1.3 The switched reluctance motor. - Warwick WRAP

1.3 The switched reluctance motor. - Warwick WRAP
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THE DESIGN OF SWITCHED RELUCTANCE MOTORS
FOR EFFICIENT ENERGY CONVERSION
Alexandros M. Michaelides
Thesis submitted for the examination of degree of Doctor of Philosophy
Department of Engineering
University of Warwick
Coventry, CV4 7AL
September 1994
This copy of the thesis has been supplied on condition that anyone who consults
it is understood to recognize that the copyright rests with its author and that no
quotation from the thesis and no information derived from it may be published
without the prior written consent of the author or the University (as may be
appropriate).
To my family,
Michael, Androulla
and
Vangelis.
11
TABLE OF CONTENTS
Acknowledgements List of figures and tables xi
xii
List of symbols
Abstract
Preface
xxix
Chapter 1 The switched reluctance drive: an overview
1
1.1 Historical background to the reluctance motor.
1
1.2 A present day switched reluctance drive. 3
1.3 The switched reluctance motor. 5
1.4 Existing power converter circuits for the switched
reluctance drive.
9
1.4.1 Power converter with bifilar motor windings. 9
1.4.2 Power converter with split dc supply.
11
1.4.3 Capacitor dump power converter.
11
1.4.4 Power converter with the asymmetric half-bridge.
13
1.4.5 Shared switch, asymmetric half-bridge power
converter.
1.5 Rotor position measurement techniques.
14
16
1.5.1 Slotted disk arrangements.
16
1.5.2 Optical shaft encoders.
17
1.5.3 Brushless resolvers.
18
1.5.4 Sensorless position detection.
18
1.6 Phase current measurement and control.
18
1.7 Market applications of the switched reluctance drive. 20
Chapter 2 The switched reluctance drive: aspects of
design, construction and testing
2.1 Switched reluctance motor design.
22
22
2.1.1 Low phase numbers.
23
2.1.2 Higher phase numbers - a new motor design. 27
2.2 Introduction to electromagnetic finite element analysis.
28
2.2.1 The need for finite element modelling.
28
2.2.2 Electromagnetic field equations.
29
2.2.3 Finite element model creation.
30
2.2.4 Field values computed using the finite element
analysis package.
32
I. Flux linkage computation.
32
II. Energy considerations.
35
III. Instantaneous static torque: the Maxwell
36
stress tensor.
2.3 Construction of power converter circuits. 37
2.3.1 Overview of semiconductor devices for power
converters.
37
I. The ideal switch.
37
II. The thyristor.
38
III. The bipolar transistor.
39
IV. The MOSFET.
39
V. The insulated gate bipolar transistor (IGBT).
40
2.3.2 Selection of type and rating of the semiconductor
40
devices.
2.3.3 Gate drive circuits for power MOSFETs. iv
41
I. Selection of the gate drive isolating device.
41
II. Gate drive circuit design for a top switch.
42
III. Bottom switch gate drive circuit design.
44
2.3.4 Snubber circuits.
2.4 The control board.
2.4.1 Current sensing and control.
44
46
47
I. Hysteresis type current chopping regulator. 47
II. Fixed frequency pwm current regulator. 47
2.4.2 The implementation of logic functions - XILINX.
49
2.5 Experimental arrangements.
50
2.5.1 Description of the test rigs.
50
2.5.2 Flux linkage measurement.
51
I. Measurement of rising current.
51
II. Measurement of decaying current.
53
III. Biasing the electromagnetic field.
53
2.5.3 Measurement of static torque.
54
I. The dc generator test rig.
54
II. The eddy current test rig.
54
2.5.4 Measurement of dynamic torque. 54
I. The dc generator test rig.
54
II. The eddy current test rig.
55
2.6 Review of fundamental aspects of switched reluctance
motor technology.
55
Chapter 3 Electromagnetic analysis of the switched
reluctance motor.
3.1 Electromechanical energy conversion theory.
3.1.1 Singly excited systems. 3.1.2 Exciting two phases simultaneously - a new
57
58
58
modelling procedure.
61
I. Flux patterns in the 4-phase motor.
61
II. Computation of coenergy in a doubly excited
61
system.
68
3.2 The 150W 4-phase motor.
3.2.1 Single phase excitation.
68
3.2.2 Simultaneous excitation of two phase windings in
the 4-phase machine - normal machine operation.
3.2.3 Bulk saturation effects.
70
72
3.3 Electromagnetic design of switched reluctance motors for
low torque ripple - a new alternative. 77
3.4 The 4kW 7-phase switched reluctance motor.
80
3.4.1 Electromagnetic field considerations. 84
3.4.2 Instantaneous / average torque considerations.
87
3.5 Summary of fundamental modelling considerations.
89
Chapter 4 The effect of end-core flux on the performance
of the switched reluctance motor
91
4.1 The need for three-dimensional modelling. 91
4.2 Three-dimensional effects in the switched reluctance machine. 93
4.3 Comparison between two-dimensional and three-dimensional
finite element analysis results with experimental results.
95
4.3.1 Flux linkage.
95
4.3.2 Static torque.
99
4.4 Correction charts for two-dimensional finite element modelling. 101
101
4.4.1 Flux linkage.
4.4.2 Comparison with a 140mm stack 7-phase switched
106
reluctance motor.
106
4.4.3 Static torque.
vi
4.5 Discussion on other effects. 109
4.5.1 Anisotropy.
109
4.5.2 Conductor overhang / inside coil radius.
112
4.5.3 Sources of error.
113
115
4.6 Conclusions.
Chapter 5 The SRDESIGN package: Modelling and
Simulation
116
5.1 Modelling magnetisation curves for singly excited systems. 118
5.1.1 'Extreme' (aligned and unaligned) rotor positions. 118
5.1.2 Intermediate rotor positions.
119
I. Low excitation.
119
II. High excitation.
120
5.2 Modelling magnetisation curves for switched reluctance
motors with two phases simultaneously excited. 122
5.2.1 'Extreme' rotor positions.
122
5.2.2 Intermediate rotor positions.
123
5.3 Dynamic operation considerations.
125
5.3.1 Base speed estimation.
127
5.3.2 Commutation.
127
5.3.3 Maximum speed for a given current.
131
5.3.4 Variation of current with angle.
132
5.3.5 Time stepping algorithm for current prediction. 133
5.4 Computation of output power and losses.
135
5.4.1 Computation of the rms phase current I.
135
5.4.2 Copper losses.
136
5.4.3 Iron losses.
138
5.4.4 Output power, input power and efficiency.
140
5.5 Structure of the SRDESIGN package.
vii
141
5.5.1 Unit CONSTANT.
141
5.5.2 Unit CURRCALC.
142
5.5.3 Unit DRAW.
142
5.5.4 Unit GLOBALS.
143
5.5.5 Unit INPUTS.
143
5.5.6 Unit MENUS.
143
5.5.7 Unit RESULTS.
143
5.5.8 Main Program.
144
144
5.6 Summary.
Chapter 6 SRDESIGN verification: dynamic testing of
switched reluctance motors
146
6.1 The use of X, / i diagrams in SRDESIGN.
146
6.2 Testing the 4-phase 150W motor.
148
6.2.1 Experimental arrangement.
148
6.2.2 Test presentation.
149
6.2.3 Sources of error.
158
6.3 Testing the 4kW 7-phase motor. 159
6.3.1 Experimental arrangement.
159
6.3.2 7-phase motor testing.
159
164
6.4 SRDESIGN practicality.
Chapter 7 The 5-phase switched reluctance drive:
design, construction and performance 169
169
7.1 5-phase motor design.
7.1.1 Selection of stator pole arc and back-iron width.
169
7.1.2 Stator / rotor pole arcs.
174
7.1.3 Rotor slot depth.
179
viii
7.1.4 Choice of steel grade.
180
180
7.2 5-phase motor construction.
7.2.1 Construction procedure.
180
7.2.2 Potential improvements of the constructed
185
5-phase motor.
7.3 Measurement of flux linkage and static torque.
186
7.4 Static performance comparison between the 5-phase
prototype and the 4-phase Oulton motor.
188
7.5 Dynamic performance prediction. 190
7.6 Experimental arrangement. 196
7.7 Test presentation.
197
7.7.1 On-state angle analysis.
199
7.7.2 Maximum drive efficiency analysis. 202
7.7.3 Drive and motor efficiency considerations. 206
7.8 Comparison of experimental results with simulated data. 208
7.9 Market applications of the 5-phase switched reluctance
drive.
211
Chapter 8 Conclusion
215
8.1 Main conclusions and author's contribution to knowledge. 215
8.2 Areas of further work.
217
References
219
Appendices
226
A. Electromagnetic equations governing the finite element
analysis software.
A.1 The two-dimensional finite element code
ix
226
(OPERA-2D).
226
A.2 The three-dimensional algorithm (OPERA-3D /
TOSCA).
227
B. Data sheets for power semiconductor devices used in
this project.
229
C. Comparison on the basis of equal copper losses. 236
D. Loss data and BH curves for Losm 500-50.
238
E. Operating principles of stepping motors.
240
E.1 The variable reluctance stepping motor.
240
E.2 The permanent magnet (PM) stepping motor.
240
E.3 The hybrid stepping motor. 241
F. A brief description of the induction motor. 244
ACKNOWLEDGEMENTS
I would like to thank Dr. Charles Pollock for his supervision and support
throughout the project. Thanks are also due to the technical staff at the University,
(especially Andy Leeson, Stuart Edris and Colin Major) and at Vector Fields Ltd
for help in times of need, and to Electrodrives Ltd for support during the motor
assembly stage. I would also like to thank my colleagues Po Wa Lee, Kevin
Richardson, Helen Pollock, Chi-Yao Wu, Mike Barnes and Cliff Joliffe for useful
discussions, but most of all Antigoni for continuous help and encouragement.
xi
LIST OF FIGURES AND TABLES
Chapter 1
Fig. 1.1
Principle of Davidson's six-step reluctance motor.
Fig. 1.2
Block diagram of a switched reluctance drive.
Fig. 1.3
Plan of the laminations of a typical 4-phase motor.
Fig. 1.4
a) Equivalent circuit of a switched reluctance motor phase winding.
b) Typical waveforms.
Fig. 1.5
Power converter with bifilar motor windings.
Fig. 1.6
Power converter with split dc power supply.
Fig. 1.7
Capacitor dump power converter.
Fig. 1.8
Power converter with asymmetric half-bridge.
Fig. 1.9
Shared switch, asymmetric half-bridge converter.
Table 1.1
Shared switch converter switching algorithm.
Chapter 2
Fig. 2.1
A 2-phase 4/2 motor.
Fig. 2.2
The 2-phase 4/2 motor with a stepped gap, showing self-starting
xii
capability.
Fig. 2.3
3-phase 12/10 motor with 2 teeth per stator pole.
Fig. 2.4
3-phase 12/10 motor, with short flux paths.
Fig. 2.5 The proposed machine configuration. A 5-phase 10/8 motor showing
short flux-paths both producing positive torque. Phases 1 and 2 are
simultaneously excited.
Fig. 2.6
a) The two-dimensional finite element mesh for the 150W 4-phase
motor.
b) The three-dimensional finite element mesh for the 150W 4-phase
motor (air regions not shown for clarity).
Fig. 2.7
a) The upper switch drive circuit.
b) The lower switch drive circuit.
Fig. 2.8
A complete turn off-snubber circuit.
Fig. 2.9
A hysteresis type current chopping regulator.
Fig. 2.10
The constructed fixed frequency pwm current regulator.
Fig. 2.11
The dc generator test bed.
Fig. 2.12
Circuit arrangement for flux linkage measurement.
Fig. 2.13
Flux linkage measurement in a biased field.
Chapter 3
Fig. 3.1
A 2-phase 4/2 motor, illustrating movement through a rotor step.
Fig. 3.2
X / i diagram of an ideal excitation cycle.
Fig. 3.3
a) Flux pattern in a singly excited 4-phase motor.
b) Flux pattern in a doubly excited 4-phase motor.
c) Resulting primary B-field in a doubly excited 4-phase motor.
d) Geometrical considerations in a 4-phase motor.
e) Excitation sequence in the 4-phase motor.
Fig. 3.4
Integration path in a doubly excited system.
Fig. 3.5
X / i diagram (4-phase motor, 1 phase excited).
Fig. 3.6
X / 8 diagram (4-phase motor, 1 phase excited).
Fig. 3.7
TI9
Fig. 3.8
System X, / i diagram (4-phase motor, 2 phases excited).
Fig. 3.9
X / 0 diagram (4-phase motor, 2 phases excited).
Fig. 3.10
TI
Table 3.1
Average torque figures for the 150W 4-phase motor.
Table 3.2
Dimensions of the 4-phase motor models.
Fig. 3.11
X / 0 diagram (4-phase motor, leading phase). -
diagram (4-phase motor, 1 phase excited).
0 diagram (4-phase motor, 2 phases excited).
xiv
Fig. 3.12
X / i diagram (4-phase Mk II motor).
Fig. 3.13
TI 0 diagram (4-phase motor, 2 phases excited).
Fig. 3.14
TI 0 diagram (4-phase Mk II motor).
Table 3.3
Average torque figures for the 4-phase motor models.
Fig. 3.15
a) The 4kW 7-phase motor laminations.
b) Excitation patterns in the 7-phase motor.
c) Flux distribution in the 7-phase motor (long loops).
d) Flux distribution in the 7-phase motor (short loops).
10A).
Fig. 3.16
Energy conversion loop for low speed cycle (7-phase,
Fig. 3.17
Energy conversion loop for high speed cycle (7-phase, ibias = 10A).
Fig. 3.18
X / 0 diagram in the leading phase (7-phase motor, i= 10A).
Fig. 3.19
TI 8 diagram (7-phase motor, i= 5A and 10A).
Table 3.4
Average torque figures for the 7-phase motor.
ibias
Chapter 4
The computed and experimental X / i diagram for an 8/6 4-phase
Fig. 4.1
motor.
Fig. 4.2
a) Flux distribution in an excited stator pole with the rotor in the
aligned position (i= 3A).
b) Flux distribution in an excited stator pole with the rotor in the
XV
unaligned position (i = 3A).
c) Flux distribution in the 4-phase motor (aligned position).
Fig. 4.3
Computed and experimental static torque profile of the 4-phase 8/6
motor. (i = 5A and 10A).
Fig. 4.4
Variation of end-core flux with rotor position in the experimental
motor.
Fig. 4.5
Chart showing the correction factor which needs to be applied to
two-dimensional solutions to account for end-core flux (aligned
position).
Fig. 4.6
Percentage increment in flux linkage due to end-core effects as a
function of rotor position.
a) i = 5A
b) i = 10A
Fig. 4.7
a) X / 0 diagram for the 7-phase machine (i = 10A).
b) Flux linkage increment / rotor position diagram (7-phase motor,
i = 10A).
Fig. 4.8
Percentage increment in static torque due to end-core effects as a
function of rotor position.
a) i = 5A
b) i = 10A
Fig. 4.9
Illustration of the difference in two-dimensional modelling results
using different scaling approaches to account for anisotropy.
Fig. 4.10
X / i diagrams for the experimental motor model assigned different
xvi
packing factors.
Fig. 4.11
Illustration of overhang and inside coil radius.
Fig. 4.12
Variation of end-core flux with inside coil radius and overhang
(aligned position).
Fig. 4.13
Corrected X / i diagram based on a two-dimensional model of the
experimental machine.
Chapter 5
Fig. 5.1
Structure of the SRDESIGN program.
Fig. 5.2
Obtaining magnetisation (X, / i) curves for singly excited systems.
Fig. 5.3
X / 0 variation in singly excited systems.
Fig. 5.4
Obtaining system X Ii characteristics for switched reluctance motors
with two phases simultaneously excited.
Fig. 5.5
X, / 0 curves for doubly excited switched reluctance motors.
Fig. 5.6
Dynamic operation considerations.
Fig. 5.7
Illustration of principal winding dimensions.
Fig. 5.8
Slot filling in the switched reluctance motor.
xvii
Chapter 6
Fig. 6.1
Flux linkage / current diagram (4-phase motor, 1 phase excited).
Fig. 6.2
The experimental 4-phase drive.
Table 6.1
Sample SRDESIGN printout for the 150W 4-phase motor.
Fig. 6.3
Notation used throughout chapter 6.
Fig. 6.4
Torque / speed curve (4-phase motor, fixed commutation angles).
Fig. 6.5
Power loss in the 4-phase motor (fixed commutation angles).
Fig. 6.6
Maximum torque / speed characteristic (4-phase motor, angular
conduction period = 15°).
Fig. 6.7
Maximum torque / speed characteristic (4-phase motor, angular
conduction period = 20°).
Fig. 6.8
a) Experimental i / 0 profile @ 450rpm.
b) Experimental i / 0 profile @ 1500rpm.
c) SRDESIGN i / 0 profile @ 450rpm.
d) SRDESIGN i / 0 profile @ 1500rpm.
Fig. 6.9
a) SRDESIGN X / 0 diagram @ 450rpm.
b) SRDESIGN X / i diagram @ 450rpm.
Fig. 6.10
The experimental 7-phase drive.
Fig. 6.11
Maximum torque / speed characteristic (7-phase motor, short loops).
xviii
Fig. 6.12
Efficiency curve (7-phase motor, short loops).
Fig. 6.13
Maximum torque / speed characteristic (7-phase motor, long loops).
Fig. 6.14
Efficiency curve (7-phase motor, long loops).
Fig. 6.15
a) SRDESIGN i / 0 profile @ 1000rpm (short loops).
b) SRDESIGN i / 0 profile @ 1000rpm (long loops).
c) SRDESIGN / 0 diagram @ 1000rpm (short loops).
d) SRDESIGN X / 0 diagram @ 1000rpm (long loops).
e) SRDESIGN X / i diagram @ 1000rpm (short loops).
I) SRDESIGN X / i diagram @ 1000rpm (long loops).
Chapter 7
Fig. 7.1
Dimensions of a 10/8 5-phase motor.
Fig. 7.2
Variation of stator bore with average torque (constant stator pole
arc).
Fig. 7.3
Variation of average torque with stator pole arc / pitch ratio.
Fig. 7.4
Illustration of the 'zero torque period' concept.
Fig. 7.5
a) Excitation cycle in the 5-phase motor.
b) B-field distribution in the 5-phase motor (short flux loops, 6° rotor
position).
c) B-field distribution in the 5-phase motor (long flux loops, 6° rotor
position).
Fig. 7.6
a) Illustration of fringing effects in the unaligned position.
xix
b) Rotor slot depth considerations.
Fig. 7.7
Final drawing of the 5-phase motor laminations.
Table 7.1
Dimensions of the experimental 5-phase motor.
Fig. 7.8
The 5-phase construction process, through a set of photographs.
Fig. 7.9
Flux linkage / current diagram (5-phase motor, 1 phase excited).
Fig. 7.10
Static torque profile for the 5-phase motor (i = 12.75A).
Table 7.2
Static torque developed by the 4-phase Oulton and 5-phase prototype
motors (equal copper loss).
Fig. 7.11
a) Torque / speed curve predicted by SRDESIGN (asymmetric halfbridge converter).
b)Efficiency / speed curve predicted by SRDESIGN (asymmetric
half-bridge converter).
Table 7.3
SRDESIGN simulated data for the 5-phase short flux loop motor
(asymmetric half-bridge converter).
Fig. 7.12
a)Torque / speed curve predicted by SRDESIGN (shared switch
converter).
b)Efficiency / speed curve predicted by SRDESIGN (shared switch
converter).
Table 7.4
SRDESIGN simulated data for the 5-phase short flux loop motor
(shared switch converter).
XX
Fig. 7.13
a) Section from the experimental 5-phase drive.
b) Photograph of the 5-phase drive.
Fig. 7.14
a) Efficiency contours at half load (long loops,
conduction angle = 18°).
b) Efficiency contours at half load (short loops,
conduction angle = 18°).
Fig. 7.15
a) Efficiency contours at half load (long loops,
conduction angle = 13.5').
b) Efficiency contours at half load (short loops,
conduction angle = 13.5').
Fig. 7.16
a) Variation of torque and efficiency with speed (300V, long loops).
b) Variation of torque and efficiency with speed (300V, short loops).
Fig. 7.17
a) Experimental current profile at 900rpm, 25Nm (long loops).
b) Experimental current profile at 900rpm, 25Nm (short loops).
Fig. 7.18
Torque / speed profile (firing angle = 0°, unaligned position).
Fig. 7.19
Representation of the phase current pulse at w = 1283rpm,
T = 21.7Nm.
Fig. 7.20
Comparison of experimental results with SRDESIGN (firing
angle = 1.5°, short loops, conduction angle = 13.5°).
Fig. 7.21
a) Experimental current profile at 800rpm (short loops).
b) SRDESIGN simulated phase current profile at 800rpm
(short loops).
xxi
Fig. 7.22
a) SRDESIGN simulated / 8 diagram at 800rpm (short loops).
b) SRDESIGN simulated / i diagram at 800rpm (short loops).
Table 7.5 Comparison of the 5-phase drive efficiency with competing induction
motors and switched reluctance drives (all constructed in D112
frames).
Appendix E
Fig. E.1
A 2-phase PM stepping motor.
Fig. E.2
A 4-phase hybrid stepper motor.
Fig. E.3
Hybrid stepper operating principles.
Appendix F
Fig. F.1
The 3-phase inverter-fed induction motor.
LIST OF SYMBOLS
A
Magnetic vector potential.
A
Cross-sectional area.
AoArea enclosed by the operating trajectory on the X / i diagram.
A,
Area on the X / i diagram representing energy returned to the supply.
Flux density.
Commutation ratio.
Capacitance.
Co
Zero crossing of a function.
Diameter.
Displacement current.
Electric field strength.
Frequency.
Force.
airgap length.
Magnetic field intensity.
xxiii
i, I
Current.
Current density.
khe
Back-emf constant at high excitation.
kie
Back-emf constant at low excitation.
Coil fill factor.
Ke
Eddy current constant.
Kh
Hysteresis constant.
Slot fill factor.
1
Length.
Winding inductance.
Slope (gradient) of a function.
Efficiency.
Number of turns per phase.
N,.
Number of rotor poles.
Number of stator poles.
Power.
xxiv
PCu
Copper loss.
Pf,
Windage and friction loss.
'Fe
Iron loss.
P1
Phase 1 of the switched reluctance motor.
pf
Packing factor.
Number of phases.
Rotor pole pitch.
Winding resistance per phase.
Radius.
step
Step angle.
Stator pole pitch.
Vector describing a surface.
Sa,b,c
Switching devices.
Time.
t.
Stator pole width.
t3i
Sampling interval.
XXV
Torque.
v, V
Voltage.
Vb
Back-emf.
v,
Volume.
Energy.
Stator back-iron (yoke) thickness.
Temperature coefficient of resistance.
Stator pole arc.
Ps
Rotor pole arc.
13,
13.f,
Coefficients of the sigmoidal function.
Electric permittivity.
0
Rotor (angular) position.
X
Winding flux linkage.
1-t
Permeability.
Resistivity.
a
Conductivity.
xxvi
T
Maxwell stress tensor.
(i)
Reduced scalar potential.
oztoMagnetic flux.
tli
Total magnetic scalar potential.
(.0
Rotational speed.
Wb
Base speed.
f2.l
A region in space containing current.
xxvii
ABSTRACT
A new switched reluctance motor configuration is proposed, in which the windings
are arranged to encourage short magnetic flux paths within the motor. Short flux
path motor configurations have been modelled extensively using electromagnetic
finite element analysis. It is demonstrated that short flux paths significantly reduce
the MMF required to establish the B-field pattern in a motor; as a result copper
losses are reduced. In addition, hysteresis and eddy current losses are decreased
as the volume of iron in which iron losses are generated is reduced.
Short flux paths are formed when two adjacent phase windings, configured to give
neighbouring stator teeth opposite magnetic polarity, are simultaneously excited.
In order to accurately model short flux path machines, a thorough electromagnetic
analysis of doubly excited systems is adopted. The proposed modelling theory
forms the basis for design considerations that can optimise the performance of the
4-phase and 5-phase switched reluctance motors.
The electromagnetic theory of doubly excited systems is used in conjunction with
a dynamic simulation program, written in Turbo Pascal, to design a 5-phase
switched reluctance motor that exploits the advantages of short flux paths. Test
results from the constructed prototype confirm that short flux paths significantly
improve the efficiency of the switched reluctance motor. The 5-phase prototype
achieves higher efficiency than all known prior art switched reluctance motors and
industrial induction machines constructed in the same frame size. At the
[1300rpm, 20Nrn] operating point the efficiency of the 5-phase drive was measured
to be 87%. The corresponding motor efficiency was in excess of 89.5%.
PREFACE
The switched reluctance motor (SRM) is an electric motor consisting of a salient
pole stator with concentrated excitation windings and a salient pole rotor with no
conductors or permanent magnets. Torque is produced by the tendency of the
rotating member to move to the position which maximises the flux linking the
excited stator phase. Rotation is maintained by switching on and off the current
in the phase windings in synchronism with the position of the rotor. The direction
of the torque does not depend on the sign of the flux and current, but only on the
sign of the rate of change of reluctance with rotor position. This offers the
advantage of simple, unipolar power converter circuits.
Switched reluctance motors of three and four phases have received considerable
attention in recent years, as low cost robust variable speed drives. The 3-phase 6/4
(i.e. 6 poles on the stator and 4 poles on the rotor) motor ensures starting capability
in either direction. However, the torque profile of this motor contains a significant
amount of ripple. In contrast, the 4-phase 8/6 configuration can operate with two
phases simultaneously excited which helps to minimise the problem with torque
dips. The penalty incurred is that of increased iron loss, due to the higher
fundamental switching frequency.
This thesis describes the design and development of a 5-phase 10/8 switched
reluctance drive. The 5-phase motor exploits the advantages of a new winding
configuration which encourages short flux paths within the motor. Short flux paths
reduce the MMF required to establish the B-field pattern in the motor, leading to
a significant reduction in copper losses. In addition, the volume of iron in which
hysteresis and eddy current losses are generated is reduced considerably. The
proposed 5-phase motor can operate with (at least) two phases excited at any time
to produce smooth torque with high efficiency.
A thorough electromagnetic analysis of doubly excited systems, which relates to
switched reluctance motors operating with two phase windings conducting at any
time, is proposed in this thesis. Mutual coupling and saturation effects are
investigated. Accurate electromagnetic modelling forms the basis for design
considerations that can optimise the performance of the 4-phase and 5-phase
switched reluctance motors.
Electromagnetic finite element analysis (FEA) is used extensively to model the
static performance of a number of different switched reluctance drives. The finite
element analysis program is used not only as a motor design tool but also as a
means of validating the electromagnetic theory of doubly excited switched
reluctance motors. Switched reluctance motor structures are modelled using two
and three-dimensional finite element analysis. The effect of end-core flux on the
performance of the switched reluctance motor is investigated.
Finite element analysis is employed in the lamination design of the 5-phase
prototype together with a sizing / dynamic simulation program, which is developed
in Turbo Pascal. Test results from the constructed 5-phase motor confirm the
significant benefits arising when the machine is configured for short flux paths.
The thesis has eight chapters, a list of references and six appendices. Chapter 1
gives a historical background to the reluctance motor before describing in more
detail the components of the present day switched reluctance drive.
Chapter 2 describes the more usual switched reluctance motor designs and
highlights their merits and shortcomings. The new motor design is subsequently
described in which the windings are configured for short flux paths. The
advantages of the proposed configuration over prior art motors are highlighted. In
addition, the chapter introduces finite element analysis, the 'software tool' used for
electromagnetic design of switched reluctance motors. The design and construction
of 'hardware tools', such as drive circuits for power converters and controller
components is also described. These were employed to test a number of different
XXX
switched reluctance motors throughout the project. The chapter concludes with an
account of the experimental procedures which have been adopted.
Chapter 3 introduces an electromagnetic analysis of doubly excited systems which
relates to switched reluctance motors operating with two phases excited at any
time. The new modelling procedure includes the effects of mutual coupling and
accounts for the increased flux density, present in some parts of the magnetic
circuit when two phases are simultaneously excited. The chapter focuses on the
implementation of the modelling theory on a 150W 4-phase and a 4kW 7-phase
machine. The design of 4-phase switched reluctance drives for low torque ripple
is proposed. Finite element analysis results from a 4kW 7-phase motor, configured
for long and short flux paths, highlight the advantages offered by the latter
configuration.
Chapter 4 describes the effect of end-core flux on the performance of the switched
reluctance motor. The chapter begins with a description of three-dimensional
effects in the switched reluctance motor. The superiority of three-dimensional
modelling is asserted by comparing test results from the 150W 4-phase motor with
two-dimensional and three-dimensional finite element modelling results. Correction
charts are set up to account for end-core flux at a range of rotor positions and
excitations, to alleviate the need for three-dimensional modelling of the switched
reluctance motor. An extensive discussion into three-dimensional modelling of
anisotropic material structures is also given. In addition, a useful description of the
effect of end-core flux on instantaneous static torque production is presented.
The following chapter describes the work that was undertaken in this project to
develop SRDESIGN; a program written in Turbo Pascal for dynamic simulation
of switched reluctance drives. The principal mathematical formulations
incorporated in the program are described.
The accuracy of the dynamic simulation program is verified in chapter 6, where
simulated data from the 150W 4-phase and 4kW 7-phase motors is compared with
experimental results.
Chapter 7 describes the design, construction and testing of the 5-phase switched
reluctance drive. Finite element analysis is used to compare the static performance
of the 5-phase motor with that of a 4-phase machine (based on the Oulton motor).
Test results from the 5-phase prototype are compared with simulated data obtained
using SRDESIGN. The performance of the 5-phase motor is compared to that of
a 'standard' and 'high efficiency' induction motor of the same frame size.
The main conclusions of the work are highlighted in chapter 8. The author's
contribution to knowledge is described and areas of future work are proposed.
The list of references is followed by appendices containing mathematical
derivations and power device data sheets. 'Members' of the stepping motor family
are also reviewed and a brief description of operation of the induction motor is
given.
Chapter 1
THE SWITCHED RELUCTANCE DRIVE:
AN OVERVIEW
1.1 Historical background to the reluctance motor.
The operation of the switched reluctance motor relies on the 'alignment principle'
which gives rise to reluctance torque. When a salient pole rotor is turned from the
position of alignment with the excited phase of a salient pole stator, a torque
tending to realign the members will be developed. The phenomenon has been
known ever since the first experiments on electromagnetism. In the first half of
the 19th century, scientists all over the world were experimenting with this effect
in order to produce an electromechanical energy conversion device. Their early
designs were named 'electromagnetic engines'. In a book [1] published in 1859,
H. M. Noad describes much of this early development work. Some of the early
designs which he describes show remarkable similarity to the switched reluctance
motor of today.
In 1838, W. H. Taylor obtained a patent for his electromagnetic engine in the
United States and subsequently, on the 2' of May 1840, he was granted a patent
[2] in England for the same engine. The structure was composed of a wooden
wheel, on the surface of which were mounted seven pieces of soft iron, called
armatures, equally spaced around the periphery. The wheel rotated within a
suitable framework in which four electromagnets were mounted. The soft iron
pieces could pass over each electromagnet in turn without touching it. In his
description of the engine, Taylor said that "the magnets must also be so fixed in
the framework that when the centre of one of them is opposite the centre of an
armature, another magnet shall have one of its edges just opposite the edge of an
armature, and the third its contrary edge opposite a contrary edge of another
1
armature and the fourth magnet directly in the centre between the two". This
arrangement ensured that there was always at least one of the electromagnets
capable of producing torque irrespective of the direction of rotation. It is for the
same reason that today's reluctance motors have different numbers of rotor and
stator poles. Taylor's wheel had a mechanical commutator which magnetised an
electromagnet until a soft iron pole piece was brought into alignment and then
demagnetised that electromagnet when its "attractive power" ceased to "operate
with advantage". A lever arrangement on the commutator allowed the turn-on
angle of the electromagnets to be altered so that the engine could be stopped and
reversed. Taylor also pointed out that current needs only to flow through the
electromagnet in one direction, making the connection to the power source a
simpler task. A detailed account of this engine was given in the Mechanics
Magazine [3] in 1840. This resulted in many other scientists describing similar
work which they had completed.
One such person was Robert Davidson of Aberdeen who wrote to the editor of
Mechanics Magazine [4] claiming priority over Taylor's invention, as he had built
a very similar machine himself. Davidson pursued his ideas further and in
September 1842 successfully powered an electric locomotive on the Edinburgh to
Glasgow Railway [5,6], using a six-step reluctance motor. The motor comprised
of two electromagnets, mounted 180 mechanical degrees apart in space, as shown
in fig. 1.1. Between them was a wooden rotor on which three equally spaced
rectangular bars of iron were fixed. Switching between the two electromagnets
was being synchronised to appropriate rotor angles by a commutator. The
commutator consisted of a disk, divided into twice as many parts as there were
armatures, each part being alternately copper or some non-conducting material.
The disk was mounted on the motor shaft and revolved at the rotor speed. One
end of the winding on each 'stator pole' was connected to the negative battery
terminal. The other "extremity" of each winding made contact with the rotating
disk. The disk also made contact with a wire feeding into the positive battery
terminal.
2
One problem faced by all the early inventors was the size of the batteries which
were required to power their machines. Another major problem was likely to have
been heating losses in the iron which was not laminated. In addition, the
unbalanced nature of the magnetic forces required very rigid construction or very
large air gaps in order to avoid contact between the stationary and moving parts.
Fig. 1.1. Principle of Davidson's six—step reluctance motor.
The latter solution led to unnecessarily high copper losses. Davidson's locomotive
reached a disappointing 4 mph over a distance of 1.5 miles. Current in the motor
windings fell off with time due to lack of proper cooling arrangements. Other
electromagnetic engines with similarities to reluctance motors were constructed by
Bain, Wheatstone and Henley [1]. However these motors all suffered from torque
pulsations and were soon superseded by the invention of the dc machine.
1.2 A present day switched reluctance drive.
One hundred and twenty years after these early experiments, the switched
reluctance motor began to realize its full potential. The modern era of power
electronics and computer-aided design brought the switched reluctance motor into
the variable speed drive market [7,8]. The simple brushless structure of the motor
3
makes it very reliable in operation and keeps construction costs at bay. High
permeability-low loss materials and rigid construction, which allows a small air gap
between the stationary and rotating members, have increased the motor efficiency.
The unipolar power converter which has replaced the mechanical commutator is
reliable and robust.
A block diagram of a typical switched reluctance drive is shown in fig. 1.2.
Unlike induction motors or dc motors the switched reluctance motor cannot run
directly from an ac or de supply. The flux in the switched reluctance motor is not
constant, but must be established from zero every working step. A power
converter circuit must supply unipolar current pulses, timed accurately to coincide
with the rising inductance period of each phase winding. It is therefore
advantageous to feed rotor position information from a shaft mounted sensor back
to the control board. The power converter must also regulate the magnitude of the
current, to meet the (torque and speed) demand placed on the drive by the load.
A phase current measuring device and current regulator should therefore be present.
USER
CONTROL
CONTROL
CIRCUITS
UNIPOLAR
POWER
CONVERTER
CURRENT
MEASUREMENT
POSITION
SENSOR
SR MOTOR
Fig. 1.2. Block diagram of a switched reluctance drive.
4.
The major parts of the switched reluctance drive shall be described in more detail
in subsequent sections of this chapter.
1.3 The switched reluctance motor.
The switched reluctance motor has a salient pole stator with concentrated excitation
windings and a salient pole rotor with no conductors or permanent magnets. A
plan view of a typical 4-phase switched reluctance motor is shown in fig. 1.3. The
4-phase motor has eight stator poles and six rotor poles. A coil is wound around
Fig. 1.3. Plan of the laminations of a typical 4—phase motor.
each stator pole and is connected, usually in series, with the coil on the
diametrically opposite stator pole to form a phase winding; e.g. coils 1 and 1' form
phase Pl. The reluctance of the flux path between the two diametrically opposite
5
stator poles varies as a pair of rotor poles rotates into and out of alignment. Since
inductance is inversely proportional to reluctance, the inductance of a phase
winding is a maximum when the rotor is in the aligned position, and a minimum
when the rotor is in the unaligned position. In fig. 1.3 the position of the rotor is
such that two rotor teeth are aligned with the stator teeth of phase Pl. This is the
position of minimum reluctance and hence maximum inductance. The stator teeth
of phase P3 are shown to be facing the rotor interpolar air slots. This is the
position of maximum reluctance (minimum inductance) in phase P3.
The equivalent circuit of a switched reluctance motor phase winding (neglecting
mutual interaction with other phases) comprises the winding resistance, R, and the
variable winding inductance, L, as shown in fig. 1.4a. The winding inductance, L,
varies not only with rotor position, 0, but also with current, i. This is because the
magnetic circuit becomes substantially saturated when the phase current, i, is high
and there is significant overlap between the excited stator poles and the associated
rotor pole pair. The equivalent circuit satisfies Faraday's voltage law,
dt
where the flux linkage, X, is given by
X, = L(0,i)i
(1.2)
Typical phase current and flux linkage waveforms are shown in fig. 1.4b. A pulse
of positive torque is produced if current flows in a phase winding as the inductance
of that phase winding is increasing. The 'lines of force' acting on the structure
behave like stretched elastic bands and attempt to pull the members into alignment.
In the aligned position the magnetic forces will tend to close the air gap by pulling
opposite members together. The stator is, under such conditions, subjected to
compressive forces while the rotor is under tension. A negative torque contribution
is avoided if the current is reduced to zero before the inductance starts to decrease
again. Rotation is maintained by switching on and off the current in the stator
phase windings in synchronism with the rotor position. The rotor speed can be
6
L(4,i)
I
Vs
Fig. 1.4a. Equivalent circuit of a switched
reluctance motor phase winding.
aligned
unaligned
Idealised
inductance L
1
if
voltage V
flux linkage A
phase current i
commutation
H
conduction period
I-
Fig. 1.4b. Typical waveforms.
7
varied by changing the frequency of the current pulses.
Switched reluctance motors can operate with any number of phase windings;
however there are some guidelines governing the choice of stator and rotor pole
numbers [7,8] and therefore phase windings. To ensure starting torque in either
direction there should be at least three stator phases. Additionally there should be
different numbers of stator and rotor pole pairs. Usually there is one more stator
pole pair than rotor pole pairs, though many other combinations are possible. Both
the stator and rotor should be made of laminated steel to reduce the iron losses in
the motor. The number of stator and rotor poles has a significant influence on the
performance of the switched reluctance motor, and a choice must be made with the
particular application in perspective. Low torque ripple may be achieved by
increasing the number of stator and rotor teeth. As a penalty, the higher switching
frequencies 'fluxing' this structure would incur excessive eddy current losses at
very high speeds. It is for this reason that low cost, single phase switched
reluctance machines have been developed [9] and successfully operated at speeds
up to 20,000rpm. In addition, configurations that encourage short flux paths within
the switched reluctance motor have been reported [10], reducing losses overall
while retaining low torque ripple capability.
The absence of permanent magnets or coils on the rotor means that there are no
excitationl forces acting on the structure. Torque is produced purely due to the
variation of reluctance in the magnetic flux path, introduced by the saliency of the
rotor laminations. The direction of the reluctance torque is irrespective of the
direction of the B-field through the rotor, and hence the direction of current in the
stator phase windings is not important. The need for unipolar phase current in the
switched reluctance motor results in simpler and more reliable power converter
circuits.
1 Excitation forces are induced when a permanent magnet or wound rotor is present in a stator
roduced magnetic field.
8
1.4 Existing power converter circuits for the
switched reluctance drive.
The purpose of the power converter circuit is to provide some means of increasing
and decreasing the supply of current to the phase windings. Many different power
converter circuits have been proposed for the switched reluctance motor. The
circuits which have been proposed, tested and most widely used shall be described
and the advantages and disadvantages of each highlighted.
1.4.1 Power converter with bifilar motor windings.
Much of the early research work on switched reluctance drives concentrated on the
development of power converter circuits for motors with bifilar windings [11,12].
The single motor winding is replaced by two closely coupled bifilar windings. One
of these windings is connected to a single switching device and the other to a
freewheeling diode as shown in fig. 1.5. When the switching device is turned on,
current builds up in the main winding. The voltage across the secondary winding
reverse biases the diode. When the switch turns off, current flow transfers to the
secondary winding. A potential difference dV above the applied voltage V
required to forward bias the diode and allow stored magnetic energy to flow back
into the supply. Depending on the degree of coupling between the two windings
and their turns ratio, the voltage across the main switching device may rise to over
twice the supply voltage at the instant of turn-off. The switching device must be
rated to withstand this.
Although this power converter utilises only one switch per phase, the voltage rating
of that device must be at least twice the rating of the motor windings. A second
disadvantage of this power converter lies in the inefficient use of the copper in the
motor since only one of the bifilar windings in each pair can carry current at any
time.
9
+Vs
•
••••
bifilar
windings
41111.
••••
••••
•
0
Fig. 1.5. Power converter with bifilar motor windings.
+Vs/2
Db
P2
riMP—•
P1
•—rinni"
a(
Cs
—Vs/2 o
T
Sb
•
Fig. 1.6. Power converter with split dc power supply.
10
1.4.2 Power converter with split dc supply.
One of the simplest power converter circuits suitable for controlling the unipolar
phase current in a switched reluctance motor uses a split dc supply [13,14]. Figure
1.6 shows the simplest form of this power converter. Two phase windings are
connected to the central tap point of a bipolar dc supply. The other ends of the
two phase windings are each connected to a switching device and associated
freewheeling diode. The switching device and diode associated with each phase
winding are connected in opposite positions to ensure that there isno power flow
imbalance between the two supply capacitors. This arrangement means that this
power converter circuit is only suitable for motors which have an even number of
phases.
This power converter requires only one switching device and associated
freewheeling diode per phase. Each switch and diode must be rated to withstand
the complete supply voltage plus any transient voltages due to the switching.
However only half this voltage can appear across the motor winding in the positive
or negative direction. The available supply voltage is therefore under-utilised.
1.4.3 Capacitor dump power converter.
This power converter, shown in fig. 1.7, has been proposed [15] in an attempt to
minimise the number of switching devices per phase, while ensuring that the
switches do not have to be rated much in excess of the motor voltage rating. Each
phase has a main switch (Sa, Sb and Sc) which can be turned on to increase the
current in the respective phase winding. When the switch is turned off, the stored
energy in the phase winding is transferred to the dump capacitor C. A buck
chopper circuit is used to return energy from the dump capacitor to the supply.
However the mean capacitor voltage must be maintained well above the supply rail
in order to rapidly reduce the phase current to zero after commutation. The main
switches and freewheeling diodes must therefore be rated in excess of the motor
voltage. The low reverse voltage dV impressed across the phase winding upon
11
Fig. 1.7. Capacitor dump power converter.
Fig. 1.8. Power converter with asymmetric half—bridge.
12
commutation may limit the drive performance, especially at high speeds. The
chopper circuit adds to the C-dump converter component count; however this is not
as high as the component count of the asymmetric half-bridge power converter
which is described below.
1.4.4 Power converter with the asymmetric half-bridge.
Some papers [16,17] have proposed using the asymmetric half-bridge as the power
converter for the switched reluctance drive. The asymmetric half-bridge is shown
in fig. 1.8 connected to one phase winding of a switched reluctance motor. One
switching device, Sa, connects the positive supply rail to one end of the phase
winding. This switch is called the upper or floating switch since the drive circuit
for such a switch must be isolated from the lower supply rail. The second
switching device, Sb, connects the other end of the phase winding to the lower
supply rail and is referred to as the lower switching device. The inductive nature
of the motor phase windings means that the asymmetric half-bridge must also
incorporate a freewheeling diode for each switching device. Each diode provides
a path for freewheeling motor current when the associated switching device is
turned off. The switches and diodes must be rated to withstand the supply voltage
plus any switching transients. The motor windings are rated at the supply voltage.
This circuit therefore allows the motor to be rated close to the maximum switch
voltage. This is important where the dc supply voltage or the available switch
voltage may be limited.
The asymmetric half-bridge has three main modes of operation. The first, a
positive volt loop, occurs when both switching devices, Sa and Sb, are turned on.
The supply voltage is connected across the phase winding and the current in the
phase winding increases rapidly, supplying energy to the motor. The second mode
of operation is a zero volt loop. This occurs if either of the two switching devices
are turned off while current is flowing in the phase winding. In this case the
current continues to flow through one switching device and one diode. Energy is
neither taken from nor returned to the dc supply. The voltage across the phase
13
winding during this time is equal to the sum of the saturation voltages of the two
semiconductor devices. This voltage is very small compared to the supply voltage
and so the current in the phase winding decays very slowly. The final mode of
operation is a negative volt loop. Both the switching devices are turned off. The
current is forced to flow through both the freewheeling diodes. The current in the
phase winding decreases rapidly as energy is returned from the motor to the
supply. The asymmetric half-bridge thus offers three very flexible modes for
current control. The zero volt loop is very important in minimising the current
ripple at any given switching frequency. The zero volt loop also tends to reduce
the power flow to and from the motor during chopping by providing a path for
motor current to flow without either taking energy from or returning it to the
supply capacitors.
The major advantage with this circuit is that all the available supply voltage can
be used to control the current in the phase windings. As each phase winding is
connected to its own asymmetric half-bridge there is no restriction on the number
of phase windings. However as there are two switches per phase winding it is best
suited to motors with few phase windings.
1.4.5 Shared switch, asymmetric half-bridge power converter.
A family of power converter circuits has been developed [18] which are based on
the asymmetric half-bridge, but use less than two switches per phase. A section
from the simplest form of the power converter circuit is shown in fig. 1.9. Two
phase windings are connected to three switching devices. The central switch in the
diagram, Sb, is connected to two phase windings and must therefore be rated to
withstand at least twice the motor phase current. The operation of this switch
affects the flow of current in either of the two phase windings to which it is
connected. This imposes a restriction on the operation of the circuit as a positive
volt loop in one phase cannot be accompanied by a negative volt loop in the
adjoining phase. By carefully selecting the phase windings which are connected
to the same switch it is possible to ensure that this restriction does not impose a
14-
severe limitation on the operation of the drive.
Fig. 1.9. Shared switch, asymmetric half—bridge converter.
The switching steps involved in the excitation of phase windings P1 and P2 are
shown in Table 1.1. Current i, can be built up in a positive volt loop by
simultaneously switching devices Sa and Sb on. When current i1 reaches a
predetermined level, /fli, it can be maintained constant by chopping switch Sb at
high (-201(1-1z) frequency. The duty cycle of the pwm voltage waveform is
dependent on the magnitude of I.. In order to subsequently increase the current
i2 in a positive volt loop, devices Sb and Sc must be switched on. Therefore the
chopping operation of i1 is transferred to Sa. Current i2 can be maintained at a
constant level 4, by chopping switch Sc. During this period the top switching
device Sb is carrying the sum of the currents i1 and i2, i.e. 24 and must be rated
accordingly.
It is possible to subsequently decrease the current in P1 while maintaining the level
of i2, by switching device Sa off and interchanging the functions of Sb and Sc. At
this time, phase winding P1 is impressed with an average negative voltage, Keg,
where
15
- Vc(1.3)
Keg =
The term vc denotes the average voltage that is impressed across phase winding P2
during chopping, and is dependent on the magnitude of i2 and the back-emf seen
by P2.
ii
12
Sa
Sb
Sc
incr
zero
on
on
off
hold
zero
on
chop
off
hold
incr
chop
on
on
hold
hold
chop
on
chop
decr
hold
off
chop
on
Table 1.1 Shared switch converter switching algorithm.
1.5 Rotor position measurement techniques.
For motoring operation the phase current pulses must be carefully timed to
coincide with the rising inductance period of each phase winding. This means that
the controller requires information on the position of the rotor relative to the stator
phases. Depending on the performance required and speed of operation various
techniques may be suitable [19]. A selection of rotor position measurement
techniques shall be presented in this section.
1.5.1 Slotted disk arrangements.
One of the most common techniques is to use a slotted disk, driven by the motor
shaft, in conjunction with optoelectronic devices. The optoelectrOnic devices are
fixed, with the optical transmitter on one side of the disk and the receiver on the
16
other side. As the disk rotates, a tooth or a slot is between the optotransmitter and
the receiver arrangement, hence producing an on / off signal. The resolution of
such a system is dependent on the number of optical devices used.
The optoelectronic devices may be replaced by RF transducers in dusty
environments. As an aluminium tooth reaches an RF transducer, eddy currents are
induced which alter the transducer coil inductance. The coil is fed with a high
frequency ac waveform so as to amplify eddy current effects.
Alternatively, a permanent magnet rotating element may be employed which is
attached to the shaft. The rotating magnetic field can then be sensed using search
coils or Hall effect transducers. The Hall effect transducers must be used if
information about the stationary position is required. This information is usually
necessary for the switched reluctance drive to determine which phase to excite at
start up. Slotted disk arrangements are cost effective and robust and need only be
as complicated as the system demands.
1.5.2 Optical shaft encoders.
Optical shaft encoders may be purchased as a complete unit. Incremental encoders
consist of a disk divided into (fine) alternate opaque and transparent sectors. The
disk is mounted on the shaft and a single light source / detector arrangement is
used as the sensing device. The disadvantage of this arrangement is that the
angular information is stored in an external counter. If the information in the
counter is lost, the angular position cannot be extracted. Furthermore, at start up
the disk must be rotated through one revolution marker to determine the shaft
angle. These problems are overcome by the use of absolute encoders. The
absolute encoder disk is radially divided into N sectors, each sector also being
divided up along its length into opaque and transparent sectors. This arrangement
forms a digital word of maximum count 21' representing rotor position. Encoders
constitute a more expensive option than a few discrete optical devices but provide
more accurate position information if it is required.
17
1.5.3 Brushless resolvers.
Very fine position information can be provided by the combination of a brushless
resolver and resolver to digital converter [20]. The simplest form of resolver has
a rotating member with a single phase winding and a stationary member with two
windings at 90° to each other. The resolver and resolver to digital converter
arrangement exploits the sinusoidal relationship between the shaft angle and output
voltage to produce a (typically) 12 bit digital word representing the angular
position. Such systems are costly and are therefore only suitable for very high
performance drives.
1.5.4 Sensorless position detection.
It is possible to derive rotor position information from the phase windings of the
motor. In one sensorless position detection method a 'mini' high frequency square
wave voltage is applied to an unexcited phase [21-24]. The resulting current pulse
magnitude increases as the phase inductance decreases to reach a minimum at the
unaligned position. A threshold current level may be set which relates to a
particular rotor position and upon detection a particular phase winding may be
excited or commutated. Such readings may however be affected by mutual
coupling effects between phase windings. Alternatively, it is possible to monitor
the current in the (active) phase winding during chopping to determine the rotor
position from the rate of change of current [21]. This however implies that the
range for which position detection is possible is restricted to low speeds else the
motor back-emf will affect accuracy. Sensorless position detection is an ongoing
research area which exploits the recent advances in digital signal processing.
1.6 Phase current measurement and control.
Current pulses must be applied in a phase winding of the switched reluctance
motor when a pair of rotor poles is approaching alignment. The timing, duration
18
and magnitude of the current pulses determine the torque output and machine
efficiency. However, the nonlinear relationship between torque, current and rotor
position presents complications in feedback control systems for the switched
reluctance drive. Several control models have been proposed for the drive [25,26],
though some simplification of the nonlinear characteristics is usually made.
Programmable gate arrays offer increased potential in this area, allowing a large
amount of logic circuitry to be implemented in a single device. The flexibility of
user programming reduces the risks involved in changing a circuit design. More
complex control may be required for high-power switched reluctance drives,
particularly where a wide speed range is required at constant power, and
microprocessor controllers have been developed and used to this effect [27,28].
At low speeds, the back-emf is small and the current must be limited with the aid
of either a 'hysteresis type' current chopping regulator or a fixed frequency pwm
current regulator. A Hall effect current transducer can be used to measure the
phase current in the switched reluctance motor. Hall effect transducers can be
multiplexed between several phase windings. These transducers are relatively
expensive and therefore not suitable for small, low cost drives. Recently,
MOSFETs, called SENSEFETs, have become available, in which part of the silicon
substrate is used to measure the current. These devices, successfully employed in
switched reluctance drives [21], offer the possibility of switches modulating the
current flowing through them.
The base speed, cob, is the highest speed at which maximum current can be supplied
at rated voltage with fixed firing angles. If these angles are kept fixed beyond cob,
the maximum torque at rated voltage decreases significantly. However, if the
conduction angle is increased by advancing the turn-on angle, maximum current
can still be forced in the motor windings. This sustains the torque level high
enough to maintain a constant power characteristic over a considerable speed range.
19
1.7 Market applications of the switched reluctance
drive.
The switched reluctance drive offers many advantages over competing drives. The
structure of the motor is simple, robust and hence very reliable in operation.
Manufacturing costs are also kept at bay. Starting torque can be very high and,
under running conditions, the bulk of the losses occur on the stator where they can
readily be dissipated. The motor is, in addition, very competitive on power /
weight and power / cost ratios.
The requirement for unipolar phase current means that the SRM can employ simple
power converter circuits. These power converters do not exhibit shoot-through
problems and therefore prove more reliable and easier to protect. The need for
some form of position feedback and current feedback increases circuit complexity
and cost, but once added can offer useful control features such as optimisation of
the developed torque at all operating speeds.
The major disadvantage of the switched reluctance motor is the inherent torque
ripple that is produced by the stepping action of the motor. However, efforts have
been made which illustrate the potential of the motor to produce low torque ripple.
One technique requires the precise wave-shaping of phase current, which must be
stored in electronic memory and subsequently forced in the phase winding [8]. It
has been shown [29] that neural networks are capable of learning the current
profiles required to minimise torque ripple. In a treatment of multi-tooth per pole
structures Wallace and Taylor [30] demonstrated how maximum torque and
minimum torque ripple can be achieved by the same motor design.
High levels of acoustic noise are also caused by the pulsed nature of torque
production, though research at the University of Warwick [31] has shown that the
problem can be reduced by 'clever switching'. The new active control technique
employs two complimentary effects to minimise stator vibration. Firstly, the
20
magnitude of any step change in the voltage is minimised, particularly at turn-off.
Secondly, at commutation, if the voltage across the phase winding is decreased in
two successive steps, with the second occurring half a resonant cycle after the first,
the resulting vibrations will be out of phase and therefore cancel.
Many applications for switched reluctance drives have been considered. These
range from traction [32,33] and battery powered vehicles [34] to small drives for
domestic appliances [17]. High performance drives have also been constructed for
servo drive applications [35] and spindle drives [16]. These papers all show that
switched reluctance drives are suitable for a range of applications providing the
cost of the power converter and the control electronics can be kept to a minimum.
21
Chapter 2
THE SWITCHED RELUCTANCE DRIVE:
ASPECTS OF DESIGN, CONSTRUCTION
AND TESTING
Some switched reluctance motor design principles shall be described in section 2.1.
Basic considerations aim at justifying the traditional design methodology. At the
same time, shortcomings of existing designs are highlighted. A new switched
reluctance motor design is then presented, which offers significant advantages over
prior art motors.
Section 2.2 of this chapter aims at introducing finite element analysis, the software
tool that was used in this project to model existing motor configurations and design
the proposed switched reluctance motor. The hardware tools employed to test the
constructed switched reluctance prototype and prior art motors are subsequently
described. A detailed account of all experimental procedures is presented.
2.1 Switched reluctance motor design.
The relationship between the fundamental switching frequency and speed is derived
from the fact that, if the poles are wound oppositely in pairs to form the phases,
then each phase produces a pulse of torque on each passing rotor pole. The
fundamental switching frequency in one phase is therefore
f=TIN,
(2.1)
where 11 is the rotational speed in rev/s. If there are q phases, the step angle is
2TE
step = qN
22
(2.2)
The non-uniform nature of torque production leads to torque ripple and contributes
to acoustic noise. The torque ripple can be reduced by increasing Nr, the number
of rotor teeth. However, the resulting increase in the fundamental switching
frequency will induce higher core losses.
It can be shown that peak static torque in multiphase stepping motors can be
obtained when half the phases are simultaneously excited [36], i.e. in a machine
with q phases the static torque is maximised if
phases excited = qI2 for q even
(2.3a)
phases excited = (q±1)/2 for q odd
(2.3b)
The overlap between current pulses of adjacent phase windings leads to smoother
torque production capability.
2.1.1 Low phase numbers.
The simplest switched reluctance motor and power converter is single phase. A
2/2 1-phase motor is practical only if the starting problem can be overcome. In 1phase motors zero torque zones are inevitable and sufficient load inertia must exist
to push the rotor through them. Single phase motors can, however, operate at
extremely high speeds [9] before their performance is limited by excessive eddy
current losses.
Zero torque zones can be minimised with a low cost, 2-phase 4/2 machine. A
primitive form of the 2-phase motor is shown in fig. 2.1. The rotor is shown to
reside in a zero torque position. In theory, an infinitesimal displacement of the
rotor is needed to enter the rising inductance region of phase 1. In practice though,
the torque output is small for several degrees on either side of this point.
Some form of starting assistance or parking mechanism should be present in the
4/2 2-phase motor. A stepped airgap structure [37], shown in fig. 2.2, has been
23
Fig. 2.2. The 2—phase 4/2 motor with a stepped gap [37],
showing self—starting capability.
24-
suggested for this purpose. The authors of reference [37] suggested that this
structure extended the region of positive inductance variation, to provide positive
dL I
c/0 for at least one of the phase windings at any rotor position.
The most commonly described forms of switched reluctance motor are those with
stator / rotor pole numbers of 6/4 (3-phase) and 8/6 (4-phase). The 6/4 3-phase
machine has starting torque capability in either forward or reverse direction. The
12/8 3-phase machine (a 6/4 'multiplied' by 2) offers the advantages of shorter end
windings and shorter flux paths which lead to reduced copper and iron losses
respectively.
A 12/10 3-phase structure shown in fig. 2.3, with two teeth per stator pole, was
developed by Harris and Finch [38]. In comparison to the 6/4 3-phase motor, the
authors reported a significant increase in torque per ampere. On the other hand,
the increase in steps / rev resulted in higher core losses. In addition, the stator
pole structure restricted the winding area available. Therefore, the benefits of this
configuration were thought to be restricted to low speeds [39].
Hendershot [40] reported a similar 12/10 3-phase machine, in the form shown in
fig. 2.4, in which the stator had unevenly spaced teeth. The stator teeth were
energised as pairs of adjacent poles having opposite magnetic polarities so as to
create a magnetic circuit between each pole pair. The induced short flux paths
reduced the core losses in the machine. However, the unevenly spaced teeth on
the stator resulted in restrictions in the winding area available. Therefore, the
torque developed by this 3-phase 12/10 motor is expected to be reduced.
The 4-phase 8/6 switched reluctance motor ensures starting torque from any rotor
position and, in addition, delivers smoother torque compared to its 3-phase
counterpart (ref. eqn. 2.3).
25
26
2.1.2 Higher phase numbers - a new motor design.
The use of the shared switch power converter was demonstrated in the control of
a 7-phase switched reluctance motor [41]. It was shown that the efficiency of the
motor was improved considerably by arranging the windings to encourage short
flux paths. Michaelides and Pollock [10] described results of research into
computer-aided modelling of short flux paths. It was demonstrated that the MMF
required to produce the nominal flux linkage level in the excited stator poles was
reduced significantly by configuring the motor for short flux paths.
Figure 2.5 illustrates the flux distribution in a section of a 5-phase switched
reluctance motor. If the phase windings are arranged so that adjacent stator poles
have opposite magnetic polarity, then the B-field associated with any two adjacent
arrows show
magnetic polarity
Fig. 2.5. The proposed machine configuration. A 5—phase
10/8 motor showing short flux—paths both
producing positive torque. Phases 1 and 2
are simultaneously excited.
27
phase windings forms a short magnetic circuit linking the excited stator poles via
the rotor teeth. Short flux paths can only be realised in switched reluctance motors
with an odd number of phases, if a discontinuity in the B-field distribution is to be
avoided. Furthermore, to benefit fully from this technique, there should be
considerable overlap between current pulses in adjacent phase windings. Sufficient
overlap does not occur in the 3-phase motor. Five-phase and 7-phase motors are
therefore thought to be suitable, cost effective configurations. Experimental results,
taken from the 7-phase motor, demonstrated the superior performance offered by
the short flux loop configuration. A 5-phase motor, that would exploit the
advantages of short flux loops in a simpler 'package', is now proposed. The 10/8
structure can ensure improved torque production and lower torque ripple compared
to its 4-phase 8/6 counterpart. Although the fundamental switching frequency is
increased, lower iron losses can be expected from the 10/8 structure because the
motor is excited with short loops.
The stator and rotor poles of the proposed 10/8 and 14/12 structures are
symmetrical about their centre lines and equally spaced around the stator and rotor
periphery. This poses no restriction to winding area or torque output. A detailed
analysis of the 7-phase machine and the design and development of a 5-phase
prototype will be described in subsequent chapters of this thesis.
2.2 Introduction to electromagnetic finite element
analysis.
2.2.1 The need for finite element modelling.
Modem electrical machines must be designed to meet specified operating
conditions that are set by the load demand, while maintaining optimum efficiency
and reliability. In addition, the power / cost and torque / volume ratios must be
maximised. In order to meet these requirements, reliable machine performance
predictions at the design stage must be established. An accurate model of the
28
switched reluctance motor magnetic circuit cannot be constructed using simple
analytical functions or equivalent circuit representations. This is due to the
complexity introduced by the doubly salient structure and the highly nonlinear
relationship between the stator phase current and flux. In recent years, numerical
techniques have been developed that can overcome certain limitations of analytic
methods such as their restriction to linear, steady state problems, and provide
efficient solutions to a wide range of problems. For example, it has been possible
for several years to compute the magnetic forces acting on the members of a
switched reluctance motor, taking into account the three-dimensional geometry and
saturation effects of the material, using the finite element method.
Finite element analysis is the most widely used numerical method for transient and
steady state solutions to two and three-dimensional electromagnetic problems. The
enormous capabilities of this technique are largely due to considerable advances
in computers. This computer-based numerical technique for solving partial
differential equations is implemented by representing the domain of the problem
under consideration by a collection of finite elements. The nodes associated with
each element are the points in space where the field values are calculated.
Governing equations for each element are set up and subsequently combined in
order to describe a global property (variable).
2.2.2 Electromagnetic field equations.
The governing laws of electromagnetism can be concisely expressed by Maxwell's
equations [42]. In differential form, these are
VxE = -
aB
(2.4)
at
VxH = J+
and
29
ap
-7
(2.5)
(2.6)
.D = p
(2.7)
V .B = 0
Maxwell's equations form the basis of two and three-dimensional finite element
programs. When the frequency is low, displacement currents can be neglected.
Equation 2.5 is therefore reduced to
(2.8)
V xH = J
The magnetic flux density, B, is related to magnetic field strength, H, by
B = p,(H - H c)
(2.9)
where p, denotes the material permeability. The magnetic field remanence,
relates only to permanent magnet materials and may therefore be omitted in the
treatment of the switched reluctance motor model. The displacement current D is
related to electric field strength by
D = cE
(2.10)
and the current density, J, is expressed as
J = GE
(2.11)
Throughout this project, the software used for two and three-dimensional
electromagnetic modelling of the switched reluctance machine was supplied by
Vector Fields Ltd. The basic electromagnetic field theory on which the packages
are based [43,44] follows from the laws of electromagnetism and may be found in
Appendix A.
2.2.3. Finite element model creation.
In OPERA-3D the finite element model of a switched reluctance motor is created
by describing the projection of the required three-dimensional geometry onto a
two-dimensional XY plane cross section. The three-dimensional mesh is then
30
formed by extruding the section in the third dimension. The level of discretisation
in the third dimension is dependent on the stack length of the individual model and
the required accuracy.
Boundary conditions can provide a way of reducing the size of the finite element
representation of symmetrical problems. Symmetry considerations reveal that the
three-dimensional finite element model of a typical switched reluctance motor may
be divided into four identical regions by means of two bisecting planes. The first
plane bisects the model parallel to the XY plane, mid-way along the stack length
of the machine. The second, a ZX plane divides the base plane into two
semicircular regions. Only one of these four regions is therefore modelled. A pair
of matching surfaces is identified, namely the ZX and Z(-X) surfaces, where the
potential values have the reverse sign but equal magnitude. These surfaces are
assigned a negative periodicity boundary condition. This implies that field values
along the Z axis are assigned to zero.
During the early stages of the project only the 3D software was available.
However, a two-dimensional model of the switched reluctance machine could be
constructed in OPERA-3D / TOSCA. This consists of a single element slice
through the machine. The conductors are defined as long parallel bars intersecting
the mesh at right angles. The symmetry boundary condition is specified on the ZX
and Z(-X) surfaces. The faces of the slice have the Neumann (default) boundary
condition imposed on them i.e.
(2.12)
This is a weak boundary condition setting the direction of the flux to be tangential
at these boundaries. With the tangential flux direction imposed, these boundaries
can be considered as reflection boundaries, with a mirror image of the solution on
either side of the boundary. Hence the slice appears to be one (in the middle) of
a stack of similar slices. This produces the effect of an infinite model in the axial
direction. The setup of a typical two-dimensional and three-dimensional model of
31
a 4-phase switched reluctance motor is illustrated in fig. 2.6a,b respectively.
Two independent finite element meshes are created and subsequently 'stitched',
namely the stator and rotor meshes. The conductors do not form a part of the
finite element mesh. The air regions, in which the conductors resided, are assigned
the reduced scalar potential formulation whereas magnetic volumes are assigned
the total scalar potential formulation. The finite element mesh may be created such
that solutions to the problem at different rotor positions can be obtained by
allowing the rotor to rotate, in steps of one degree, with respect to a fixed stator
position. The appropriate symmetry boundary conditions are then imposed and the
model submitted for analysis. The analysis is completed using the TOSCA
computer algorithm, which is briefly described in Appendix A.
2.2.4 Field values computed using the finite element analysis
packag e.
I. Flux linkage computation.
The flux of B over a surface element dS regarded as a vector, is given by the
product of the component of B normal to the surface, and the area of dS. Hence,
the magnetic flux, c1), over a finite stator pole area, Si,, is
(I) = .fB.dS.
(2.13)
This integral can be readily obtained in OPERA by the use of a POLAr or
CARTesian patch that computes field values over a predetermined surface (capital
letters in the text represent the command that must be typed in). The flux linkage,
X, associated with a phase winding of N turns is defined as
=
32
(2.14)
33
-o
co
<L
LU
0
34
II. Energy considerations.
Poynting's theorem [45] finds its source from the vector identity
(2.15)
V.(ExH) = H.(VxE) - E.(VxH)
Substitution of Maxwell's equations yields
aB
ap
- E.J - E
at
at
V .(ExH) = H
(2.16)
Integrating over a volume, vo, and applying the divergence theorem on the term on
the left hand side of the equation gives
(ExH).dS = f(E.J+ HL
B + E aD )dv
at
V„
at
°
(2.17)
If there were no power sources within the volume considered, then the first integral
on the right of eqn. 2.17 would represent the total Ohmic power dissipated within
the volume. If sources are present within the system, then the result of integrating
over the volume of the source represents the input power into the system. The
second and third terms on the right represent the total power stored in the magnetic
and electric fields. The sum of the terms on the right equals the total power
radiated out of the volume. In the treatment of the magnetostatic switched
reluctance motor model using the finite element analysis package, an ideal 'no
loss' system is considered. The radiation power is therefore assumed to be zero.
The displacement current term is only significant at high frequencies and is
therefore ignored.
The electrical energy, WE, input to the switched reluctance motor system is equal
to the stored magnetic energy, Wm, that is
.dA dvo = TH.dB
The system coenergy, Wc, is defined as
35
(2.18)
Wc. = fB.dH dvo
(2.19)
In linear systems, the stored magnetic energy and coenergy terms are equal, i.e.
1
IH.dB dv o = fB .dH dvo =
IB
.H dvo
(2.20)
v.
In nonlinear systems, such as the switched reluctance machine,
IB.Hdvo = fH.dB dvo +
JB .dH dvo
(2.21)
The energy terms can be readily obtained in OPERA by typing ENERgy.
Electromechanical energy conversion principles may be applied in order to extract
information on the torque production of the machine. It is also useful to note that,
in singly excited systems, the flux linking the stator pole phase winding can be
computed using energy considerations.
III. Instantaneous static torque: the Maxwell stress tensor.
The Maxwell stress tensor is defined as
1
2 (B-By2 -Bf)
1
=—
BBy
BA
BA
li(BBB)
2"
BA
BB
y z
(2.22)
X 4
BA
1-(B2-B2-B2)
2
4 X Y
The diagonal terms in the matrix are equivalent to tensions whilst off diagonal
terms represent shear stresses. The forces acting on the rotor of a switched
reluctance machine, at a particular rotor position and excitation, may be found by
SELEcting the rotor surface and computing the INTEgral of the Maxwell stress
tensor over the selected surface. The resultant torque about a specified pivot point
(centre of shaft) is also computed.
36
Inaccuracies in the calculation of forces using Maxwell stresses occur when the
selected surface is an interface between air and a magnetic body. This is because
finite element analysis results give a poor approximation to reality at a corner of
the body. In order to accurately compute the forces acting on the rotor, it is
advisable to mesh the airgap of a switched reluctance motor with four layers of
eight-node brick elements. The iron structure (rotor) is selected, and subsequently
enclosed by two layers of air elements. This gives the best possible chance of the
integration of forces over the selected surface being accurate [44].
2.3 Construction of power converter circuits.
This section describes the construction of the power converter circuits which were
used for dynamic testing of switched reluctance motors. The power converter
components, i.e. the power switches, power diodes, drive circuits and snubbers,
were selected / constructed in the early part of the project. The same components
were employed in the dynamic testing of different switched reluctance machines,
rated from 150W to over 4kW. Different power converter configurations could be
realised by making the appropriate connections to the power switches and diodes.
2.3.1 Overview of semiconductor devices for power converters.
I. The ideal switch.
Several types of semiconductor power devices, including B.ffs, MOSFETs, GTOs
and IGBTs, can be turned on and off by control signals applied to the control
terminal of the device. These devices are known as controllable switches. No
current flows when the switch is off, and when it is on, current can only flow in
one direction.
The ideal controllable switch has the ability to block arbitrarily -large forward and
reverse voltages with zero current flow when off. Furthermore, it can conduct
37
arbitrarily large current with zero voltage drop when on. An ideal device switches
from on to off or vice-versa instantaneously when triggered and requires negligible
power from the control source in order to be triggered [46].
Semiconductor switches are not ideal, but have certain operational characteristics.
There is a maximum rated voltage which can be applied across their terminals in
the off-state before the devices breakdown. They do not offer zero impedance in
the on-state and hence there is usually a maximum forward current rating to avoid
damage to the semiconductor. Semiconductor switches also have a finite transition
time between states so there are power losses in the device during this time. This
imposes a limit on the operating frequency of the switch.
II. The thyristor.
The thyristor is a semiconductor device which comprises four semiconductor
layers, and operates as a switch having two stable states, on and off. There are
many variants in the thyristor family, two in particular being the most common, the
silicon controlled rectifier (SCR) and the gate turn-off thyristor (GTO). The
thyristor is triggered into the on-state by a short duration gate current pulse,
provided that the device is in its forward blocking state. Once the device begins
to conduct, it is latched on and the gate pulse can be removed. The major
difference between the SCR and the GTO is in their turn-off mechanism. The SCR
can only be turned off by reducing the main current through the device below a
holding current level to allow forward blocking to take place. This commutation
requires additional components to divert the principal current. The GTO however
has a simpler turn-off process which can be initiated by a negative gate current
pulse, reducing the amount of extra circuitry required.
Both these devices are capable of supporting large voltages and carrying large
currents. They are generally the most cost efficient way of switching very large
powers. However they have low switching speeds which limits their operating
frequency to below 51thz. When used for motor control applications, this low
38
switching frequency may produce unacceptable audible harmonics in the motor
windings. The SCR was used in some of the early power converter designs [11],
but the complicated commutation circuitry meant that it was superseded by designs
using the GTO [13,14].
III. The bipolar transistor.
The bipolar transistor is the most widely available power semiconductor device and
is therefore quite competitively priced. It is available in both nn and pnp types,
thus offering flexible circuit design choices. A sufficiently large base current,
dependent on the collector current, results in the device being fully on. The BJT
is a current controlled device, and base current must be continuously supplied to
keep it in the on-state. This requirement, however, adds to the cost of the base
drive circuitry. There is a wide range of device ratings available although, in the
higher power range, better silicon utilisation is offered by the thyristor. Below
10kW bipolar transistors can offer higher switching frequencies than thyristors,
though not quite high enough to put the switching noise into the ultrasonic range.
The on-state voltage of the power transistor is usually in the 1-2V range and hence
conduction power loss is small.
IV. The MOSFET.
The name MOSFET stands for a Metal Oxide Semiconductor Field Effect
Transistor. A power MOSFET has a vertically oriented, four layer structure of
alternating p-type and n-type doping. This switching device requires continuous
application of a gate-to-source voltage, of magnitude higher than the threshold
voltage Vrh, in order to be in the on-state. No gate current flows except during the
transitions from on to off or vice-versa, when the gate capacitance is being charged
or discharged. Upon application of a gate-to-source voltage of appropriate
magnitude, a load current conduction channel is initiated from drain to source.
The MOSFET exhibits very fast switching speeds and can be operated at ultrasonic
39
switching frequencies. However, at higher voltages (>250V) the on-state losses of
this switch exceed those of the BJT. The MOSFET offers poor utilisation of the
silicon area compared to the bipolar transistor and can therefore be more expensive
if the manufacturing volume is low. This can be offset by snubberless operation
and as a result the MOSFET has been used in low power switched reluctance
drives [17].
V. The insulated gate bipolar transistor (IGBT).
This is a relatively new device which combines the low current, gate voltage
control requirement of the MOSFET with the high off-state and low on-state
voltage characteristics of the bipolar transistor. The switching times of this device
are better than those of the bipolar transistor, in particular the turn-on time. IGBTs
have not yet reached their full potential but are a very suitable device for all
switched reluctance drives. Voltage ratings up to 2000V and current ratings of
several hundred amperes are projected. At present, pre-packaged IGBT modules,
in which several devices are connected in parallel to increase the total currentcarrying capability, are manufactured.
2.3.2 Selection of type and rating of the semiconductor devices.
Power MOSFETs were selected to construct the power converter circuit.
MOSFETs simplify the drive circuitry considerably because they are voltage
controlled devices, and offer high switching speeds. They have great ruggedness
due to the absence of the second breakdown mechanism present in bipolar
transistors.
The rating of the power switches was chosen with the feasible power converter
configurations in mind. Two configurations were considered, namely the
asymmetric half-bridge and the shared switch converter [18]. The former
configuration was employed in the proposed 5-phase • drive, as it provided
maximum control flexibility (see chapter 1) and could therefore be used to optimise
the performance of the 5-phase motor. The latter configuration reduced the number
40
of switches required to operate the drive, posed no compromise to the winding area
and could power a motor of any phase number. It was therefore used to control
the current in the circuits of the 7-phase motor. However, the top switches of the
shared switch converter would have to be rated at approximately twice the motor
current. The largest motor that required testing was in excess of 4kW, designed
to operate at 600V and carry a maximum phase current of 15A. All switches
ought to be able to withstand the supply voltage plus any switching transients. The
top switching devices of a shared switch converter ought to carry current in excess
of 30A. SEMIKRON SKM 181F power MOSFETs were therefore selected for the
construction of the power converter circuits. BYT 261 fast recovery power diodes
were also employed in the power converter circuits. The data sheets for these
semiconductor devices may be found in Appendix B.
2.3.3 Gate drive circuits for power MOSFETs.
I. Selection of the gate drive isolating device.
The top switching devices of any power converter configuration must have their
gate drive circuit referenced to the source rather than to the ground. The drive
circuit may be 'floated' with respect to ground by means of a pulse transformer,
an optocoupler or an optical fibre.
When pulse transformers are employed, the control signal may be modulated by
a high frequency (1MHz) oscillator output before being applied to the primary
terminals of a compact HF transformer. The secondary terminals can then be
connected to a full wave rectifier and filter capacitor arrangement. The output
signal is commonly applied to a totem pole amplification stage.
The optocoupler is a semiconductor device consisting of a light emitting diode, an
output transistor and often a built-in schmitt trigger circuit. The "capacitance
between the LED and the base of the receiving transistor within the optocoupler
must be as small as possible. This is to avoid re-triggering of the power MOSFET,
at both turn-on and turn-off, due to the jump in potential between the floating
41
source terminal and the ground of the control board. Electrical shields are
frequently used to reduce this problem. As an alternative fibre-optic cables can be
used, where the LED is kept on the control board and the fibre-optic cable
transmits the signal to the receiving transistor which is placed on the drive circuit
board.
Optocouplers are low cost, compact units which reduce the gate drive component
count and were hence chosen to isolate the MOSFET gate drive. As a
precautionary measure, opto-isolators were employed on both top and bottom
switch drive circuits. The optocouplers that were to be incorporated in the power
MOSFET drive circuits ought to have the following characteristics:
a) High common mode transient immunity (CMR figure). Typically, the MOSFET
is capable of switching 600V within 0.1 IIS though additional protection devices,
such as snubbers, limit the dv I dt rate. The requirement for high CMR was posed
only on the top switch drive.
b) High speed; typically, a propagation delay time of 500ns is tolerated.
Very few optocouplers featured high common mode transient immunity at a high
test voltage. Testing of devices also revealed that the guaranteed CMR figure
drops dramatically when the optocoupler is subjected to a voltage higher than the
test voltage.
II. Gate drive circuit design for a top switch.
The top switch gate drive circuit, shown in fig. 2.7a, was powered from a +15V 5V supply. The -5V rail was incorporated to speed up the gate discharge path at
turn-off. The input on / off signal was isolated from the main control board by the
high speed, TTL compatible HCPL2611 optocoupler. The on / off 5V control
signal on the optocoupler output was fed to a voltage translation stage. A Baker's
clamp [47] circuit diverted excess current from the base of the BC 109 transistor
into the collector, to ensure that the device was not driven hard into saturation.
The Baker's clamp increased the speed of the circuit considerably. A totem pole
amplification stage followed the voltage translation stage. A gate resistor value of
4.2
15V0
100.0AF elec.
0.1/AF eel
5V logic
signal
O
330pF
47OR
E
0.1ALL
E
.-
T
3312F tant
'UT-- . ,
ip
ZTX651
1K
IN4148
470R
220pF Co
(:_
(..)
x
12R
Gate
I1
I •
2K2 IN4118
ZTX751
BC109
Source
..,,31
__Lii 1000
2K2
0.1
5Vo
(N.1
o
Fig. 2.7a. The upper switch drive circuit.
15V a
1000AF elec.
T
33AF tank
O
TiT
i
1
5V logic
signal
1220pF
0.1AF cer.
E
ZTX651
4.7nF
Gate
I-1
I
I-0
680R
12R
HCPL2200
I
820R
• E
ZTX751
Source
Li
0.1/2F1
I
1000 F
—1/4-1-
68r
OV
=
•
—5V 0
Fig. 2.7b. The lower switch drive circuit.
,..
43
•
o
12C2 was chosen, to damp out oscillations in the circuit while maintaining an
acceptable switching speed.
The modes of operation of the circuit are given below:
0"On-state": The optocoupler output is low and the BC109 transistor is switched
off. The ZTX651 npn transistor is switched on, base current being provided
through the totem pole 11(0 base resistor. Taking into account the voltage drop
across the 1211 gate resistor and the collector-emitter junction of the ZTX651, the
gate is charged to approximately 14V.
b)"Off-state": The optocoupler output is high and the BC 109 transistor is switched
on. The collector-emitter junction of the BC109 may be regarded to be shorted,
i.e. the transistor acts as a closed switch. The ZTX751 pnp transistor is switched
on, discharging the gate capacitance.
III. Bottom switch gate drive circuit design.
The bottom switch gate drive circuit, shown in fig. 2.7b, was powered from a
+15V -5V supply. The input on / off signal was isolated from the main control
board by the high speed, CMOS compatible HCPL2200 optocoupler. CMOS
compatibility removes the need for a voltage translation stage. The optocoupler
output was fed to a totem pole amplification stage. The signal was then applied
between the gate and source terminals of the MOSFET.
2.3.4 Snubber circuits.
Snubber circuits are employed in order to reduce transistor switching stresses and
losses by improving their switching trajectories. There are three basic types of
snubbers:
a) Turn-off snubbers
b) Overvoltage snubbers
c) Turn-on snubbers
The goal of a turn-off snubber is to provide a zero voltage across the transistor
44-
while the current in the device reduces to zero. Overvoltage snubbers are
employed to minimise overvoltages at turn-off caused by stray inductances in the
circuit. Turn-on snubbers are used to reduce turn-on losses at high switching
frequencies.
Compact Rs-Cs snubber units were employed to reduce the turn-off switching losses
and protect the power MOSFET from excessive
dv I dt
rates and overvoltages. A
complete turn-off snubber circuit is shown in fig. 2.8. As the switch opens, current
is diverted into the initially uncharged snubber capacitor which limits the value as
well as the rate of rise of the switch voltage. This allows the drain current to
reduce significantly, before the voltage across the device rises to an appreciable
level. Switching losses are therefore reduced. At turn-on, the snubber capacitor
discharges through a closed switch. The discharge current is limited by the
snubber resistor, connected in series with the snubber capacitor. The energy stored
in the snubber capacitor is dissipated as heat in the snubber resistor. Therefore, no
additional energy dissipation due to the snubber occurs in the transistor.
45
The presence of the snubber resistor is detrimental at turn-off; unnecessary heating
losses are incurred though the resistor provides good damping. The energy
associated with stray inductances in the circuit is absorbed in the
Rs.-C,
network,
thereby containing the voltage overshoot to a safe level and guarding against
excessive dv I dt rates. If desired, the snubber resistor may be shunted by a diode.
Snubber circuits reduce power losses in the switching device. However, snubber
losses are incurred at turn-on as the capacitor stored energy is dissipated as heat
through the snubber resistor. It is therefore important to select appropriate values
for the snubber resistor and capacitor so that the snubber reduces switching losses
and stresses considerably but does not cause excessive heating losses. A simple
mathematical model was developed and incorporated into a Turbo PASCAL
program to simulate the response of the system at turn-off. Theoretical predictions
were supported by laboratory work. At turn-off, it was found that the drain voltage
rise time is very much dependent on the capacitance of C. For a given load and
current the larger the snubber capacitor, the slower the drain voltage rises. Large
valued resistors provide good damping in the system though the smaller the
snubber resistor, the slower the drain voltage rises. Experimental work also
suggested that the transistor current fall time at turn-off, and the drain voltage fall
time at turn-on are dictated primarily by the characteristics of the switching device.
The values of the capacitance and resistance of the turn-off snubber that was
selected are given below:
= 0.0047f polypropylene. Polypropylene capacitors can withstand high
voltage, fast rise time pulses and have an excellent high frequency performance.
Rs =
13.6O. Five 2W carbon film resistors were connected in parallel to provide
a power dissipation capability of 10W.
The fast recovery power diodes were also `snubbered' for protection.
2.4 The control board.
The information extracted from the rotor position sensor and the current measuring
46
devices is fed back to the drive controller. The controller must then produce the
correct switching signals for the power converter to supply timely, magnitude
regulated current pulses to the motor phase windings. The design of a 'clever'
controller can maximise the performance of the drive.
2.4.1 Current sensing and control.
I. Hysteresis type current chopping regulator.
In its basic form, the circuit consists of two amplifier comparator circuits and an
SR bistable, as shown in fig. 2.9. A small percentage perturbation about the
required phase current level is chosen, and the appropriate current limit signals (Cin
and imax) are set. Level imi„ is fed into the inverting input of comparator I, while
level imax forms the input to the non-inverting terminal of comparator II. The
measured current level forms the input to the second terminal of each comparator.
The output signals from the comparators are fed into the SR bistable. The SR
bistable truth table, given in fig. 2.9, reveals how the current is contained within
the prescribed levels.
This circuit is simple and robust. However, having set limits imin and in.,' the
circuit has no control over the chopping frequency. The power switch may
therefore be subjected to excessive switching stresses. For this reason, a fixed
frequency pwm current regulator was preferred. This circuit will now be described
in more detail.
II. Fixed frequency pm current regulator.
An inverting amplifier and potentiometer arrangement was used to set the required
phase winding current, as shown in fig. 2.10. The device was calibrated so that
if
OV
then
req =
OA
cd = -12V
then
„q =
20A
V cd =
4.7
+v.
R2
R3
•
COMPARATOR
R4
Out
C
Condition
SR out
'In >i min,
;in > i max
OFF
i in > i min .
i in <imax
SAME
< i min,
i in < i max
ON
i in > i min .
iin <i max
SAME
'in
SR
BISTABLE
1min
R59
R6
•
0-00 .1=-0
Fig. 2.9. A hysteresis type current chopping regulator.
220K
PHASE 1 47K FIOK
• 0
1K
074 OpAm
n 10K
10K
010K
1011141-1=1—'
LM311N
10/IF
ex.
47K
MEASURED
SIGNAL
IN
220K
PHASE 2 47K
•
0
10K
10K
10K
TRIANGLE
VOLTAGE
GENERATOR
rue_L___w_
<8
c
100nFI.10K
—15V
074
OpAm
§
47K
Z2(5.6V) Irk
Z2(5.6V)y
CURRENT
DEMAND
SETTING
Fig. 2.10. The constructed fixed frequency pwm current regulator.
46
where vcd denotes the current demand signal and
i„q
the interpreted phase current
requirement. The current demand signal was fed into the inverting input of an
adder (inverting summing amplifier). Current flowing in the motor phase windings
was sensed by LEM Hall effect transducers. The measured phase current signal
from the LEM module board was also fed to the inverting input of the adder. The
resulting error signal was equal to the difference between the current demand and
the actual current measurement. This was compared to the instantaneous amplitude
of a triangle wave. An operational amplifier comparator, together with an
integrator was used to generate the triangle waveform, shown in fig. 2.10. The
frequency of the triangle wave set the chopping frequency of the power switch, and
could be altered by trimming a variable resistor pot. A TTL on / off signal was
transmitted from the current feedback board to the digital control board. As an
example, if the error signal was OV ( 1p41 = ireq) a square wave of 50% pulse width
would be transmitted. This would indicate that the chopping power switch ought
to be on half the time in order to maintain the present current level.
2.4.2 The implementation of logic functions - XILINX.
Recent breakthroughs in logic architectures have resulted in Application Specific
Integrated Circuits (ASICs) which can be configured by the user [48]. These user
programmable gate arrays offer the logic integration benefits of custom VLSI. The
flexibility of user programming allows easy design changes.
The )(MINX development system consists of three stages namely the design entry,
design implementation and design verification. The design entry software consists
of libraries and netlist interfaces for standard CAE software (e.g. FutureNet). The
programmable gate array libraries allow design entry with standard UL gates and
Boolean equations. The design implementation software converts schematic
netlists and Boolean equations into efficient designs for programmable gate arrays.
The software includes sub-programs to perform gate minimisation, placement and
routing, and interactive circuit editing. The design verification stage may be
performed using simulation software (SILOS) or testing on XILINX demonstration
boards. The XILINX development system was used to implement the control logic
49
in the 5-phase and 7-phase drives.
2.5 Experimental arrangements.
This section describes the experimental arrangement that was employed for static
and dynamic tests on the switched reluctance motors.
2.5.1 Description of the test rigs.
A `dc generator test rig', shown in fig. 2.11, was designed to carry out extensive
testing on integral kW switched reluctance machines. The prime mover was
mounted on the test bed and coupled via a VibroMeter torque transducer to the
Flexible
Couplings
SR MOTOR
Fixture for
static torque
measurement
Speed and
Torque
—
— Transducer
Load Machine
(dc generator)
H
Resistor
Bank
TEST BED
Fig. 2.11. The dc generator test bed.
load machine. The torque transducer measuring shaft was supported by the
transducer housing which was bolted directly to the test bed. Double element
flexible couplings were used to connect the measuring shaft to the test and load
machines. The torque transducer was used in conjunction with the ISC 228 signal
conditioner to measure the rotational speed and average torque produced by the test
machine. The load machine was a separately excited dc generator. A small
resistance-high power load was connected across the terminals of the dc generator
50
armature. As an accessory, a mechanical fixture could be mounted to lock the
rotor of the prime mover. This was useful for static torque and phase winding flux
linkage measurements.
Sub-kW switched reluctance machines were mounted on an 'eddy current test bed'.
The shaft of the test machine was connected to the shaft of the eddy current brake
via a flexible coupling arrangement.
23.2 Flux linkage measurement.
This section describes the experimental procedure that was adopted in order to
measure the flux linking a phase winding of the switched reluctance machine. The
required rotor position was selected with the aid of a position sensor and / or an
LCR meter, and the rotor was clamped using the mechanical fixture arrangement.
The electric circuit arrangement, shown in fig. 2.12, consisted of a power
MOSFET, the source terminal of which was connected to one terminal of the phase
winding undergoing measurement. The other end of the phase winding was
connected to the negative terminal of a dc power supply and decoupling capacitor
arrangement. A freewheeling diode, connected across the motor winding, provided
a path for the current once the main switching device was turned off. The other
phase windings of the switched reluctance motor were left open-circuit.
I. Measurement of rising current.
The switching device was turned on and measurement commenced. A step
increase in voltage across the circuit terminals caused an (approximately)
exponential rise in the phase current waveform, the profile of which was dictated
by the instantaneous value of the time constant
R I Lin„.
The measurement was
terminated once the phase current waveform attained the value experienced by the
motor at full load,
I..
The phase winding voltage and phase current waveforms
were recorded. Faraday's voltage equation, in integral form, was applied in order
to compute the winding flux linkage i.e.
51
i
'on board'
computation
facilities
_n_
gate
circuit
V
1
1-0
c
IMM=MMI
MMillIMIM
MrAMIIMNIII
MIMI" 0 0
Fig. 2.12. Circuit arrangement for flux
linkage measurement.
voltage
source
‘,/
current
source
measurement
phase P1
biased
phase P2
Fig. 2.13. Flux linkage measurement in a biased field.
52
A
v,
fc12 = Tv dt - R fidt
(2.23)
where A denotes the flux linking the phase winding when i(t) reaches I.. The
initial flux linkage value X(0) = 0, as both v(t) and i(t) were zero at t = 0. The two
integrals on the right hand side of eqn. 2.23 were computed using measurement
facilities on-board a Gould digital oscilloscope. An accurate reading of the circuit
resistance, R, was taken using a 4-terminal ohmmeter. Although the circuit
resistance varied with temperature, the effect was minimised by conducting the
experiment on a 'single shot' basis.
II. Measurement of decaying current.
A step voltage was applied to the test winding and, once the phase current attained
a steady-state value, the switching device was turned off. The winding was
disconnected from the voltage source and the profile of the decaying current was
recorded. The measurement was terminated when the phase current was reduced
to zero. Faraday's equation was used to compute the winding flux linkage. At t
= 0, the boundary conditions were specified as v(0) = V, i(0) = I. and A.,(0) = A.
III. Biasing the electromagnetic field.
Switched reluctance motors of 4 and 5 phases operate with two phase windings
simultaneously excited. In order to measure the flux linking phase winding Pl,
while the neighbouring phase P2 is carrying rated current I., the following
procedure was adopted: it was necessary to connect phase P2 across the terminals
of a constant current source and not a voltage source, as shown in fig. 2.13. The
current source ensured that level I. was maintained in phase P2, irrespective of
step changes in the voltage across phase Pl. Therefore P2 was connected across
an asymmetric half-bridge arrangement. A separate high-voltage power supply
powered the bridge and a pwm current regulator, operating at 20kHz, maintained
53
a constant current chopping level of Subsequently the flux linkage in phase P1
was measured as described in section I.
2.5.3 Measurement of static torque.
I. The dc generator test rig.
The required rotor position was selected with the aid of a position sensor, and the
rotor was locked mechanically. The appropriate phase winding(s) was (were)
excited with dc current, and the static torque was obtained from the torque
transducer / signal conditioner arrangement.
II. The eddy current test rig.
No suitable mechanical fixture was provided to lock the rotor of the test machine.
The eddy current brake was decoupled from the prime mover and a pulley-andweights arrangement was mounted on the shaft of the test machine. The
appropriate phase winding(s) was (were) energised and the necessary force was
applied on the pulley in order to keep the rotor in position. The rotor position was
subsequently recorded using a position sensor.
2.5.4 Measurement of dynamic torque.
I. The dc generator test rig.
The level of torque presented to the prime mover was varied by varying either the
field current, i.e. the strength of the magnetic field on the stator of the separately
excited dc generator, or the armature resistance. The power developed was
dissipated, in the form of heat, in a load resistor connected across the armature of
the dc machine.
54
II. The eddy current test rig.
The eddy current brake develops load torque by the interaction of a de magnetic
field, produced by stator winding excitation, and induced eddy currents in a solid
rotor [49]. The power developed is dissipated in the form of heat. The level of
torque presented to the prime mover by the brake was varied by varying the
strength of the magnetic field on the stator. The torque developed in the machine
was transmitted to the stator, which was free to rotate over a limited arc. The
degree of rotation of the stator frame was recorded on a spring- balance. Torque
could therefore be directly measured on a scale. Torque indicating scales could be
changed so as to alter the range of the instrument.
A digital tacho was used to record rotational speed, (0. The shaft power output was
obtained by computing the product of Ta„
CO.
The electrical input power was
measured with a Voltech power analyzer connected across the dc link capacitor.
2.6 Review of fundamental aspects of switched
reluctance motor technology.
This chapter has reviewed the fundamental motor design methodology of previous
researchers. The 'traditional' phase numbers and pole combinations i.e. 3-phase
6/4 or 12/8 and 4-phase 8/6 structures have been described. A new design of
switched reluctance motor has been proposed, in which the windings are arranged
to encourage short magnetic flux paths. It was demonstrated that switched
reluctance motors of five and seven phases can be configured for short flux paths.
This is achieved by arranging the phase windings such that each stator pole has
opposite magnetic polarity to its neighbouring poles, and simultaneously exciting
two adjacent phase windings.
Furthermore, this chapter has illustrated the use of the finite elemdnt method, in the
prediction of phase winding flux linkage and static torque in the switched
55
reluctance motor.
The construction of the power converter and control electronics, that were common
to all the drives tested, has been described. Power MOSFET switching devices
were chosen to provide high switching speeds and simplify gate drive electronics.
Simple Rs-C, snubbers were connected across the MOSFETs to decrease switching
losses and stresses. The design of the opto-isolated gate drivers for the upper and
lower switching devices has been presented.
The control board featured LEM Hall effect current measuring devices. A fixed
frequency pwm current regulator was constructed to provide current magnitude
regulation. Implementation of logic equations was performed in logic cell arrays.
The experimental procedures for static and dynamic testing of switched reluctance
machines has been described. All experimental results that will be presented in
subsequent chapters have been obtained by adopting the procedures described.
56
Chapter 3
ELECTROMAGNETIC ANALYSIS OF THE
SWITCHED RELUCTANCE MOTOR
This chapter focuses on electromechanical energy conversion theory and its
application to the switched reluctance motor. The virtual work principle, as
applied to singly excited electromagnetic systems, is described. The virtual work
principle is frequently used by designers to compute the average torque produced
in a switched reluctance motor. The established modelling procedure works well
for 1, 2 and 3-phase switched reluctance motors (referred to in the thesis as singly
excited motors) where there is no (or little) overlap between phase current pulses.
The chapter introduces a thorough electromagnetic analysis of doubly excited
systems which relates to switched reluctance motors operating with two phases
simultaneously excited [50]. These include the 4-phase 8/6 and 5-phase 10/8
switched reluctance motors. The new modelling procedure that is proposed
includes the effects of mutual coupling and increased flux density present in some
parts of the steel when two phases are excited at any time. The variation of
winding flux linkage with phase current and rotor position is described for such
motors. The accurate electromagnetic modelling proposed forms the basis for
design considerations that can optimise the performance of switched reluctance
motors. The design of 4-phase motors for low torque ripple is described. Finite
element analysis results from a 4kW 7-phase motor configured for long and short
flux paths are also presented. It is shown that short flux loops significantly
improve the torque production capability of the 7-phase machine.
57
3.1 Electromechanical energy conversion theory.
3.1.1 Singly excited systems.
In a lossless electromechanical energy conversion device operating as a motor, an
incremental change in the electrical energy input, dW„ will cause one component
of energy, dWp to be stored in the field and another component, dWmech, to be made
available to the load. The energy balance equation is
(3.1)
dW
e = dW f + dWmeeh
Introducing Faraday's law, dWf may be expressed as
dW =
(3.2)
- T dO
where i denotes the current in a particular phase winding and X its associated flux
linkage; the term T represents (average) torque while d0 denotes angular
displacement. By application of the chain rule the increment in field energy, dWp
can also be expressed in terms of the flux linkage, X, and rotor position, 0, as
aw
aw
dW
=,
dA + ao
e=const
I
X.const
do
(3.3)
Comparison of eqn. 3.2 with eqn. 3.3 reveals that
aw (x 0)
T= -
f
(3.4)
ae
The system coenergy, W, can be defined as
W c = fX(i3O)di
0
(3.5)
The coenergy may be expressed in terms of the stored energy by
Wc =
- Wf(3.6)
Torque, T, is also given by the rate of change of coenergy with respect to the rotor
58
angle, at constant excitation i.e.
T-
aw (i3O)
(3.7)
a0
In order to estimate the average torque produced in the switched reluctance motor,
it is essential to know how the phase winding flux linkage, X, varies with phase
current, i, and rotor position, O. The change in coenergy, AW,, during one
repetitive excitation cycle of duration AO, is equivalent to the area enclosed by the
operating trajectory described on the X / i diagram. The average torque is given
by
Tave = AW, N
(N - Ar)
(3.8)
Figure 3.1 illustrates the laminations of a typical 2-phase switched reluctance motor
with four teeth on the stator and two teeth on the rotor. This machine is operated
by ensuring that one stator phase winding is conducting at any time. Referring to
fig. 3.1 (consider solid lines), the stator teeth of phase P1 face the interpolar airgap
depth. This is known as the 'unaligned' rotor position which marks the beginning
of the excitation cycle. The stator teeth of P2 are aligned with the rotor teeth.
This is known as the 'aligned' rotor position which, in the 2-phase motor, marks
the end of the (repeatable) excitation cycle.
The ideal excitation cycle can be described with the aid of a A. / i diagram, shown
in fig. 3.2. The start of the excitation cycle is marked upon application of full
positive volts across the terminals of phase Pl. In the ideal case the current rises
to its maximum value I. instantaneously. This current level is maintained
throughout the duration of the excitation cycle by means of a current chopping
regulator. The rotor poles rotate to take up a position of minimum reluctance, that
is, to align with the magnetised stator teeth (ref. dashed lines in fig. 3.1). During
this time the phase winding flux linkage rises from A. to A.al. At alignment, after
the rotor has moved by 90 0 , full negative volts are impressed on the terminals of
phase P1 to instantaneously reduce the current to zero. At the same time, full
positive volts are impressed on the terminals of P2 to move the rotor 90° further.
59
Fig. 3.1 A 2—phase 4/2 motor, illustrating
movement through a rotor step.
60
3.1.2 Exciting two phases simultaneously a new modelling
procedure.
I. Flux patterns in the 4-phase motor.
The 4-phase 8/6 switched reluctance motor is fundamentally a doubly excited
system, as two phase windings are carrying current at any time to produce
continuous torque. Fig. 3.3a illustrates the flux pattern arising in the motor if
phase winding P1 is excited. The B-field links the excited stator poles via the
rotor body and stator yoke. The stator yoke carries half the flux linking the excited
stator poles. However, at this rotor position phase P2 is also in the torque
producing region, as shown in fig. 3.3b. The B-fields produced by the two excited
phases cause most parts of the magnetic circuit to be driven at higher flux
densities. In the stator yoke the B-fields oppose each other only in the sections
that lie between adjacent excited poles. In these sections a balancing flux exists,
complementing the resulting B-field flux pattern as shown in fig. 3.3c.
The effective torque zone for each phase of the 4-phase 8/6 motor is 30 0 , as
illustrated in fig. 3.3d. However, the stepping action which results in the B-field
pattern described in fig. 3.3c is repeated every 15°. This is confirmed by the plot
of the ideal phase current pulses in the four phases, shown in fig. 3.3e. The
stepping action will be referred to as the excitation cycle.
II. Computation of coenergy in a doubly excited system.
The energy balance equation that was introduced in section 3.1.1 can be re-written
for a system with two excitation sources as
dWf = iidX,i + i2dA.,2 - Td0
(3.9)
The increment in field energy, dWp can also be expressed in terms of Al, dA,2 and
de as
61
Fig. 3.3a. Flux pattern in a singly excited 4—phase motor.
P1
B—field
cancellation
B—field
associated
with P1
8—field
— — — associated
with P2
B—field
cancellation
Fig. 3.3b. Flux pattern in a doubly excited 4—phase motor.
P1
Resulting
primary B—field
— — — Balancing
B—field
Fig. 3.3c. Resulting primary B—field in a doubly excited
4—phase motor.
62
30'
/tIfi/\
ri
7\14(Sr
turn—off (30') position
turn—on ( 0') position
Phase current conduction period
(Effective torque zone)
30
Fig. 3.3d. Geometrical considerations in a 4—phase motor.
PHASE
P1
P2
P3
P4
4
excitation
cycle
(step)=15'
conduction period= 30'
Fig. 3.3e. Excitation sequence in the 4—phase motor.
63
.1
dW, =
a w
ax,
dX, +
.2 ,u = con
aw
A,,,O=con
dX2 +
aw
a0 I,Ad.2=con de
(3.10)
As a result
T— -awfai,x2,0)
(3.11)
ae
Similar expressions may be derived using the coenergy 147c, where
Wc
(3.12)
X2i2 Wf
The torque, T, is given by the rate of change of coenergy with respect to the rotor
angle, 0,
T = awc(i1,12,8)
(3.13)
ae
In order to obtain the coenergy Wc of a doubly excited system, such as a switched
reluctance motor with two phases simultaneously excited, at a particular rotor
position and winding excitation, the integral idwc must be evaluated in steps, as
illustrated in fig. 3.4. It is assumed that the rotor is turning in an anticlockwise
direction; rotor position P marks the beginning of the conduction cycle in the 4phase machine. At this position phase P2 has been conducting maximum current
1/4, for 15° of rotor rotation and the current in phase P1 now increases from 0 to
It is therefore necessary to first compute the coenergy associated with the
excitation of the leading phase P2, before attempting to calculate the coenergy
associated with the excitation of P1 in the presence of i2p:
1. Step OA; i1 = i2 = 0 and 0 varies from zero to Op:
Now di 1 = di2 = 0 and T = 0 , therefore
A
A
PIK = f(Xidii + X2di2 + TdO) = 0
0
0
2. Step AB; i, = 0, 0 = Op and i2 varies from zero to i2p:
64-
(3.14)
i2p
(3.15)
fdw,
A
3. Step BP; i2 = i2p ,8 =
Op
0
and i1 varies from 0 to i1p:
(3.16)
dWc = fX1BP4il
i
0
Hence
2P
(3.17)
Wc (i 1p' i2p' e p) = fkABdi2
0
fX1BPdil
0
where
AtAB
X1BP =
p)
(3.18)
1 ( i2 = i2p' i l' 0 p )
(3.19)
A.2(ii = 0, i 2,
Equation 3.17 dictates that two separate integrals i.e.
JA,2di2
and fAlciii must be
computed in order to estimate the coenergy at the start of the excitation cycle.
First, the integral of flux linkage in the leading phase (X 2) wrt to current i2 is
calculated, assuming that the trailing phase is carrying no current (i 1 = 0).
Subsequently the integral of flux linkage in the trailing phase (X1 ) is computed wrt
ip assuming that the leading phase is conducting full current (i 2 = i2p). These are
then added together to give the total coenergy associated with the two excited
phases.
The average torque output of the 4-phase machine can be determined by evaluating
the change in the coenergy of the system from position P at the start of the
conduction cycle, to position P' at the end of the cycle, as shown in fig. 3.4. At
position P', the integral fc/147, may be evaluated in steps following any suitable
integration path to obtain
65
i4.1
i2p1
W
(i i 8 ) = .12t, di +
c le 2p" p i1/11131 1
TX
2.1311)i
(3.20)
d1 2
0
0
where
X m,B , = 21. 1 (i2 = 0,
(3.21)
ii3 Op,)
X213 1PI =
(3.22)
At(i i = i lp" i2' ° pi)
'1
leading phase
leading phase
trailing phase
trailing phase
position P'
Fig. 3.4. Integration path in a doubly excited system.
The rotor has moved one complete step between positions P and P' and is now in
the same position relative to phase Pl, as it was to phase P2 at position P.
Examination of equations 3.17 - 3.22 reveals that
66
(3.23)
assuming
Therefore, the change in coenergy over the conduction cycle
is given by
i2pf
14
(3.24)
WC/
WC
= j.k2B /P itii2
0
fklBPdi 1
0
where
2B ,p ,
21.
k
=
lBP =
X2(i 1 = i,p„ i2, Op,)
(3.25)
1 (i2 = i2p' i 1' Op )
(3.26)
Computation of the first integral in eqn. 3.24 yields the X, / i curve at the end of
the excitation cycle ('aligned' characteristic). In order to obtain this integral the
rotor is positioned at P', a bias current i1p . is applied to phase P1 and the flux
linkage of phase winding P2 is integrated for different excitations up to i2 = i2p, =
1/4).
The second integral in eqn. 3.24, which represents the X, / i characteristic at the
start of the cycle, can be obtained in a similar fashion as dictated by eqn. 3.26. In
this doubly excited system the area enclosed by the system / i characteristic that
is defined by these curves is equal to the electrical energy per step that is
converted to mechanical work.
Results obtained from two-dimensional electromagnetic finite element modelling
shall be presented in subsequent sections of this chapter. Two switched reluctance
motors were extensively modelled; a 150W 4-phase machine and a 4kW 7-phase
motor. These motors were available for testing and their dimensions could readily
be obtained. The switched reluctance motor models were created and analysed
using OPERA / TOSCA, as described in chapter 2. The performance of these
motors was characterised by implementation of the electromechanical energy
conversion theory presented in this section.
67
3.2 The 150W 4-phase motor.
The 4-phase switched reluctance motor that was modelled, was constructed as part
of earlier development work in the laboratory. The analysis that follows includes
flux linkage and static torque computations on the 4-phase motor, for a range of
rotor positions and current levels. For comparison purposes the analysis includes
results into modelling of the 4-phase motor with one and two phases excited at the
same time. Magnetic interaction effects between simultaneously excited phase
windings are investigated.
Magnetic interaction effects include mutual coupling between adjacent phase
windings and saturation. Mutual coupling arises when flux generated from current
flowing in one phase winding is linked by an adjacent phase winding. Saturation
must be taken into account since some parts of the magnetic circuit will carry
increased flux when two phases are excited. Magnetic saturation degrades the
performance of the switched reluctance motor. In a saturated 4-phase structure
operating with two phases simultaneously excited, the flux linking a phase winding
at a specified rotor position and excitation would increase if the second phase was
switched off. This is because the stator and rotor yokes would operate at a lower
flux density.
3.2.1 Single phase excitation.
The / i characteristic for one phase of this machine at the aligned and unaligned
positions is shown in fig. 3.5. In comparison to measurement, two-dimensional
model solutions consistently underestimate the flux linkage value. The effect is
particularly noticeable at positions where the excited stator poles face the interpolar
airgap depth. This error can be attributed to end-core flux, which is not accounted
for in two-dimensional modelling. A full analysis of three-dimensional effects in
the switched reluctance motor will be presented in chapter 4.
66
FIG. 3.5 FLUX LINKAGE / CURRENT DIAGRAM (4-PH MOTOR, 1 PH EXCITED)
0.25
Current (A)
FIG. 3.6 FLUX LINKAGE / ROTOR POSITION (4-PH MOTOR, 1 PH EXCITED)
5
unaligned
10
<
15
Rotor Position (deg)
69
20
25
>
30
aligned
The / 0 characteristic for one phase of the 150W, 4-phase motor is illustrated in
fig. 3.6. When the excitation is low, the relationship between flux linkage and
rotor position in the region where the excited stator poles and associated rotor
poles overlap (henceforth referred to as the overlap region) is linear. This is
because, although the reluctance of the magnetic circuit decreases as the rotor poles
reach alignment, the excitation is not high enough to saturate the iron. At high
excitations, the relationship between flux linkage and angular position in the
overlap region may be characterised by a linear followed by a sigmoidal function.
The degree of saturation depends on path reluctance and excitation.
The measured static torque produced by the experimental 4-phase machine, as a
function of rotor position, is illustrated in fig. 3.7. Also shown is the static torque
profile of the machine, predicted by the two-dimensional finite element model, At
a particular rotor position and excitation, static torque was computed by evaluating
the Maxwell stress integral over the rotor surface. Finite element analysis
predictions show good agreement with experiment, though there is a tendency to
underestimate the measured static torque value at early rotor positions (0 = 0°-15°).
This may again be attributed to three-dimensional effects which shall be
investigated in chapter 4.
3.2.2 Simultaneous excitation of two phase windings in the 4phase machine - normal machine operation.
The system X, / i characteristic, drawn by adopting the new field computation
procedure for motors with two phases simultaneously excited, is shown in fig. 3.8.
In order to obtain the characteristic that marks the end of the excitation cycle, the
rotor was positioned such that a pair of rotor poles was aligned with phase P2 (see
position P' in fig. 3,4). The selected bias cunent was then applied to phase P1 and
the flux linking P2 was measured for different excitations up to 10A. The
(unaligned) characteristic that marks the beginning of the excitation cycle was
obtained by applying similar considerations to phases P1 and P2 at rotor position
P. A system X / i diagram was also constructed for a 5A phase current bias.
70
FIG. 3.7 STATIC TORQUE / ROTOR POSITION (4-PH MOTOR, 1 PH EXCITED)
3
*
2.5
0.5
5
10
unaligned
<
20
15
Rotor Position (deg)
25
>
30
aligned
FIG. 3.8 (SYSTEM) FLUX LINKAGE / CURRENT DIAGRAM (4-PH MOTOR, 2 PH EXCITED)
0.25
1
2
3
4
5
Current (A)
71
7
8
10
The variation of flux linkage with rotor position in the doubly excited 4-phase
motor is shown in fig. 3.9. The excitation cycle of a 4-phase switched reluctance
motor spans 15°. In one cycle the rotor poles associated with the leading phase
move from the 15° rotor position to the 30 0 (aligned) position. In the same cycle,
the rotor poles associated with the trailing phase are displaced from the 0°
(unaligned) position to the 15° rotor position, as shown in fig. 3.3d,e. The X, /
profile of both the trailing (0°-15°) and leading (15°-30°) phases is depicted. The
characteristic is similar to that of a typical, singly excited switched reluctance
motor. In the overlap region, from 0 = Obo to 0 = ebo 13, / 2 (where 0„ denotes
the beginning of the overlap), the A, / 0 characteristic follows a linear relationship.
From 0 = O bo
Ds
/ 2 to 8 = ebo P s the profile follows a sigmoidal relationship.
The static torque profile of the 4-phase motor, with two phases conducting
simultaneously, is illustrated in
fig.
3.10. The
TI
0 profile is drawn with respect
to the absolute rotor position, i.e. the unaligned rotor position of the trailing phase.
The characteristic, obtained by evaluating the Maxwell stress integral at discrete
positions, spans one rotor step angle. Average torque can be computed by
averaging the instantaneous static torque values over the step angle.
step
Tave
1
TO)
de
(3.27)
step 0
This is in close agreement with the value obtained by the use of the coenergy
principle as applied to doubly excited systems. A comparison between the
different methods of computing average torque in the 4-phase motor (coenergysingly excited, coenergy-doubly excited and Maxwell stress) is given in Table 3.1.
Table 3.1 suggests that if mutual coupling and saturation effects are neglected,
average torque values calculated by the coenergy method are overestimated.
3.2.3 Bulk saturation effects.
Extensive finite element analysis of doubly excited switched reluctance motors has
revealed a departure from the customary X, / 0 characteristic when the stator and
72
FIG. 3.9 FLUX LINKAGE / ROTOR POSITION (4-PH MOTOR, 2 PH EXCITED)
0.25
overlap region
I<---
0.2
1
eading phase
-- 2D FEA 5A
- 2D FEA OA
trailing Phase
0.05
-------------
0
5
10
30
25
20
15
Rotor Position (deg)
FIG. 3.10 STATIC TORQUE / ROTOR POSITION (4-PH MOTOR, 2 PH EXCITED)
5
4.5 .................... ......
....................
...
.....................
............ ......
4
2D FEA 10A
3.5
........ ...........
3
2.5 .............
•• ....... ...
2 ...................
.....
.... _ .......
.......
....... ....
1
.........
.. .......
..... .........
.......
............
.............
... ............
..... ............
1.5
.... ....
......
..... ..........
...........
............
..... .............
...... ... ...
.......
...................
2D FEA
0.5
o
...
o
2
4
......
6
...........
..
......
8
10
Absolute Rotor Position (deg)
73
........
.........
••• ..........
........
... •
.............
12
... .... ....
........
.
.... ......
........
14
/ or rotor yoke sections are heavily saturated. In order to investigate the effects of
stator yoke saturation, the back-iron width of the 4-phase fmite element model was
varied by changing the stator slot depth. The stator bore and pole arc were held
constant. The geometry of the 4-phase finite element models, referred to as Mk
I, II and III, may be found in Table 3.2.
Torque
Torque
Torque
Overestimation
(coenergy
(coenergy
(Maxwell
by singly
singly
doubly
stress)
excited theory
excited)
excited)
5A
1.05Nm
1.00Nm
0.99Nm
6.4%
10A
3.65Nm
3.52Nm
3.5Nm
4.0%
Current
Table 3.1. Average torque figures for the 150W 4-phase motor.
Mk I
Mk II
Mk III
stator diameter (mm)
106.5
106.5
106.5
stator back-iron width (mm)
10.0
7.00
5.00
stator pole arc (rad)
0.365
0.365
0.365
stator pole height (mm)
14.775
17.775
19.775
airgap length (mm)
0.6
0.6
0.6
rotor diameter (mm)
55.75
55.75
55.75
rotor pole arc (rad)
0.436
0.436
0.436
stack length (mm)
50.0
50.0
50.0
packing factor
0.92
0.92
0.92
turns per phase
220
220
220
Table 3.2. Dimensions of the 4-phase motor models.
74
The customary X / 0 relationship can be 'distorted' in cases where the magnetic
circuit is heavily saturated. Consider the X / 0 characteristic of the 4-phase Mk I,
II and III motors, shown in fig. 3.11. The diagram only shows the flux linkage in
the leading phase, as this is the one most affected by saturation. In the Mk I motor
the flux linkage reaches a peak at the aligned position. In the Mk II and III
motors, the flux linkage value reaches a maximum before the approaching rotor
poles reach alignment. The peak flux value occurs earlier as the back-iron width
is reduced. Beyond this peak, and while the overlap angle increases, the flux
linking the leading stator phase P1 decreases. In contrast, it can be shown that the
flux linkage of the trailing stator phase P2 continues to rapidly increase so that the
energy balance equation
w.
=
i2x2
(3.28)
is adhered to.
Long flux loop motor configurations are more susceptible to saturation effects
because the stator yoke constitutes a significant part of the overall magnetic flux
path length. Magnetic interaction between adjacent phases becomes more
pronounced as the back-iron width is reduced, largely due to saturation. Figure
3.12 shows the system X / i characteristic of the 4-phase Mk II motor; also
demonstrated is the significant error that arises if the effects of mutual coupling
and saturation, brought about by exciting the second phase, are ignored.
These and subsequent comparisons between the 4-phase Mk I, II and III assumed
equal copper loss. This was found to be most appropriate because a comparison
based on equal MMF (excitation) would not take into account the increased copper
area which becomes available as the yoke thickness is decreased. The
mathematical analysis that describes the setup of finite element models for equal
copper loss can be found in Appendix C.
75
FIG. 3.11 FLUX LINKAGE / ROTOR POSITION DIAGRAM (4-PH MOTOR,LEAN NG PHASE)
0.2
0.18 .....
.............
0.16
0.1 ..................
.....
...
0.14
0.12 ..........
............ .........
.................................. ............
- Mk I 2D FEA
.... ....................
.......
- Mk 11 21) FEA
Mk
0.08
D FEA .. .....
..... ....................
.....
0.06 0.04 ....
0.02
16
...................
.................................... ...........
18
20
22
24
26
30
28
Rotor Position (deg)
FIG. 3.12 FLUX LINKAGE / CURRENT DIAGRAM FOR THE 4-PH MK 11 MOTOR
0.25
4
6
Current (A)
76
8
10
3.3 Electromagnetic design of switched reluctance
motors for low torque ripple - a new alternative.
Figure 3.13 shows the variation of static torque with rotor position for the three
different 4-phase motors. Instantaneous static torque was computed by integrating
the Maxwell stress tensor over the rotor surface. Figure 3.13 illustrates that the
back-iron width not only affects the average torque for a given copper loss but also
controls the shape of the static torque profile. In this case a flatter torque / angle
characteristic may be achieved by compromising the yoke thickness.
The choice of the appropriate yoke thickness coupled with 'clever' switching can
extend the flat torque period. This observation is particularly useful in applications
where low torque ripple is a principal requirement. The variation of static torque
with rotor position in the 4-phase Mk II motor is illustrated in fig. 3.14. When the
rotor pole associated with the trailing phase is at the 9 0 position, the leading phase
is commutated. The conduction period of each phase is therefore 24° (15°+9°)
rather than the usual 30 0 . In fig. 3.14 it can be seen that while the rotor turns from
9° to 15 0 (relative to the trailing phase) the torque output of the motor is increased
by switching off the excitation of the leading phase and reducing the motor to a
singly excited system. While the static torque increases in doing so, the copper
losses decrease! By commutating the current before alignment, the deeply
saturated stator yoke is 'relieved' magnetically. A lower reluctance path is set up
for the overlapping (trailing) phase which, for the same MMF, now produces
significantly higher torque. The magnetic flux path, set up when the leading phase
is energised during the 24° - 30° period, could be thought of 'absorbing' MMF.
Furthermore, at rotor positions near alignment, the B-field produced by the leading
phase causes predominantly tensile rather than shear forces to act on the rotor. As
a result P1 does not contribute significantly to torque production.
The commutation of the leading phase before alignment also results in substantially
reduced torque ripple. The Mk II 4-phase motor design for low torque ripple does
77
FIG. 3.13 STATIC TORQUE / ROTOR POSITION (4-PH MOTOR,2 PH EXCITED)
5
4.5 4
3.5 3
s.s
....
2.5
ss
2
ss
- Mk1
1.5 2D PEA
Mkil 2D FBA
MIclil 2D FEA
1 0.5 2
4
6
8
10
12
14
Absolute Rotor Position (deg)
FIG. 3.14 STATIC TORQUE / ROTOR POSITION (4-PH MkliE MOTOR)
5
4.5
4
3.5
.................... .........
...
- COAdUCtion period
= 30 d g.
-- Conduction period = 24 deg.
1.5
1
0.5
o
o
2
4
8
6
10
Absolute Rotor Position (deg)
76
12
14
not compromise the average torque output as Table 3.3 suggests. For a 24° phase
current conduction period the 4-phase Mk II model achieves comparable torque to
Mk I for equal copper loss and lower operating current density.
Torque
Torque
Torque
Torque
(Maxwell
(Maxwell
(coenergy
(coenergy
stress)
stress)
doubly
singly
excited)
excited)
e = 30°
Oc=26°
e=30°
8c=30°
Mk I
3.51Nm
3.46Nm
3.52Nm
3.64Nm
Mk II
3.06Nm
3.44Nm
3.04Nm
4.35Nm
Mk III
1.90Nm
-
1.85Nm
4.30Nm
Table 3.3. Average torque figures for the 4-phase motor models.
A smooth torque characteristic can be achieved by careful selection of critical
motor dimensions i.e. the stator yoke and rotor pole arc. Dynamic operation
parameters such as the rated speed and resulting commutation angles must also be
considered. Phase current profiling has been suggested as a means of achieving
smooth torque (ref. discussion in [8]), though the electromagnetic design of a 4phase motor for low torque ripple proposed in this thesis should simplify phase
current control.
Table 3.3 lists average torque values for the three 4-phase finite element models,
computed for equal copper loss. It is demonstrated that the virtual work principle
applied to doubly excited systems yields average torque values which compare
favourably with torque computed from Maxwell stress (ref. 0,=30° columns).
Significant errors can arise using traditional coenergy methods in which magnetic
interaction effects are neglected.
79
3.4 The 4kW 7-phase switched reluctance motor.
In chapter 2, it was shown that motors with an odd number of phase windings can
be configured to encourage short magnetic flux patterns. It was asserted that this
configuration would decrease the MMF required to establish the flux in the airgap
while also decreasing the iron losses in the machine. A 4kW 7-phase 14/12
prototype machine was constructed in order to investigate the performance of small
step-angle structures and evaluate the effectiveness of the shared switch,
asymmetric half-bridge converter [41]. It was therefore suitable to model this
machine in finite element analysis, in order to examine the advantages offered by
short flux loops and be able to validate FEA predictions with experimental results.
The design of the 7-phase machine, illustrated in fig. 3.15, was not optimised.
This is because the stator and rotor laminations were stamped out of existing
induction motor laminations. This lead to a significant compromise in the stator
yoke width and pole depth. Results will be presented from two-dimensional
modelling of the machine, configured for short and long flux loops.
Short flux loops can be established by simultaneously exciting at least two phase
windings. Equation 2.3 dictates that in order to obtain peak static torque from the
7-phase machine, three phase windings need to carry current at the same time.
However, the switching algorithm that was developed for the shared switch
converter allows the current in only two phase windings to be simultaneously
controlled [18]. The current in the third phase winding would have to be partially
dependent on the voltage across one of the other two. This would be an
undesirable feature and therefore modelling of the 7-phase machine was confined
to simultaneous excitation of two phases.
In the analysis, two excitation cycles as described below shall be considered. In
the 7-phase machine the beginning of the repeatable excitation cycle is defined as
the point in space where a particular phase winding P1 is energised, while a second
phase winding P2 has been conducting for one rotor step. The end of the cycle is
80
All dimensions
in mm
Fig. 3.15a. The 4kW 7—phase motor laminations.
. short flux paths
-.... long flux paths
Fig. 3.15b. Excitation patterns in the 7—phase motor.
61
B2
CO
0
0
co
go)
°
c co
N.
o
E
o
c3.
83
marked by the de-energisation of P2, one step angle later, while a third phase
winding is being energised. At high speeds a phase winding must be excited at the
unaligned position so as to provide sufficient time for the current to build up in the
phase winding. The excitation cycle in which a phase is fired at the unaligned
position and conducts for two rotor steps will be referred to as the high speed
cycle. At lower speeds firing may be delayed until just prior to the overlap period
between the excited stator and associated rotor poles, such that the conduction
period lies entirely within the pole overlap period. A low speed cycle will be
examined in which firing is delayed by 3°.
3.4.1 Electromagnetic field considerations.
The ideal X / i trajectory assumes square current pulses and spans an angle equal
to two rotor steps. It can be constructed by the use of magnetic circuit
considerations developed for motors operating with two phases conducting at any
time. Figure 3.16 shows a plot of the system X / i diagram for the 7-phase
machine, configured for long and short flux loops and operating in the low speed
excitation cycle. A phase current bias of 10A is assumed. A similar plot
describing the high speed excitation cycle is shown in fig. 3.17. The area enclosed
by the A, / i trajectory is a measure of the average torque developed in the switched
reluctance motor (see eqn. 3.8). It is therefore evident that short flux loop
excitation results in higher torque output. It is also noted that the benefit is greater
where the reluctance of the iron constitutes a substantial part of the total magnetic
circuit reluctance.
The X / 0 characteristic of the leading phase of the 7-phase machine, configured
for long and short flux loops, and excited with 10A is shown in fig. 3.18. In
comparison with the 4-phase (Mk I) motor, the magnetic interaction between the
excited phase windings in the 7-phase machine is more acute. This is due to the
close proximity of one stator pole winding to another which implies a higher level
of mutual coupling between adjacent phases. In addition, the simultaneous
excitation of two phase windings rapidly saturates the stator yoke (the thickness of
84
FIG. 3.16 ENERGY CONVERSION LOOP FOR LOW SPEED CYCLE (7-PH,Ibias=10A)
0.6
4
5
6
7
8
9
10
Current (A)
FIG. 3.17 ENERGY CONVERSION LOOP FOR HIGH SPEED CYCLE (7-PH,Ibias=10A)
0.6 0.5
- short loops 2D FEA
- ldng loops 2D FEA
0.4
0.3
0.2
0.1
.10
Current (A)
85
FIG. 3.18 FLUX LINKAGE / ROTOR POSITION IN THE LEADING PHASE (7-PH, I=10A)
0.6 - short loops (20 FEA)
* sliort loops (experiment)
log .loops . (21) FEA)
0.5
+ Icing loops (experiment)
+
+
.......................
+
..........
.................
..
0.4
...............
0.3
............. ........
.................
0.2
........
0.1
2
4
6
8
10
12
14
Rotor Position (deg)
FIG. 3.19 STATIC TORQUE / ROTOR POSITION DIAGRAM (7-PH MOTOR, I=5A and WA)
40
- short loops 2D FEA
-- long loops 20 FEA
35
* short loops UXPERJMENT
+ long loops EXPERIMENT
30
25
20
5
15
...
10
I = 5A
................
5 ............. ............ .............. .............................
o
o
1
2
3
4
5
6
Absolute Rotor Position (deg)
86
7
8
9
10
which is insufficient) hence degrading performance.
For the same current level, a significant increase in phase winding flux linkage
resulted by configuring the motor for short flux loops. The flux linking the excited
stator poles of the long flux loop machine was limited by bulk saturation of the
stator yoke sections. The phase winding flux linkage reached a maximum of
0.44Wbt, 50 before alignment; beyond this point it began to decrease though the
overlap between the stator and rotor poles increased. The lower reluctance path
set up in the short flux loop machine allowed the phase winding flux linkage to
rise to 0.55Wbt; no significant decrease in X was noted toward alignment. The
static torque production of the long flux loop configuration was therefore severely
compromised due to saturation effects, in sharp contrast to the short flux loop
configuration.
Referring to the long flux loop configuration (see fig. 3.15), the B-field is
essentially encouraged to separate in two long loops that link stator coils 1-2' and
l'-2. Both long and short flux loop configurations attempt to maximise the mutual
B-field linking the excited stator coils. However, the latter configuration
encourages the B-field to follow a short path to link coils 1-2 and 1'-2'. In a
sense, this is the natural B-field path of minimum reluctance. The short flux loop
configuration is significantly less sensitive to back-iron thickness because only a
small arc of the stator periphery forms part of the magnetic pattern. This feature
offers an additional design advantage since, for a specified rotor diameter, the
back-iron width of the machine can be reduced to offer larger copper area.
3.4.2 Instantaneous / average torque considerations.
The measured static torque produced by the 7-phase machine, as a function of rotor
position, is illustrated in fig. 3.19. Measurements were taken for phase currents of
5A and 10A in two adjacent phase windings. Also shown is the static torque
profile of the machine, predicted by the use of the two-dimensional finite element
analysis model. The long and short flux loop characteristics considered are similar
87
at rotor positions early in the excitation cycle. In this region the reluctance of the
magnetic circuit is dominated by the interpolar airgap depth facing one of the
excited stator phases. As the associated rotor poles move into alignment with the
excited stator poles, the reluctance of the iron becomes more significant, and
substantially higher torque is produced by the short flux loop motor configuration.
Good agreement between the instantaneous static torque predicted by the twodimensional model and measurement, was obtained for the short flux loop
configuration. End-core effects in the 7-phase machine are minor because the stack
length is large. However, in the long flux loop configuration, finite element results
consistently overestimated measured values. The dimensions of the machine,
including the sensitive airgap length, were accurately entered during the model
creation stage. In any case, errors in geometry would affect both long and short
loop configurations. Referring to fig. 3.15, the grooves in the back iron of the
machine were not included in the finite element model. This is an 'innocent'
omission which is frequently made. However, in this particular machine, the backiron thickness is small and the grooves randomly positioned with respect to the
poles. This was a design restriction, set by the use of existing induction motor
laminations. The grooves may have therefore increased the magnetic path
reluctance enough to cause a noticeable error in the results. This would only be
visible in the long flux loop configuration, where the back-iron periphery
constitutes a significant part of the path reluctance.
The average static torque may be evaluated by averaging the instantaneous static
torque values over the angle that the excitation cycle spans. The results of this
study are summarised in Table 3.4. Also tabulated is the average torque, computed
using the coenergy principle as applied to doubly excited systems. Long and short
flux loop configurations were considered. Good agreement is noted between
results obtained by the two methods.
88
High Speed Cycle
Low Speed Cycle
Torque
Torque
Torque
Torque
(Maxwell
(coenergy
(Maxwell
(coenergy
stress)
doubly
stress)
doubly
excited)
excited)
Long
20.77Nm
20.85Nm
25.73Nm
28.53Nm
Short
32.48Nm
33.69Nm
28.73Nm
30.30Nm
Table 3.4. Average torque figures for the 7-phase motor.
3.5
Summary of fundamental modelling
considerations.
A new procedure of applying the virtual work principle to switched reluctance
motors which operate with two phases conducting at any time has been described.
The electromagnetic theory of doubly excited systems does not neglect magnetic
interaction effects between simultaneously excited phases, hence leading to more
accurate modelling of the switched reluctance motor. The procedure which has
been described shall facilitate the modelling of short flux loop machines, but can
also be applied to the 'traditional' 4-phase 8/6 structure. The method proposed
allows much of the existing dynamic modelling theory to be adopted providing the
correct X1 characteristics are computed.
It has been shown that in 4-phase switched reluctance motors the stator yoke
thickness must be carefully chosen to allow for the overlap of phase current pulses.
If the chosen yoke thickness is small, bulk saturation effects will severely limit
torque production. This phenomenon, however, will not 'show up' in the
modelling if the virtual work principle as applied to singly excited systems is
adopted.
89
It has also been illustrated that careful selection of the yoke thickness, coupled with
matching commutation angles, can optimise the performance of the 4-phase drive.
Although the 4-phase switched reluctance motor is doubly excited (the effective
torque zone is equal to twice the step angle) the back-iron width need not be equal
to the stator pole width. The yoke thickness can be reduced to allow for more
copper area, and the commutation angles appropriately adjusted to give optimum,
low ripple torque production.
Modelling of the 7-phase motor with the windings configured for long and short
flux paths, has demonstrated the benefits of the latter configuration. The torque
developed by the switched reluctance machine was computed by the methods of
virtual work or Maxwell stress. Good agreement was obtained between the two
methods when applied to the 4-phase and 7-phase motors, providing the new
modelling theory for doubly excited motors was adopted.
\/.
90
Chapter 4
THE EFFECT OF END-CORE FLUX ON THE
PERFORMANCE OF THE SWITCHED
RELUCTANCE MOTOR2
4.1 The need for three-dimensional modelling.
Finite element analysis is considered to be highly suited to handle the modelling
complexities introduced by the deeply saturated, doubly salient iron structure of the
switched reluctance motor. Having decided to use commercially available finite
element analysis software, the question posed by researchers is whether the
switched reluctance machine can be modelled, with sufficient accuracy, using a
two-dimensional code. A useful, early discussion on inductance estimation and
three-dimensional effects in switched reluctance motors may be found in [51].
Simkin and Trowbridge [52] reported that inductance calculations on a stepping
motor using a two-dimensional computer program had shown good agreement with
measurement when the rotor teeth were aligned with the excited stator teeth.
However in the 'unaligned' position, that is, the position at which the rotor slots
are aligned with the excited stator teeth, values for computed and measured
inductances disagreed. In the latter position the airgap facing the excited stator
poles is large causing strong axial components of field to arise. These were not
modelled by the two-dimensional program and the errors were thought to be caused
by this.
Williamson and Shaikh [53] demonstrated the superiority of three-dimensional
models for calculating A. / i diagrams for the switched reluctance motor and
2This chapter is based on a paper, written by A. Michaelides and C. Pollock, which has been
accepted for publication in IEE Proc. B.
91
concluded that the difference between the results obtained using two-dimensional
and three-dimensional models cannot be accounted for by assuming a single-valued
end winding inductance. However, the authors of the paper did not explicitly
suggest a suitable procedure for estimating the end winding flux at any rotor
position or excitation.
Despite these observations, finite element analysis packages that employ twodimensional formulations are established as the primary tool in switched reluctance
motor design. Users of finite element analysis packages have found that twodimensional models require far less cpu time to solve and occupy little disk space
in contrast to three-dimensional models. Typically a two-dimensional nonlinear
problem (one particular excitation level and rotor position), processed on a Sun
Sparcstation10, requires twenty minutes of cpu time to solve and occupies 2Mb of
disk space. Its three-dimensional counterpart would require six times the cpu time
and occupy up to ten times the disk space. In addition, most two-dimensional
formulations are today available in PC form, which makes them more attractive.
It is widely accepted that the two-dimensional formulation for electromagnetic
finite element analysis is easier to implement and expand. Recently C.
Biddlecombe [54] and D. Roger [55] have reported advances in the twodimensional code to include heat and bending calculations. Implementation of
these advances in three dimensions is a few years away, mainly due to the
complexity of the three-dimensional algorithm. The description of basic equations
on which two and three-dimensional algorithms are based (see Appendix A)
illustrates this: in two dimensions, a simple equation relating A z to the applied
is solved for the magnetic field.
The purpose of this chapter is to illustrate the effect of end-core flux on the / i
/ 0 diagram and on the predicted values of static torque in the switched reluctance
motor. The phase winding flux linkage and static torque of a 4-phase 8/6 switched
reluctance motor are determined as a function of phase current and rotor position
using a two-dimensional finite element model. The base- plane lamination is
extruded to different stack lengths to form three-dimensional finite element models.
92
The flux linkage and static torque characteristics of each model are determined and
compared with results obtained from the two-dimensional model. An experimental
motor of stack length exactly equal to one of the models is used to verify
computed results. Correction charts are set up providing appropriate coefficients,
to allow users of two-dimensional software to account for three-dimensional
effects, at a range of excitations and rotor positions. The sensitivity of the endcore flux value to magnetic circuit parameters such as applied MMF, conductor
overhang and magnetic saturation is also examined. An application to an
alternative 7-phase 4kW switched reluctance motor is presented. OPERA -3D /
TOSCA was used throughout this work [44].
4.2 Three-dimensional effects in the switched
reluctance machine.
There are three different three-dimensional effects that must be carefully considered
in order to correctly compute phase winding flux linkage and static torque:
a) anisotropy of the laminations,
b) end winding flux and
c) axial fringing.
Like most electrical machines, the switched reluctance motor is laminated in order
to minimise eddy current losses. Finite element modelling of the individual
laminations and the interlamination insulation would require a mesh of unrealistic
element number. In the three-dimensional finite element code, laminated structures
can be solved by specifying the packing factor, pf, and the direction normal to the
laminations. These parameters enable the program to calculate the effect of the
laminations using anisotropic material properties, i.e. by assigning a high
permeability in the direction parallel to the laminations and a considerably lower
permeability in the direction perpendicular to them. In directions parallel to the
laminations, the program uses
93
= pf vi,„„
+ ( 1 —PDI-Lo
(4.1)
and normal to the laminations
1-10
pf
Pjron
+ (1
(4.2)
-pnilimn
whereuiron is the relative permeability of iron obtained from the BH curve data.
The value of the relative permeability is dependent on the magnetic field intensity
at any point in space. The symbol 1.i.0 denotes the absolute permeability.
In a two-dimensional finite element model, the effect that the laminated structure
of the machine has on stator flux linkage and static torque production may be
accounted for in one of two different approaches:
Method A: The original BH curve data may be used and the field values per unit
length, obtained from finite element model solutions, multiplied by the stack length
times the packing factor.
Method B: The BH curve data can be manually scaled by multiplying the value
of the flux density, at all MMFs, by the packing factor. This approach closely
approximates the method employed in the three-dimensional code (ref. eqn. 4.2).
Once two-dimensional model solutions have been correctly scaled to account for
anisotropy, the remaining discrepancy between corrected two-dimensional solutions
and measurement must be due to end-core flux.
End-core flux can be accounted for by considering three-dimensional effects that
arise at the ends of the machine stack. The dominant effect is end winding flux
i.e. the B-field lines generated from current flowing in the conductor region which
extends beyond the lamination stack, and link the phase winding via the main
magnetic circuit. One other end-core effect is axial fringing, or bulging of flux in
the axial direction. The B-field lines, fringing axially from the ends of the stator
pole stack into the rotor pole ends, can be lines generated from both h and hp.,
(end winding) current. The phenomenon is minimal in the unaligned position, and
occurs as a pair of rotor teeth align with the excited stator teeth. The effect that
94-
this magnetic flux path has on the phase winding flux linkage, is accounted for
only in three-dimensional modelling.
In order to accurately determine end-core effects, three-dimensional model
solutions were compared with corresponding solutions from a two-dimensional
model that was prepared using BH curve data scaled by the packing factor (method
B). This scaling method was solely used for comparison purposes. A second twodimensional model was prepared using the original BH curve data; scaling method
A was imposed on solutions of this model. It is the intention of the author to
provide information on the difference between two-dimensional model solutions
obtained by the use of these two scaling approaches.
4.3 Comparison between two-dimensional and
three-dimensional finite element analysis results with
experimental results.
The base plane used for the two and three-dimensional finite element models
corresponds to the lamination of the experimental 150W 4-phase 8/6 switched
reluctance motor. Comparisons will now be presented between two-dimensional
model solutions, solutions from a three-dimensional model of stack length equal
to that of the experimental machine, and measurement. Scaling method A was
employed for two-dimensional model solutions.
4.3.1. Flux linkage.
The X / i characteristic for one phase of this machine at the aligned and unaligned
positions is shown in fig. 4.1. Two and three-dimensional finite element model
predictions are shown alongside experimental results. A significant error in
computing X, using two and three-dimensional finite element cOde, was noted at
very low currents. This was thought to be caused by the 'reverse curvature'
95
relationship that magnetic materials exhibit at very low values of H. This was not
included in the definition of the BH curve, in order to assist convergence in
nonlinear problems (it is advisable that 1.1 decreases monotonically with H). At
higher current levels, flux linkage calculations using two-dimensional and threedimensional modelling show good agreement with experimental results when the
rotor pole is aligned with the excited stator pole (high flux linkage position).
However, in the unaligned position results from two-dimensional modelling of the
machine are in error while calculations using a three-dimensional model maintain
good agreement with measurement. Two-dimensional model solutions consistently
underestimate the flux linkage value, the effect being particularly noticeable at
positions where the excited stator pole faces the interpolar airgap depth. These
findings are in agreement with observations made by previous authors [52,53].
FIG. 4.1 EXPERIMENTAL 4-PH MOTOR : FLUX LINKAGE / CURRENT DIAGRAM
0.25
Figure 4.2a illustrates the flux linking the excited stator pole when this is aligned
with a rotor pole while fig. 4.2b shows the flux linking the same Pole, for the same
excitation, in the unaligned position. Strong axial fields arise due to end windings,
96
-0
OD
co
c\.1 r,
.q.
in a)
71 NU)
-
7
4 7--.
1- Ø (\I
L°
co
co '7J-
co
N (3)
Ntr) r•-1 .,_ LO
LC)
N
Lü
C°
(7)
I
1-1; C\j
i-f5
"71C°
r.--co
w
71-
•,: -
C
0)
0)
0)
0)
co r,
co
co
c=3.
co 1-1)
1_6
co co N
CY)
4
Lci
-7r
00 -cr in
06
Lo.
cIj
cUH-
("\!
Lo
N
,r•
co
• o
•
co
o
C0
C\!
c\!
97
cc
cy)
co 71Ls) o
cO
7t-
0
Ti;
0
OD Lo
u)
uJ
a_
CL
0
. 11
9.
a°
cr)
71- co
N. co
a) LO
N. ,I.
,—
LO
• isi
tri A
i
,
(3)
.1- c°
,t- co
0)N
(NI
N- c\I
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0) 1-0
LC)
N- °I1
N. .1-.
7
In.
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7 '71-•(NI
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n
N L
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c\I
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In: cr
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..i-
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cli
'En
cp .a)
d 85
96
especially in the latter case. However, as the motor structure is laminated and the
permeability in the (Z) direction normal to the laminations is low, B-field lines find
it difficult to penetrate the magnetic material axially. High flux densities therefore
appear at the ends of the structure, where flux is encouraged to follow a path
parallel to the laminations. These effects are not accounted for in two-dimensional
modelling. A view of the B-field distribution in the 4-phase motor is shown in fig.
4.2c; the rotor is in the aligned position, where axial fringing effects are
pronounced. This is confirmed by the increased flux density appearing at the stator
and rotor pole tips.
4.3.2. Static torque.
The static torque produced by the switched reluctance motor at a particular rotor
angle and excitation can be obtained by computing the integral of the Maxwell
stress tensor t over the appropriate surface. In order to accurately compute the
forces acting on the rotor, the airgap of the machine was meshed with four layers
of eight-node brick elements. The iron structure (rotor) was selected, and enclosed
by two layers of air elements before computing the integral of the Maxwell stress
tensor. This gave the best possible chance of the integration of forces over the
selected surface being accurate.
The measured static torque produced by the experimental 4-phase machine, as a
function of rotor position, is illustrated in fig. 4.3. Also shown is the static torque
profile of the machine, predicted by the use of two-dimensional and threedimensional finite element models. Figure 4.3 is drawn for phase currents of 5A
and 10A. Superior agreement with experimental results was obtained from threedimensional model solutions.
99
100
FIG. 4.3 EXPERIMENTAL 4-PH MOTOR: STATIC TORQUE / ROTOR POSITION
3
2.5
-- 2D FEA
- 3D FEA
* experiment
0.5
0
15
10
unaligned
20
25
Rotor Position (deg)
30
aligned
4.4 Correction charts for two-dimensional finite
element modelling.
The base plane lamination of the 4-phase 8/6 machine was extruded to create two
further three-dimensional models, 100mm and 150mm in stack length. The A, / i
/ 0 characteristic and static torque profile of the machines modelled was
determined and compared with the characteristic that was obtained using twodimensional modelling. For comparison purposes, scaling approach B was imposed
on two-dimensional model solutions, as described in section 4.2.
4.4.1 Flux linkage.
The end-core flux, 4) e, was obtained by subtracting the value of flux linking the
excited stator poles computed on a two-dimensional model, from the
101
corresponding value computed using a three-dimensional model. The value of
end-core flux is not constant over the excitation range. In the linear region of
operation, 40 e increases in proportion to excitation. The end-core flux reaches a
peak value when the excited stator poles are operated at the 'knee' point of the BH
curve (measurements taken at the centre of the core). Beyond this point gi e begins
to decrease due to the marked decrease in the permeability of iron.
The variation of end-core flux with rotor position in the experimental 4-phase
motor is illustrated in fig. 4.4. It is seen to be heavily dependent on the excitation.
At high excitations (i = 10A),
(1) e
decreases monotonically as a rotor pole moves
into alignment with the excited stator pole. This is due to the fact that the machine
is driven harder into saturation as the overlap of the poles increases and the end
windings 'see' a low permeability, high reluctance path resulting in less end-core
flux. In contrast, at lower excitations (i = 5A) the relative permeability is constant
(at most rotor positions) and the reluctance of the magnetic circuit decreases as the
overlap of the poles increases. The end-core flux is therefore found to increase as
the rotor poles move into alignment with the excited stator poles, only decreasing
slightly due to saturation near alignment.
Figure 4.5 indicates the correction factor which needs to be applied to a twodimensional solution to account for end-core flux. The chart shows the percentage
increment in flux linkage due to end-core effects, as a function of current, when
a rotor pole is aligned with the excited stator pole. Depending on the airgap length
and structure of a machine, the MMF required to establish the necessary flux
linkage value (or flux density over the appropriate magnetised pole surface) varies.
It must therefore be emphasised that the correction diagram should be used as a
function of flux density in the stator pole, and not as a function of current. It is
for this reason that the nominal value of flux density in the excited stator pole is
also depicted on the diagram. The flux density values were extracted from twodimensional model solutions and were equal to those of three-dimensional model
solutions taken midway along the stack.
102
FIG. 4.4 EXPERIMENTAL 4-PH MOTOR: END CORE FLUX / ROTOR POSITION
50 = 10A
45
40
35 ......................... ......................... ...........................
...............
30
. ............
= 5A
S 25
........................... .........................
20 15
10
5
o
o
5
10
unaligned
15
20
30
25
Rotor Position (deg)
>
aligned
FIG. 4.5 CORRECTION CHART: FLUX LINKAGE INCREMENT / CURRENT (ALIGNED POSN)
10
1172 1.7 '8 1.84
1 63
0 27 0 54
1 345 153
081
1:08
Flux density (T)
9
50mm stack
8
100nun stack
................
................ ................ ...... ........ ...........
s'ss,
150mm tack
ss„
............ ..............
2
* 7-ph motor (stack=140rnm)
1
2
3
4
5
Current (A)
103
6
7
8
9
10
The reluctance of the path which the end winding B-field must follow can be
separated into two parts. Firstly, there is the air region which B-field lines must
penetrate to reach the stator teeth. The reluctance of this path is essentially
constant. Secondly, there is the main (iron) magnetic circuit linking the
magnetised stator poles via the rotor body and back iron. The reluctance of this
path increases with excitation. Hence, at low excitations the current flowing in the
end windings has a more significant impact on the value of the phase winding flux
linkage because the permeability of the magnetic material is high. In the saturation
region the permeability of iron approaches unity and the end winding effects are
small. The error in two-dimensional finite element model solutions is greater when
a machine of short stack length is modelled due to the fact that the end winding
constitutes a significant part of the conductor.
Figures 4.6a and 4.6b illustrate the percentage increment in flux linkage due to
end-core effects, as a function of rotor position, for an excitation level of 5A and
10A respectively. Two-dimensional modelling incurs significant errors at rotor
positions where the excited stator pole faces the interpolar airgap depth (0 0 being
the unaligned position), though maintaining good accuracy at positions where there
is complete overlap between the magnetised stator pole and a rotor pole (30° being
the aligned position). In the unaligned position, the error incurred in twodimensional model solutions is very much constant over the excitation range as the
interpolar airgap depth dominates the magnetic circuit reluctance. In the overlap
region the error decreases as the rotor poles move into alignment.
In order to predict the percentage increase in flux linkage due to three-dimensional
effects at any rotor position, the end-core flux at the unaligned and aligned rotor
positions must be known; an appropriate function must then be fitted to
approximate the profiles of fig. 4.6. It can be observed that, at high excitations,
straight line approximations can be adopted. At the unaligned and aligned rotor
positions, the appropriate correction factors at any excitation level can be
readily obtained from fig. 4.5 - 4.6. The correct value of average torque can then
be computed from the amended 2 / i diagram upon application of the coenergy
104
FIG. 4,6a CORRECTION CHART: FLUX LINKAGE INCREMENT / ROTOR POSITION (I=5A)
20 18
50mm stack
....
16
14
12
0
coot
........
10
----------
8
........... ..............
100mm stack
.........
........... .......
6
4
...........
150mm stack
2
o
5
o
10
15
20
aligned
Rotor Position (deg)
unaligned
30
25
FIG. 4.6b CORRECTION CHART: FLUX LINKAGE INCREMENT / ROTOR POSITION (I=10A)
20
18
50mm stack
16
14
12
10
N
O 00mm stack
S.
4
150mm stack
2
o
............. .........................
.....................
t
...... ......
o
5
unaligned
10
15
Rotor Position (deg)
105
20
.............
25
30
aligned
principle.
4.4.2 Comparison with a 140mm stack 7-phase switched
reluctance motor.
The guidelines and correction charts have been verified on a 4kW 7-phase switched
reluctance motor. This motor has 14 stator poles and 12 rotor poles. Although the
dimensions of the 7-phase motor are completely different to the 8/6 configuration
that was used to produce the correction charts, it has been found that it
demonstrates the same percentage increase in flux linkage due to end-core flux, at
a given mid-stack stator pole flux density. This machine has a stack length of
140mm and an airgap length of 0.4mm. The percentage increment in flux linkage
due to end-core flux was plotted as a function of flux density in the excited stator
pole. The profile fits the correction chart convincingly (see fig. 4.5).
Solutions of a two-dimensional and a three-dimensional model of the 7-phase
machine at different rotor positions revealed a similar trend to that obtained from
solutions on the 4-phase switched reluctance motor model. In the unaligned
position, a small variation of the percentage increment in flux linkage due to endcore effects was noted for different excitations (6.4 to 7.11%). This result is
consistent with earlier findings on the 4-phase machine (ref. fig. 4.5 and fig. 4.6
at 0 = 00 ) . At constant (high) excitation, end-core flux decreased linearly in the
region where the stator and rotor poles overlap to reach a minimum at alignment.
Results for an excitation of 10A are given in fig. 4.7.
4.4.3. Static torque.
The percentage increment in static torque due to end-core flux as a function of
rotor position, for low and high excitation levels, is illustrated in fig. 4.8a, b. The
discrepancy in static torque calculations performed using a two-dimensional finite
element model is not analogous to errors in flux linkage calculations. The
relationship that governs static torque production in the switched reluctance motor
106
FIG. 4.7a FLUX LINKAGE / ROTOR POSITION DIAGRAM (7-PH MOTOR, I=10A)
0.6
2
unaligned
4
6
8
12
10
Rotor Position (deg)
<
>
14
aligned
FIG. 4.7b FLUX LINKAGE INCREMENT / ROTOR POSITION (7-PH MOTOR, I=10A)
10 9
8
_
-
2
o
o
unaligned
2
4
<
8
6
Rotor Position (deg)
107
10
12
>
14
aligned
FIG. 4.8a CORRECTION CHART: STATIC TORQUE INCREMENT / ROTOR POSITION (I=5A)
6
5
50mm stack
100mm stack
„
„....-•-•
,
,
-•-•
...........................
.
150mm stack
E-12
1
o
o
5
unaligned
10
15
20
Rotor Position (deg)
25
30
aligned
FIG. 4.8b CORRECTION CHART: STATIC TORQUE INCREMENT / ROTOR POSITION(110A)
4
3
2
sss,
......................... .....................
'
stack .
................
.... 100mm
- .....
................
... ........................... ..............
50Inn.1 . sta.& . .........................
-2
4
................. .........
............ ........................... ..................
-3
0
unaligned
5
10
15
Rotor Position (deg)
106
20
25
30
aligned
dictates that the axial field Be, a strong component of which is induced by end
windings, does not contribute to positive torque. Torque is maximised by
optimising the shearing force 'r on the rotor, a direct consequence of
maximising the tangential component of flux density on the rotor, B. The radial
component Br, tends to keep the rotor in position, by subjecting it to tension or
compression. It must be pointed out that not only the direction but also the
magnitude of the flux density components is important. This is the reason why
maximum torque is obtained in the region where there is significant overlap
between the excited stator and rotor poles (0 = 10 0 -20 0 ), and not earlier in the
excitation cycle.
End windings induce all three components of flux density (Br, By, and Be). The
first two components acting parallel to the XY plane contribute to torque.
However, at high excitations and towards alignment a higher value of static torque
was predicted by two-dimensional model solutions. This is thought to be due to
the fact that in positions close to alignment the radial component of flux B,.
produced by end windings may be more dominant than component B.
4.5 Discussion on other effects.
4.5.1 Anisotropy.
In three-dimensional finite element models of the switched reluctance motor using
anisotropic materials, the iron permeability in the axial direction is assigned a low
value, making flux penetration in this direction difficult. As a result, a significant
axial component of field arises solely at the ends of the excited stator poles. Flux
is forced to penetrate iron parallel to the plane of laminations where the relative
permeability is very high. However, at very high excitations as the iron becomes
saturated, more flux penetrates the iron axially. In field solutions of the machine
using isotropic materials, the axial component of flux is at its highest value at the
ends of the excited stator poles and decreases more uniformly toward the middle
109
of the stack. The net flux linking the stator windings is higher in the isotropic
materials machine due to the higher permeability, although higher flux densities
appear at the pole edges of the laminated structure. Therefore, in the threedimensional finite element code, the equations governing the behaviour of the
magnetic field in an anisotropic structure appear to provide a faithful
representation. However, one might argue that parallel to the plane of each
lamination the permeability of iron should not be affected. This leads to the two
approaches used to scale two-dimensional model solutions. Figure 4.9 illustrates
the X / i diagram of the experimental machine, computed using two-dimensional
models that were either set up by scaling the BH curve data (method B) or
prepared using the original BH curve data and scaling field solutions per unit
length by the stack length times the packing factor (method A). When the rotor
poles are aligned with the excited stator poles, the results produced by the two
methods converge as the excitation increases due to the marked decrease in iron
permeability, but they are never equal.
This trend may be understood more easily if the case is considered where threedimensional models, structurally identical, were assigned packing factors of 0.96,
0.92 and 0.88 and solved for different excitations. Figure 4.10 shows that at low
excitations, field values calculated in all three variants were in close agreement,
somewhat higher values being obtained from the model that was assigned the
highest packing factor. This is because the motor was operated in the linear, high
permeability region and the iron was 'seen' as infinitely permeable in comparison
to air. At higher excitations, as the relative permeability of iron approaches that
of air, the field values obtained from the three variants diverged and the loss in
performance due to a poor packing factor was evident.
Referring to fig. 4.9, the reader will notice that the X / i diagram computed using
scaling method B is in closer agreement with measurement. This, however, is
misleading. It must be remembered that end-core flux has not been accounted for.
The use of the original BH curve data to set up a two-dimensional model, and the
subsequent scaling of the field values per unit length by the stack length times the
110
FIG. 4.9 FLUX LINKAGE / CURRENT DIAGRAM FOR VARYING SCALING METHODS
0.25
- method A
0.2
0.15
°
ba
0.1
0.05
Current (A)
FIG. 4.10 FLUX LINKAGE / CURRENT DIAGRAM FOR VARYING PA
CKING FACTORS)
0.25
- pf = 0.88
0.2
''' ''' .. ... . ........
--p =0.9
pf = 0.92
0.15
0.05
1
2
3
4
5
Current (A)
111
6
7
8
9
10 _
packing factor (method A), constitutes a more realistic scaling approach. It
provides information on the true flux densities that drive the machine by assuming
no change in the magnetic properties of a single lamination. Despite the fact that
this approach yields higher field values in the post-processor, it still predicts lower
overall (scaled) values of flux linkage and static torque when compared to solutions
of finite element models prepared using scaling method B.
The three-dimensional model consistently yields more accurate field solutions of
the motor, at any rotor position and excitation, in comparison to the twodimensional model. However, flux linkage and static torque values are, even
marginally, overestimated by three-dimensional model solutions. One reason for
this discrepancy could be the properties assigned to anisotropic material structures,
and in particular eqn. 4.2. The margin of error is still very acceptable though, and
defining a three-dimensional model with layers of iron and air interleaved would
be unnecessarily expensive, if not impossible.
4.5.2. Conductor overhang / inside coil radius.
The variation in length of the conductor overhang and inside coil radius, shown
diagrammatically in fig. 4.11, has little effect on the end-core flux linking the
excited stator poles of the switched reluctance motor. Three models were set up
with a conductor overhang of 3mm and an inside coil radius of 3mm, 4.5mm and
6mm respectively. The value of end-core flux plotted against excitation, when the
rotor poles are aligned with the excited stator poles, is shown in fig. 4.12. As the
inside coil radius increases the end-core flux decreases, but only marginally,
because the end conductors are positioned further away from the stator poles.
The results suggest that the overhang, present in all machines, plays the most
significant role in producing the marked increase in flux at the ends of the excited
stator pole. The B-field lines generated by current flowing in the overhang, follow
a shorter path through air in order to 'creep into' the stator poles. These findings
were confirmed by extending the end windings a considerable distance away from
112
the pole ends (the overhang was set to lOmm) and repeating the computation of
flux linkage. The results are superimposed on fig. 4.12 and demonstrate clearly
that the dominant cause of the end-core flux is the coil overhang and not the
tangential (XY) part of the end winding.
inside
radius
stator
pole
overhang
phase
winding
Fig. 4.11. Illustration of overhang and inside coil radius.
4.5.3. Sources of error.
The most significant source of error in finite element modelling is that incurred due
to the level of discretisation. In order to minimise this, the discretisation of the
two-dimensional (base plane) mesh was repeatedly refined until field solutions
obtained from the most finely discretised model were within 1.0% of the previous.
Discretisation in the third dimension was also optimised, although a very fine mesh
here would produce a model of unrealistic element size. The ends of the machine
were more finely discretised in order to 'capture' the end effects. This is important
when dealing with anisotropic structures, where there are abrupt changes in field
values at the excited stator pole ends. A small margin of error should however be
allowed to the results presented to account for discretisation ei-rors.
113
FIG. 4.12 VARIATION OF END CORE FLUX WITH COIL RAD. / OVERH. (ALIGNED POSN)
35
!
!
- radius = 3 mm
oVerhang 3 nun
10
Current (A)
FIG. 4.13 FLUX LINKAGE/CURRENT DIAGRAM (OBTAINED USING 2D FEA AND CORRECTED)
0.25 * eiperiment
- 31) FEA
0.2
-- CORRECTED 2D FEA
g 015
0
0.05
5
Current (A)
114
7
10
4.6 Conclusions.
The effect of end-core flux on the performance of switched reluctance motors has
been presented. Experimental results from a 4-phase motor verified the superiority
of three-dimensional modelling. The percentage increment in flux linkage due to
end effects was found to be maximum when the excited stator poles face the
interpolar airgap depth. The percentage increment in flux linkage due to end
effects decreased linearly as the overlap between stator and rotor poles increased,
reaching a minimum value in the aligned position. The correction charts that were
set up for different machine lengths may be used to account for end-core flux at
a range of rotor positions and excitations. An application to an alternative 4kW
7-phase machine confirmed the reliability of the charts. The value of end-core flux
was found to be heavily dependent on excitation, rotor position and magnetic
saturation. An extensive discussion into the modelling of anisotropic material
structures was put forward.
It is thought that the most realistic approach of accounting for three-dimensional
effects when modelling switched reluctance machines in two dimensions,
constitutes the scaling of field values per unit length by the stack length times the
packing factor and, at a particular rotor position and stator pole flux density,
adding the end-core flux value provided by the correction charts. This procedure
was applied to the experimental four phase machine, and the resultant X / i
diagram, shown in fig. 4.13, compares favourably with measurement (except at
very low current, as explained earlier). A similar procedure may be followed for
static torque estimation.
115
Chapter 5
THE SRDESIGN PACKAGE: MODELLING
AND SIMULATION
SRDESIGN is a computer simulation program, written in Turbo Pascal by C.
Pollock and A. Michaelides to characterise the performance of the switched
reluctance motor under running conditions. This chapter shall describe
fundamental design and modelling considerations supported in SRDESIGN.
The structure of SRDESIGN, shown in fig. 5.1, is based on screen menus which
control the flow of data and sequence of calculations. A design entry interface and
a facility for design changes in the lamination geometry or the power converter
specification is provided. Once a complete switched reluctance drive specification
has been entered, the program offers the choice of either (internally) computing the
magnetisation curves at 'extreme' rotor positions, or importing them from finite
element analysis. Magnetisation curves at intermediate rotor positions are
subsequently computed within SRDESIGN. Information on the operating speed
and level of excitation is used to calculate the output torque, power input and
efficiency. A collection of additional data that may be of interest to the designer
is also provided. Included are the operating flux density in different parts of the
magnetic circuit, the rms current and current density and information on the stator
slot area, winding resistance and slot fill factor.
With the aid of mathematical formulations, this chapter will predominately describe
the work that was undertaken only in this project to improve SRDESIGN.
116
Design entry
and
modification
Estimation
of machine
constants.
Computation
(or import) of
magnetisation
curves at 'extreme'
rotor positions
Specification
of current
chopping level
and
operating speed
or range of speeds)
1
Computation
of developed
torque, efficiency
etc at the
specified speed
Computation
of developed
torque, efficiency
etc at each of the
specified speeds
1
V
Presentation of
results at the
specified speed
Presentation of
results at the
specified range
of speeds
Fig. 5.1. Structure of the SRDESIGN program.
117
5.1 Modelling magnetisation curves for singly
excited systems.
5.1.1 'Extreme' (aligned and unaligned) rotor positions.
The X / i diagrams for the aligned and unaligned rotor positions play a significant
role in the modelling structure. It is therefore advantageous to obtain these curves
from a finite element analysis program. A PASCAL routine has been written to
import X / i data calculated by finite element analysis into the SRDESIGN package.
The PASCAL program interpolates linearly between the imported A, / i array, as
needed. If finite element software is not available, the curves can be computed
within the package, with routines which find their source in [51].
Figure 5.2 shows the laminations of a 2-phase switched reluctance motor. The
magnetic flux pattern in the unaligned position is illustrated. The unaligned X, / i
characteristic is shown to be approximated with a straight line. The magnetic path
reluctance is highest at this position because of the large interpolar airgap between
the rotor and the excited stator teeth. The magnetic circuit is not subject to
saturation effects and therefore
un =
Lun i
(5.1)
where A„ and Lu„ denote the flux linkage and inductance in the unaligned position.
In the aligned position the reluctance of the magnetic circuit is at its lowest; for a
constant excitation level the phase winding flux linkage is therefore at its highest.
At very low excitation the flux linkage varies linearly with current. The iron paths
are highly permeable, with a relative permeability, v r, of over 6000. 'Reverse
curvature effects' are neglected to aid the convergence of nonlinear finite element
problem solutions. At high current levels the magnetic circuit becomes saturated,
with the iron relative permeability II r decreasing rapidly.
118
aligned position
current i
unaligned position
Fig. 5.2. Obtaining magnetisation (Vi) curves
for singly excited systems.
5.1.2 Intermediate rotor positions.
I. Low excitation.
As a pair of rotor poles turn from the unaligned position to the point where they
begin to overlap with the excited stator poles, there is a small_ increase in the flux
linking the excited stator phase. The large rotor interpolar airgap facing the excited
stator poles maintains a high magnetic circuit reluctance. B-field lines tend to
119
fringe from the stator pole tips to the approaching rotor teeth. Fringing effects
become more pronounced near the onset of overlap. Fringing B-field lines account
for the small increase in flux linkage from X„„ to k o in this region. The flux
linkage at the beginning of overlap, ko, is estimated using an empirical formula
derived from finite element analysis studies; X bo varies linearly with excitation i.e.
X
ho
Lho i
(5.2)
A sharper increase in phase winding flux linkage is noted with the onset of
overlap. As the excitation is low, X varies linearly with 0, throughout the overlap
region as shown in fig. 5.3a. The reluctance of the magnetic circuit decreases as
the rotor teeth approach the excited stator poles, though the excitation is never high
enough to saturate the magnetic circuit. The slope of this linear function is
expressed as
=
22. —Xho
(5.3)
s
Byrne and Lacy [56] recognised the gradient of this profile to be analogous to the
back-emf constant of a dc motor, and appropriately assigned the symbol k to it.
II. High excitation.
At higher current levels, the X / 0 profile in the overlap region can be
approximated by a linear function followed by a sigmoid. The rotor travel angle
may be separated in four regions as shown in fig. 5.3b. The slope of the linear
region (II) is similar to that of the idealised (trapezoidal) inductance characteristic,
i.e.
khe =
Ada 1 — Li
(5.4)
s
This observation was first made by Miller and McGilp [57]. It must, however, be
pointed out that the slope k is not constant; it varies with excitation from kie to khe.
120
Aba = 'al
slope= K
Abo
Aun
ob.
.61ba
No-
al
Ps
a. Low excitation.
X
Aba = Aal
slope of two
lines similar
Aho
Ab
Au linear function
region I
I sigmoidal function
region ll
d un
region Ill
ho
15tb a
al
Ps
LCM
C\-1?
b. High excitation.
Fig. 5.3. NS variation in singly excited systems.
121
19.
A sigmoidal function has been chosen to describe the flux linkage variation with
rotor position in region III. This is of the form [58]
a1 02
X=
+y
02 + f3
f
f
(5.5)
The starting gradient of the sigmoid at 0 = eh, was set to be the slope of the X /
0 characteristic in region II. This defines two points on the sigmoidal function.
A third point is needed to define the shape of the sigmoid, and this is extracted
from the aligned magnetisation curve, at the specified current level. The 'Gauss
routine' within the SRDESIGN package uses this information to compute constants
ai, flf and yf and therefore completely define the sigmoidal variation of flux linkage
with rotor position in the overlap region. Although a similar approach can be used
to define a sigmoidal X / 0 characteristic in region I, it was thought that a linear
function description would suffice.
5.2 Modelling magnetisation curves for switched
reluctance motors with two phases simultaneously
excited.
5.2.1 'Extreme' rotor positions.
When modelling switched reluctance motors with two phases simultaneously
excited, the advantage of importing X, / i diagrams for the 'extreme' rotor positions
from finite element analysis is more pronounced. The analytical technique which
is embodied in the SRDESIGN package does not account for magnetic interaction
effects. In finite element analysis the system A, / i characteristic is drawn by
following the new field computation procedure for motors with two phases excited
at any time. The procedure, described in chapter 3, is graphically illustrated in fig.
5.4. Referring to fig. 5.4,
122
ph
IB
X2(al) = N
X 1(un)
= N
Ph
l nt,
ds i = I
iBds
varying i2
i2 = 'm' varying il
(5.6a)
(5.6b)
where I. denotes the set current chopping level.
increase
current
in P2
P1 biased
with Im
position P•
P2 biased
with Im
increase
current
in P1
current i
position P
Fig. 5.4. Obtaining system Vi characteristics for SR motors
with two phases simultaneously excited.
5.2.2 Intermediate rotor positions.
The modelling structure presented in section 5.1.2 is valid for motors with two
123
phases excited at any time, provided no part of the magnetic circuit is heavily
saturated. There are cases where bulk saturation of the yoke sections may distort
the usual 2 / 0 curve. This phenomenon was extensively discussed in chapter 3.
Long flux loop machine configurations are more susceptible to yoke saturation
effects because of the flux path nature. The X, / 0 curve of a deeply saturated
motor with two phases excited at any time is reproduced in fig. 5.5. The phase
• points used to define a second
order function (heavy saturation)
+ points used to define sigmoid
function in SRDESIGN
second order
function
A max
Aba = Aal
1
sigmoid
function
linear
function
Al)
ho
15/bo
low
1.9
15Iba401
Fig. 5.5. A/15( curves for doubly excited SR motors.
winding flux linkage in the leading stator phase increases rapidly with rotor
position in the overlap region. However, the flux linkage value reaches a
maximum before the approaching rotor poles reach alignment. Beyond this peak
towards alignment, and while the system energy increases, the flux linking the
leading stator phase decreases.
It is possible to use a second order function to fit a heavily saturated X, / 0
124.
characteristic within the SRDESIGN package so as to obtain an accurate model of
the behaviour of the motor. However, additional data needs to be imported from
finite element analysis in order to perform this task. In addition to the
magnetisation curves at the extreme rotor positions, the maximum flux linkage,
Xm., and the rotor position at which it is obtained must be entered. This operating
point moves along the 0 axis with changing excitation. The data is therefore valid
for a single operating current, In,• The approximate curve fitting procedure is
illustrated in fig. 5.5.
5.3 Dynamic operation considerations.
Under running conditions, it is necessary to commutate the current in the phase
winding before the approaching rotor teeth align with the excited stator poles.
Early commutation ensures that the current and associated flux linkage reduce to
zero before the rotor teeth move beyond alignment, as shown in fig. 5.6.
When the rotor speed is low, the supply voltage exceeds the motor back-emf. It
is therefore essential to limit the phase current to its rated value with the aid of a
current chopping regulator. There exists a speed, known as the base speed wb, at
which the applied voltage is equal to the back-emf. In theory, at this speed a flat
topped current pulse may be maintained without chopping. In practice this cannot
be achieved as the back-emf constant varies with rotor position, as illustrated in
section 5.1.2.
When the motor is running above base speed, the supply voltage is not enough to
overcome the back-emf. In this case the phase current rises to a set value and
immediately decreases as the approaching rotor teeth begin to overlap with the
excited stator poles. Figure 5.6 demonstrates how the electrical energy that is
converted to mechanical work during each working stroke decreases with speed.
125
Fig. 5.6. Dynamic operation considerations.
126
5.3.1 Base speed estimation.
If the phase current is constant, and a linear variation of inductance with rotor
position is considered in the overlap region, the back-emf is also constant. The
speed at which the back-emf is equal to the supply voltage is known as the base
speed.
As the rotor turns through an angle equal to the stator pole arc, f3„ the flux linkage
increases from kb , to ka. The time taken to complete the move is given by f3/ co,
where Co represents the average speed of rotation. If the motor is running at base
speed, wb, the current must have risen to (and maintained) a constant value under
the influence of the supply voltage, V. Hence
P
al -
(5.7)
Xbo = (Vs - In,R) —
co
where R denotes the phase winding resistance. The base speed is therefore given
by
=
-
/R )13
'1ph(al —
(5.8)
Cob)
(I) denotes the flux linking the excited stator phase at the rotor position specified
by the subscript. In this form, eqn. 5.8 indicates to the switched reluctance motor
designer that the key parameters which must be considered when tailoring the base
speed are the supply voltage, V„ and the number of turns per phase,
Nph.
5.3.2 Commutation.
The rotor angle, beyond the onset of overlap, at which negative ( or zero ) voltage
is applied across the phase winding in order to decrease the current and flux
linkage to zero is defined as the commutation angle. The commutation angle may
be expressed as the product of the stator pole arc, f3s, and the commutation ratio,
c,
where 0 < c 1. Upon commutation, the angular duration available for the
127
current to decrease to zero is equal to ofall, where
° fall
=
Pr
CI3
(5.9)
Commutation must be delayed as much as possible in order to 'capture' the
maximum possible area within the ideal (square current pulse) energy conversion
loop. There is therefore an ideal commutation angle for each rotational speed and
current level. If the ideal commutation angles are adhered to in practice, the drive
efficiency is optimised and the power converter kVA rating is kept to a minimum.
Here it must be stressed that the commutation angles proposed in SRDESIGN may
not always be ideal. The program assumes that commutation must be delayed as
much as possible but regeneration must be completely avoided. However, there
may be cases where the motor performance stands to gain by delaying
commutation even further. If the extra time the current has been maintained at I.
lies in the peak torque producing region, then substantially higher torque will be
developed. This would overwhelm any negative torque produced as the current tail
enters the generating region.
The commutation ratio prediction is dependent on the choice of the unipolar
converter that powers the switched reluctance motor. Full negative volts (-Vs) can
be impressed on a phase winding connected to the asymmetric half-bridge
converter. In power converters with a split de rail, only half the supply voltage
(-Vs / 2) is available for commutation. A more complicated situation arises when
the shared switch converter is employed. The switching algorithm which allows
current control in two phase windings connected to the same switching leg was
presented in chapter 1. One disadvantage of this technique is the increased current
fall time in phase P1 due to the switching requirements of the adjacent phase, P2.
During the current fall time in Pl, negative volt loops are interspersed with zero
volt loops, each time the adjacent phase P2 requires a positive volt loop to
maintain the current at its rated value.
The computation of the commutation angles for the asymmetric half-bridge, split
dc and shared switched converter will serve as an illustrative example. In this
128
example it is assumed that the motor is running below base speed, and therefore
current chopping is required in order to maintain a predetermined current level.
It is appropriate to derive an expression for the average voltage, vc , that is
impressed across the motor winding during chopping. The average voltage during
chopping, vc, is equal to the sum of the generated back-emf and the resistance drop
in the phase windings. Faraday's law states that, at a rotational speed co, below the
base speed wb , the average chopping voltage Vc must satisfy
—
= (vc — Im R) 70.
(5.10)
It has also been shown that
PS
-X 0 (
— Ir7nR)_
(5.11)
Equating 5.10 and 5.11, and rearranging to give an expression for ve at a rotational
speed below cob yields
Vc = V
+ Im R(l -
co b
.)
(5.12)
(I b
A straight substitution for V in Faraday's equation gives the rate of change of flux
linkage during chopping
ca
=
(Vs - ImR)
(5.13)
wb
dt
The time taken for the rotor to turn through the commutation angle, ci3„ is equal
to Os / o.). The flux linkage at commutation A,„,, is therefore given by
X,COM
xbo
CO
-
cf3
b
or
129
IR)
m
(5.14)
cr•
(5.15)
= Xho + (Vs - ImR)
b
De-energisation of the phase winding follows the chopping mode. The time,
tfall
available for the current to fall to zero is given by
13 r — cf3 s
tfall
(5.16)
co
The equation governing the fall of flux linkage in a phase winding, connected to
an asymmetric half-bridge converter is
0
= f(- V k .„,
(5.17)
iR)dt
o
The second term of the integral on the right hand side of the equation may be
evaluated upon application of the trapezoidal rule. An expression for A„,„, may be
obtained as follows
A.
COM
Im R
)(
= (Vs +
13 — cf3
2
(5.18)
S)
co
Equating 5.15 and 5.18 yields an expression for the commutation angle, assuming
an asymmetric half-bridge converter:
vs
o
ImR
r +
(3 r — C Lbolm
2
c13
(5.19)
co
or)
+
vs (1 +
- -
C° b
Should a split dc rail converter be used, eqn. 5.19 is modified, to
n
ImR
2
2 r
c =
V
_1(1 +
2
b
bo rn
r
+I
(5.20)
R(1 -
2
co b
)
Upon commutation, the average negative voltage V„„ that is impressed on a phase
130
winding connected to a shared switch converter is given by
V
fleg
= Vs - Vc
(5.21)
Substituting for V, (see eqn. 5.12),
Vneg = (Vs - Inz R)(1 -
(5.22)
6-) b
K eg arises
because the lower switching device, to which the commutated phase is
connected, is off whereas the top switching device is chopping. The top switching
device is shared with the adjacent phase which carries the rated current.
The equation that governs the fall of flux linkage is given below:
)
= 1(73 - Im R)(1 -
+
f3 1( r
2
co
I R
b
P
(5.23)
)
Equations 5.15 and 5.23 may be equated and rearranged to yield an expression for
the commutation angle, assuming a shared switch converter
V3 0 s (1 Cf3
L
i) )
(-1) b
=
-
/mRP s (1 - ._
°) ) - Lb 10)
b
2
os.)
(5.24)
I R
Vs. - m
2
This section has illustrated how an SRDESIGN routine can be employed to
automatically compute the phase current commutation angle at any speed co,
chopping current level,
/m ,
and supply voltage V,. The user does, however, reserve
the option of manually specifying the commutation angles, as an attempt to further
optimise the torque production capability of a motor design.
5.3.3 Maximum speed for a given current.
Once the stator and rotor poles begin to overlap, the motor back-emf increases
substantially and, depending on the running speed, can limit or decrease the
current. It is therefore desirable to increase the current to the desired value before
131
the onset of overlap. Speed limit o.)..a is computed on this basis, and represents
the maximum speed at which current of magnitude I. can be switched in (but not
necessarily out of) the winding at the specified supply voltage. Similar
considerations must be adopted for commutation. Negative motoring torque is
avoided if phase current I. is reduced to zero before the rotor poles move beyond
alignment, into the generating region. If necessary, commutation may be brought
forward to c = 0 (i.e. 0,„„, 0 1,0). This defines a second speed limit cu„, 2 . The
maximum speed routine compares Wmi and (0„,„,2 and warns the user of the smaller
speed limit for the chosen current level.
The algorithm chosen to compute the maximum speed limit depends on the type
of converter employed in the switched reluctance drive and on the switching
technique adopted, that is, whether the firing and commutation angles are fixed by
the drive electronics or calculated by the SRDESIGN program.
5.3.4 Variation of current with angle.
The current profile can be predicted, having specified the current chopping level
and running speed. The time, t„ taken for the current to rise to a specified value
is computed using
a.,
t
517 sdt - R fidt
0
0
(5.25)
0
where X,. lies between xu„ and kw The trapezoidal rule is used to compute the
second integral on the right hand side. The time interval, t, can be expressed as
a function of rotor angle and rotational speed,
=
0
(5.26)
When the rotational speed, co, is lower than the base speed, co,„ the phase current
rises to the predetermined chopping level and maintains a 'flat top' until it is
commutated. At commutation,
132
c
X,„. -Xb Q = (V -
Im R)
(5.27)
s
If the rotational speed is higher than the base speed, the switched reluctance motor
back-emf exceeds the supply voltage in the overlap region and, as a result, causes
the current to decay though the flux linkage increases. At the onset of overlap the
program enters a time stepping algorithm which estimates the phase current and
winding flux linkage during the angular period c0,..
This time stepping algorithm, which was written in a general format, is also used
to predict the current fall in the phase winding during the commutation period cps).
5.3.5 Time stepping algorithm for current prediction.
The variation of phase current with time must always obey Faraday's law
= iR
+
aX(i3O)
ao
ax(i e)
dO
I,--const. di
di
le--const. —
dt
(5.28)
The second term on the right represents the motor back-etnf, Vb. The rate of
change of flux linkage with current at a specified rotor position is otherwise known
as the incremental inductance, Lin,. Equation
5.28
can therefore be rewritten as
(5.29)
V, iR + Vb +
The discrete time equivalent of eqn.
5.29
may be obtained by taking finite
differences to give
Vs =
+ vbt
L
Inc
i t
it_i
t
(5.30)
where t t represents the discrete time (sampling) interval. Solving for the phase
current it, at time t,
133
it = (V, - Vb t)t
LI.nc it -1
Rtsi. + L .
Rt.si + Lino
(5.31)
In the overlap region, and at a specified current level, the back-emf of a nonsaturated motor is constant. The back-emf constant,
k,
can be found by evaluating
the gradient of the / 0 characteristic at that current level. Therefore, the backemf is equal to
vb = Xcd — Lbo Im
(5.32)
PS
or, in the customary dc machine equation format
(5.33)
Vb = kw
This quantity plus the resistive drop may be regarded as the applied voltage that
would be required to maintain the specified current value constant at a given speed.
The back-emf of a saturated motor varies with position in the overlap region. The
variation of flux linkage with rotor position is described by a linear followed by
a sigmoidal function. At a specified current level, the corresponding A, / 0 diagram
is drawn with the aid of the 'Gauss routine' and the gradient of the
X, /
0 curve is
then computed at a given rotor position to give k.
Information on the incremental inductance, Lino is also needed to predict the phase
current value, it. In the overlap region and at constant excitation, the incremental
inductance of a non-saturated motor increases linearly with position from Lba to
Lai.
A PASCAL routine has been written to interpolate between aligned X, / i data
imported from FEA, in order to compute ki at any phase current value. At the
operating point (i[t-1 ] ,k[t-11),
Lino = L bo
where the ratio
r
r (Lai
is expressed as
134-
- Lbo)
(5.34)
r=
Mt — 1] — i[t-1]40
A.,a1 - i[t-1]Lbo
(5.35)
The incremental inductance of a saturated motor is found by computing the
gradient of the 2t., / i diagram at the required rotor position and phase current value.
SRDESIGN generates three arrays namely Aphase, lphase and Fphase which
contain instantaneous values for rotor position, phase current and winding flux
linkage respectively.
5.4 Computation of output power and losses.
5.4.1 Computation of the rms phase current 4„,•
The profile of the phase current pulse is defined by two arrays, namely
lphase[count] and Aphase[count], which contain values for the instantaneous
current magnitude and the corresponding rotor angle.
The equation of the line joining two consecutive points (Aphase[count],
Iphase[count]) and (Aphase[count+1], Iphase[count+1]) is arranged in the form
Iprof (0)
= MO + Co
(5.36)
where M denotes the profile slope
M -
lphase[count+1] - Iphase[count]
Aphase[count+1] - Aphase[count]
(5.37)
and Co is the zero crossing.
Equation 'prof (A) is squared and integrated with respect to the rotor angle. The
process is repeated for all values of variable 'count', from count = 0 to count =
Tcount. The integrals are summed and the total is divided by the phase current
repetition angle, before finally taking the square root, i.e.
135
Tcount-
dO)
E(CI
prof
I
rtns
(5.38)
count.0
=
27c
N,.
5.4.2 Copper losses.
The switched reluctance motor copper losses,
Pc,
' may be computed from
(5.39)
Pcu = 4
2 ' sRq
where q represents the number of phases. The phase winding resistance, R, is
given by
R=
where l
p
(5.40)
the copper wire length and A H, its cross-sectional area.
An average turn length of copper wire, 1„e , wound around the stator tooth is
considered in order to compute the total length of the phase winding. Referring
to fig. 5.7,
I ave =
21„k
+
41oh
A-
2ts + 2rc
rave
(5.41)
and
1w = Nph 1 ave
(5.42)
The slot area, Aslot of the motor is also calculated and, for a specified number of
turns, the maximum (standard) copper wire diameter is estimated. An empirical
approach to the slot fill factor computation is taken. In production, switched
reluctance motor coils can be pre-wound and slid over the poles without interfering
_
with each other, as shown in fig. 5.8. Hence the actual coil area il. 011 is
compromised. Each wire takes up a slot area fractionally higher than the area of
136
Fig. 5.7. Illustration of principal winding dimensions.
Fig. 5.8. Slot filling in the switched reluctance motor.
137
a square with a side equal to the wire diameter. This accounts for the insulating
varnish coating the copper wire. The coil fill factor IC, is therefore equal to
2
IL
K = c
4(r
=
(5.43)
0.7
+
where r„, denotes the copper wire radius and tv the thickness of the varnish. The
overall slot fill factor, K5, is equal to
KA
=
c coil
A
(5.44)
slot
This parameter works out to approximately 0.4 for a 4-phase machine, but
increases with increasing number of stator poles. It is also acknowledged that
methods may be found by which the fill factor is increased. The SRDESIGN
package therefore allows the user to input the copper wire diameter from the
keyboard, should one choose to do so.
The resistivity of copper, p, is a function of the operating temperature O cp. R
increases with temperature at the rate of about 20% for every 50°C rise in the
copper windings according to
R op
R20°C [1 + a
-
132001
(5.45)
where a denotes the temperature coefficient of resistance of copper. The program
computes R20.c and Rop given a nominal operating temperature. The skin effect is
neglected.
5.4.3 Iron losses.
Hysteresis losses, Ph, can be expressed as
B rnax f
p =K
h "
h
p
(5.46)
where Bmax is the maximum flux density in the iron, p is the mass density of iron
138
and Kh is the hysteresis constant [59]. This expression holds for a system excited
with a sinusoidal waveform of frequency f. The exponent n may not necessarily
be constant.
Eddy current losses are expressed as
Pe =
K B 2 f2
(5.47)
e "
where Ke is the eddy current constant.
Loss data in WIKg for different lamination materials is provided by the
manufacturers for frequencies ranging from 50 to 500Hz. These curves were used
to obtain constants Ke and Kh. Exponent n was found to be a second order function
of the flux density
B, yielding values between 1.5 and 2.5 in the region of 0 to 2T.
Hence, a general analytical expression was formed, predicting core losses at any
excitation frequency, and assuming the iron to be excited with sinusoidal
(alternating) current. In the switched reluctance motor the flux waveforms in
different parts of the magnetic circuit are non-sinusoidal, and as a result, an error
in the calculation of the iron losses is expected.
Hysteresis and eddy current losses are calculated from eqns. 5.46 and 5.47 in WIKg
and multiplied by the weight of the iron of the respective magnetic circuit section.
This procedure requires some information on magnetic circuit parameters. The
'active' (or 'excited') volume of iron, Vaci, is equal to
Vact [section] = l[section] A[section]
(5.48)
where l[section] and A[section] represent the length and cross-sectional area of
different sections of the magnetic circuit (such as the stator pole and stator yoke).
The program incorporates a routine to compute V on the motor winding
configuration (short or long flux paths).
139
5.4.4 Output power, input power and efficiency.
The area Ao enclosed by the operating trajectory on the flux linkage / current
diagram of the switched reluctance motor system is equal to the electrical energy
per 'stroke' that is converted to mechanical work. The net power delivered by the
motor shaft is given by
qNr \co
P — A
out
where P
p
fiv
2rc
p
Fe
(5.49)
friction and windage loss and P Fe is the sum of hysteresis and
eddy current losses. The average torque output is expressed as
Pout
Tave
(5.50)
CO
In each working stroke, energy is delivered to the switched reluctance motor from
the power supply during the transistor conduction period. A proportion of the total
energy supplied is converted to mechanical work during this period while the
remainder is stored in the magnetic field. During the diode conduction period,
some of the stored field energy is converted to mechanical work and the remainder,
111, is returned to the power supply. It is not possible to convert all the electrical
energy supplied during one working stroke to mechanical work. The ratio of the
energy converted to mechanical work, A o, to the electrical energy supplied in each
working stroke is known as the energy ratio, E [7].
A
E= (5.51)
Ao + A r
This ratio is computed in the SRDESIGN package because it reveals information
on the rating of the power converter.
The total power input to the motor may be computed by summation of all power
loss components of the system, P and the power made available to the motor
shaft, Pout.
140
(5.52)
Pin = P
out + 'loss
where
loss = Cu
P
Fe
(5.53)
P fiv
The motor efficiency is given by
P out
(5.54)
P out + P in
5.5 Structure of the SRDESIGN package.
The implementation of the modelling theory presented in previous sections has
made use of the modular (or 'unit') structure within Turbo Pascal. This has helped
to subdivide the programming task to manageable sections. The contents and
purpose of each unit will now be described in brief.
5.5.1 Unit CONSTANT.
Information on the geometry of the machine and the number of turns per phase is
used in this unit, in order to calculate the variation of flux linkage with current in
the unaligned and aligned rotor positions. The X, / i diagram computation is based
on the procedure described in [51], which applies to singly excited systems.
System X / i diagrams for switched reluctance motors with two phases
simultaneously excited can be computed, with sufficient accuracy, using finite
element analysis. Unit CONSTANT was therefore written such that the X, / i
diagram can be imported from finite element analysis, should the user choose to
do so. The characteristic is stored in two arrays, namely 'Flux Linkage' and
'Current'.
141
The length of the magnetic flux pattern (short or long flux paths) is estimated and
used for subsequent iron loss computations. Geometrical considerations also allow
the maximum diameter of copper wire that can be used (for a given number of
turns per phase) to be estimated. This information is used to compute the
resistance of the phase winding at room and operating temperatures.
5.5.2 Unit CURRCALC.
The phase current and flux linkage profiles, as a function of rotor position, are
computed within unit CURRCALC. Information on the maximum phase current,
speed of rotation and type of converter employed in the drive is used to calculate
optimum turn-on and commutation angles. Alternatively these parameters can be
keyed in.
Subsequently, the variation of current and flux linkage with rotor position is
predicted within a time stepping algorithm, based on the theory presented in
sections 5.1-5.3. At each time step, the values of the rotor angle, phase current and
winding flux linkage are stored in arrays Aphase, lphase, Fphase. Unit
CURRCALC could be thought of as the 'heart' of SRDESIGN.
5.5.3 Unit DRAW.
This unit makes use of pre-written graphic routines within Turbo Pascal in order
to display graphics on the screen. A plot of any two arrays of the same size
against each other may be created, displayed on the screen and subsequently sent
to a printer if required. The plot facility features automatic scaling of the axes.
The unit was written in a general format such that plots of the variation of all
major parameters with speed (such as torque) and rotor angle (such as flux linkage)
may be obtained.
142
5.5.4 Unit GLOBALS.
All variable and constant definitions are included in this unit, and it is accessed by
all other units including the main (control) program.
5.5.5 Unit INPUTS.
Unit INPUTS allows the user to interactively key in the geometry of the machine
which is to be analyzed. Information on the power converter configuration and
rating is also essential. A machine design may be stored as a file on / or retrieved
from the disk. A built-in facility checks the machine design for errors and prompts
the user for corrections.
5.5.6 Unit MENUS.
Unit MENUS comprises four procedures that activate and display an 'Input Panel
Menu', an 'Operating Conditions Menu' and two 'Results Menus'. The 'Input
Panel Menu' lists user options regarding data input from the keyboard or disk, such
as motor geometry entry and modification. The 'Operating Conditions Menu'
prompts the user to specify the operating speed (or range of) and maximum phase
current for the present run. Presentation of results and user options for a 'single'
or 'batch' run are controlled within the appropriate 'Results Menus'.
5.5.7 Unit RESULTS.
Program results may either be displayed on the screen or sent to a printer. In
'batch mode' the motor performance is predicted, for a specified maximum phase
current value, at a range of speeds. The program tabulates results, indicating the
variation of rms phase current, average torque, total machine losses and efficiency
with speed. A 'single run' examines the motor performance at a specified motor
speed and maximum phase current. A detailed results file is provided for a single
143
run, listing additional information on phase winding resistance, average flux density
values in the iron parts and commutation angle(s).
5.5.8
Main Program.
The main program acts as a data flow controller. Data flow control is achieved by
sequentially calling key procedures within the units. The program also contains
short procedures which use data supplied from units INPUT, CONSTANT and
CURRCALC to compute the average torque, power output, power losses and
machine efficiency.
5.6 Summary.
This chapter presented the 'back bone' theory supported in SRDESIGN.
SRDESIGN is used for sizing and dynamic simulation of the switched reluctance
motor. The program is capable of computing the motor magnetisation curves using
internal (analytical) routines (ref. Unit CONSTANT). However, it does also offer
the facility of importing the curves from finite element analysis.
The A. / 0 characteristic is subsequently computed within SRDESIGN. At low
excitations the A. / e diagram is approximated by a linear function. At higher
excitations, a set of linear and sigmoidal functions are calculated to accurately
define the variation of flux linkage with rotor position. These observations and the
resulting mathematical formulations are the product of extensive finite element
modelling of the switched reluctance motor.
The phase current and flux linkage variation with rotor position is estimated with
the aid of a time stepping algorithm within Unit CURRCALC, having specified the
current chopping level In, and operating speed.
The area enclosed by the operating trajectory described on the A, / i diagram yields
14.4-
the average torque developed in the motor. Program MAINSR includes a
procedure to calculate this. MAINSR also includes procedures to calculate motor
losses and efficiency. SRDESIGN is thought to be a valuable tool to a switched
reluctance motor designer. At the design stage the performance of a motor may
be completely characterised within minutes. The geometry of the motor (stator /
rotor pole width, rotor diameter etc) can then be altered to improve its
performance. More accurate results from a 'reasonable' design may subsequently
be sought by obtaining a finite element model of the motor and importing
magnetisation curves into SRDESIGN. This is advisable in cases where a switched
reluctance motor operating with two phases simultaneously excited is examined.
145
Chapter 6
SRDESIGN VERIFICATION: DYNAMIC
TESTING OF SWITCHED RELUCTANCE
MOTORS
The previous chapter described in detail the 'back bone' structure of SRDESIGN.
The accuracy of this dynamic simulation program was verified by testing the
switched reluctance machines that were available in the laboratory: a 150W 4phase motor and a 4kW 7-phase motor. This chapter will present a comparison of
simulated data and experimental results obtained from these machines. The
strengths and weaknesses of SRDESIGN, which was used for the design of the 5phase prototype, are identified.
6.1 The use of A / i diagrams in SRDESIGN.
Chapter 3 demonstrated that when modelling switched reluctance motors with two
phases excited at any time, electromagnetic theory of doubly excited systems ought
to be adopted. The proposed procedure of computing system X, / i diagrams for
doubly excited switched reluctance motors was implemented using finite element
analysis. The 150W 4-phase motor is operated with two phases conducting
simultaneously. Therefore, X / i diagrams at the 'extreme' rotor positions were
imported from FEA to SRDESIGN for dynamic simulation of the experimental
motor. Two-dimensional finite element modelling was used to obtain the
magnetisation curves; end-core flux correction was applied, as described in chapter
4. The magnetisation (X / i) curves at intermediate rotor positions were computed
within SRDESIGN using mathematical formulations described in chapter 5. A
similar procedure was adopted for the 4kW 7-phase motor configured for long or
short flux loops.
146
In SRDESIGN, it is possible to compute X, / i diagrams at the 'extreme' (unaligned
and aligned) rotor positions, for singly excited switched reluctance motors. This
would be applicable to 1,2 and 3-phase motors. In order to assess the accuracy of
the SRDESIGN algorithm, the X / i diagram of the 150W 4-phase motor (assumed
to operate with one phase excited at any time for comparison purposes) was
computed. This was compared with the corresponding plot obtained using twodimensional finite element analysis and corrected for end-core effects. Figure 6.1
illustrates that, at any excitation level, SRDESIGN tends to yield a lower value of
flux linkage, especially in the unaligned position. However, taking into account
the vast difference in computation speed (SRDESIGN yields the X / i curve within
seconds), the results are satisfactory.
FIG. 6.1 FLUX LINKAGE/CURRENT DIAGRAM (4-PH MOTOR, 1 PH EXCITED)
0.25
SRDESIGN COMPUTATION
0.2 aligned
- CÖRREC10ED 2D FEA
0.15 g
0.1 bnaligned
............... ............... ............... ................ ................ ...
.........
...........
0.05 .....
---5
Current (A)
147
6
10
6.2 Testing the 4-phase 150W motor.
6.2.1 Experimental arrangement.
The purpose of testing the 4-phase motor was to assess the accuracy of the
simulation package in predicting the dynamic performance of a switched reluctance
motor. The SRDESIGN algorithm that is implemented on a motor powered by an
asymmetric half-bridge converter is simpler in comparison to the shared switch
converter algorithm. As a first step, it was therefore thought appropriate to analyze
a drive that employs an asymmetric half-bridge converter. This power converter
was chosen further because it reduces the complexity of the digital controller and
provides increased flexibility.
The SKM181F power MOSFETs that were made available for the research project
were rated at 800V / 32A, suitable for driving a 4kW motor. The gate drive
circuitry has been described in chapter 2. The on-state losses of the SKM181F
modules may well have been higher than the losses that a smaller device, suitable
for a 150W motor, would exhibit. This however was not considered important as
the aim of the exercise was to validate a computer model and not to optimise the
drive efficiency.
Rotor position sensing was present in the 4-phase drive in the form of (four)
optical sensors and a shaft mounted slotted disk. This method produced a
resolution of 7.5°, though this was improved with digital electronic circuits
integrated into the drive controller.
The switched reluctance drive energy ratio, E, is significantly reduced when the
motor is driven in saturation. It was shown by Miller [8] that in a magnetically
linear motor
E
(k1 / ku ) - 1
2(X 1 /
148
)-1
(6.1)
The energy ratio improves with increasing a1 /
X'un
but can never exceed 0.5. In
the saturating motor an energy ratio of 0.6 - 0.7 can be achieved and this reduces
the converter volt ampere requirement.
Finite element studies and flux linkage measurement indicated that the 150W 4phase motor must be excited with a peak phase current of 10A in order to be
driven into saturation. This, however, could not be achieved in practice due to
thermal limitations. The frame that was constructed for the motor was not finned
and no provision was made for a shaft mounted fan. As a result, heat generated
by copper and iron losses was only removed by natural (and not forced)
convection. The current level in the 4-phase motor winding was limited to 5A
with the aid of a pwm current regulator. The pwm current regulator circuit
diagram and description of operation have been presented in chapter 2. One LEM
Hall effect current sensor was used for each phase winding in order to simplify
current control. The experimental 4-phase drive is shown in fig. 6.2.
6.2.2 Test presentation.
A series of tests were carried out to validate the SRDESIGN program. In order to
optimise the motor performance, the onset of excitation was retarded and the phase
current commutation angle was varied. A selection of experimental results together
with computer-aided predictions shall be presented in this section. The reader is
reminded of the notation that is used throughout this section in fig. 6.3.
The predicted and experimental torque / speed curve obtained for I.= 5A Of = 10
and Oo„ = 15° is illustrated in fig. 6.4. The power loss in the motor as a function
of speed is shown in fig. 6.5. Sample SRDESIGN printouts, listing the most
important operating parameters are given for a running speed of 1500rpm in Table
6.1.
A series of tests was conducted in which the on-state angle was kept constant (80„
= 15°, 1m = 5A). Measurements on the 4-phase motor were repeated for a firing
149
Fig. 6.2. The experimental 4—phase drive.
150
Value Units
Parameter
Number of stator poles
Number of rotor poles
Air gap length at alignment
Inter-polar air gap depth
Rotor diameter
Stator outside diameter
Stator back iron width
Core length
Stator pole arc
Rotor pole arc
Shaft diameter
Supply voltage
Turns per phase
Chosen wire diameter
Switching strategy
Angle control technique
Stepping mode
Winding configuration
Step angle
Maximum wire diameter
Actual wire diameter
Resistance of each winding (atTop= 80°C)
Total mass of steel
Total mass of copper
Minimum inductance Phase current
RMS phase current
Peak current density
RMS current density
Maximum speed at this current
Base speed for flat topped current
Running speed
Commutation Ratio
Current at commutation Flux linkage at commutation
Flux linkage at alignment Current at alignment
Average torque
Average torque per rms phasecurrent Stator heat loss
Windage and friction losses
Hysteresis and eddy current losses Total losses in machine Bridge rating
Power returned to supply
Net power input
Shaft power output Efficiency
Energy ratio
No. of phases conducting at one time Flux density in stator poles
Flux density in air gap
Flux density in rotor poles
Flux density in rotor body
Flux density in stator yoke
8 poles
6 poles
0.615 mm
9.500 mm
56.000 mm
106.500 mm
10.000 mm
50.000 mm
0.365 rad
0.436 rad
14.000 mm
100.000 Volts
220 Turns
Auto
Normal
Predefined Commutation angles
Single
Long flux loops
0.262 rad
0.730 mm
0.710 mm
2.021 Ohms
1.676 kg
0.536 kg
6.800 mH
5.000 A
2.480 A
12.629 Aimmimm
6.264 A/mm/mm
2413.753 r/min
3205.109 r/min
1500.000 r/min
0.425
5.000 A
0.088 Wb Turns
0.000 Wb Turns
0.000 A
0.540 Nm
0.218 Nm/A
49.711 W
2.069 W
5.545 W
57.324 W
252.423 W
110.312 W
142.111 W
84.787 W
59.662
0.336
1 phases
0.835 T
0.706 T
0.716 T
0.377 T
0.434 T
Table 6.1. Sample SRDESIGN printout for the 150W 4-phase motor.
151
angle of Of =
0°
to Of = 5°. At low speed it was found that for approximately
equal losses, higher average torque is obtained by retarding the excitation. As the
speed increased, it was more beneficial to impress the supply voltage across the
phase winding early so as to allow sufficient time for the current to rise to
In,•
Figure 6.6 illustrates the maximum torque / speed characteristic that was derived
from this exercise. A similar experiment was performed for
In, =
5A, 0„„ = 200;
figure 6.7 shows the resulting maximum torque / speed curve.
°on
(on—state angle)
°on
0
unaligned Vf
position (firing angle)
= 'a corn —.Of
'acorn
(commutation angle)
'hand
(conduction angle)
Fig. 6.3. Notation used throughout chapter 6.
Two simulated phase current pulses are shown in fig. 6.8 and compared with
measurement at a rotor speed of 450rpm and 1500rpm. The current pulse on-state
angle, 00„, was set to 15°. The simulated X, / 0 and X / i curves at 450rpm are also
illustrated in fig. 6.9a,b respectively.
152
FIG. 6.4 TORQUE / SPEED CURVE (4-PH MOTOR,FIXED COMMN ANGLES)
1
0.9
0.8
0.7
0.6
0.5
f
E- * EXPERIMENT
- SRDESIGN
0.4
0.3
0.2
0.1
o
o
600
400
200
800 1000 1200 1400 1600 1800 2000
Speed (rpm)
FIG. 6.5 POWER LOSS IN THE 4-PH MOTOR (FIXED COMM ANGLES)
120
100
* EXPERIMENT
- SRDESIGN
80
60
**
**
40
20
0
0
200
400
600
800 1000 1200
Speed (rpm)
153
1400
1600
1800
2000
FIG. 6.6 MAX.TORQUE/SPEED CHARACTERISTIC (4-PH,CONDN PERIOD=15 DEG.)
1
0.9 0.8 0.7 ,a,
.,
*
*
0.6 N
0.5 Os:
Fi
0.4 * EXPERIMEN
- SRDE IGN
0.3 0.2 0.1 o
o
200
400
600
800
1000 1200 1400 1600 1800 2000
Speed (rpm)
FIG. 6.7 MAX.TORQUE/SPEED CHARACTERISTIC (4-PH,CONDN PERIOD=20 DEG)
1
0.9
0.8
0.7
1 0.6
z
E.
0.4
0.3
0.2
0.1
0
0
200
400
600
800
1000 1200 1400 1600 1800 2000
Speed (rpm)
154.
PLOTTED:
Jan 14/94
15:25:12
10mU :2ms
TR1:
!ACQUIRED:
:Jan 14/94
i 15:25:12
1A/div
GND
Fig. 6.8a Experimental i / 0 profile @ 45Orpm.
PLOTTED:
Jan 14/94
15:35:31
TR1: 10mU :0.5ms
:ACQUIRED:
Jan 14/94
15:35:31
1A/div
Fig. 6.8b Experimental i / 0 profile @ 1500rpm.
155
Current
A
6.00-
5.00-
4.00-
I
3.00-
2.00-
1.00-
0.00 0.00
0:10
0:20
0.30
I Angle
0.40 rad
Fig. 6.8c SRDESIGN ii 0 profile @ 450rpm.
Current
A
6.00-
5.00
4.00-
3.00-
2.00-
1.00-
0.00
0.00
0.110
0.3 0
0.120
Fig. 6.8d SRDESIGN i / 0 profile @ 1500rpm.
156
0:40
, Angle
0.50 rad
Fig. 6.9a SRDESIGN X, / 0 diagram @ 450rpm.
Flux Linkage
Turns
Wb
*
0.10-
0.08-
0.06
0.04
0.02
0.00
0.00
1.00
2.00
3.00
4.00
5.00
Fig. 6.9b SRDESIGN A, / i diagram @ 450rpm.
157
,
Current
6.00 A
6.2.3 Sources of error.
The spring balance and torque indicating scale arrangement, mounted on the eddy
current test rig, did not provide an accurate reading of the torque applied on the
eddy current brake shaft. Although the equipment was repeatedly calibrated, a
margin of error on the torque reading must be allowed.
In SRDESIGN, average torque is computed using the 'virtual work' method which
involves the computation of the area enclosed by the operating trajectory on the A,
/ i diagram during each stroke. Linear and sigmoidal functions are used to
interpolate between the 'unaligned' and 'aligned' magnetisation curves, and some
error is expected from this.
Errors may also occur in the estimation of power losses using SRDESIGN. Power
losses mainly comprise of copper and iron losses. At low speeds, the heat
dissipated in the copper windings forms the major source of power loss. The
estimation of rms phase current /,„.. and phase winding resistance R has been found
to be very accurate. However, the absence of a thermal model prevents the
prediction of temperature rise in the copper winding and its effect on R. A
transducer mounted on the coil surface measured temperature and this was used as
a guideline in determining R0
running conditions, since the temperature
coefficient of resistance for copper was known. Finally, as the operating speed is
increased the eddy current loss component becomes more pronounced. SRDESIGN
uses the Steinmetz formulae to compute iron losses. However, no modifications
were made to account for the non-sinusoidal flux waveforms encountered in
switched reluctance motors.
158
6.3 Testing the 4kW 7-phase motor.
6.3.1 Experimental arrangement.
The shared switch power converter was employed in the 4kW 7-phase drive.
Figure 6.10 shows seven phase windings connected to eight switching devices and
associated freewheeling diodes. Two series diodes block unwanted current when
more than two switches in the circuit conduct simultaneously. The series diodes
are slow recovery, rectifying diodes because the voltage across them only reverses
at the phase current frequency, not at the chopping frequency seen in the fast
recovery freewheeling diodes.
The motor was designed to operate at a de link voltage of 600V and a peak phase
current of 10A. The top switching devices of the shared switch converter ought
to be rated to withstand twice the motor rated current. These criteria were met by
the SKM181F MOSFET devices.
A brushless resolver was mounted on the shaft of the 7-phase motor and was used
in conjunction with the 11RS260 resolver to digital converter, to provide rotor
position feedback. The digital converter offered 12 bit (0.0879°) resolution, thus
allowing very fine control of the phase current firing and commutation angles.
6.3.2 7-phase motor testing.
Measurements were carried out on the 7-phase motor for a range of operating
speeds up to 1500rpm. A test voltage of 200V and maximum phase current of
10A were chosen. This reduced the motor base speed below the rated speed of
1500rpm and allowed SRDESIGN 'above base speed' algorithms to be verified.
The on-state angle, Oon, was set to 8.57° (twice the step angle). At low speeds
improved performance could be achieved by setting 0 0„ up to three step angles.
However the shared switch converter algorithm allowed the current in only two
159
Fig. 6.10. The experimental 7—phase drive.
160
phase windings to be simultaneously controlled. The current in the third phase
winding would be dependent on the voltage across one of the other two excited
phases. This would be an undesirable feature.
Short and long flux loop configurations were examined. At each running speed
and for a constant O the current firing angle Of was advanced (or retarded)
in steps of 0.7°. The torque, input power and rms phase current were recorded and
the optimum firing angle (i.e. the firing angle for which maximum torque was
obtained) was established. The results of this experimental procedure shall next
be analyzed.
The maximum torque / speed characteristic describing the 7-phase motor
configured for short flux loops is given in fig. 6.11. Also shown is the SRDESIGN
predicted curve, which was drawn having specified the firing angle, commutation
angle and maximum current /„, at each operating speed. Good agreement between
simulated and experimental results is achieved. In the short flux loop
configuration, the 7-phase motor achieved a maximum efficiency of 78%, as shown
in fig. 6.12.
The maximum torque / speed curve obtained by winding the motor for long flux
loops is shown in fig. 6.13. Significantly lower torque was produced by the long
flux loop configuration, although the rms phase current at each test speed was kept
constant. Configuring the 7-phase motor for long flux paths also resulted in an
increase in iron losses. As a result, the motor efficiency decreased significantly,
as shown in fig. 6.14.
At any speed, the torque output was limited by one of two factors. Firstly, there
was a limitation on the amount of losses that could be dissipated by the motor
frame, if the temperature in the stator windings was to be kept within an acceptable
level. This was addressed by controlling the rms phase current. At higher speeds
torque production was limited by the back-emf which exceeded the supply voltage.
161
FIG. 6.11 MAX.TORQUE/SPEED CHARACTERISTIC (7-PH MOTOR,SHORT LOOPS)
30
* EXPERIMENT
- SRDESIGN
25
20
3
0
15
cr
E-(
10
200
400
600
800
1000
1200
Speed (rpm)
FIG. 6.12 EFFICIENCY CURVE (7-PH MOTOR,SHORT LOOPS)
400
600
800
Speed (rpm)
162
1000
1200
1400
Fig. 6.13 MAX.TORQUE/SPEED CHARACTERISTIC (7-PH MOTOR,LONG LOOPS)
30
200
400
800
600
1000
1200
1400
Speed (rpm)
Fig. 6.14 EFFICIENCY CURVE (7-PH MOTOR,LONG LOOPS)
400
600
800
Speed (rpm)
163
1000
1200
1400
A collection of SRDESIGN-generated graphs that describe the 7-phase motor
'behaviour' at 1000rpm is given in fig.
6.15.
It is interesting to note that at 1/„. =
200V the motor is running above base speed when configured for short flux loops.
In contrast, the same drive runs below base speed when configured for long loops.
This is because the system 2 / i characteristic predicted by finite element analysis
was different for the two machine configurations. Base speed may be expressed
as
(Vs - / R)13
?tt
(6.2)
b
al —
bo
The difference Xal A.,bo was greater in the short flux loop machine configuration.
This example demonstrates yet again the adverse implications of neglecting
magnetic interaction effects. Had the magnetisation curves at the aligned and
unaligned positions been constructed using the virtual work method as applied to
singly excited systems, no information on the modified A, / i curve, which results
by exciting a second phase or configuring the machine for short loops, would be
conveyed to the user.
Referring to the simulated phase current profiles shown in fig.
6.15,
the current
rises to 8.5A (chosen chopping level) and maintains this value until the rotor teeth
begin to overlap with the excited stator teeth. In the overlap region, if the backemf exceeds the supply voltage (short flux loops) the current decreases though flux
linkage continues to increase. If the supply voltage exceeds the back-emf (long
flux loops) then the current is maintained constant (with the aid of a current
chopper in practice). Upon commutation, the phase current decreases in a zero volt
loop; flux linkage also decreases, with a slower rate of fall though. Full negative
volts subsequently force a faster rate of fall of flux linkage.
6.4 SRDESIGN practicality.
The purpose of SRDESIGN is to provide a design and simulation facility for
switched reluctance motors. SRDESIGN is capable of completely characterising
164-
Current
A
10.00-
8.00-
6.00-
4.00-
2.00-
0.00
0.00
0.10
0.20
, Angle
0.40 rad
0.30
Fig. 6.15a SRDESIGN i / 0 profile @ 1000rpm (short loops).
Current
A
10.00-
8.00
6.00
4.00
2.00
0.00 0.00
0.110
0.120
, Angle
0.40 rad
0.30
30
Fig. 6.15b SRDESIGN i / 0 profile @ 1000rpm (long loops).
165
Flux Linkage
Wb * Turns
0.30-
0.25-
0.20-
0.15-
0.10-
0.05-
0.00
0.00
0.10
0.20
I Angle
0.40 rad
0.30
Fig. 6.15c SRDESIGN X / 0 diagram @ 1000rpm (short loops).
-Fig. 6.15d SRDESIGN X / 0 diagram @ 1000rpm (long loops).
166
Fig. 6.15e SRDESIGN X / i diagram @ 1000rpm (short loops).
Fig. 6.15f SRDESIGN X, / i diagram @ 1000rpm (long loops).
167
the performance of a switched reluctance motor within minutes. However, with
how much accuracy is the analysis performed?
This very much depends on the starting point: the X /
i
diagram at the unaligned
and aligned rotor positions. If the magnetisation curves are imported from finite
element analysis, preceding sections demonstrated that the predicted motor torque
at any speed or commutation angle is within 10% of the measured value. This is
very acceptable considering that the X, / 0 curves are computed analytically within
SRDESIGN. In addition, the simulated
i I
0 profile at any speed compares
favourably with traces obtained experimentally.
However, importing
A, / i
diagrams implies additional man hours to produce the
finite element model. Accurate results may only be obtained by computing the X
/ i diagram within SRDESIGN, if switched reluctance machines operating with
only one phase excited at any time are being examined. This subject was
addressed in section 6.1.
Switched reluctance motor losses are also calculated within a 10% accuracy,
though this is achieved by manually entering the (measured) operating temperature
in the copper windings. The absence of a thermal model suggests that an
SRDESIGN user must have some basic knowledge on the permissible current
density that can appear in the motor in order to avoid overheating. SRDESIGN
supplies information on -
peak
and 4... Miller [8] provides some guidelines on
maximum permissible current densities for a range of motor types.
168
Chapter 7
THE 5-PHASE SWITCHED RELUCTANCE
DRIVE: DESIGN, CONSTRUCTION AND
PERFORMANCE
The design, construction and testing of the 5-phase switched reluctance drive are
presented in this chapter. The electromagnetic theory of doubly excited systems
is used in the motor lamination design process. Finite element analysis is
employed to model the static performance of the 5-phase prototype. This is
compared with the static performance of a 4-phase motor based on the Oulton3
motor design. SRDESIGN was employed for the dynamic simulation of the 5phase drive. Experimental results from the constructed 5-phase drive are compared
with simulation data. Market applications of the 5-phase switched reluctance drive
are discussed.
7.1 5-phase motor design.
The task was to design a switched reluctance motor, to be constructed inside a
standard D112 induction motor frame. An outer stator diameter constraint of
165mm was therefore imposed. The existing D112 frame also set a constraint on
the stack length of approximately 150mm. The main aim was the electromagnetic
design of an energy efficient switched reluctance motor.
7.1.1 Selection of stator pole arc and back-iron width.
A 10/8 5-phase motor, showing motor dimensions is depicted in fig. 7.1. The
choice of stator pole arc and stator back-iron width must be a compromise between
3The Oulton motor is a well known motor design, manufactured by Graseby Controls.
169
rotor pole pitch (rad)
stator pole pitch (rad)
ds stator outside diameter (mm)
ts stator pole width (mm)
stator back—iron thickness (or stator yoke)
y
ps stator pole arc (rad)
dr rotor diameter (mm)
Pr rotor pole arc (rad)
g airgap (mm)
d b=d r +2g
Fig. 7.1. Dimensions of a 10/8 5—phase motor.
170
the requirement for a low reluctance iron path and the need for sufficient space for
the copper conductors. A comprehensive study on the sensitivity of stator and
rotor pole arc / pole pitch ratios on 3-phase switched reluctance motors has been
reported [60]. It was illustrated that average torque may be maintained at high
levels if the stator pole arc / pole pitch (0, I s) ratio is between 0.35 and 0.45.
Faiz and Finch [61] reported that maintaining ps I s within 0.42-0.47 would
maximise torque production though this must be reduced, subject to Ohmic loss
constraints. Miller [8] reports that the optimum
13, /
s ratio increases with the
number of poles. However, these observations should only be used as guidelines.
The stator pole arc ought to be chosen in conjunction with the stator bore, db.
These two dimensions set the pole width, ts according to
db
= 2(_.
2
f3
(7.1)
2
which dictates the path reluctance.
In switched reluctance motors the stator bore is found to increase with increasing
pole numbers. In order to establish the stator bore, suitable for the 5-phase short
flux path motor, finite element models of varying bore were constructed. The
stator pole arc, r3s , and stator pole width / yoke thickness ratio (t, / y) were held
constant. As a result ts increased with increased db. It was found that a db I d =
0.535 design produced significantly less average torque, as shown in fig. 7.2.
These and subsequent comparisons between different 5-phase motor designs
assume equal copper loss. The db I d,= 0.535 structure also exhibited the highest
operating flux densities. The results depicted in fig. 7.2 were by no means
conclusive. Thermal considerations dictate that the conductor current density must
be maintained at low levels in order to limit the temperature rise in the windings.
Therefore the lowest db I d, ratio possible that would not limit T was chosen: db
I d, was set to 0.6.
In a subsequent design exercise 13, / s was varied from 0.42 to 0.45, for a constant
stator bore to stator outer diameter ratio (db I d„) of 0.6. It was found that
171
FIG. 7.2 VARIATION OF STATOR BORE WITH AVERAGE TORQUE (CONSTANT POLE ARC)
35
34.5
34
33.5
33
0
32.5
0
F
32
31.5
31
30.5
30
0 5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
Stator bore / outer dia. ratio
FIG. 7.3 VARIATION OF AV. TORQUE WITH STATOR POLE ARC / PITCH RATIO
34
33.8 ...............
.........
LOSS
EQUALCOPPER
.
33.6
> Decreasing current ensity
33.4 .............
33.2 ......................
> Increasing flux density
...
.........................
33
0
32.8 .............
................
32 .6 _ .........................
.......... .........................
........... ......................
32.4 .....................
.........
32.2
32
0.42
0.425
0.43
0.435
0.44
Stator pole arc / pole pitch ratio
172
0.445
0.45
marginally lower torque was produced by the [3, / s 0.42 tooth design in
comparison with higher 13, Is ratio designs, as shown in fig. 7.3. This design would
also exhibit marginally higher iron loss. However, the current density in the coil
would be somewhat lower. It was decided to strike a balance between high flux
density and high current density by setting p s I s to 0.435. A design validation
exercise was subsequently performed. Additional finite element models were
defined in which the db / ds. ratio was set to 0.58 and 0.62 and Ps / s was varied.
No significant change in performance was noted.
The back-iron thickness must be specified having considered the magnetic flux
patterns that arise in the switched reluctance motor. If the system is singly excited
(e.g. a 2-phase 4/2 motor), the back-iron need only be as thick as approximately
half the stator pole width. The two 180° yoke sections can then share the flux
linking the diametrically opposite excited stator poles. The stator yoke thickness
must be increased in 3-phase 6/4 designs to account for the partial overlap between
phase current pulses. In motors with two phases excited simultaneously (such as
the 4-phase 8/6), the back-iron thickness ought to be (approximately) equal to the
stator pole width. If however a switched reluctance machine is designed for short
flux paths, the back iron does not constitute a significant part of the magnetic
circuit. The back-iron thickness can therefore be decreased for the benefit of
increased copper area (and hence reduced copper loss). Alternatively, for the same
slot area, the stator bore of a short flux loop machine can be increased, resulting
in a linear increase in torque production.
Finite element studies have shown that, as the back-iron thickness of the 5-phase
10/8 motor is reduced from ts. to 0.65t„ the average torque per unit copper loss is
increased when the motor is configured for short flux loops. This is because the
benefit that arises from the increased copper area overwrites the penalty incurred
by narrowing the stator yoke and, as a result, increasing the yoke reluctance. This
result does not hold for the long flux path-configured 5-phase motor. The
reluctance of the long B-field path around the stator yoke increases significantly
when the yoke thickness is reduced beyond 0.8t„ and the average torque output is
173
compromised.
In contrast to the electromagnetic design, it is required mechanically that the stator
yoke is thick in order to maximise the stiffness of the stator against compressive
forces. This is important in reducing acoustic noise. Therefore, a compromise
between the two requirements (bigger slot area or stiffer structure) was reached.
The copper area was shaped for rectangular coil sections and the coil was designed
to make contact with both the stator pole side and the back-iron for improved heat
transfer capability. The average stator yoke thickness in the 5-phase motor was set
to O.8 t.
7.1.2 Stator / rotor pole arcs.
A simple 'rule of thumb' that is applicable to singly excited switched reluctance
systems states that the rotor and stator pole arcs ought to be approximately the
same. The 'useful' energy converted to mechanical work, is equal to the difference
in the system coenergy at the 'aligned' and 'unaligned' rotor positions. If for
example pr was to be increased significantly beyond 13 there would be no
noticeable increase in the 'aligned coenergy'. In contrast, the 'unaligned coenergy'
would be increased, hence decreasing the torque output of the machine.
Referring to fig. 7.4, as the rotor moves from position 1 (0 = 13,) to position 2 (0
= Pr) the phase winding flux linkage (at constant excitation) remains constant i.e.
I
d0 = 0. This is the 'zero torque period' that compromises the average torque
produced by the motor. However, the 'zero torque period' offers more time for the
flux in the aligned pole to be forced to zero before negative torque is produced.
The rotor pole width of the 5-phase motor was designed marginally bigger than the
stator pole width. More time was therefore made available to force the flux to zero
upon commutation. This design feature would prove especially useful if the shared
switch asymmetric half-bridge converter was connected to the 5-phase motor. This
converter does not allow full negative volts to be impressed across the motor
winding at commutation. The torque production capability of the motor is not
174
compromised by this choice; an 18° conduction period ensures that both excited
phases are always in the torque producing region.
Position 1
Position 2
a go
0=fi's
19=16r
Fig. 7.4. Illustration of the 'zero torque period' concept.
The excitation cycle of the proposed 5-phase motor is shown in fig. 7.5a. The
distribution of the B-field in the motor configured for short or long flux paths is
shown in fig. 7.5b,c respectively. The rotor is positioned at 6° with respect the
unaligned position of the trailing phase.
Duration of excitation cycle (in deg.) = 9°
Phase current conduction angle = 18°
Beginning of excitation cycle
(0° position)
End of excitation cycle
(9° position)
Fig. 7.5a. Excitation cycle in the 5—phase motor.
175
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178
7.1.3 Rotor slot depth.
Minimum airgap permeance data for doubly slotted structures has been presented
by D. Tormey and others [62]. The authors suggested that the ratio of rotor slot
depth to rotor slot arc ought to be higher than 0.4. Additionally a rotor slot to
stator pole arc ratio of 1.5 or higher ensures low airgap permeance. However,
there is no point in making the rotor slot too deep because, in unaligned the
position, B-field lines from the stator pole tend to fringe into the rotor teeth edges
as shown in fig. 7.6a. Finite element studies on the 5-phase motor have verified
the notion that a semicircularly shaped rotor slot, shown in fig. 7.6b, is adequately
deep to provide low airgap permeance, provided the rotor slot to stator pole arc
ratio is higher than 1.5. In the 5-phase motor, it was further ensured that there was
enough clearance in the unaligned position to build up the current to its full load
value at the rated speed of 1500 rpm.
stator pole
arc
rotor slot
arc
n
I
1
rotor slot arc > 1.5 stator pole arc
Fig. 7.6b. Rotor slot depth considerations.
179
7.1.4 Choice of steel grade.
The choice of silicon steel grade to be employed in a switched reluctance motor
is dependent on the number of phases (i.e. fundamental frequency of excitation)
and the motor rated speed. High speed machines employ low loss TRANSEL grade
steel in order to limit eddy current losses. Low speed machines employ
NEWCORE grade steel which is highly permeable in order to reduce copper losses.
The 5-phase switched reluctance motor can be configured for short flux loops.
This excitation pattern reduces core losses substantially. The need for expensive
TRANSIL grade steel was therefore removed. A LOSIL 500-50 (0.5mm in
thickness) grade, which is between the NEWCORE and TRANSIL grades, was
readily available from European Electrical Steels and was considered suitable for
use in the construction of the 5-phase prototype.
Figure 7.7 illustrates the final drawing drafted for the 5-phase switched reluctance
motor, and Table 7.1 lists the full specification. The number of turns per phase
was set to 160; the maximum current level in the winding was not to exceed 15A.
7.2 5-phase motor construction.
7.2.1 Construction procedure.
The 5-phase motor laminations were laser-cut from long sheets of silicon steel.
SUBCON laser cutting undertook the fabrication of the laminations. The
laminations were cut to a guaranteed tolerance of 0.1mm. However, the specified
guaranteed tolerance was not satisfactory for critical dimensions such as the stator
bore, db, and rotor diameter, dr, Dimensions dr and db set the length of the airgap
which was designed to be 0.25mm. Within the specified tolerance the airgap could
be reduced to 0.05mm or increased to 0.45mm; this was unacceptable. SUBCON,
however, agreed to cut sample laminations which were sent- to Warwick for
inspection. 'Batch production' commenced once all dimensional requirements were
180
•
5 0 . =
1
I
I
I jyt
ii
n
I 10!
it
lr.
i
21
41110
,ir.tilitm
Apr
ein
1
i
i
q
111:1
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tEr
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0,
1.
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di
4
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tt,,g
v-4L.Nor
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v
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2
a
v
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0A
0
l1it4i
4A
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181
t
met, and the quality of the laser cut was up to standard: free of burrs and burns.
number of stator poles
10
number of rotor poles
8
stator diameter
165 mm
stator pole arc
0.275 rad
stator pole height
20 mm
airgap length
0.25 mm
rotor diameter
100 mm
rotor pole arc
0.34 rad
stack length
150 mm
160
turns per phase
maximum phase current
15 A
maximum supply voltage
600 V
Table 7.1 Dimensions of the experimental 5-phase motor.
A stacking fixture, shown in fig. 7.8, was made in order to stack the stator
laminations. The fixture consisted of two parallel plates through which four
circular cross-section bars run. Each bar located at two points on the stator
lamination: on the side of a stator pole and yoke section. This arrangement
ensured that there was no skew on the stack. The mechanical fixture allowed
access to the circumference of the stator laminations.
It was thought initially that the stack could be held together by spring-steel strips,
located in the pre-fabricated grooves on the outside diameter. This was a 'clean'
method that is successfully adopted in induction motors. However, the facilities
182
Stator and rotor laminations.
The stacking fixture for the stator laminations.
Fig. 7.8 The 5-phase motor construction process through a set of photographs.
183
The wound stator assembly.
-MCI=
milmmoN011n11=NIR
The rotor assembly.
Fig. 7.8 (cont.) The 5-phase motor construction process through a set of
photographs.
184
at Warwick workshops proved inadequate to fit the strips finnly in place. 'This job
was also made difficult by the unevenness of the grooves, presumably caused by
the poor laser-robot repeatability. Therefore, once the stacking fixture plates were
pressed on, the laminations were welded at two points on the outside diameter.
The quality of the MIG weld proved poor in comparison to resistance welds
adopted on a manufacturing process in industry. A stacking factor of 0.945 was
achieved for the stator stack.
The 5-phase motor outside diameter and stack length was designed to shrink-fit
into a standard D112 induction motor frame. The aluminium cast frame was
supplied by Electrodrives Ltd. The assembly procedure involved heating up the
frame to 100°C at which temperature the aluminium expanded and the stator stack
was pushed in. The arrangement was left to cool at room temperature and the
aluminium frame contracted to fit onto the stack. Once the lamination assembly
was rigid, the mechanical stacking fixture was dismantled. Subsequently, 80 turns
of 1.32mm diameter copper wire were wound around each stator pole. The slot
fill factor of 0.45 estimated by the SRDESIGN program was achieved.
The rotor laminations were stacked on the shaft and located on the shaft key. The
laminations were subsequently pressed into position using two steel endplates.
Endcaps placed on each end of the stack ensured that the rotor laminations were
held firmly in place. A stacking factor of 0.93 was achieved for the rotor stack
assembly.
7.2.2 Potential improvements of the constructed 5-phase motor.
Welding the back of the core introduces paths for eddy currents to flow and
potentially degrades material properties at the weld area. Holding the stack with
spring-steel strips would be preferable.
The copper slot fill factor of 0.45 that was estimated in SRDESIGN proved overcautious. Having examined the wound stator, it was thought that 80 turns of
185
1.4mm diameter wire could have been wound around the stator poles, hence
increasing K, to 0.5. In addition, ample space was allowed at the ends of the stack
for end windings and terminating connections. In retrospect, the motor stack
length could have been increased from 150mm to 160mm.
The stacking factors achieved, though satisfactory, could be improved significantly.
Stacking factors as high as 0.98 are achieved in industrial manufacturing processes,
where appropriate tools are available to apply high pressure on the laminations and
eliminate 'air pockets'.
All these factors would potentially improve the efficiency of the 5-phase prototype.
7.3 Measurement of flux linkage and static torque.
The static magnetisation curves at the unaligned and aligned rotor positions were
measured and compared with calculated values. The measurement of
magnetisation curves is based on the integration of Faraday's voltage equation, as
described in chapter 2. Measurement on all phases was carried out in order to
investigate the degree of potential imbalance in flux linkage (and hence torque) in
the five phases. The results are depicted in fig. 7.9. It is concluded that some
degree of imbalance does exist in the phase windings; the two extreme cases
(phases with highest and lowest A) are shown. Imperfections in the mechanical
assembly account for this phenomenon and the results are very acceptable on the
whole, considering that no subsequent stack-machining operations were performed.
Figure 7.9 also illustrates the magnetisation curves calculated using twodimensional finite element analysis. An average stacking factor of 0.94 was
assumed for modelling purposes. Three-dimensional effects are not pronounced in
the 5-phase prototype (such was also the case with the 7-phase prototype) because
the stack length / outside diameter ratio is high. Good agreement between finite
element analysis results and measurement is noted.
The predicted static torque profile is superimposed on the measured characteristic
166
FIG. 7.9 FLUX LINKAGE / CURRENT DIAGRAM (5-PH MOTOR, 1 PH EXCITED)
0.7
*,+ EXPERIMENT
- 2D FEA
0.6
0.5
0.4
I
0.3
0.2
0.1
10
8
12
14
Current (A)
FIG. 7.10 STATIC TORQUE PROFILE FOR THE 5-PH MOTOR (I=12.75A)
40
35
„
30
3
a)
25
+ EXPERIMENT (long loops)
20
* EXPERIMENT (shortloops)
- 2D FEA (long loops)
- 2D FEA (short-loops)
15
iTav(shott)=30Nm
10
Tav(long)=25Nru
Copper loss = 265W
5
o
o
1
2
3
4
5
6
Absolute Rotor Position (deg)
187
7
8
9
10
in fig. 7.10. The
TI
0 characteristic was obtained by simultaneously exciting the
two phase windings that were in the torque producing region with 12.75A. Short
and long flux loop configurations were examined. At any rotor position, higher
torque is obtained when the motor is configured for short flux paths. Figure 7.10
indicates the maximum average torque T
T., =
1
step
at this excitation level where
fTde , step =
90
(7.2)
Some error is noted between predicted and experimental results. In finite element
analysis, the Maxwell stress integral was computed to yield forces acting on the
rotor surface and hence torque at any rotor position. Although the mesh was
refined in the airgap region, an error is expected from this computation which may
be amplified when two phases are producing torque. The magnetic imbalance
caused by imperfect mechanical construction may have also resulted in a
discrepancy between predicted results and measurement.
7.4 Static performance comparison between the 5phase prototype and the 4-phase Oulton motor.
For comparison purposes, the static performance of a 4-phase motor based on the
`Oulton.' motor design was examined in finite element analysis. Unlike the 5-phase
prototype, the outer diameter of the 4-phase motor was 180mm. The comparison
between the 4-phase and 5-phase motors was therefore performed on a 'torque per
unit volume' basis and for equal copper loss (ref. Appendix C). Both machines
were assumed to have an airgap of 0.25mm and a stack length of 150mm.
Table 7.2 lists the results of this static performance comparison. It is interesting
to note that the 4-phase motor stands to gain significantly by commutating well
before alignment. This technique, first proposed in chapter 3, results in higher
torque development and less copper loss. Table 7.2 confirms that, at its best, the
4-phase motor develops 17% less torque per unit volume compared with the short
flux path machine. In addition, the iron losses of the 5-phase machine will be
188
Ta,
per
Ta,
per
Tay per
Motor
unit volume
unit volume
unit volume
type
0,=18°
Oc=300
Oc=26°
(Nm / m3)
(Nm I m3)
(Nm / m3)
7225
8510
4-phase
Oulton
5-phase
short loops
10289
Table 7.2 Static torque developed by the 4-phase Oulton and 5-phase prototype
motors (equal Pci, loss).
significantly lower compared with the iron losses of the 4-phase motor, because the
5-phase machine is excited with short flux paths. Manipulation of the Steinmetz
core loss formulae [59] can produce an approximate comparison on the core loss
per Kg exhibited by the 4-phase and 5-phase machines. The Steinmetz formulae
can be written as
'Fe = Kh fBnnla. Ke f2 Bm
2
(7.3)
The fundamental frequency of excitation can be written as
f=
co AT,(7.4)
Constants Kh and IC depend on material properties and active volume, and may be
rewritten as
= C e v o(7.5)
Kh
ChVo
(7.6)
where v, is the active (or 'excited') material volume, equal to the magnetic circuit
length 1m times the cross-sectional area A. Geometrical considerations were used
to compute the magnetic circuit length of a 4-phase long flux loop machine and a
159
5-phase short flux loop machine. The approximate core loss equations for the two
machines were therefore found to be
1 Fe_4ph = 0.61 C h A 6w B:ax
= 3.66chA w B
PFe_5ph = 0.25chA 8co
+
+
0.61ceA 36 co2Bm2.
(7.7)
21.96ceA co 2 Bm2a„
13L +
0•25ceA 64(0 2 Bm2.
(7.8)
= 2chA w B, + 16ceA co 2 Bm2a„
These equations confirm that significantly lower iron losses are exhibited by the
5-phase motor, though this benefit decreases with speed. The cross-sectional area
of the magnetic circuit, A, dictates
13,7,„,
and is dependent on the motor design.
The comparison did not consider temperature rise effects in the phase windings;
it should be noted that the current density in the 4-phase motor was marginally
lower.
7.5 Dynamic performance prediction.
SRDESIGN was used to model the performance of the 5-phase prototype under
running conditions. Outlined in this section shall be the simulated results obtained
for the rated voltage of 600V (rectified 3 - 0, 415V, ac mains).
The 5-phase motor can be fed from an asymmetric half-bridge or a shared switch
power converter. In either case SRDESIGN was instructed to compute optimum
firing and computation angles, using the procedure described in chapter 5. A
current chopping level
I.
was specified in SRDESIGN for which full load torque
(25Nm) would be produced at the rated speed of 1500rpm. The current chopping
level,
was dependent on the type of power converter employed.
The torque / speed curve predicted by SRDESIGN, assuming an asymmetric half190
bridge converter is shown in fig. 7.11a. At each operating speed the rms current,
commutation ratio, output power and losses (as predicted by SRDESIGN) are given
in Table 7.3. A current chopping level of 13.425A is sufficient for the motor to
produce 25.5Nm of torque at 1500rpm. The torque output is maintained fairly
constant for a wide range of operating speeds. Beyond 750rpm, torque begins to
fall (but not significantly) as the commutation ratio is reduced from 1.0 to 0.761
at 1500rpm. The efficiency curve for the asymmetric half-bridge powered motor
is given in fig. 7.11b. It is shown that the motor efficiency climbs to above 80%
at 500rpm and reaches 91% at the rated speed of 1500rpm. Every confidence was
placed on the computation of copper loss at room temperature, as the phase
winding resistance was computed to be equal to the measured value of 0.812.
However it must be pointed out that any temperature rise in the phase winding and
its resultant effect on winding resistance was neglected in this exercise. An 80°C
increase in winding temperature is specified as the maximum level for class B
motor operation. The 5-phase motor rated rms current density never exceeds 6.5A
/ mm2. This figure is modest for a fan-cooled industrial drive [8] and winding
temperature was therefore not expected to exceed the specification. It was
estimated that at 1500rpm, efficiency would fall to 90.05%, if the winding
temperature was to rise to 100°C.
The simulated torque / speed curve of the 5-phase prototype employing the shared
switch power converter is shown in fig. 7.12a. SRDESIGN simulated performance
data is given in Table 7.4. It is demonstrated that a higher current chopping level
of 14.5A is required to maintain full load torque at 1500rpm. This is due to the
operating requirements of this converter which result in reduced negative volts
upon commutation. Therefore, in order to reduce the phase current to zero before
entering the regenerative region, commutation is advanced. As a result, torque falls
off faster as the speed increases, from 31.5Nm at 200rpm to 25.5Nm at rated
speed. However, this requirement does not impose a penalty on the efficiency of
the 5-phase motor, as fig. 7.12b suggests. The additional copper losses incurred
are counterbalanced by the reduced iron loss resulting from lower operating flux
densities. Efficiency is maintained above 90% at rated speed.
191
Torque
Nn
30.00-
25.00-
20.00-
15.00-
10.00-
5.00-
0.00
0.00
5001.00
1000.00
Speed
1
1500.00r/nin
Fig. 7.11a Torque / speed curve predicted by SRDESIGN (asymmetric half-bridge
converter).
Efficiency
%
100.00-
80.00-
60.00-
40.00
20.00
0.00 0.00
500.00
1000.00
Speed
1500.00r/nin
Fig. 7.11b Efficiency / speed curve predicted by SRDESIGN (asymmetric halfbridge converter).
192
Value Units
Parameter
10 poles
8 poles
0.250 mm
15.000 mm
100.000 mm
165.000 mm
10.750 mm
150.000 mm
0.275 rad
0.340 rad
40.000 mm
600.000 Volts
160 Turns
1.320 mm
Normal
Automatic angle selection
Single
Short flux loops
Number of stator poles
Number of rotor poles
Air gap length at alignment
Inter-polar air gap depth
Rotor diameter
Stator outside diameter
Stator back iron width
Core length
Stator pole arc
Rotor pole arc
Shaft diameter
Supply voltage
Turns per phase
Chosen wire diameter
Switching strategy
Angle control technique
Stepping mode
Winding configuration
Speed results for phase current of
(r/min)
Torque
(Nm)
100.000
200.000
300.000
400.000
500.000
600.000
700.000
800.000
900.000
1000.000
1100.000
1200.000
1300.000
1400.000
1500.000
28.808
28.762
28.716
28.670
28.624
28.577
28.620
28.372
27.996
27.635
27.230
26.801
26.373
26.017
25.523
Speed
corn
ratio
1.000
1.000
1.000
1.000
1.000
1.000
0.977
0.946
0.917
0.888
0.861
0.834
0.809
0.784
0.761
RMS
current
7.974
8.003
8.033
8.062
8.091
8.120
8.050
7.950
7.856
7.764
7.677
7.593
7.511
7.429
7.355
Pout
(W)
301.678
602.389
902.134
1200.912
1498.723
1795.568
2097.929
2376.883
2638.573
2893.910
3136.638
3367.903
3590.308
3814.324
4009.095
13.425A.
Power
Loss/W
Efficiency
(%)
266.863
277.427
288.957
301.454
314.917
329.347
337.011
342.719
349.137
355.958
363.270
370.962
378.889
386.884
395.332
53.062
68.468
75.740
79.935
82.636
84.501
86.159
87.398
88.314
89.047
89.621
90.078
90.454
90.791
91.024
Table 7.3 SRDESIGN simulated data for the 5-phase short flux loop motor
(asymmetric half-bridge converter).
193
Torque
Nn
40.00-
30.00-
20.00-
10.00-
0.00
0.00
5001.00
1 ooO
.00
1500.007;:ln
Fig. 7.12a Torque / Speed curve predicted by SRDESIGN (shared-switch
converter).
Efficiency
%
100.00-
80.00-
60.00-
40.00-
20.00-
0.00 0.00
Speed
1500.00r/min
1
1000.00
Fig. 7.12b Efficiency / Speed curve predicted by SRDESIGN (shared-switch
converter).
194
Parameter
Value Units
10 poles
8 poles
0.250 mm
15.000 mm
100.000 mm
165.000 mm
10.750 mm
150.000 mm
0.275 rad
0.340 rad
40.000 mm
600.000 Volts
160 Turns
1.320 mm
Novel Switching Algorithm
Automatic angle selection
Single
Short flux loops
Number of stator poles Number of rotor poles
Air gap length at alignment Inter-polar air gap depth
Rotor diameter
Stator outside diameter
Stator back iron width Core length
Stator pole arc
Rotor pole arc
Shaft diameter
Supply voltage
Turns per phase
Chosen wire diameter
Switching strategy
Angle control technique Stepping mode
Winding configuration Speed results for phase current of
Speed
(r/min)
100.000
200.000
300.000
00.000
500.000
600.000
700.000
800.000
900.000
1000.000
1100.000
1200.000
1300.000
1400.000
1500.000
Torque
(Nm)
31.433
31.386
31.338
31.291
31.244
31.191
31.012
30.511
29.939
29.332
28.642
27.804
26.969
26.116
25.499
corn
ratio
1.000
1.000
1.000
1.000
1.000
0.990
0.949
0.908
0.868
0.827
0.786
0.745
0.704
0.663
0.633
RMS
current
8.613
8.647
8.682
8.717
8.754
8.748
8.600
8.458
8.312
8.164
8.014
7.864
7.709
7.553
7.443
Pout
(W)
329.170
657.346
984.528
1310.716
1635.909
1959.814
2273.302
2556.116
2821.711
3071.677
3299.292
3493.917
3671.388
3828.733
4005.361
14.500A.
Power
Loss/W
310.296
321.535
333.838
347.210
361.658
373.656
374.955
376.782
378.488
379.916
380.900
381.464
380.960
379.623
382.312
Efficiency
(%)
51.476
67.153
74.678
79.058
81.895
83.987
85.841
87.153
88.173
88.993
89.650
90.157
90.599
90.979
91.287
Table 7.4 SRDESIGN simulated data for the 5-phase short flux loop motor (shared
switch converter).
195
Finally it must be pointed out that the D112 frame supplied by Electrodrives Ltd
is designed to dissipate approximately 800W when cooled by a shaft mounted fan
at the rated speed of 1500rpm [63]. SRDESIGN simulated data suggests that
power losses are maintained below 400W, irrespective of the type of power
converter employed. It therefore follows that the 5-phase prototype is capable of
producing in excess of 4kW at rated speed.
7.6 Experimental arrangement.
The simulation program dictated that the 5-phase switched reluctance drive,
employing either an asymmetric half-bridge or a shared switch converter, is capable
of delivering 4kW at 1500rpm with a motor efficiency in excess of 90%. This
prediction was based on the assumption that the power converter dc link voltage
was 600V (3 - 0, 415V, rectified).
A SORENSEN DCR 600V-16A power supply, capable of meeting the converter
requirement, was available in the laboratory. However, it was (repeatedly!) found
that this power supply could not cope with the
dv I dt
rates imposed by this type
of load. The next option available was the Electronic Measurements TCR power
supply. This supplied a maximum of 2.25kW at 300V (1 -
0,
240V, rectified) and
proved reliable in operation. At higher speeds two TCR power supplies were
connected in parallel ('master' / 'slave' configuration) to increase the supply of
current. However, the 'master' did not share current equally with the 'slave'. A
peak power of approximately 3.5kW could be drawn from the power supplies. The
available dc power supplies therefore imposed a limitation in testing the motor
above 3.5kW input power.
The load machine (dc generator) was capable of generating 7.5kW at 1500rpm.
Large resistor banks were connected across the armature terminals of the dc
machine.
A schematic from the experimental 5-phase switched reluctance drive is illustrated
196
in fig. 7.13a. A photograph of the drive is also shown in fig. 7.13b. The drive
employed an asymmetric half-bridge power converter with ten SKM181F MOSFET
devices and associated freewheeling diodes. This arrangement provided the
flexibility in operation needed to optimise the efficiency of the motor at the
reduced supply voltage of 300V. Increasingly important became the ability of
impressing full negative volts across the commutated phase winding, especially at
higher running speeds. The shared switch converter can only supply full negative
volts interspersed with zero volts upon commutation. The commutation point must
therefore be advanced in order to avoid regeneration. The SRDESIGN simulation
program predicted that at 173. = 300V and 1m = 15A, the 5-phase drive would not
deliver the rated torque of 25.5Nm at high speeds if a shared switch converter was
employed.
All logic functions were performed in XlLINX. Five optoelectronic devices in
conjunction with a shaft mounted slotted disk provided rotor position feedback to
the XILINX control board. The resolution of this system was 4.5°. Phase current
was measured by an LEM Hall effect transducer. The current demand was
compared with the measured value and the error signal was converted to a digital
PWM signal and passed to the XILINX control board. The correct switching
signals were subsequently fed from the control board to the gate drivers.
7.7 Test presentation.
Measurements were taken on the 5-phase motor for a range of torque loadings and
operating speeds up to 1500rpm. At each running speed and torque loading, the
total input power to the drive was measured in order to compute the drive
efficiency. The phase current waveform and rms phase current value were also
recorded. A thermocouple, fitted on the surface of a motor coil, provided an
approximate value of winding temperature.
Short and long flux loop winding configurations were examined for comparison
purposes. At each running speed and torque loading, the efficiency of the short
197
HALL EFFECT
CURRENT
MEASURING
DEVICE
1
PHASE
[I TERMINALS
5—PH MOTOR
0
TOP
SWITCH
DRIVE
CIRCUIT
I
I
I
I
SLOTTED DISK
AND OPTICAL
SENSOR
BOTTOM I
SWITCH I
DRIVE
CIRCUIT I
L
— — —
—NI — — —
XLINX CONTROL'
BOARD
dPWM CURRENT
REGULATOR
Fig. 7.13a. Section from the experimental 5—phase drive.
V— • /...Gdite /
A
-----q
"IEW
vfM,...01120•MMOINN1111-----t
smog
;;;L:Will
- ,i_t_ialtallam. wag
apoit 1_4_ MEI
MIR
KitivialWksi
emmue,
aro slam
ow
,71140,14111111
...,
a
Photograph of the o — pnase anve.
196
and long flux loop motor configurations was recorded for two on-state angles (ref.
fig. 6.3), eon = 13.5° and 18°. This choice of on-state angles was dictated by the
resolution of the position sensing system. However, it was possible to alter the
firing angle, Of (and hence the commutation point) by changing the position of the
shaft mounted slotted disk with respect to the optoelectronic devices.
7.7.1 On-state angle analysis.
In order to assess the implications in drive performance of changing the on-state
angle from 13.5° to 18°, measurements at a constant torque of 5Nm, 10Nm and
12.5Nm (half-load torque) were taken for the short and long flux loop
configurations. Operating points of equal efficiency were joined on a torque /
speed diagram. Figures 7.14a,b illustrate the performance of the 5-phase drive
(configured for long or short flux loops respectively) for the on-state angle of 18°.
Drive efficiency contour plots for 00n = 13.5° are shown in fig. 7.15a,b for long
and short flux paths respectively. It is demonstrated that the long flux path
configuration operates inefficiently when an 18° on-state angle is adopted. The
long flux loop drive efficiency increases when 0 is set to 13.5°. The short flux
path configuration maintains high efficiency at e on 18°, though performance is
still improved by reverting to e o„ = 13.5°. This trend can be understood by
examining the static torque profile of the 5-phase motor, shown in fig. 7.10. It is
shown that, although short flux paths result in higher static torque output at any
rotor position, the benefit is more significant as the rotor poles move toward
alignment with the excited stator poles (i.e. at rotor positions toward the end of the
excitation cycle). The static torque profile and the (dynamic) experimental results
presented suggest that, in the short flux path configuration, performance may be
improved even further (depending on speed) by choosing an on-state angle in
between 13.5° and 18°. However, such resolution was not offered by the present
slotted disk and optical sensor arrangement.
199
FIG. 7.14a EFFICIENCY CONTOURS AT HALF LOAD (LONG LOOPS, COND.=18 DEG)
14
12
75%
10
•
•
•
8
•
•
••
•
55,
6
67.5%
4
70%
2
o
o
200
400
600
800
1000
1200
1400
Speed (rpm)
FIG. 7.14b EFFICIENCY CONTOURS AT HALF LOAD (SHORT LOOPS, COND.=18 DEG)
14
12
I
;I
•
80%
t
82.5%
1
%.
10
rfg
•
8
•
6
67.5%
4
70%
75%
2
o
o
200
400
600
800
Speed (rpm)
200
1000
1200
1400
FIG. 7.15a EFFICIENCY CONTOURS AT HALF LOAD (LONG LOOPS, COND.=13.5 DEG)
14
12
3
I 80%
10
1
1
fIi
8
1
1
1
1
1
6
1
•
67.5% 70%
4
75%
2
o
o
200
400
800
600
1000
1200
1400
Speed (rpm)
FIG. 7.15b EFFICIENCY CONTOURS AT HALF LOAD (SHORT LOOPS, COND.=13.5 DEG)
14
::
12
85%
1
\ 80%
I.
10
0
6
ssss
70%
4
75%
2
o
o
200
400
600
800
Speed (rpm)
201
1000
1200
1400
7.7.2 Maximum drive efficiency analysis.
Following on from the on-state angle analysis, measurements at higher torque
loadings (15, 20 and 25Nm) were taken to examine the variation of the 5-phase
drive efficiency with torque and speed. The maximum torque / speed profiles
(within the constraints of the power supplies) obtained by configuring the 5-phase
motor for long or short flux paths are shown in fig. 7.16a,b respectively. The
profiles were obtained for a firing angle, Of , of 1.5° and an on-state angle, 0, of
13.5°. This firing angle was chosen because it was found that for Oon = 13.5°,
higher efficiency was obtained by retarding the excitation (making O f > 0).
At operating speeds ranging from 200rpm to approximately 1000rpm, the current
chopping level, /„„ was set to the value necessary to maintain full load torque
(25Nm). Beyond 1000rpm there was not enough time for the current to rise to /„,
before the onset of overlap because the drive operated from a reduced dc link
voltage of 300V. In the overlap region, the back-emf severely limited the rate of
rise of current and hence the torque developed. Therefore, beyond 1000rpm the
average torque developed by the motor fell rapidly from 25Nm to less than 15Nm.
In the 1000 to 1500rpm region, where the current followed its 'natural' profile
higher torque was developed when the motor was configured for short flux paths.
At lower speeds, a lower current chopping level was required to produce 25Nm
when the motor was configured for short flux paths. This is confirmed by
experimental current profiles shown in fig. 7.17; these were obtained at an
operating speed of 900rpm. The lower current chopping level implies reduced
copper loss. In addition, at any speed iron losses are decreased when the motor
is configured for short flux paths hence resulting in a significant increase in motor
efficiency.
In addition to the maximum torque profiles, the graphs of fig. 7.16 show contours
joining the operating points of equal drive 4 efficiency and thus indicate the
'Drive efficiency includes the losses in the power converter.
202
FIG. 7.16a VARIATION OF TORQUE AND EFFICIENCY WITH SPEED (300V, LONG LOOPS)
30
0
Speed (rpm)
FIG. 7.16b VARIATION OF TORQUE AND EFFICIENCY WITH SPEED (300V, SHORT LOOPS)
30
25
20
s‘s
80%
sS•
10
5
o
75%
70%
o
200
400
600
800
Speed (rpm)
203
1000
1200
1400
2A/div
A
,
OND
Fig. 7.17a Experimental current profile at 900rpm, 25Nm (long loops).
T
_
k
2A/div
GND
II
Fig. 7.17b Experimental current profile at 900rpm, 25Nm (short loops).
204
variation of efficiency with torque and speed. At any operating point, higher
efficiency is obtained from the short flux loop configuration. At the [1300rpm,
20Nm] operating point the 5-phase drive configured for short flux loops achieves
an efficiency of 87%. There is also a general tendency (subject to experimental
error) for the efficiency to increase slightly with torque, but more significantly with
speed. Hence, the 5-phase drive efficiency is likely to increase further as the full
load [1500rpm, 25I\Im] operating point is approached.
In order to develop higher torque beyond 1000rpm the firing angle, Of, was set to
0 0 (firing at the unaligned position). This allowed more time to increase the
current to in, before the onset of overlap. The result of this exercise is shown in
fig. 7.18. Comparison of the maximum torque profiles of figures 7.16b and 7.18
FIG. 7.18 TORQUE SPEED PROFILE (FIRE AT 0 DEG-UNALIGNED POSITION)
30
SHORT FLUX LOOPS, COND. ANGLE 13.5 DEG
/
=
25 60%
70%
80%
85%
20 cr
15 87.5%-
1-4
10 5
o
o
200
400
600
800
1000
1200
1400
Speed (rpm)
reveals that the experiment was successful. However it was still not possible to
reach the 4kW [1500rpm, 25Nrn] operating point. Beyond 1100rpm output power
was limited by the maximum input power of 3.5kW that the two TCR supplies
205
could deliver when connected in parallel. Beyond approximately 1300rpm the
reduced voltage of 300V was not enough to force maximum phase current before
the onset of overlap. A maximum drive efficiency of 87.5% was recorded in this
experiment at the [1450rpm, 16.8Nm] operating point.
The motor frame was cooled with a shaft mounted fan. At low speeds though, fanforced cooling is minimal. Losses are therefore dissipated through 'natural
convection'. At low speeds and rated (25Nm) torque output, the temperature in the
motor winding attained a steady state at approximately 80°C. This is well within
the Class B operating specifications, which dictate that the winding temperature
should not exceed 105°C. The temperature rise in the coil would be even further
decreased, had the winding been impregnated. Winding impregnation significantly
increases the rate of heat transfer from the copper to the iron. The steady state
temperature of the frame at low speeds and rated torque was found to be
approximately 50°C. At 1500rpm, 15Nm a steady-state coil temperature of
approximately 58°C was recorded. Temperature measurements were cross-checked
by measuring the resistance of the phase winding at the operating temperature, and
comparing this with the room temperature resistance. This all implies that the
motor is capable of producing more than 25Nm without exceeding Class B
temperatures.
7.7.3 Drive and motor efficiency considerations.
Although the maximum drive efficiency contour was not reached, it was shown
that the 5-phase prototype drive configured for short flux paths did achieve an
efficiency of 87% at approximately 1300rpm, 20Nm. This figure is higher than the
efficiency of all known prior art switched reluctance drives of the same rating. It
is known that a 3-phase 12/8 switched reluctance design, currently manufactured
in industry, achieves a drive efficiency of 85% at full load (1500rpm, 25Nm).
In order to obtain an approximate figure for the 5-phase motor efficiency, an
estimation of the power converter loss component has been made. As an example,
206
the analysis for the operating point [0) = 1283rpm, T = 21.7Nm, 8 = 0°, 0 =
13.5°] will be presented. At this operating point the phase current followed its
'natural' profile, as it was limited by the motor back-emf. Both switching devices
connected across each phase winding were therefore continually conducting during
the angular period The
The current chopping regulator was inactive and hence
switching losses were small and can be neglected.
rp = rotor pole pitch
45°
1.9
cond
Fig. 7.19. Representation of the phase current pulse at
w= 1283rpm, T = 21.7Nm.
The current profile can be divided into two periods: the switch conduction period
and diode conduction period, as shown in fig. 7.19. The area A enclosed by the
current profile, the horizontal datum and the vertical limits of 0 = Of and e =
207
-
can be used to compute the rms current, Inns, 'seen' by the switching devices as
follows:
on
rms
=
(7.9)
aye
rp
where
•
lave
=
Asw
0 com - O f
(7.10)
The nns current can then be squared and multiplied by the on-state resistance of
the MOSFET to yield the on-state power loss in each MOSFET. The power loss
in each freewheeling diode was computed by the BYT230 power loss formula (ref.
Appendix B). Switching losses in the power devices and the snubbers were
neglected to make this a conservative estimation. In this example, the losses in the
power converter total approximately 108W. The drive efficiency at this operating
point approaches 87%; the corresponding motor efficiency is therefore
approximately 89.7%. Motor efficiency is known to increase with speed and
therefore at 1500rpm it is expected to comfortably exceed 90%.
7.8 Comparison of experimental results with
simulated data.
SRDESIGN was used for the dynamic simulation of the prototype 5-phase short
flux path motor. This section aims at drawing a brief, sample comparison between
experimental results and simulation data obtained from SRDESIGN, in order to reassess the accuracy of the computer program. For precise simulation, the X, /i
diagram at the 'extreme' rotor positions was imported from finite element analysis
to SRDESIGN.
Figure 7.20 shows the maximum torque produced by the shOrt flux path motor, for
a range of speeds up to 1500rpm. The profile was obtained at the reduced supply
208
voltage of 300V, and for 01 = 1.5°, 0,„ = 13.5°. Also shown in fig. 7.20 is the
torque profile predicted by SRDESIGN. At each running speed, the current
chopping level (recorded during the experiment), firing and commutation angles
FIG. 7.20 COMPARISON OF EXPERIMENTAL RESULTS WITH SRDESIGN
30
SHORT LOOPS, FIRE AT 1.5 DEG, C0/4D.ANGLE=13.5 DEG
25
20
* EXPERIMENT
- SRDESIGN
10
200
400
600
800
1000
1200
1400
Speed (rpm)
were keyed in SRDESIGN. The simulation program yielded average torque within
a 10% accuracy, though there was a general tendency to underestimate
experimental torque values. The experimental and predicted torque profiles
converged at higher running speeds. An experimental current pulse, recorded at
800rpm is compared with the SRDESIGN simulated pulse in fig. 7.21.
SRDESIGN simulates the experimental phase current profile with sufficient
accuracy. The rms current estimation at any speed also compares favourably with
the digital oscilloscope recording. Therefore, copper loss computation within
SRDESIGN is expected to be accurate. However, only motor (and not drive)
efficiency can be estimated in SRDESIGN, because an algorithm has not been
written to compute losses in the power converter. No comparison can therefore be
drawn with experimental drive efficiency figures. SRDESIGN simulated ?t, / 0 and
1
11111111111111111111111111
rillill11111111111111
Ell
/
E
2A/div
GND
Fig. 7.21a Experimental current profile at 800rpm (short loops).
Current
A
15.00-
10.00
5.00
0.00
0.00
:10
0.120
0:30
Angle
0.40 rad
Fig. 7.21b SRDESIGN simulated phase current profile at 800rpm (short loops).
210
Fig. 7.22a SRDESIGN simulated X / 0 diagram at 800rpm (short loops).
Flux Linkage
Wb * Turns
0.50-
0.40-
0.30-
0.20
0.10
0.00 0.00
5.00
00
10 (:)(1
i Current
15.00 A
Fig. 7.22b SRDESIGN simulated A, / i diagram at 800rpm (short loops).
211
X / i characteristics at 800rpm are given in fig. 7.22 for reference.
7.9 Market applications of the 5-phase switched
reluctance drive.
The switched reluctance motor is identical in construction to a single stack variable
reluctance stepping motor (VRM). As the name suggests, in a stepping motor the
rotor moves in discrete steps. The angular rotation is determined by the number
of current pulses fed to the stator winding during each revolution. There are two
further stepping motor arrangements: the permanent magnet (PM) stepping motor
and the hybrid stepper. The basic operating principles and characteristics of these
motors are described in Appendix E.
The physical construction and / or operating characteristics of the VR, PM and
hybrid stepping motors make them differ from the switched reluctance in the
applications they are suited for (ref. Appendix E). In fact, the constructed 5-phase
switched reluctance prototype is targeting the industrial variable speed drive market
which is currently dominated by the 3-phase induction motor.
The 3-phase inverter-fed induction motor, described in Appendix F, is now well
established as an industrial variable speed drive. The rugged rotor structure and
simple power electronic converter have contributed significantly to its success. In
terms of performance, polyphase excitation of appropriately designed stator
windings produces a symmetrical rotating field which leads to smooth torque
development and low noise levels. However, the stator end winding in the
induction motor is long and contributes significantly to copper losses. In addition,
copper losses are incurred in the rotor and are more difficult to dissipate.
'Standard efficiency' 4kW 3-phase induction machines develop 26.5Nm at
1420rpm, with a motor efficiency of 83%. The 'energy efficient' design, which
uses low-loss steel laminations, achieves an efficiency of 85.3% at full load [63].
212
The switched reluctance motor structure is rugged and potentially cheaper to build
in comparison to the induction motor. The salient pole stator has concentrated
excitation windings with short end turns. The phase winding resistance is therefore
reduced and the active core length occupies a higher proportion of the overall
frame length than in the induction motor. There are no windings on the rotor and
therefore rotor losses are lower than in induction motors. The bulk of the losses
occur in the stator and can be dissipated easily through the motor frame.
5-phase 10/8
5-phase 10/8
Most
Energy
prototype
prototype
efficient
efficient
(measured)
(projected)
3-phase 12/8
3-0
1300rpm
1500rpm
motor design
induction
20Nm
25Nm
known
motor
150Orpm
25Nm
Motor
89.75%
efficiency
(appr.)
Drive
87%
above 90%
above 88%
85.3%
85%
81%
(appr.)
efficiency
Table 7.5 Comparison of the 5-phase drive efficiency with competing induction
motors and switched reluctance drives. (All constructed in D112 frames).
In addition to the switched reluctance motor advantages mentioned above, the
proposed 5-phase drive offers the significant advantages associated with short flux
paths. Short flux paths reduce the MMF required to establish the flux in the airgap
and hence decrease copper losses. Hysteresis and eddy current losses are also
decreased as the 'active' iron volume is reduced. The 5-phase switched reluctance
motor was constructed inside a standard D112 induction motor frame. SRDESIGN
simulation data suggested that, at the rated supply voltage of 600V and a peak
phase current of approximately 13.5A, the 5-phase prototype would develop
213
25.5Nm at 1500rpm with a motor efficiency in excess of 90%. Experimental
results demonstrated that, at the reduced supply voltage of 300V, the 5-phase motor
developed 20Nm at 1300rpm with a drive efficiency of 87% and a corresponding
motor efficiency of approximately 89.75%. The 5-phase prototype therefore
achieved far superior performance in comparison with the 'energy efficient'
induction motor before reaching the maximum drive efficiency operating point(s).
Table 7.5 summarises efficiency figures for the 5-phase prototype and competing
induction motors and switched reluctance drives of the same frame size.
With eight poles on the rotor low ripple torque can be achieved with the 5-phase
motor. The high starting torque available shall be most useful in traction
applications (crane and lift drives). The high efficiency also makes the 5-phase
drive suitable for battery operated vehicles or other applications where the power
/ weight ratio is important and permanent magnet motors are not appropriate.
However, the fundamental excitation frequency of the drive increases significantly
at higher speeds and exaggerates the eddy current loss component. It is for this
reason that it is thought the 5-phase drive can be established more comfortably as
a variable speed drive running up to 3000rpm. In general, specialised applications
are more likely to employ switched reluctance drives. This is because a dedicated
power converter and control system must be designed for a switched reluctance
motor. In contrast, any induction motor can operate from a standard 3 - 0
inverter. This makes the induction motor particularly attractive, as a general
purpose variable speed drive.
214
Chapter 8
CONCLUSION
8.1 Main conclusions and author's contribution to
knowledge.
A new configuration of switched reluctance motor has been described, in which the
windings are arranged to encourage short flux paths within the motor. Short flux
paths reduce the MMF required to establish the B-field pattern in the motor,
leading to a significant reduction in copper losses. In addition, iron losses are
decreased because the volume of iron in which hysteresis and eddy current losses
are generated is reduced.
It has been demonstrated that short flux paths can be encouraged if the phase
windings of a switched reluctance motor with an odd number of phases are
arranged so that adjacent stator poles have opposite magnetic polarity. In the
proposed configuration, the B-field associated with two adjacent phase windings
simultaneously excited forms a short magnetic circuit, linking adjacent stator poles
via the rotor teeth.
A thorough electromagnetic analysis of doubly excited systems, which relates to
switched reluctance motors operating with two phase windings conducting at any
time, has been proposed. The analysis includes the effects of mutual coupling and
the increased flux density, present in some parts of the steel when two phases are
excited simultaneously. This electromagnetic theory of doubly excited systems was
used to accurately model switched reluctance machines configured for short flux
loops, as well as the more common 4-phase 8/6 machine. It has been demonstrated
that the virtual work principle, applied to doubly excited systems as proposed in
this thesis, yields average torque values which consistently compare favourably
215
with torque computed using the Maxwell stress tensor. It has also been shown that
significant errors can arise if mutual interaction effects, frequently neglected by
previous researchers, are not accounted for. A performance optimisation study on
the 4-phase motor was undertaken. The design of 4-phase motors for low torque
ripple has been proposed. A smooth torque characteristic was achieved by correct
specification of critical motor dimensions (stator yoke thickness and rotor pole arc)
coupled with an appropriate phase current conduction period.
Switched reluctance motor structures have been modelled using two and threedimensional finite element analysis. Three-dimensional effects, i.e. anisotropy, end
winding flux and axial fringing have been investigated. An extensive discussion
into modelling of anisotropic material structures has been put forward. A series
of correction charts account for end-core flux at a range of rotor positions and
excitations. The value of end-core flux has been found to be heavily dependent on
rotor position, excitation and magnetic saturation. The percentage increment in
flux linkage due to 'end effects' was found to be maximum when the excited stator
poles face the interpolar airgap depth. The percentage increment in flux linkage
due to 'end effects' decreased linearly in the overlap region to reach a minimum
at alignment.
The 'back bone' structure of SRDESIGN, a computer simulation program written
in Turbo Pascal to characterise the dynamic performance of switched reluctance
drives, has been presented. Fundamental mathematical formulations supported in
SRDESIGN have been described. The accuracy of dynamic simulation data
obtained from SRDESIGN was verified by testing switched reluctance drives that
were available in the laboratory. In order to obtain accurate simulation data for
doubly excited switched reluctance motors, X / i diagrams at 'extreme' rotor
positions (computed by implementing the proposed electromagnetic theory for
doubly excited systems) were imported from finite element analysis. SRDESIGN
estimated the magnetisation curves at intermediate rotor positions and yielded
values for average torque and motor losses, always within 10% of the measured
value. It was also asserted that the performance of singly excited switched
216
reluctance motors could accurately be simulated in SRDESIGN, with the 2 n., / i
diagrams at unaligned and aligned rotor positions computed within the program.
The design and development of a 5-phase 10/8 switched reluctance drive, which
exploited the advantages of short flux paths, has been described. The 5-phase
motor design procedure, which included new proposals for motors with two phases
simultaneously excited, has been thoroughly presented. The static performance of
the 5-phase motor, with the windings configured for short or long flux paths, was
modelled using finite element analysis. It was shown that, for equal copper loss
and reduced iron loss, the short flux loop motor configuration developed 16%
higher average torque. In addition, the 5-phase motor configured for short flux
paths was found to develop 20% higher torque per unit volume, when compared
to a 4-phase machine based on the design of the Oulton motor.
Although the maximum drive efficiency contour was not reached, it has been
demonstrated that the 5-phase prototype drive, with the motor configured for short
loops, achieved an efficiency of 87% at the [1300rpm, 20Nm] operating point.
This figure, which corresponds to a motor efficiency in excess of 89.7%, is
significantly higher than the efficiency of all known prior art switched reluctance
drives and induction drives of the same frame size.
8.2 Areas of further work.
The principal aim of this project was the electromagnetic design of a high
efficiency switched reluctance motor. This aim has been achieved. However,
further work is needed to realise the full potential of the 5-phase drive.
A more advanced control system ought to be designed for the 5-phase motor. The
angular resolution of the position sensor ought to be improved in order to optimise
the drive efficiency. In addition, speed feedback could be provided. These
functions can be performed within a microprocessor-based controller.
217
The available dc power supplies imposed a limitation in testing the motor above
3.5kW input power. Measurements ought to be taken to establish the maximum
power output of the 5-phase drive. A power supply capable of delivering 600V 16A would be required to perform these tests. In addition, the 5-phase drive
employing six power switches in the shared switch converter configuration ought
to be experimentally evaluated. However, the dc link voltage impressed across the
shared switch converter would need to be increased beyond 300V 5 for the drive
to develop 25Nm at a phase current chopping level of 15A.
Further work is needed to improve the computer simulation program SRDESIGN.
Thermal modelling could be added to help predict the maximum continuous rating
of a motor. Some form of model should be developed to predict the losses in the
power converter. Information on the drive efficiency (rather than just motor
efficiency) can then be conveyed to the user. An analytical procedure of predicting
2.
/ i diagrams for doubly excited switched reluctance motors should also be
developed.
5The EM TCR power supply that was available in the laboratory could supply a maximum of
300V.
218
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APPENDIX A
Electromagnetic equations governing the finite
element analysis software.
A.1 The two-dimensional finite element code (OPERA-2D).
A magnetic vector potential,
A, may be defined such that
Vx A
B
(A.1)
Maxwell's first law (eqn. 2.4) may be rewritten in terms of the magnetic vector
potential as
A
(A.2)
Vx[E + L ] = 0
at
Introducing the electrostatic potential, V, the electric field strength is expressed as
E +
aA
(A.3)
- VV
at
Current density, J, may be separated into two components, namely the source
current density, L, and induced current density, Je, where
•
(A.4)
-VV
aA
•
(A.5)
= —a7
The term a denotes conductivity. Expanding the source and induced current
density components in eqn. 2.8 and expressing the magnetic field strength in terms
of the flux density gives
vx—B +
P,
aA
at
(A.6)
s
This equation describes eddy current phenomena in terms of a specified source
226
current density and relevant material properties. The magnetostatic model of the
switched reluctance motor has coils with known current density. The current
density is therefore prescribed and the conductivity is set to zero. In OPERA-2D,
the equation to be solved for the static magnetic field using the magnetic vector
potential, is derived by substituting for the flux density, B, in eqn. A.6 [43]. In
two dimensions, this simplifies to
1
Vx( __ VxA z ) =
(A.7)
A.2 The three-dimensional algorithm (OPERA-3D / TOSCA).
Stationary magnetic fields consist of both solenoidal and rotational components.
The field produced by electric currents has a rotational component inside the
volumes where currents flow. In the exterior space the field is solenoidal but the
scalar potential is multi-valued. The field produced by magnetised volumes is
solenoidal. It is convenient to separate the total field into two parts in order to
obtain a description of the field in terms of the scalar potential. The total field
intensity H may be expressed as the sum of the source field intensity Hs and the
reduced field intensity Hill
H Hs + Hm(A.8)
The source field can be obtained directly from the Biot-Savart law by integration
over the region SI j containing current
JxR
(A.9)
Hs 1, IR 1 3 " j
The field satisfies
V x Hs J
so that
227
(A.10)
V x Hm = 0
(A.11)
The reduced field intensity can now be represented using the reduced scalar
potential, 4),
(A.12)
HM = -V4)
The divergence of the flux density B is always zero. Introducing the permeability
tensor, p, and combining the expressions for the source and reduced field
intensity, gives the partial differential equation for the reduced scalar potential
v.i_cvq) - v r.fxR
do„) = °
(A.13)
IR13
This equation can easily be solved using the finite element method. However, in
magnetic materials the two parts of the field HM and Hs tend to be of similar
magnitude but opposite direction. Therefore, cancellation occurs in computing the
field intensity H, that results in a loss in accuracy [44]. The errors can be
completely avoided by combining the total and reduced scalar potential
representations. Hence, exterior to the volumes where currents flow the total field
can be represented using the total magnetic scalar potential IP
(A.14)
H = -VT
where the total magnetic scalar potential satisfies
=0
(A.15)
The minimal combination consists of using the reduced scalar potential only inside
volumes where current flows and the total potential everywhere else.
226
APPENDIX B
Data sheets for power semiconductor devices
used in this project
SIEMENS
BSM 181 F (C)
BSM 181 FR
SIMOPAC* MOSFET Modules Ifos = 800 V
= 34 A
RDS(onl = 0.32 0
•
•
•
•
•
•
•
Power module
Single switch
FREDFET
N channel
Enhancement mode
Package with insulated metal base plate
Circuit diagram: Fig. la')
1VP•
BSM 181 F(C)
BSM 181 FR
Ordering code
C67076-A1052-A2
C67076-A1057-A2
Maximum Ratings
Parameter
Symbol
Values
Unit
Drain-source voltage
VD*
800
V
VEKAR
800
Vos
± 20
ID
34
Pulsed drain current Tc xi 25 °C
/ow.
136
Operating and storage
temperature range
Ti
7",,,
—55...+150
Total power dissipation, Tc = 25 °C
P,,,,,
700
Thermal resistance
Chip-case
Case- heat sink
Ri ti jc
R,,, c,,
5 0.18
IS
V,
2500
Vic
—
16
film
Drain-gate voltage,
R05 off 20
kO
Gate-source voltage
Continuous drain current, Tc
Isolation test voltage),
= 25 °C
A
''C
W
KM
t
= 1 min.
Creepage distance, drain-source
0.05
—
11
DIN humidity category. DIN 40 040
—
F
IEC climatic category, DIN IEC 68-1
—
55/150/56
Clearance, drain-source
.
See chapter Package Outlines.
—
2) Isolation test voltage between drain and base plate referred to standard climate 23/50 In ace. with DIN 50014.
IEC 146, pars 492.1.
219
cc
IL U.
CO
CO
7-
c71
r
CO
CO
Csl
N
2 2
ci.
a
.0
2
....e
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BYT 230 PI(V)-1000
FAST RECOVERY RECTIFIER DIODE
•
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VERY HIGH REVERSE VOLTAGE CAPABILITY
VERY LOW REVERSE RECOVERY TIME
VERY LOW SWITCHING LOSSES
LOW NOISE TURN-OFF SWITCHING
INSULATED : Capacitance 45pF
DESCRIPTION
Double rectifiers suited for switching mode power
supply.
ABSOLUTE RATINGS
Symbol
Value
Unit
VI:11:mA
Repetitive Peak Reverse Voltage
Parameter
1000
V
VFism
Non Repetitive Peak Reverse Voltage
1000
V
A
Repetitive Peak Forward Current
tp 5 10u.s
375
Innms
RMS Forward Current
per leg
70
A
I F(AV)
Average Forward Current
TC810 . 50°C
5 .0.5 per leg
30
A
Surge Non Repetitive Forward Current
tp .10ms
Sinusoidal
200
A
Power Dissipation
Teals. ... 50°C
60
W
— 40 to 4. 150
°C
I FR0,4
I F sm
P
per leg
Ts t g
T,
Storage and Junction Temperature Range
THERMAL RESISTANCES
Symbol
Parameter
Junction-case
Rth (1-C)
per leg
total
Coupling
June 1989
Value
Unit
1.6
0.8
°C/W
0.1
°C/W
1/6
S.15
if*
233
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APPENDIX C
Comparison on the basis of equal copper losses.
The switched reluctance motor copper losses Pci, may be computed from
(C.1)
Pc. = 1.
2sR
where I denotes the rms value of the phase current and R the resistance of the
phase winding. Assuming square pulses, the rms phase current can be expressed
in terms of the peak phase current, I,,,, as
Ton
(C.2)
where T denotes the period (1 /f) of the current pulse train and Tc,„ represents the
on-state time. The following relations also hold
(C.3)
= J. A
and
R=
p Aw
(C.4)
where A., denotes the cross-sectional area of copper and l,, the length of copper
wire. Equation C.1 can therefore be rewritten as
2 2 4 T
Pc. = JA1
=
(q
lw
(C.5)
To
n)(I) )
T
w
The conductor length can be assumed constant in motors of equal stack length,
though the length of the end winding is dependent on the stator tooth width. As
236
an approximation, the resistivity
p
is taken as constant. It is known however that
p is temperature dependent, and the rate of temperature rise in the phase windings,
which plays a significant role in the copper loss, increases with current density.
In addition, the heat transfer coefficient from the conductor to the iron is higher in
machines that exhibit lower iron losses. It is evident that an accurate loss model
can only be obtained by conducting a thorough thermal analysis of the switched
reluctance motor. This is beyond the scope of this argument, therefore
P c. c.= (4,A) (q
To
n )
T
(C.6)
In finite element modelling, area A„, is taken to be that of the largest rectangular
(single turn) coil that can be slipped over the pole without interfering with its
neighbouring coils.
237
APPENDIX D
Loss data and BH curves for LOSIL 500-50.
tesla
Peak Magnetic Flux Density
0 . 01
1•0
0•1
_
100
-
=-
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3 J
100
,98
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10
0• 1
0.01
0-0 1
0• 1
1.0
238
Magnetic Flux Density B tesla
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APPENDIX E
Operating principles of stepping motors.
E.1 The variable reluctance stepping motor.
The construction of a single-stack variable reluctance stepping motor is identical
to that of the switched reluctance motor. However, the VRM is designed to
operate 'open loop' (i.e. without position sensing) and maintain accurate positioncontrol. In contrast, switched reluctance machines operate with position feedback.
This is needed to produce a variable speed drive of high efficiency.
A multi-stack type of variable reluctance stepping motor is also manufactured.
Each stack corresponds to a phase and is misaligned with respect to its
neighbouring stacks. The stator and rotor have the same tooth pitch.
E.2 The permanent magnet (PM) stepping motor.
A stepping motor that uses a permanent magnet in a cylindrically shaped rotor is
called a permanent magnet stepping motor. The operating principle of this type
of motor can be illustrated by means of a cross-section of a 2-phase structure,
shown in fig. E.1. The rotor consists of four radially magnetised permanent
magnet sections, namely N-S-N-S. The stator has eight poles around which coils
are wound to make up two phase windings. The phase windings need to be
excited with positive and negative current polarities, and hence the requirement for
a bipolar power converter circuit arises. This type of converter utilises more power
devices than unipolar configurations and suffers from the danger of shoot-through
faults.
Rotation in one direction can be achieved if the excitation sequence
jA+ iB+ IA- iB- jA+
240
is adopted. Electromagnetic torque is produced by the interaction of the magnetic
fields produced by the stator windings and the permanent magnet sections
comprising the rotor. This gives rise to 'excitation' forces acting on the structure.
The phase windings are excited in turn to produce the correct magnetic polarities
in the stator poles which pull the rotor in place. The stepping action is illustrated
in fig. E.1. The step angle of this motor is 45°.
Fig. E.1. A 2—phase PM stepping motor.
The PM stepping motor exhibits good torque per unit volume and high efficiency.
The main disadvantage associated with the use of a permanent magnet is the
additional cost and weight penalty that is incurred. The torque / inertia ratio of the
PM stepping motor is low.
E.3 The hybrid stepping motor.
Hybrid stepping motors are operated under the combined principles of the variable
reluctance and the permanent magnet type of stepping motors. The construction
of a 4-phase hybrid stepper is illustrated in fig. E.2. A cylindrically shaped
permanent magnet lies in the core of the rotor and is magnetised along the length
of the machine (axially). Two end sections, consisting of equal numbers of poles,
are fitted on each end of the magnet. The teeth of the two sections are misaligned
241
with respect to each other by half a tooth pitch. The stator structure is similar to
that of the switched reluctance type, though the winding connections are different.
In the hybrid stepper, coils of two different phases may be wound on one pole.
stator core
windings
rotor core
•IIII111111111111111111111111•
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S
10
shaft
N
1
magnet
11111111
DI IIS
end cap
III 11111
coil
Fig. E.2. A 4—phase hybrid stepper motor.
T. Kenjo [64] demonstrates most effectively the operating principles of the hybrid
stepper with the aid of a 'split-and-unrolled' model of a 4-phase motor, reproduced
in fig. E.3. Dotted curves represent flux due to the magnet. Field distributions
produced by excitation of phase windings are represented by solid curves. When
pole II is excited as a north pole N, and pole IV as a south pole S, a driving force
toward the left appears in the south pole cross-section because in the toothed
structure under pole II the fields produced by the excitation windings and the
permanent magnet sections act in the same direction. Field components oppose
one another in the toothed structure under pole IV hence weakening the rightoriented force. A left-oriented force is also produced in the north pole crosssection. An equilibrium position is reached after the rotor has moved by one
quarter tooth pitch. The stator excitation -can now be transferred to poles I and III
so as to maintain rotation.
242
strengthen
each other
Ir
neutralize
1911
16
each other •9
•9.1.11,9
4441
Aviv
permanent magnet S
000
(
8%
permanent magnet N
Fig. E.3. Hybrid stepper operating principles.
The tooth structures on the rotor and stator of the hybrid stepper are designed to
realise small step angles which alleviates the need for position feedback. This type
of stepping motor has been used extensively in positioning applications i.e. robot
arms and XY tables. A high level torque output is achieved from a small volume,
though the cost and weight of the permanent magnet has limited production to
machines rated at only a few kW (maximum).
243
APPENDIX F
A brief description of the induction motor.
In the induction motor, the coils forming the stator winding are arranged so that
conductors are distributed in slots around the stator periphery. The rotor can be
of the 'wound' or (more commonly) 'squirrel cage' type. In the 'squirrel cage'
type, solid aluminium bars are cast into the rotor slots and short circuited. This
type of rotor construction is more rugged and reliable than the 'wound' type.
Power electronic circuits are used to control rotor speed.
Fig. F.1. The 3—phase inverter—fed induction motor.
In the induction motor, alternating current is supplied directly to the stator
windings and by induction (or transformer action) to the rotor windings. The stator
244
produced magnetic field interacts with the currents induced in the rotor windings
and gives rise to excitation forces according to Lorenz's law
F = JxB
(F.1)
Simple single phase motors are used extensively in industry, where rugged fixed
speed drives are required. The 3-phase inverter-fed induction motor, shown in fig.
F.1, holds a significant share of the variable speed drive market. Torque and speed
control can be achieved in an inverter-fed induction motor by varying the voltage
and frequency respectively.
245
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