ANALYSIS AND DESIGN OF DOUBLYSALIENT RELUCTANCE AND PERMANENT
MAGNET MOTORS
み
SHETH NIMITKUMAR KIRITKUMAR
Department of Electrical Engineering
Submitted
In Ju/fl//men' ofthe requirements of the 凌箸ree of
DOCTOR OF PHILOSOPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY DELHI
June 2007
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CERTIFICATE
This is to certify that the thesis entitled, "Analysis and Design of Doubly Salient
Reluctance and Permanent Magnet Motors," being submi如d 句 Mr. Sheth
Nim itku mar 硲ritkumar for the award ofthe degree ofDoctor of Philosophy is a record
of bon面de research work carried out by him in the Electrical Engineering Department of
Indian Institute of Technology, Delhi.
Mr. Nimit Sheth worked under my guidance and supervision and has fuiffihled the
requirements for the submission of this thesis, which to my knowledge has reached the
requisite standard. The results obtained here in have not been submitted in part or in full to
any other University or Institute for the award of any degree.
(Prof. K. R. Rai agopal)
Electrical Engineering Department
Indian Institute of Technology Delhi
Hauz姉as, New Delhi-i 10016, INDIA
ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to my supervisor, Prof. K. R.
Rajagopal, for his support, patience and encouragement through out my research and
course work at lIT Delhi. It is not often one ffinds a supervisor, who always ffinds the time
for listening to the little problems and roadblocks, which unavoidable crop up in the
course of performing research. His technical, non-technical and editorial advice was
essential for the completion of this dissertation. OEe advices provided by him has helped
me a lot in my overall growth as a researcher and helped me to look forward to the 釦ture
with enthusiasm and conffidence in my ability.
My thanks are due to my research committee, particularly to Prof. B. P. Singh,
Prof. R. Balasubramanian, and Dr. I. N. Kar for providing me many valuable suggestions
that improved the content ofthis dissertation.
I wish to extend my warmest thanks to Mr. Meharban Singh, Mr. Srichand, Mr.
Puran Singh and Mr. Gurucharan Singh for their support in the laboratory and for creating
homely working atmosphere in the laboratory d面ng my tenure.
I also would like to express my gratitude to my former lab members Mr. A. R. C.
Shkharbabu, Dr. Parag Upad取ay, Mr. Vipul Pate!, Mr. Kamal Pandey, Mr. Shashank
Tandon for the cooperation, ffliendly behavior and invaluable help. The cooperation fflom
all the present lab members Mr. Madhan Mohan, Mr. Sanjay Gairola, Mr. Satishbabu, Mr.
Sathaiah and Mr. Illamparithi is also greatly appreciated.
I am thankful to the management of Institute of Technolog了， Ninna University of
Science and Technology, Ahmedabad, for sponsoring me to carry out research at lIT
Delhi. I am also thankful to Indian Institute of Technology Delhi, Indian National Science
111
Academy, Crnmcil for Scientiffic and Industrial Research, Department of Science and
Technology and All India Council for Technical Education for providing me ffinancial
s叩port to attend and present my research work at international conferences.
Additional energy and vitality for this research was provided externally through
my involvement in several social activities. For that, I express my thanks to Prof. N. K
Jamn, Mrs. Veena Jamn, Dr．瓦ran Momaya, Mrs. Manisha Momaya, Mr. Bhavik, Mr.
Sanj習，Mr・Rajesh, Mr・Rajen, Mr・Bhavesh, and their families・
My heartfelt thanks go to my parents and brother, for their love and understanding,
the encouragement and the sacriffice they have made d面ng the entire course of my life.
Without their overwhelming positive influence on my life, I would not have been able to
achieve my goals.
I acknowledge my sincere thanks to my wife and my soul mate Priyanka, whose
faith and belief in my capability gave me immense inspiration. She always is being my
pillar of strength, patience, inspiration and encouragement. She devoted her valuable
youth time injust eagerly waiting for me in days and nights, months and years. I can never
forget her dedicati叫加d support for my research work.
Lastly, I must thai止 God for giving me the strength, the patience and the ability to
accomplish this work.
Date: 4-6-2007
倒imit K Sheth)
lIT Delhi, New Delhi
2002REEO i 2
1V
ABSTRACT
s面tched reluctance motor (SRM) is a doubly-salient motor usually having
concentrated windings on the stator poles. The rotor is made out of soffi magnetic material
and doesn't have any 面nding or permanent magnets on it. It has the advantages of rugged
construction, high effficiency and tailored torque-speed characteristics. Compared to an
induction motor, SRM has higher power density and higher staring torque. The absence of
cogging and crawling torques gives the advantage of fast dynamic response for the SRM
with respect to the permanent magnet brushless dc (PM BLDC) motor and induction
motor. Unipolar drive requirement in the SRM in comparison to the bipolar drive in the
PM BLDC motor makes the converter immune to shoot through fault. The drawbacks of
this motor are the necessity of a rotor position sensor and presence of large torque ripple.
Research is going on worldwide to get rid of these drawbacks by having a sensorless
operation and reduced torque ripple either by appropriately designing the tooth geometry
or by suitable control methods. Research aimed at improving the performance indices like
torque-to-volume, torque-to-power and torque-to-mass ratios is also ON. SRM is
considered a good alternative to conventional and PM BLDC motors in the domestic
applications like washing machine, vacuum cleaner, electric vehicle, robotics, and also in
aerospace and industrial drives. Doubly-salient permanent magnet motor (DSPM) is the
latest addition in the category of brushless motors. In a DSPM motor, the magnets are
located on the stator, eliminating the problems of demagnetization and also the assembly
related issues for higトspeed applications. Still, it has the inherent advantages of PM
BLDC motors such as high effficiency and power density. Rotor of the DSPM motor is
similar to that of an SRM, providing the advantages of simple construction and robustness.
A comprehensive literature survey on these motors leads to the opportunities for
v
developing better design concepts for these motors for achieving compact and efficient
designs.
Calculating the outer dimensions based on available standards for the induction
motors, accurate estimation of the flux-linkage and inductance characteristics for v面ous
rotor positions and excitations, loss calculation based on the actual excitation, and
computing the actual torque proffile of the motor based on the actual phase excitations are
some of the requirements towards better designs of SRM. For the calculation of the
average torque of the motor a new concept of best step angle is presented in this thesis.
Invariably, in all the literature related to the design ofmulti-phase SRM, the unaligned and
aligned flux-linkage characteristics only are considered in calculating the torque, and
thereby assuming that all the torque developed over this half-cycle period of the static
torque proffile is available as the output torque from the phase. This is not true as the phase
excitation generally exists only for a step angle, which happens to be only one-third of one
cycle of the static torque proffile in case of the 6/4 SRM (which is 300), and one-fourth of
one cycle of the static torque proffile in case of the 8/6 SRM (which is i 50). The
commutation aspects needing excitation for a little more time to raise or commutate the
current need not be misunderstood as the phase excitation for a longer period as these will
keep on changing based on the varying speed and torque requirements. To ai田ve at a
situation that the sequential excitations of the phases of the SRM really results in the
highest possible average torque having low ripple content for the same phase currents, the
phase excitation should ideally start fflom the rotor position when approaching rotor pole
just starts overlapping with the stator pole that is going to be excited.
From the experience obtained after conducting several ffinite element (FE) analyses
of the multi-phase SRM, it is observed that for the calculation of actual flux-linkage
vi
characteristics, the rotor position for the half rotor pole pitch 一 fflom the 飼ly aligned to
fully unaligned-can be divided in to three possible regions viz. (i) fully unaligned to
starting of the pole over lap, (ii) partial pole over lap to full pole overlap and (iii) fflom
pole overlap to fully aligned condition. These three regions are identiffied in such a
that each one of these can be accurately modeled using a predetermined
of flux
tubes, which is decided 雄er analyzing the flux plots of the motor obtained fflom the FE
analysis for all rotor positions and various excitations. Core loss calculated based on the
actual waveform of flux in various parts of the motor and the copper loss based on the
waveform considering the ffinite rise and fall time gives more accurate
actual
results than the core loss calculated based on the assumption of triangular flux in stator
pole and hence gives more accurate estimation of effficiency of the motor.
Putting all these information together, a computer aided design (CAD) program for
the design of multi-phase SRM is developed in this work. A GA based optimization
technique has been explored for the design optimization of the SRM and a compact motor
for the same torque has been obtained. For the constant stator and rotor pole arcs, increase
in the number of variables increases the torqueんolume of the motor. The designs obtained
fflom the CAD program as well as the GA based optimized ones are veriffied using the twodimensional (2-D) FE analyses.
It is observed that the SRM having maximum aligned to unaligned inductance ratio
is not always giving the highest developed torque due to the fact that the actual inductance
variations in between the fully aligned and unaligned positions also do play a major role in
deciding the average and ripple torques. Considering the importance of effect of stator and
rotor pole geometry on the torque production of the SRM, an extensive 2-D FE analysis is
vil
carried out on a typical 8/6 SRM with various tooth shapes of the stator and rotor. The
study shows that for the dovetail kind of the stator or rotor pole, the optimum values of the
rotor outer pole arc and the stator inner pole arc in cases ofthe analyzed motor are 300 and
250 respectively. For this motor, the optimum values of the rotor and stator outer pole arc
are 280 and 20.20, when the pole geometry in both the cases is parallel-sided. Harmonic
analysis of static torque for optimum pole arcs shows that the optimum values of the pole
arcs will give more average and fundamental torque with reduced ripple and harmonic
torques in both the cases. With the increase in the stator or rotor pole arc, the value of the
unaligned and aligned inductance increases. Novel pole shapes like the slanted stator pole
having flattened pole face and the noncircular stator pole face with varying airgap under a
pole for the SRM are also investigated. FE analysis of the motor with such pole geometry
shows that the torque developed by both of these poles is higher for the unidirectional
operation. For a typical 8/6 SRM considered in this work, for a slant of 50 on the stator
pole face, the average torque goes up to i i .84 Nm and for an airgap having a 30% lift on
one side, the average torque goes up to 9.88 Nm fflom the nominal value of 9.41 Nm. But
in both the cases, the ripple content in the developed torque goes up.
The analysis conducted to study the effects of airgap nonuniformity on the
performance of the multi-phase SRM has revealed that with the increase in concentricity
error in the positive d妙ction, the average to現ue and to円ue ri即le increase. For the
positive concentricity error, the motor with the elliptical rotor producesaverage
torque compared to the motor having error in one half of the rotor, but with higher ripple.
The airgap nonuniformity caused by the relative eccentricity between the stator and rotor
axes 面11 result in higher fundamental torque and higher average torque in SRM but 面th
higher ripple. The rate of increase in average torque is more for relative eccentricity more
vill
than 25%, but with drastic increase in the ripple content. The airgap nonuniformity
changes the static torque characteristics of the different phases of the motor, so an accurate
for
for
of the static torque characteristics of the motor
all the phases separately
must be measured and used in arriving at appropriate logic
the reliable and accurate
pe雨rmance ofthe motor. Airgap nonuniformity 面11 lead to more noise and vibration.
Being a very promising motor for future robotic and industrial applications where
special torque versus rotor position characteristics is required, the DSPM motor also needs
careful investigations. In this work, a CAD program for the design of multi-phase DSPM
motor has been developed. A new factor for incorporating the effects of the stator poles
having different proximity with the permanent magnets is suggested and added in the
power equation considered in the CAD program. Two i hp, 6/4 DSPM motors-one with a
normal rotor and the other with a skewed rotor-are designed using the developed CAD
program and the design output data are validated for both the motors using 2-D and 3-D
FE analyses.
An extensive FE analysis has been carried out to study the effects of fault in phase
winding on the performance of both the doubly salient motors. The analysis revealed that
the inter-turn fault reduces the average torque and phase inductance with an increase in the
ripple content in both the doubly salient motors. The DSPM motor has an inherent
advantage of partial withstand to inter-turn faults. The study on the effect of phase to
phase fault indicates that it reduces the average torque and increases the torque ripple in
both the motors, but the phase independence makes SRM more immune to such faults.
When one of the phases of the 8/6 SRM is open-circuited, then the reduction in the
average torque is 25%, while in case of 6/4 DSPM motor it is 66%. The phase
independence of SRM makes it more immune to open phase fault.
lx
Some investigations are also carried out on v面ous methods such as skewing of the
rotor, appropriate excitation proffiles,and tapered rotor poles for the improvement of
performance of the multi-phase DSPM motors using 2-D and 3-D FE analyses. The
analysis shows that in case of the typical 8/6 DSPM motor, skewing the rotor 句 120to 150
will lead to minimum detent torque and reduced torque ripple without much reduction in
the torque capability of the motor and a combination of sinusoidal excitation and rotor
skew angle of 120 to 150 will lead to further reduction in the torque ripple and
improvement in the torque proffile. The results of a 3-D FE analysis carried out on the
same motor shows that at all rotor skew angles, the sinusoidal stator excitation with twophase excitation mode is giving more average torque in comp耐son to the rectangular
current excitation; this is also true for lesser torque ripple if the skew angles less than 240.
This analysis also indicates that rotor ske面ng reduces the phase flux-linkage and for the
skew angle more than halfofrotor pole pitch the amount oftiux-linkage is very small with
negligible variation. Skewing the rotor also reduces the difference between the phase
inductance when phase excitation is aiding or opposing the permanent magnet excitation.
The 2-D analysis carried out to study the effect of rotor pole tapering shows that the
tapered rotor pole gives higher average torque than the parallel sided rotor poles for 8/6
DSPM motor. The maximum average torque in both the cases, occur when the stator inner
and the rotor outer pole arcs are same, with the reduced torque ripple for tapered rotor
pole. For the analyzed 8/6 DSPM motor, for rotor outer pole arcs of less than the optimum
220, the tapered c ase is better; at 1 50 pole arc, the average torque developed by the motor
is 14.8% higher than the corresponding value of parallel-sided case. The analysis also
reveals that DSPM motor is immune to the type of restrictions like requirement of larger
rotor pole arc compared to the stator pole arc prevalent in SRM for having non-zero torque
zones.
CONTENTS
CERTIFICATE
ACKNOWLEDGEMENT
ABSTARCT
LIST OF FIGURES
LIST OF TABLES
LIST OF SYMBOLS
CHAPTER-IINTRODUCTION
2Switched Reluctance Motors
3Doubly Salient Permanent Magnet Motors
i .4. 1 Switched Reluctance Motors
1.4.1.1 Tooth Geometry
1.4.1.2 Design
i .4. 1 .3 Modeling and Analysis
i .4. 1 .4 New Topologies
1.4.2 Doubly Salient Pennanent Magnet (DSPM)
1.4.2.1 Design
i .4.2.2 Modeling and Analysis
5Scope of Work
6Outline of Chapters
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1 11 1 1 2 2 2
2 2
4Literature Survey
つ」【ノ
iGeneral
FLUX-LINKAGE CHARACTERISTICS OF THE MULTI27
PHASE SRM BY FLUX TUBE METHOD
CHAPTER-Il
Methodology
2.3
Inductance for Region-I
2.3
Calculation for Tube i and 5
一】
2.2
71 00 11
うつ「11j1
2 2
General
2.3.3 Calculation for Tube 3
2.3.4
Calculation for Tube 6 and 7
2.3.5
Calculation for Tube 8
2.3.6
Calculation for Tube 9
2.4
Inductance for Region-II
2.4.1
Calculation for Tube 1
2.4.2
Calculation for Tube 2
2.4.3
Calculation for Tube 3
2.5
Inductance for Region-III
2.5.1
Calculation for Tube i
2.5.2
Calculation for Tube 2
2.6
Conclusions
CHAPTER-Ill
へつ
1
7 0 2 7 9 11 2
4 6 71 9
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4 4 4 4 IIJ IIJ に J IIJ IIJ く J 一 66
2.3.2 Calculation for Tube 2 and 4
DESIGN OF MULTI-PHASE SWITCHED RELUCTANCE
MOTORS
64
3.1
General
64
3.2
CADofSRM
65
3.2.1
Output Equation of Multi-Phase SRM
66
3.2.2
Stator Pole Height Calculation
67
3.2.3
Stator Winding Design
68
3.2.4
Flux-Linkage Characteristics
69
3.2.5
Average Torque Calculation
69
3.2.6 Best Excitation Region for the SRM
71
3.2.7 Design Data ofthe 8/6 SRM
72
3.3
Calculation ofActual Phase Current Proffile and Average
Torque
74
3.4
Estimation of the Actual Copper Loss
76
3.5
Estimation ofthe Actual Core Loss
77
3.6
Actual Performance ofthe Designed 8/6 SRM
84
3.7
Validation ofthe Developed CAD Program and the Final Design
ofthe 8/6 SRM using FE Analysis
84
3.8
Genetic Algorithm Based Design Optimization of SRM89
3.9
Conclusions
xii
98
『 11
一 11
4.2.2 Effects of Change in Rotor Outer Pole Arc
一 11
4.2.2.1 ELects on Flux Densities
一 11
一 11 111
0 0 11
4.2.2.2 Effects on Static Torque Proffiles
4.2.2.3 Effects on Inductances
4.2.3 Effects of Change in the Stator Inner Pole Arc
噌 11
4.2.3.1 Effects on Flux Densities
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11111
111
4.3.2 Optimum Stator Pole Arc
4.4
Analysis with Modiffied Pole Shapes for Improved Average
Torque
2
4.3
Analysis for Optimum Values ofthe Rotor and Stator Pole
Arcs for Parallel Sided Poles
4.3
Optimum Rotor Pole Arc
一 11
一 11
4.2.4.4 Analysis ofthe Motor 面th Both the Stator and
Rotor Pole Arcs are Varied
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1
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4.2.4.3 Performance ofMotor with Optimum Stator Inner
Pole Arc
■11
4.2.4.2 Performance ofMotor with Optimum Rotor Outer
Pole Arc
2
4.2.4.1 Performance ofthe Original Motor
唾 且
1
4.2.4 Performance 面th Practical Current Waveforms
一 11
1 1
4.2.3.3 E査とcts on Inductances
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111
General
4.2
Analysis for Optimum Values of the Rotor and Stator Pole
Arcs for Tapered Poles
4.2
Analysis ofthe Original Geometry
4.2.3.2 Effects on Static Torque Proffiles
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CHAPTER-IV ANALYSIS OF VARIOUS POLE SHAPES FOR IMPROVED
PERFORMANCE OF THE SWITCHED RELUCTANCE
MOTOR
138
4.4.1 Motor having Noncircular Airgap due to Elevated Rotor Poles 138
4.4.2 Motor having Noncircular Stator Pole Faces with Varying
Airgap under a Pole
4.5
Conclusions
CHAPTER-V
4 4
4 4
General
142
一 11
411
EFFECTS OF AIRGAP NONUNIFORMITY ON THE
PERFOR八厘ANCE OF SWITCHED RELUCTANCE
MOTOR
i 40
5.4
5.5
Analysis ofthe Motor having Concentricity Errors on the
Rotor
I 59
Conclusions
167
General
6.2
Output Equation
CAD of DSPM Motor
■1
1
6.5
6.6
CHAPTER-Vil
Design Data ofthe 6/4 DSPM Motors
Validation ofthe Developed CAD Program ofthe DSPM
Motor using FE Analysis
Conclusions
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7.3.3 Effect on Pole Flux Densities
Performance of SRM on Phase to Phase Fault
7.4
b 11
7.3.1 Effect on Static Torque Proffiles
7.3.2 Efたct on Phase Inductances
一
Performance ofDSPM Motor with Inter-turn Fault
0
7.3
06 009 9
7.2.3 Effect on Pole Flux Densities
ノ
7.2.1 Effect on Static Torque Proffiles
7.2.2 Effect on Phase Inductances
ノ
Performance of SRM with Inter-turn Fault
11 11 11 11 噌 11 111 11 11 つ L
7.2
一
0
6
General
0
00ハ
7.1
1111
EFFETCS OF FAULTS IN PHASE WINDING ON THE
PERFORMANCE OF MULTI-PHASE DOUBLY-SALIENT
MOTORS
L 11 11
6.3
6.4
11
6.1
1 11
DESIGN OF MULTI-PHASE DOUBLY SALIENT
PER八壇ANENT MAGNET MOTORS
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CHAPTER-VI
1
5.3.2 Effects of Relative Eccentricity on Flux Densities
111
5.3.1 Effects of Relative Eccentricity on the Torque Proffiles
11
5.3
Airgap Nonuniformity
Analysis ofthe Motor having Relative Eccentricity
j
4 6ワ 1「 lJ
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4
4 一4
一 11
且
1
5.2
7.5
Performance of DSPM Motor on Phase to Phase Fault
207
7.6
Performance of SRM and DSPM Motor on an Open-Phase
Fault
213
Conclusions
215
7.7
xlv
CHAPTER-Ylli PERFORMANCE IMPROVEMENT OF MULTI-PHASE
DOUBLY SALIENT PERMANENT MAGNET MOTORS 217
General
8.1
8.2
Two-Dimensional FE Analysis of DSPM Motor having
Skewed Rotor
8.3
Three-Dimensional FE Analysis ofDSPM Motor having
Skewed Rotor
8.3.1 Three-Dimensional Analysis ofDSPM Motor having
Skewed Rotor without Stator Excitation
8.3.2 Three-Dimensional Analysis of DSPM Motor having
Skewed Rotor with Stator Excitation
8.4
Rotor Pole Tapering of DSPM Motors
8.5
Conclusions
CHAPTER-IX MAIN CONCLUSIONS
AND SUGGESTIONS FOR
FUTURE WORKS
217
218
225
226
229
238
245
248
General
248
9.2
Main Contributions of this Research Work
249
9.3
Main Conclusions
250
Flux-Linkage
Characteristics ofthe Multi-Phase SRM by Flux
9.3
251
Tube Method
9.3.2 CAD of Multi-Phase SRM
251
9.3.3 Genetic Algorithm Based Design Optimization of SRM
252
252
9.3.4 Pole Shapes for the Improved Performance of the SRM
253
9.3.5 Effects of Airgap Nonuniformity in SRM
254
9.3.6 Design ofthe Multi-Phase DSPM motor
9.3.7 Effects of Fault in Phase Winding on the Pe雨rmance of
Multi-Phase Doubly Salient Motors
254
9.3.8 Performance Improvement ofMulti-Phase DSPM Motors
255
9.4
256
Suggestions for Future Work
REFERENCES
258
LIST OF PUBLICATIONS
270
APPENDIX-I
272
BIOGRAPHY
278