) Segmented IPM machine with DW (DW S-IPM)

(c) Constructed CW-IPM prototype (CW-IPM)

Fig. 7.31 Comparison of three UNSW IPM machines

DW S-IPM

DW IPM-I

CW-IPM


198

7.6.1 Power and Torque versus Frequency Comparison

As the CW-IPM machine has 14 poles and the two other DW-IPM machines have only

4 poles each, frequency is used as the basis of comparison instead of mechanical speed.

Fig. 7.32 shows the power versus frequency comparison between the three IPM

machines. It should be noted that while the comparison against the DW IPM-I would

not be fair due to the fact that the machine was not optimised for field weakening

performance nor for high power density. It is included to show that despite a much

lower saliency ratio, magnet volume and magnet energy density, the design is still the

most crucial in achieving good field weakening performance.

Fig. 7.32 CPSR comparison between the three UNSW IPM machines

From the results obtained, it is shown that the CW-IPM machine not only achieved a

much wider CPSR – > 6.2:1, compared to 4:1 in the S-IPM machine and almost no field

weakening capability in IPM-I – it also achieved a 56% power increase over the

constant power region as compared to the two other DW-IPM machines.

In terms of peak torque under maximum torque per unit current (MTPC) operation, the

CW-IPM machine achieved a peak shaft torque of 12.7Nm, compared to 2.25 Nm and

0100200300400500600700800900

1000

0 50 100 150 200 250 300 350 400 450

Pow

er (W

)

Frequency (Hz)

> 6.2:1 CPSR

4:1 CPSR


199

2.3Nm in the S-IPM and IPM-I respectively. For a fair comparison of torque between

the 14-pole CW-IPM machine and the 4-pole DW-IPM machines, torque is normalised.

The torque magnitude of 1p.u. is assumed in the MTPC region.

Fig. 7.33 Normalised output torque comparison between the three UNSW IPM machines

The torque versus frequency waveforms clearly show that IPM-I has almost no field

weakening capability, with torque rapidly falling at the beginning of the field

weakening region. On the other hand, it is shown that both the S-IPM and CW-IPM

have excellent field weakening capability.

7.6.2 Cogging Torque Comparison

Comparing the two DW machines the S-IPM machine uses magnets with a lower

remanent flux density of 0.78T as compared to IPM-I, which uses magnets with remanet

flux density of 1.05T. Thus the cogging torque is naturally higher in the latter. However,

despite the use of high remanent flux density magnets in the CW-IPM machine (1.04T),

the cogging torque is substantially lower compared to the DW machines due to the

elimination of periodicity of slots and poles by using fraction-slot distribution.

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400 450

Torq

ue (P

.U)

Frequency (Hz)


200

Cogging torque comparisons between the three IPM machines is shown in fig. 7.34:

Fig. 7.34 Cogging torque comparison between the three UNSW IPM machines

From the comparison of the cogging torque values, it is shown that the CW-IPM

machine produced lower cogging torque magnitude, compared to the two other DW-

IPM machines. As expected IPM-I produced the largest peak cogging torque magnitude.

As higher generated torque will make the effects of cogging torque less significant,

another important comparison is, the amount cogging torque produced as a percentage

of the total torque generated in the MTPA region. This comparison is shown in fig.7.35

as follows:

Fig. 7.35 Cogging torque as a percentage of output torque at base speed – comparison between the three UNSW IPM machines

0.038Nm(p-p)0.126Nm(p-p)

0.502Nm(p-p)

0.3%(p-p)8.1% (p-p)

24.2%(p-p)


201

7.6.3 Efficiency Comparison

Data on efficiency versus speed for IPM-I is not readily available, although it is known

to be somewhere in the 60-65% range at rated speed, so efficiency was compared only

between the CW-IPM and SEG-IPM as shown in fig. 7.36:

Fig. 7.36 Efficiency comparison between the CW-IPM and S-IPM machine up to 200Hz

The SEG-IPM machine produced 84 to 85% efficiency from base speed up to the

measured 200Hz. In comparison the CW-IPM machine produced 80.8 to 83% efficiency

from base speed up to 420Hz. Copper loss, which is 2.4 times lower in the S-IPM

machine as compared to the CW-IPM machine, was the main reason for the lower

efficiency of the CW-IPM machine. Besides copper loss, other losses were lower in the

CW-IPM machine, despite the increase in MMF harmonics created by CW.

0102030405060708090

100

0 50 100 150 200

CW-IPM SEG-IPM Poly. (CW-IPM)Effic

ienc

y (%

)

Frequency (Hz)

Base speed


202

7.6.4 Magnet Volume Comparison

Due to increasing magnet prices, the amount of magnet used for present-day machine

designs is subjected to constraints. Thus it is of interest to briefly compare the amount

of magnet used in the three machines. Fig. 7.37 compares the volume of magnet per kW

in each machine.

Fig. 7.37 Comparison of Magnet volume per kW the three UNSW IPM machines

This factor can be further improved if the efficiency of the machine is optimised. It

should be noted that, despite similar amount of magnet material used in the CW-IPM

and SEG_IPM, a magnet grade with higher energy density was chosen to compensate

for the loss in reluctance torque. This was done at the expense of higher rotor core

saturation and higher magnet losses.


203

7.7 CONCLUSION

This chapter firstly illustrated the manufacturing process of the prototype CW-IPM

machine. Problems were identified and manufacturing delays were stated as a guide to

improve the manufacturing process of future machines.

The measured performance characteristics of the constructed CW-IPM prototype were

shown and used to verify the performance of the FE model. It was shown that the

measured results from the prototype agreed with the FE results with a high degree of

accuracy. The machine parameters and performance characteristics from the FE model

were compared to two other equally sized DW-IPM machines. These results showed

that the CW-IPM outperformed the two other DW-IPM models in terms of power

density (up to 56% higher), CPSR (greater than 55%) and cogging torque performance

(almost negligible compared to the other two DW machines when compared as a

percentage of total torque). Despite the high copper loss, an 80.8% efficiency was

achieved throughout a 6.2:1 CPSR.

This chapter has verified studies and the design of the CW-IPM machine in this work.

The successful design of the first CW-IPM prototype in our labs has provided a strong

basis and confidence in the FE models.

204

CHAPTER 8EFFICIENCY OPTIMISATION AND SCALABILITY OF THE CONCENTRATED WINDING IPM MACHINE

8.1 INTRODUCTION

In previous chapters, the design and experimental verification of the CW-IPM machine

have been shown. The close correlation of the experimental and FE results gave

confidence for further designs and optimisation. On the basis of the original 800W FE

model, the scalability and efficiency optimization of the CW-IPM machine will be

studied in this chapter.

Chapter 8: Efficiency Optimisation and Scalability of the Concentrated Winding IPM Machine

205

8.2 EFFICIENCY OPTIMISATION

In chapter 7, it was shown that the CW-IPM machine operated at over 80% efficiency

throughout the CPSR. It was also shown, in chapter 5, that the majority of losses (over

90% of losses) in the CW-IPM machine were due to copper loss. With the main focus

on minimising copper loss, winding modifications and two geometric changes to the

original design are proposed to increase the efficiency of the machine.

8.2.1 Winding Modification

Two hand-winding methods were introduced in chapter 4 – the vertical-fill method and

the horizontal-fill method. The latter method was used in the prototype to reduce the

time and cost required to wind the machine. Here, for the purpose of optimising

efficiency, the vertical slot-fill method is used despite the increase in time and cost of

winding the machine. A 45% slot-fill factor was personally achieved in the prototype

stator. Thus a 45% slot-fill factor will be assumed in this optimisation study. The

difference in winding span and end winding length between these two methods is shown

in fig. 8.1 below:


206

(a) Horizontal slot-fill factor

(b) Vertical slot-fill factorFig. 8.1 Axial length comparison between two different slot-fill methods

With the vertical winding method, the overall length per turn is reduced significantly

(from 276mm per turn to 219mm per turn).

8.2.2 Proposed Designs for Efficiency Optimisation

The basic structure of the original design and the volume of the machine are preserved

in this modifications. For convenience, the first modified design will be called CW-IPM

R. For the CW IPM-R, the outer diameter and stack length of the machine is preserved

(fig 8.2a). The rotor diameter of the machine is made smaller to increase the space in the

stator for larger slots, permitting the use of larger conductors, thus lowering copper loss.

The second design will be called CW-IPM S. For the CW-IPM S, the outer diameter is

increased but the stack length is reduced by half in order to keep the volume constant

117mm axial winding length (measured)

21mm average winding span

95mm axial winding length (expected)

14.5mm average winding span

Horizontal slot-fill

Vertical slot-fill


207

(fig. 8.2b). The performance constraints are to preserve the same 6:1 CPSR and power

(a) (b)

Fig. 8.2 Designs used for efficiency optimisation indicating outer dimensions

Table 8.1 below, gives key parameters of the two optimised designs. Fig. 8.3a and 8.3b

give performance characteristics for CW-IPM R and CW-IPM S respectively.

(a)80mm

184m

m

130m

m Volume =

1063mm2

(b)40mm

Volume =

1063mm2


208

Table 8.1Key Specifications of the Two Optimised CW-IPM Machine Designs

CW-IPM R CW-IPM S

Stator outer diameter 130mm 183.85mm

Rotor outer diameter 36mm 45.7

Airgap length 1mm 1.41mm

Slot opening width 1.2mm 1.2mm

Stack length 80mm 40mm

Rated current 2.2Arms/ph 2.2Arms/ph

Current density 4.25x106A/m2 5.37x106A/m2

Conductor size AWG 20 AWG 21

No. of turns per coil 163turns 127turns

Stator resistance

Mag. remanent flux 1.13T 1.13T

Slot-fill factor 45% 45%

(a) CW-IPM R


209

(b) CW-IPM S

Fig. 8.3 Efficiency and power versus speed performance of the two efficiency optimised model

The results firstly show a significant increase in efficiency, thus increasing in output

power for both optimised designs compared to the original design (where 80%

efficiency was achieved). Comparing the two optimised designs, the CW-IPM S

achieves a higher efficiency of 93%, while the CW-IPM R achieves an efficiency of

91% throughout the CPSR. Despite a higher stator resistance, the CW-IPM S achieved a

higher efficiency, due to its capability of producing higher maximum output power. The

maximum output power in the CW-IPM R was limited by the stator and rotor outer

radius.


210

8.3 SCALABILITY OF THE CONCENTRATED WOUND IPM MACHINE

This scalability study will be divided into two steps: Firstly, the machine parameters of

the original 800W prototype will be varied to study their effects on performance. From

this, a set of general design rules will be derived to ensure that the material properties

are fully utilised and that the machine is operating with the desired field-weakening

capability. Secondly, two up-scaled versions of the 800W prototype will be created. By

implementing the design rules, it will be shown that the predicted power density and

efficiency of the scaled version can be increased significantly. FE analysis will be used

as the basis of this optimisation.

8.3.1 Airgap Length Variation

CW results in increased harmonic and sub-harmonic content in the MMF waveform,

causing localised saturation, thus, affecting the field-weakening performance of the

machine, (as explained in chapter 4). The application of double-layer stator windings as

well as a larger airgap helps lower the effects of these harmonics. From the original

800W, CW-IPM design, the effects of varying airgap length on machine performance

are investigated.

Fig. 8.4 shows the effects on the CPSR and input power, (at base speed), when airgap

length is varied from 0.6 to 1.6mm.


211

Fig. 8.4. Airgap length versus CPSR and input power

Fig. 8.5 shows the effects on total core loss, (measured at 500Hz), and overall efficiency

with the same variations in airgap length.

Fig. 8.5 Airgap length versus efficiency and core loss

From fig. 8.4, it can be seen that there is an obvious trade-off between input power and

the maximum achievable CPSR of the machine. While power falls almost linearly as

airgap length is increased, the CPSR increases exponentially with airgap length.

Fig. 8.5 shows that having a wider airgap length is beneficial in decreasing overall core

losses. However as airgap length increases, input power naturally decreases as well.

This makes the copper loss more prominent, thus reducing efficiency.


212

8.3.2 Magnet Strength and Armature Current Variation

In order to achieve optimal field weakening range, both the saliency ratio and

characteristic current values need to be considered. It was explained in chapter 3 that

saliency ratio optimisation was not effective in the CW-IPM machine. Thus,

optimisation of CPSR would be based solely on optimising the characteristic current

condition.

An increase in magnet strength results in an increase in characteristic current, (reiterated

in (8.1)). Therefore when magnets of higher remanent flux density are chosen, the

machine has to be designed with a higher rated current.

= = (8.1)

The geometry of the machine was not altered; hence Ld is kept the same (81.16mH) as

before. Fig. 8.6 shows the variation of magnet remanent flux density and the current

required to satisfy the condition (8.1) and achieve a > 6:1 CPSR. Fig. 8.6 also shows the

lossless power produced at each point. The same core material specifications used for

the prototype CW-IPM machine 35RM300 (with a saturation magnetization of 1.68T at

5000A/m) is used here.

Fig. 8.6 Magnet remanent flux density versus input current and input power


213

It can be seen from fig. 8.6 that the current required to achieve equilibrium conditions

and the input power of the machine increase linearly with magnet remanent flux density,

until the core begins to saturate, (after Is=3.3A/Br=1.32T). Fig. 8.7 shows the flux

density plot for the machine under unsaturated, (with 2.3Arms of excitation current), and

saturated conditions, (with 4.1Arms of excitation current).In order to fully exploit the

material properties of the core, the machine should be made to operate at this

equilibrium point (Is=3.3A/Br=1.32T – equilibrium is different or each design).

(a) Unsaturated conditions (b) Saturated conditionsFig. 8.7. Flux density plot of CW-IPM machine under saturated and unsaturated conditions

As magnet remanent flux and stator current are increased, the core loss increases almost

proportionately, while the copper loss increases with the current squared. It is of interest

to know the extent to which losses and efficiency are affected as the power density of

the machine increases with magnet remanent flux density. Fig. 8.8 shows the total

losses and overall efficiency of the machine as magnet remanet flux and current are

increased.


214

Fig. 8.8 Magnet remanent flux density versus total machine losses and efficiency

This section shows the effects of varying parameters – in particular, airgap length,

magnet remnant flux density and rated current – of the CW-IPM prototype machine

without significant alterations to the machine geometry. The study done here provides

designers with a set of rules to design the CW-IPM for field weakening operation.

These steps are listed as follows:

i. Decide on the desired split-ratio (the ratio of stator inner diameter to outer diameter).

A larger split-ratio would result in higher torque densities but decreased space for

stator slots, hence higher copper loss.

ii. Decide on the airgap length of the machine. A smaller airgap would result in higher

torque density and higher efficiency but a narrower CPSR.

iii. Decide on the required slot area, keeping the core saturation limits in mind. From the

FE model, ensure that the maximum flux density in the tooth and yoke are similar.

iv. Vary slot-opening width to fit desired conductor sizes. Essentially, slot-opening

widths should be kept as small as possible to achieve maximum flux linkage across

the airgap.

v. Determine the optimal equilibrium point of the machine (the point after which current

increases non-linearly with magnet remanent flux density to maintain desired CPSR).

Operating after this point yields a non-linear decrease in efficiency.


215

8.3.3 Effects of Scaling the Machine Size

The purpose of this section is to study the effects of scaling up the CW-IPM machine

size, as well as to observe the effects of applying the abovementioned design rules to

larger machines. The aim is to achieve over 6:1 CPSR, over 80% efficiency throughout

the CPSR, as well as to fully utilise the steel properties, while operating at the optimal

equilibrium point.

Two designs are created based on the proven 800W model. In the first model, only the

machine outer diameter is increased by a factor of two; the stack length remains the

same as the 800W machine (80mm). In the second model, the outer diameter is three

times that of the 800W machine and the stack length is also increased by two (160mm)

as shown in fig. 8.9.

Fig. 8.9. Comparison between the three machine sizes

The output torque ( ) on machine sizing can be determined by (8.2), where the

output torque/power of the machine increases linearly with the effective stack length

( ) of the machine, and with the square of the machine outer diameter ( ).

Size of the 800W prototype

1st model

2nd model


216

= (8.2)

Assuming the torque constant is unaltered and the entire machine is scaled up

proportionately, then the output power for the first and second scaled models should be:

1st model: = ( ) ( )( ) = 13.33 0.260.13 60 = .

2nd model: = ( ) ( )( ) ( )( ) = 13.33 0.390.13 0.160.08 60 = .

where, ( ) = Torque of the 800W prototype machine at base speed

= Base speed of the machine( ) = Diameter of the 800W prototype machine

( ) = Diameter of the 1st scaled model (refer to fig. 8.9)

( ) = Diameter of the 2st scaled model (refer to fig. 8.9)

( ) = Stack length of the 800W prototype

( ) = Stack length of the 2st scaled model (refer to fig. 8.9)

It is obvious that proportional scaling of the machine will not necessarily yield the same

CPSR. Also, the maximum flux density in the stator core will decrease as the machine

outer diameter is increased, leading to under-utilisation of the core material. Thus, the

design rules mentioned in the previous section are applied to the scaled models with the

aim of achieving at least a 6.2:1 CPSR, greater than 80% efficiency and increased

torque/power density by operating at the optimal equilibrium point of the core material.


217

By following the design steps, 5kW and 30kW can be obtained from the two models,

(3.2kW and 14.4kW), respectively. Table 8.2 shows the design specifications of the

original 800W CW-IPM prototype, in comparison to the optimised 5kW and 30kW

machines.

Table 8.2Key Specifications of the Three CW-IPM Machine Designs

0.8kWCW-IPM

5kWCW-IPM

30kWCW-IPM

Stator outer diameter 0.13m 0.26m 0.39m

Rotor outer diameter 0.080m 0.160m 0.240m

Airgap length 1.2mm 3.0mm 3.6mm

Slot opening width 1.2mm 3.0mm 4.8mm

Stack length 0.080m 0.080m 0.160m

Rated voltage 320Vrms(l-l) 320Vrms(l-l) 320Vrms(l-l)

Rated current 2.2Arms/ph 13.9Arms/ph 75.2Arms/ph

Conductor size AWG 22 AWG 13 AWG 5

No. of turns per coil 115turns 53turns 16turns

Mag. remanent flux 1.04T 1.34T 1.36T

Core saturation mag. 1.67T@5000A/m 1.67T@5000A/m 1.67T@5000A/m

Slot fill factor 41% 41% 41%

The input and output power versus speed characteristics of the 5kW and 30kW

machines are compared in fig. 8.10 and 8.11 respectively:

mailto:1.67T@5000A/m







218



The results show that the scaled designs were both able to achieve over 8:1 CPSR. The

5kW model achieved over 92.2% efficiency and 30kW model achieved over 95.8%

efficiency throughout the CPSR.

In the optimised designs, the core material operates with higher flux densities, thus core

loss would naturally increase. Despite the increase in core loss, efficiency is increased

due to the significant reduction of copper loss (which contributes to the largest portion

of losses in the machine) with a larger machine outer diameter. Fig. 8.12 shows the loss

breakdown of the three machine models:


219

Fig. 8.12. Losses in the three machine sizes as a percentage of total loss

From scaling the size of the machine, the following key points can be noted:

While increasing the machine outer diameter results in an exponential increase

in power, increasing the stack length results only in a linear increase in power, in

compliance to (8.2). Additionally, increasing the machine outer diameter

increases the efficiency of the machine.

Changing the conductor size to achieve the desired rated voltage has no effect on

copper loss and output power, as long as ampere-turns and the slot-fill factor are

unchanged.


220

8.4 CONCLUSION

This chapter has shown that the original 800W FE model can be effectively optimised

to provide high efficiency (over 93% throughout the CPSR), by the reduction of copper

loss. The comparison of two optimized models with the same volume, shows that

having a larger outer diameter and shorter stack length was effective in increasing both

efficiency and torque density of the machine.

The scalability of the machine was also studied in this chapter. Through variation of

machine parameters, a general set of design rules was illustrated to fully utilise material

properties as well as to achieve desired CPSR and power density. By applying these

design rules on two scaled models, power density in the 3.2kW and 14.4kW model can

be optimised to produce 5kW and 30kW respectively. Efficiency of over 92.2% and

95.8% were achieved by each model respectively.

221

CHAPTER 9CONCLUSION AND SUGGESTIONS FOR FUTURE WORK

9.1 CONCLUSION

The work done in this thesis has proven that the fractional-slot CW-IPM machine is a

suitable candidate for field-weakening applications. The constructed double-layer CW-

IPM machine with 14 v-shaped poles and 18-slots showed that a very wide 7.2:1 CPSR

could be achieved. Efficiency of over 80% was achieved over a 6.2:1 CPSR. The CW-

IPM also achieved a higher torque density, and much lower cogging torque compared to

two other equally sized DW-IPM machines.

In chapter 3, open-circuit characteristics of the CW-IPM machine were studied. Several

slot and pole combinations were investigated, and it was shown that the 18-slot, 14-pole

model achieved the highest induced back EMF magnitude, as compared to other 14-pole,

fractional-slot combinations. The calculated winding factor of 0.902 was confirmed by

comparison with an equivalent integral-slot DW machine model. This combination of

slots and poles also resulted in a near-perfectly sinusoidal EMF waveform, and very low

cogging torque magnitude. The comparison of two CW-IPM machines with different

magnet geometries, (rectangular and v-shaped), with the CW-SPM machine, showed

that the machine with rectangular, single-piece/pole magnets was inferior to the CW-

SPM machine in terms of torque density, and field-weakening capability. The CW-IPM

machine with v-shaped magnets, on the other hand, had improved field weakening

capability, but with slightly lower peak torque density as compared to the CW-SPM

machine, due to saturation effects.

Chapter 9: Conclusion and Suggestions for Future Work

222

In chapter 4, the CPSR of the 14-pole, 18-slot, v-shaped IPM design was optimised by

v-angle and airgap variations. It was shown that by satisfying the characteristic current

equilibrium conditions by variation of specific machine, the optimal CPSR could be

achieved. From optimisation done in this chapter, the final design was specified.

Parameters and performance characteristics of the final model were determined by FE

analysis.

In chapter 5, a detailed study of losses in the CW-IPM machine was done. It showed

how the increase in harmonics resulting from CW affected frequency related losses.

Electromagnetic losses, (consisting of core, magnet and I2R losses), and mechanical

losses, (consisting of bearing and windage losses), were studied and quantified. This

study highlighted the importance of choosing thin silicon steel laminations for the rotor

and stator core material. It also indicated that magnet losses in the CW-IPM were very

low, and that loss reduction by magnet segmentation was not as effective as magnet

segmentation in the equivalent CW-SPM machine. It was shown that the calculated

mechanical losses were low even at maximum operating speed of the machine. Chapter

5 also showed that copper loss made up for the majority of loss (> 90%) in the machine;

if the efficiency of the machine were to be improved, the main focus should be on

minimising copper loss.

Chapter 6 presented the control methodology of the CW-IPM machine. It showed the

voltage and current limits that the drive is subjected to by use of the circle diagrams. It

was shown that the widely-used trajectories calculated by Morimoto’s equations led to

the ‘over-weakening’ of the magnet fields. Thus a manually obtained current

trajectory was used in the control of the prototype CW-IPM machine.


223

Chapter 7 firstly illustrated the manufacturing process of the prototype CW-IPM

machine. Problems identified and manufacturing delays were stated as a guide to

improve the manufacturing process of future machines. The measured performance

characteristics of the constructed CW-IPM prototype was shown and used to verify the

performance of the FE model. It was shown that the measured results from the

prototype agreed with the FE results with a high degree of accuracy. The machine

parameters and performance characteristics from the FE model were compared to two

other equally sized DW-IPM machines. This comparison showed that the CW-IPM

outperformed the two other DW-IPM models in terms of power density, (up to 56%

higher), CPSR, (7.2:1 as opposed to a maximum of 4:1 achieved by the DW S-IPM), as

well as cogging torque performance, (0.3%(p-p) as compared 8.1%(p-p) and 24.2%(p-p)

achieved by the other two machines – as a percentage of total torque). Efficiency was

slightly lower in the CW-IPM machine, (80.8 to 83% over a 6.2: CPSR), as compared

with the DW S-IPM machine, (84 to 85% over a 4:1 CPSR).

With the successful design of the CW-IPM, achieving desired performance

characteristics, as well as the confidence gained from the close correlation of FE and

measured results, an efficiency optimization and scalability study was performed.

Chapter 8 showed that the original 800W FE model could be effectively optimised to

provide high efficiency, (up to 93%). Two optimised models with the same volume

were compared. It was shown that the model with larger outer diameter and shorter

stack length achieved a higher efficiency, as compared to one with the same dimensions

as the prototype machine, but with a smaller rotor. Chapter 8 also studied the scalability

of the machine. Through variation of machine parameters, a general set of design rules

were illustrated. This rules aid in designing the CW-IPM machine to achieve the desired


224

CPSR, and power density, as well as to fully utilise material properties. Two scaled up

models of the CW-IPM machine were created. Based on theoretical calculations, the

presumed output power of the two scaled models were 3.2kW and 14.4kW. However,

by application of the abovementioned design rules, the optimised models each produced

5kW and 30kW respectively.

The successful design, construction of the first CW prototype in our labs has provided a

strong basis, and confidence, in the field-weakening capability of the CW-IPM machine.

It has also created opportunities for future work to be done in this area, such as

performance optimisation, control implementation, as well as to determine the

suitability of the CW-IPM for various industrial applications.


225

9.2 SUGGESTION FOR FUTURE WORK

Due to the lack of a suitable loading generator, (capable of producing required torque

over the entire speed range), sensing equipment (torque transducer), as well as a time

constrain, the torque and field-weakening capability of the machine could not tested to

its maximum limits. With further testing using appropriate equipment, increased power

and a wider CPSR can be achieved. This work will soon be carried by a future student,

when the equipment becomes available. From simulations, it is noted that the saturation

in the steel is low (typically lower than 1.6T). This indicates that the tooth width and

yoke length can be made smaller to provide space for increased winding size- hence

lower copper loss.

In this thesis, it was shown that commonly used vector control techniques could not be

applied to the CW-IPM machine, thus a manually obtained id and iq trajectory was used

to operate the machine at optimal power throughout the speed range. With this method,

dynamic performance of this machine could not be fully tested. Therefore, a proper

control technique has to be implemented to achieve desired dynamic performance.

Subsequently, sensorless control can also be implemented. Above base speed (60rads),

common DTC control methods should work. However, due to the low saliency ratio of

1.12, achieved by the CW-IPM machine, the closed-loop observer and high-frequency

signal injection methods might not work. If a higher saliency ratio is required, the

machine can be redesigned based on rotor magnet geometry variation techniques

illustrated in appendix B, as well as the investigation of end-winding effects,

(contributing the q-axis inductance), can be done to further increase the saliency ratio.


226

Additional focus can be placed upon trying to improve the torque/power density of the

CW-IPM machine. Also, as the cost of rare earth magnets escalating, it would be

beneficial to design machines with less magnet material (NdFeB in particular).

Lastly, with a high number of poles, as well as the capability of achieving high

efficiencies, CW-IPM may by suitable for low speed applications, such as in a wind

generator.

227

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243

APPENDIX A

AC STANDSTILL TEST APPLIED TO THE FINITE ELEMENT MODEL OF THE

SEGMENTED IPM MACHINE

A.1 Results of AC Standstill Test Implemented on the Segmented IPM Machine

The AC standstill test was used for measuring inductances of the CW-IPM machine, as

it takes into account the additional leakage harmonic components. This test was

implemented in FE analysis and to determine its validity, the test carried out on the

UNSW segmented IPM machine model, as shown in fig. A.1. The results obtained from

the model was compared with other FE methods as well as the experimental AC

standstill test method. Results obtained was shown in fig. A.2.

Fig. A.1 Segmented IPM machine

Appendix A

244

Fig. A.2 AC standstill test on the S-IPM machine using FE analysis compared to other methods

Indu

ctan

ceIn

duct

ance

245

APPENDIX B

SALIENCY RATIO OPTIMISATION

B.1 Optimisation of Saliency Ratio by Variation of Rotor Magnet Shape

Since it is difficult to shape magnet poles simply by the observation of d and q-axis

paths, there are no references and rules on how the rotor pole for a CW-IPM machine

should be shaped. Thus, randomized sets of rotor magnet shapes were modelled in order

to establish certain basic rules in maximising saliency.

In the following four designs, the magnet width and thickness were kept constant to

investigate the effects of varying magnet and link section geometry.

Des

ign

1

Saliency RatioL = 5.649 mHL = 5.831 mH= = 1.032

Design Constants Magnet width = 12mm

Magnet Depth = 2mm

Des

ign

2

Saliency RatioL = 5.517mHL = 5.768mH= = 1.045

Design Constants Flux guide Design

Magnet width = 12mm

Magnet thickness = 2mm

Des

ign

3

Saliency RatioL = 6.035mHL = 6.188 mH= = 1.025

Design Constantsv-shaped magnets

Magnet width = 12mm


Des

ign

4

Saliency RatioL = 6.4274 mHL = 6.4956mH= = 1.011

Design Constants Segmented magnets

Magnet width = 12mm


Appendix B

246

It can be observed that the variation of magnet shapes did not have much effect on

increasing the saliency ratio.

In the following designs (5 and 6), the tips of the flux guides were placed closer to the

rotor surface to channel more magnet flux across the airgap. This reduced the overall

inductance and increased the saliency ratio. It is also shown that an increase in magnet

thickness also caused an increase in saliency ratio.

Des

ign

5




Des

ign

6




In the next set of designs, wider magnets were used. This resulted in an obvious

increase in saliency ratio. Various magnet shapes, positions, different number of barriers

and different magnet thickness were experimented. The outcome was that a single-

barrier structure with a basic rectangular shaped produced higher saliency ratio.

Appendix B

247

Des

ign

7



Magnet thickness = 4mmD

esig

n 8




Des

ign

9




Des

ign

10


Design Constants

Double-barrier magnets

Magnet width = 14mm


Des

ign

11


Design Constants

Magnet width = 14mm


Des

ign

12


Design Constants

Magnet width = 14mm


Although the highest saliency achieved was just above 1.13, the various designs did

show variations in the saliency ratio. This allowed basic design rules to be highlighted

via observation of the results obtained.

Appendix B

248

Thick magnets (Design 12) help in reducing d-axis inductance, thus increasing

saliency ratio

Having magnets further away from airgap increases both d-and q-axis

inductances therefore magnets should be as close to the airgap as possible,

alternatively non-magnetic barriers at magnet edges can be extended closer

towards the airgap.

Segmentation of magnets (Design 4) increases d-axis inductance hence lowers

saliency ratio

Variation of magnet shape (Design 8 and 9) including the addition of a barrier

(Design 10) has little effect on the saliency ratio

249

APPENDIX C

INDUCTANCE WAVEFORMS AND SALIENCY RATIO FOR VARIOUS SLOT/POLE

COMBINATION AND FOR DOUBLE-LAYER WINDINGS

C.1 Inductance Waveform and Saliency Ratio – Comparison of Various

Slot/pole Combinations

The saliency ratio of three different single-layer winding layouts, (with 6, 12 and 18

slots), are compared. In these three models the same 14-pole rotor is used. The AC

standstill test is used to determine the inductance waveforms of the three models.

Fig. C.1 Three 14-pole layouts used in the saliency ratio comparison

The following waveforms are for the 6, 12 and 18-slot, 14-pole, single-layer windings

as shown in the following figures:

Fig. C.2 Self- and Mutual-inductance for the 6-slot, 14-pole, single-layer model

Appendix C

250



Appendix C

251

C.2 Inductance Waveform and Saliency Ratio – Comparison with Double-Layer

Windings

Here the saliency ratio of a 6-slot, single-layer winding machine is compared with 6-slot

double-layer winding machine. The same 14-pole rotor is used.

Fig. C.5 Single- and double-layer layout used in the saliency ratio comparison

The inductance waveform for 6-slot, single-layer model was shown in fig. C.2. The

following waveform is for the 6-slot, double-layer model:

Fig. C.6 Self- and Mutual-inductance for the 6-slot, 14-pole, double-layer model

Appendix C

252

Table C.1 Summarises the achieved saliency ratios for all the above mentioned models

Table C.1Saliency ratios for various layouts

Layout

6-slot, 14-pole, Single-layer 1.059



6-slot, 14-pole, Double-layer 1.112

253

APPENDIX D

THERMAL MODEL

D.1 Thermal Model Approximating Temperature at Various Parts of the Machine

A basic thermal model was created using Motor-CAD to determine the approximate

temperature distribution in the machine. Key specifications for this thermal model is

stated in table D.1:

Table D.1Key machine parameters used in thermal model

Stator/Rotor material N.O. Silicon Steel

Core loss @50Hz/1.5T 3.40W/kg

Winding material Copper

Total no. of turns per coils 228 Turns

Stator voltage 30Vrms

Stator resistance

Stator current 17Arms

Output power 1kW

Airgap length 0.6mm

Rotor radius 42mm

Machine effective length 65mm

Machine radius 65mm

Slot fill-factor 0.5

Housing radial thickness 2.5mm

Conductor thickness AWG17

Ambient Temperature 30°C

Airgap thickness 0.6mm

Cooling arrangements Naturally cooled (no fins)

mailto:@50Hz/1.5T

Appendix D

254

Fig. D.1 Approximate model used in thermal analysis

The model as shown in fig D.1 was set to operate with 250Hz excitation frequency with

an ambient temperature of 30°C. It was subjected to the worse case scenario where the

machine was completely enclosed in the case (without fins) and made to run

continuously at full load current over a timeframe of 20 mins. The steady state

temperatures at various parts of the machine are given in table D.2:

Table D.2Estimated temperature at various parts of the machine

Housing 94°C

Rotor yoke and rotor surface 107°C

Magnet 107°C

Stator surface and stator tooth 103°C

Stator yoke 100°C

Winding 121°C

Housing 94°C

Rotor yoke

Housing

Rotor surface

Magnet

Stator tooth

Winding

Stator surfaceStator yoke

255

APPENDIX E

FINAL MACHINE DRAWINGS

E.1 ABB Casing used (with Original Induction Motor)

Appendix E

256

E.2 Stator of the CW-IPM Prototype

Appendix E

257

E.3 Rotor of the CW-IPM Prototype

Appendix E

258

Appendix E

259

E.4 Shaft of the CW-IPM Prototype

Appendix E

260

E.5 Key (shaft) of the CW-IPM Prototype

Appendix E

261

E.6 End-plates of the CW-IPM Prototype

262

APPENDIX F

EXPERIMENTAL SETUP

F.1 The Experimental Setup

The experimental setup of for testing the performance of the CW-IPM prototype,

(shown in fig. F.1), consists of the following:

(i) CW-IPM machine

(ii) Kollmorgen PM machine (loading machine)

(iii) -

(iv) Windows based PC

(v) DS1104 Controller board

(vi) 3-phase IGBT inverter

(vii) 10Nm Torque transducer (HBM – T20WN)

(viii) Position Sensor (Heidenhain ROD 426 – 5000 pulses per revolution)

(ix) Power analyser

(x) 415V Voltage regulator

Fig. F.1 Complete experimental Setup

(i)

(viii)

(vi) (x) (vi)

(iii)

(ix)(ii)

(vii)

Appendix F

263

In this setup, the inverter was supplied by 3-phase, 415V mains through the voltage

regulator. The DS1104 controller board receives feedback signals from the inverter,

(supply current from two phases), as well as from the position sensor. These signals,

together with the applied control algorithm and SVM produces the desired current

references to the inverter, (through the controller board). The controller algorithm is

written in C-code, and is applied in real-time via d-space control desk on a windows

based PC, (this interface is shown in fig. F.2). 3-phase supply is fed into the CW-IPM

machine through a power analyser, (which measures the input quantities to the motor, as

well as the power factor). The CW-IPM machine is loaded by the Kollmorgen machine,

connected to a load bank. At low speeds, the Kollmorgen machine is connected to 4:1

gearbox to achieve higher loading torque. Output shaft torque from the CW-IPM

machine is measured by the 10Nm HBM torque transducer.

Fig. F.2 d-space control desk, real-time graphical user interface

Appendix F

264

F.2 Control Algorithm

The key portion of the control algorithm, written C, and ran with d-space control desk is

shown below:

/***************************************************************************************************** Rotor Field Oriented Control of the CW-IPM (DS1104) *****************************************************************************************************/#include <c:\dSPACE\DS1104\RTLib\brtenv.h>#include <ctrl.h> /* general header for motor control */#include <vlimtfun.c>#include <svmodc.c>

/* variables for execution time measurement */int index_inc;int cnt;int index_inc;Float64 exec_time;Float64 iq_ref1;Float64 id_ref1;Float64 v_oc;Float64 Van;Float64 IaExt;Float64 scaleid=1;Float64 speed_w_base=53.0;Float64 v_om=Vam+Iam*Rs;Float64 speed_w_corner=69.0/Pp/0.168;Float64 id_man=0;

/* adjust values for timer0 */Float64 timer0_period = T_S;

/* variables for communication with Slave DSP */Int16 task_id = 0; /* communication channel */Int16 index = -1; /* slave DSP command index */

/* parameters for PWM initialization */Float64 pwm_period = T_S; /* PWM period */Float64 deadband = 2e-6; /* deadband period */

UInt16 sync_mode = SLVDSP1104_PWM3_SYNC_CENT;

/* interrupt service routine timer0 */void isr_timer0(void){

/* overrun check, enable interrupts globally */ds1104_begin_isr_timer0(); /* start interrupt service routine timer */RTLIB_TIC_START(); /* start time measurement */host_service(1, 0); /* Data Acquisition service */

/************************Rotor Position and Speed Acquisition***************************/

psn_init = psn_init1*PI/180.0;angle_limit(psn_init);

/*read with highest resolution, 1/4 line */inc_k = ds1104_inc_counter_read(1);eps_m1 = eps_m1+(double)(inc_k - inc_k1)*PI2/4.0/5000.0;eps_m =eps_m1 + psn_init;index_inc = ds1104_inc_index_read(1, DS1104_INC_IDXMODE_ON);

angle_limit(eps_m);/*calculate electrical angle between the rotor and stator *///Dan's code to limit qngle to no more than PIeps_rs = Pp * eps_m;if(eps_rs>6*PI) eps_rs=eps_rs-6*PI;else if(eps_rs<=-6*PI) eps_rs=eps_rs+6*PI;else if(eps_rs>5*PI) eps_rs=eps_rs-6*PI;else if(eps_rs<=-5*PI) eps_rs=eps_rs+6*PI;else if(eps_rs>4*PI) eps_rs=eps_rs-4*PI;else if(eps_rs<=-4*PI) eps_rs=eps_rs+4*PI;else if(eps_rs>3*PI) eps_rs=eps_rs-4*PI;else if(eps_rs<=-3*PI) eps_rs=eps_rs+4*PI;else if(eps_rs>2*PI) eps_rs=eps_rs-2*PI;else if(eps_rs<=-2*PI) eps_rs=eps_rs+2*PI;else if(eps_rs>PI) eps_rs=eps_rs-2*PI;else if(eps_rs<=-PI) eps_rs=eps_rs+2*PI;

Appendix F

265

eps_rs_k = eps_m;if ((eps_rs_k<eps_rs_k1-5000*PI/30*T_S) || (eps_rs_k>eps_rs_k1+5000*PI/30*T_S)){}else {ch_eps_rs = eps_rs_k - eps_rs_k1;}eps_rs_k1 = eps_rs_k;

speed_w = ch_eps_rs / T_S;fol(speed_w, speed_w_fol, fol_speed);speed_spd = speed_w * 60.0 / (PI2);fol(speed_spd, speed_spd_fol, fol_spd);inc_k1 = inc_k;

/**************************DC Bus Voltage and Current Acquisition***********************/

/*V_DC measurement*/ds1104_adc_mux(1);ds1104_adc_delayed_start(DS1104_ADC1);V_DC = SCALE_VOLTAGE * ds1104_adc_read_ch(1);

/* get phase currents from ADCs */ds1104_adc_start(DS1104_ADC2 | DS1104_ADC3 | DS1104_ADC4 | DS1104_ADC5 );

i_abc.a = SCALE_CURRENT * ds1104_adc_read_ch(7);i_abc.c = SCALE_CURRENT * ds1104_adc_read_ch(6);i_abc.b = -i_abc.a - i_abc.c;

Van= ds1104_adc_read_ch(8);

IaExt= ds1104_adc_read_ch(5);ia = i_abc.a;ib = i_abc.b;ic = i_abc.c;

/* convert phase currents to stator current vector */fc3_2_spec(i_abc,i_ab);

/*dq-axes current*/ sincos(eps_rs,trig_fct);vr_neg(i_ab,trig_fct,i_dq);id=i_dq.d;iq=i_dq.q;id=i_ab.alpha*cos(eps_rs)+i_ab.beta*sin(eps_rs);iq=-i_ab.alpha*sin(eps_rs)+i_ab.beta*cos(eps_rs);

/******************************PI Speed Controller******************************/

count++;

if (count >= 5){

count = 0;

u_error_spd = speed_ref-speed_w_fol;u_error_p = Kp_spd*u_error_spd;

u_error_i = Ki_spd*u_error_spd+K_anti_spd*(iq_ref-u_out_spd)+u_error_i;

if (u_error_i >= iq_max) { u_error_i = iq_max;}if (u_error_i <=-iq_max) { u_error_i =-iq_max;}

u_out_spd=u_error_p+u_error_i;iq_ref=u_out_spd;iq_max=Iam;if (iq_ref >= iq_max) { iq_ref = iq_max;}

if (iq_ref <=-iq_max) { iq_ref =-iq_max;}}

/********************************************************************************************//************************** Determination of Reference and Max id ***************************//********************************************************************************************/

id_max = -4;id_ref=id_man;if (id_ref <= id_max) {id_ref = id_max;}

/********************************************************************************************/

Appendix F

266

/******************************PI Current Controllers******************************/

//id controllerid_error =id_ref-id;id_error_p = Kp_d*id_error;id_error_i = Ki_d*id_error+K_anti_d*(vd_ref-vd_out)+id_error_i;

if (id_error_i >= 0.866*V_DC) { id_error_i = 0.866*V_DC;}if (id_error_i <=-0.866*V_DC) { id_error_i =-0.866*V_DC;}

vd_out=id_error_p+id_error_i-(0.0*Pp*speed_w_fol*Lq*iq); //Decoupling terms in bracketsvd_ref=vd_out;

if (vd_ref >= 0.866*V_DC) { vd_ref = 0.866*V_DC;}if (vd_ref <=-0.866*V_DC) { vd_ref =-0.866*V_DC;}

//iq controlleriq_error =iq_ref-iq;iq_error_p = Kp_q*iq_error;iq_error_i = Ki_q*iq_error+K_anti_q*(vq_ref-vq_out)+iq_error_i;

if (iq_error_i >= 0.866*V_DC) { iq_error_i = 0.866*V_DC;}if (iq_error_i <=-0.866*V_DC) { iq_error_i =-0.866*V_DC;}

vq_out=iq_error_p+iq_error_i+(0.0*Pp*speed_w_fol*(FLUXM+Ld*id)); //Decoupling terms in bracketsvq_ref=vq_out;

if (vq_ref >= 0.866*V_DC) { vq_ref = 0.866*V_DC;}if (vq_ref <=-0.866*V_DC) { vq_ref =-0.866*V_DC;}

/*************************Decoupling & Park's Transformation***************************/

//Decouplingvd=vd_ref;vq=vq_ref;

Ualpha=vd*cos(eps_rs)-vq*sin(eps_rs);Ubeta =vq*cos(eps_rs)+vd*sin(eps_rs);

/**************************************SVM*****************************************/

/*voltage limitation*/sv_lim(&Uab, Ualpha, Ubeta, V_DC);Ua=Uab.alpha;Ub=Uab.beta;

/*space vector modulation*/sv_mod(&dutyCycle, &sv_pwm, Uab.alpha, Uab.beta, V_DC);t1=pwm_period*sv_pwm.t1;t2=pwm_period*sv_pwm.t2;

/************************************************************************************/

exec_time = RTLIB_TIC_READ();/* overrun check end, disable interrupts globally */ds1104_end_isr_timer0();

}

/* interrupt service routine for PWM sync interrupt */void PWM_sync_interrupt(void){

/* write PWM3 duty cycle to slave DSP and test for error */error = ds1104_slave_dsp_pwm3sv_duty_write(task_id, index,sv_pwm.sector, t1, t2);if ( error != DSCOMDEF_NO_ERROR){

write_PWM3sv_error=1;}

}

main(){

init ();/* input signal for channel 1 via TTL */ds1104_inc_init(1, DS1104_INC_MODE_RS422);ds1104_inc_set_idxmode(1, DS1104_INC_IDXMODE_ON);

/* init incremental encoder channel 1 */ index_inc = 0;while (index_inc == 0) {

Appendix F

267

index_inc = ds1104_inc_index_read(1, DS1104_INC_IDXMODE_ON);}ds1104_inc_counter_clear(1);

/* initialization of slave DSP communication */ds1104_slave_dsp_communication_init();/* init and start of 3-phase PWMSV generation on slave DSP */ds1104_slave_dsp_pwm3sv_init(task_id, pwm_period, sv_pwm.sector, t1, t2, deadband, sync_mode);ds1104_slave_dsp_pwm3_start(task_id);/* registration of PWM duty cycle update command */ds1104_slave_dsp_pwm3sv_duty_write_register(task_id, &index);/* initialization of PWM sync interrupt */ds1104_set_interrupt_vector(DS1104_INT_SLAVE_DSP_PWM,(DS1104_Int_Handler_Type)

&PWM_sync_interrupt, SAVE_REGS_ON);ds1104_enable_hardware_int(DS1104_INT_SLAVE_DSP_PWM);

RTLIB_INT_ENABLE();

/* initialize control parameters */varinit();/* periodic event with timer0 */ds1104_start_isr_timer0(timer0_period, isr_timer0);/* Background tasks */while(1){

RTLIB_BACKGROUND_SERVICE(); /* ControlDesk service */}

}

/*********************************************** End ********************************************************/

F.3 3-phase IGBT Inverter

The 3-phse IGBT inverter which supplies power to the CW-IPM machine is shown fig.

F.3. Details of its circuit diagrams are shown in fig. F.4 to fig. F.5.

Fig. F.3 3-phse IGBT inverter (casing off) [174]

Appendix F

268

Fig. F.4 IGBT inverter schematic

Appendix F

269

Fig. F.5 Connections between the IGBT inverter and control boards

Appendix F

270

F.4 Kollmorgen PM Machine Specifications

Specifications of the Kollmorgen machine, (used as the loading machine), are as listed

in table F.1.

Table F.1Kollmorgen PM Machine specifications

Model AKM33H

Rated Current 5.63Arms

Rated Torque 2.88Nm

Rated Voltage 320VDC

Rated Speed 5500RPM

Rated Power 1.31kW

Stator Resistance (l-l)

Appendix G

271

APPENDIX GPUBLICATION LIST

Patents:

[1] M. F. Rahman, Rukmi Dutta, Lester Chong “Interior permanent magnet machine”, Provisional patent no. : 2011903320

Journal Publications:

[2] Lester Chong, Rukmi Dutta, M. F. Rahman, “Application of Concentrated Windings in Interior Permanent Magnet Machine”, Australian Journal of Electrical & Electronics Engineering (AJEEE) 2008. ISSN: 1448837X

[3] Lester Chong, M. F. Rahman, “Saliency Ratio Derivation and Optimization for an IPM Machine with Concentrated Windings Using Finite Element Analysis ”, Institution of Engineering and Technology (IET) 2009. ISSN: 1751-8660

[4] Lester Chong, Rukmi Dutta, M. F. Rahman, “Electromagnetic Losses in a 1kW Concentric Wound IPM Machine for Field Weakening Applications”, Journal of Applied Superconductivity and Electromagnetics (JASEM), 2010. ISSN 1836-7151

Conference Publications:

[5] Lester Chong, Rukmi Dutta, M. F. Rahman, “Application of Concentrated Windings in Interior Permanent Magnet Machine”, Australasian Universities Power Engineering Conference (AUPEC) 2007, Australia. ISBN: 978-0-646-49488-3

[6] Lester Chong, Rukmi Dutta, M. F. Rahman, “Open Circuit Analysis of Concentrated Winding in Interior Permanent Magnet Machines with Fractional Slot Distribution”, 4th IET International Conference on Power Electronics, Machines and Drives (PEMD) 2008, UK. ISBN: 978-0-86341-900-3

[7] Lester Chong, M. F. Rahman, “Comparison of d- and q-axis Inductances in an IPM machine with Integral-slot Distributed and Fractional-slot Concentrated Windings”, 18th International Conference on Electrical Machines (ICEM) 2008, Portugal. ISBN: 978-1-4244-1735-3

[8] Lester Chong, M. F. Rahman, “Saliency Ratio Optimization in an IPM Machine with Fractional-slot Concentrated Windings” 11th International Conference on Electrical Machines and Systems (ICEMS) 2008, China. ISBN: 978-1-4244-3826-6

[9] Lester Chong, Rukmi Dutta, M. F. Rahman, “Parameter Analysis of an IPM Machine with Fractional-slot Concentrated Windings, Part I: Open-circuit Analysis”, Australasian Universities Power Engineering Conference (AUPEC) 2008, Australia. ISBN: 978-0-7334-2715-2

[10] Lester Chong, Rukmi Dutta, M. F. Rahman, “Parameter Analysis of an IPM Machine with Fractional-slot Concentrated Windings, Part II: Including Armature-reaction”, Australasian Universities Power Engineering Conference (AUPEC) 2008, Australia. ISBN: 978-0-7334-2715-2

[11] Lester Chong, Rukmi Dutta, M. F. Rahman, “Design of IPM machine with Concentrated Windings for Vehicular Applications”, European Power Engineering Conference, 2009, Spain. ISBN: 978-1-4244-4432-8

Appendix G

272

[12] Lester Chong, Rukmi Dutta, M. F. Rahman, “Design and Mechanical Consideration of an IPM Machine with Concentrated Windings”, Australasian Universities Power Engineering Conference (AUPEC) 2009, Australia. ISBN: 978-1-4244-5153-1

[13] Lester Chong, Rukmi Dutta and M. F. Rahman, "Design of an interior permanent magnet machine with concentrated winding for field weakening applications," in Proc. of IEEE Int. Electric Machines & Drives Conf. (IEMDC), 2009, pp. 1985-1992.

[14] Lester Chong, Rukmi Dutta, M. F. Rahman, “Design and Thermal Considerations of an Interior Permanent Magnet Machine with Concentrated Windings”, International Conference on Electrical Machines and Systems (ICEMS) 2009, Japan. ISBN: 978-1-4244-5177-7

[15] Lester Chong, Rukmi Dutta, M. F. Rahman, “Field Weakening Performance of a Concentrated Wound PM Machine with Rotor and Magnet Geometry Variation”, Power and Engineering Society General meeting (PES) 2010, USA. ISBN: 978-1-4244-6549-1

[16] Lester Chong, Rukmi Dutta, M. F. Rahman, “Design of a Highly Efficient 1kW IPM Machine with a Very Wide Constant Power Speed Range”, International Power Electronics Conference -ECCE-Asia (IPEC) 2010, Japan. ISBN: 978-1-4244-5394-8

[17] Lester Chong, Rukmi Dutta, M. F. Rahman, “A Comparative Study of Rotor Losses in an IPM with Single and Double Layer Concentrated Windings”, International Conference on Electrical Machines and Systems (ICEMS) 2010, Korea. ISBN: 978-1-4244-7720-3

[18] Lester Chong, Rukmi Dutta, Howard Lovatt, Nguyen Quang Dai, M. F. Rahman, “Comparison of Concentrated and Distributed Windings in an IPM Machine for Field Weakening Applications”, Australasian Universities Power Engineering Conference (AUPEC) 2010, Australia. ISBN: 978-1-4244-8379-2

[19] Lester Chong, Rukmi Dutta, M. F. Rahman, Howard Lovatt “Experimental verification of Rotor Losses in a Concentrated Wound IPM Machine with V-Shaped magnets”, International Electrical Machines and Drives Conference (IEMDC) 2011, Canada

[20] Rukmi Dutta, Lester Chong, M. F. Rahman, “Analysis of CPSR in Motoring and Generating Modes of an IPM Motor”, International Electrical Machines and Drives Conference (IEMDC) 2011, Canada

[21] Lester Chong, Rukmi Dutta, M. F. Rahman, Howard Lovatt “Open Circuit Analysis of an IPM Machine with Concentrated Windings Including Experimental Verification”, International Conference on Electrical Machines and Systems (ICEMS) 2011, China

[22] Lester Chong, Rukmi Dutta, D. Xiao, M. F. Rahman “Performance Comparison between Concentrated and Distributed Wound IPM Machines used for Field Weakening Applications”, Aegean Conference on Electric Machines and Power Electronics(ACEMP) 2011, Turkey

design of an interior permanent

Documents

cwipm machine design

prototype machine

wide cpsr

constructed design

design methods

proposed design

concentrated windings

scalability study