SLOTLESS SIX-PHASE BRUSHLESS DC MACHINE DESIGN AND STEPPING
VECTOR CONTROL
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Yu Liu, B. S.
Graduate Program in Electrical and Computer Engineering
The Ohio State University
2015
Dissertation Committee:
Dr. Longya Xu, Advisor
Dr. Mahesh S. Illindala
Dr. Jiankang Wang
© Copyright by
Yu Liu
2015
ABSTRACT
Permanent magnet brushless DC (BLDC) machines have been widely used in electric
vehicles, servo systems and appliances due to their high efficiency and high torque
density. However, challenges still exist to develop high performance BLDC machines for
drive system, including machine design and machine control algorithms.
This
dissertation focuses on developing 3 kW slotless six-phase BLDC machines with high
torque density and low torque ripple. Furthermore, two control techniques are proposed
in this dissertation for BLDC machine drives, including stepping vector control (SVC)
and sensorless control.
It requires a very small cogging torque, which is less than 2% of the rating torque, for
the BLDC machine in high-performance applications. The cogging torque in BLDC
machine design can be mitigated most effectively by using slotless stator core structure.
In order to achieve high torque density, a spoke type rotor is adopted in machine design
as it can provide the largest back EMF and most balanced flux density distribution with a
given magnet size. Compared to a three-phase BLDC machine, the advantage a of sixphase BLDC machine is that a single inverter can split into two smaller power rating ones.
Although cogging torque has been mitigated in machine design, commutation torque
ripple still exists because of a mismatch between incoming and outgoing currents. To
address this issue, a novel control is proposed to combine the merits of sinusoidal current
ii
control and trapezoidal current control to improve BLDC machine performance. The
proposed control algorithm is called SVC because the vector angle changes step by step.
With the proposed algorithm, commutation torque ripple will be minimized by matched
incoming and outgoing currents. To further increase the BLDC machine’s performance, a
torque-enhanced method based on SVC is proposed.
The optimal current angle in
enhanced torque control is referred to as the stator current angle that generates maximum
torque when amplitude of stator current vector does not change. The optimal current
angle control can provide 5.4% more torque than conventional control, as though with a
drawback of torque ripple. With further investigation, the torque ripple in optimal current
angle control can be minimized by vector amplitude compensation.
In order to reduce cost and enhance mechanical robustness, a variety of sensorless
control algorithms for BLDC machines have been proposed. However, most of them fail
at zero or low speed because of the undetectable back EMFs. To solve this problem, this
dissertation presents a sensorless control algorithm for BLDC machines based on rotor
saliency. A voltage pulse injection method is used for inductance measurement and the
peak inductance current is measured to improve rotor detection accuracy. For the speed
range from zero to an arbitrarily low speed, sensorless operations of the BLDC machine
can be achieved with the proposed algorithm.
A prototype machine has been built to verify the design of a 3 kW slotless six-phase
BLDC machine. Both computer simulations and experimental results are provided to
verify the feasibility and effectiveness of proposed machine control algorithms.
iii
DEDICATION
This document is dedicated to my parents and my wife.
iv
ACKNOWLEDGMENTS
My deepest appreciation goes to my PhD advisor Professor Longya Xu for providing
me with academic guidance, funding support and encouragement during my graduate
study at The Ohio State University. His immense knowledge, profound experience,
patience, motivation, enthusiasm, and deep insight helped me to develop a creative and
critical engineering mind that I believe the most important thing in the research. I also
would like to thank my advisor for all the possible industry-related training opportunities
that I consider the bridge connecting researches to applications. His advice and personal
examples will accompany me in my future career.
I would like to express my gratitude to Professor Mahesh S. Illindala and Professor
Jiankang Wang for being committee members of my dissertation. They provided me with
numerous comments and suggestions on my research proposal and dissertation. My
special thanks go to Professor Vadim Utkin for his invaluable advice in my Candidacy
Exam and Professor Jin Wang for his insightful comments in my Qualifying Exam.
My thanks are extended to my fellow group members. I would like to thank my
senior fellow students Dr. Yuan Zhang, Dr. Thomas Tsai, Dr. Zhendong Zhang and Dr.
Ernesto Inoa for their help with my course work and research, numerous hands-on
instructions and useful discussions on research work. I also want to thank my junior
group members Dakai Hu, Haiwei Cai, Feng Qi, Miao Wang, Yazan Alsmadi, Qi Chen,
Ying Xiao and Han Yang for their friendship and enlightening discussions. I also want to
v
thank visiting scholars Professor Fei Lin, Professor Jinhua Du, Dr. Le Gao, Dr. Xikai Sun,
Professor Hui Liang, Professor Mengjia Jin, Professor Xiaolin Wang and Professor
Hongyu Wang for their valuable advice and help.
I would like to thank my following colleagues majoring in electrical engineering: Ke
Zhou, Feng Guo, Cong Li, Mark Scott, Xiu Yao, Luís Herrera, Lixing Fu, Xuan Zhang,
Ernest Davidson and Daijiafan Mao for their friendship and camaraderie.
I am always indebted to all my family members, especially my parents and my wife,
for their tremendous patience and heartfelt forgiveness. I would like to thank my parents
Xuezhi Liu and Zhongping Yu for their unconditional love and I greatly appreciate the
sacrifices and understanding of my beloved wife, Meijie. Without the endless support
from my family, the completion of my study would not have been possible.
vi
VITA
Feb. 19th, 1985..............................................Born - Qiqihar, Heilongjiang, China.
Jun. 2008.........................................................B.S. Southeast University, Nanjing, China.
Sept. 2009 - Feb. 2015 .................................Graduate Research Associate, Department of
Electrical and Computer Engineering, The Ohio State University.
Feb. 2015 - present........................................Engineer, Fisker Automotive and
Technology Group, LLC.
FIELDS OF STUDY
Major Field: Electrical and Computer Engineering
vii
TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... ii
DEDICATION .................................................................................................................. iv
ACKNOWLEDGMENTS ................................................................................................ v
VITA ................................................................................................................................. vii
FIELDS OF STUDY ....................................................................................................... vii
TABLE OF CONTENTS ............................................................................................... viii
LIST OF TABLES ........................................................................................................... xii
LIST OF FIGURES ....................................................................................................... xiii
CHAPTER 1: INTRODUCTION .................................................................................... 1
1.1
Slotless BLDC Machine Design ............................................................................ 2
1.2
BLDC Machine Commutation Torque Ripple Minimization ................................. 2
1.3
BLDC Machine Sensorless Control ...................................................................... 4
viii
1.4
Chapter Organization ........................................................................................... 5
CHAPTER 2: DESIGN OF SLOTLESS SIX-PHASE BLDC MACHINE ................. 7
2.1
Electrical and Mechanical Requirement............................................................... 7
2.2
Stator Design ........................................................................................................ 8
2.3
Stator Winding Connection Design ..................................................................... 12
2.4
Rotor Design ....................................................................................................... 17
2.4.1 Surface-Mounted Type Rotor .......................................................................... 19
2.4.2 Inset Type Rotor .............................................................................................. 20
2.4.3 Single Barrier Type Rotor ............................................................................... 22
2.4.4 Interior Type Rotor .......................................................................................... 24
2.4.5 Spoke Type Rotor ............................................................................................ 26
2.4.6 Rotor Comparison Study ................................................................................. 28
2.5
Air Gap Design ................................................................................................... 36
2.6
Inductance Calculation and Measurement ......................................................... 48
2.7
Winding Resistance Calculation ......................................................................... 57
2.8
Winding Assembling ............................................................................................ 58
2.9
Prototype ............................................................................................................. 69
2.10 Configuration ...................................................................................................... 76
2.11 Summary ............................................................................................................. 77
CHAPTER 3: STEPPING VECTOR CONTROL ...................................................... 79
ix
3.1
Stepping Vector Control of BLDC Machine ........................................................ 79
3.2
Commutation Torque Ripple Minimization of BLDC Machine ........................... 85
3.2.1 BLDC Commutation Torque Ripple Analysis ................................................. 86
3.2.2 Commutation Torque Ripple Minimization Based on SVC ............................ 88
3.2.3 Simulation Verification .................................................................................... 90
3.2.4 Experimental Verification ................................................................................ 91
3.2.5 Ramping Region of SVC ................................................................................. 93
3.3
Enhanced Torque Control of BLDC Machine ..................................................... 95
3.3.1 Optimal Current in Enhanced Torque Control ................................................ 95
3.3.2 Simulation Verification .................................................................................... 98
3.4
Summary ............................................................................................................. 99
CHAPTER 4: SENSORLESS CONTROL OF BLDC MACHINE.......................... 101
4.1
Rotor Saliency Characteristics ......................................................................... 101
4.2
Sensorless Control of BLDC Machine from Zero to Low Speed ....................... 105
4.2.1 Principles of Initial Rotor Position Estimation Algorithm ............................ 107
4.2.2 Principles of Low Speed Sensorless Algorithm .............................................110
4.3
Simulation Verification.......................................................................................112
4.4
Experimental Verification ..................................................................................116
4.5
Summary ........................................................................................................... 121
CHAPTER 5: CONCLUSIONS AND FUTURE WORKS ....................................... 123
5.1
Conclusions ....................................................................................................... 123
x
5.2
Future Works ..................................................................................................... 124
REFERENCES .............................................................................................................. 126
xi
LIST OF TABLES
Table 2.1. Rating and Parameters of Slotless Six-Phase BLDC Machine .................... 8
Table 2.2. Distribution Factors of Different Order Harmonics in Six-Phase BLDC
Machine..................................................................................................................... 10
Table 2.3. Distribution Factors of Different Order Harmonics in Three-Phase BLDC
Machine..................................................................................................................... 10
Table 2.4. Effective Air Gap Comparison ..................................................................... 47
Table 3.1. Active Phase and Inactive Phase in Six Regions ......................................... 84
Table 3.2. Rating and Parameters of BLDC Machine ................................................. 92
Table 4.1. Initial Position Estimation Comparison Procedure ................................. 109
Table 4.2. Rotor Position and Injected Voltage ........................................................... 111
Table 4.3. Rating and Parameters of BLDC Machine ................................................116
xii
LIST OF FIGURES
Figure 2.1. Slotless Stator Core and Stator Winding (1/8) .......................................... 12
Figure 2.2. Stator Winding Connection ........................................................................ 13
Figure 2.3. Half of a Single Coil ..................................................................................... 14
Figure 2.4. Connection between Two Half Coils .......................................................... 15
Figure 2.5. Phase A Winding .......................................................................................... 16
Figure 2.6. Five Types of Rotor for BLDC Machine .................................................... 18
Figure 2.7. Geometry of Surface-Mounted Type Rotor............................................... 19
Figure 2.8. Back EMF of Surface-Mounted Type Rotor ............................................. 20
Figure 2.9. Geometry of Inset Type Rotor .................................................................... 21
Figure 2.10. Back EMF of Inset Type Rotor ................................................................. 22
Figure 2.11. Geometry of Single Barrier Type Rotor .................................................. 23
Figure 2.12. Back EMF of Single Barrier Type Rotor ................................................. 24
Figure 2.13. Geometry of Interior Type Rotor ............................................................. 25
Figure 2.14. Back EMF of Interior Type Rotor ............................................................ 26
Figure 2.15. Geometry of Spoke Type Rotor ................................................................ 27
Figure 2.16. Back EMF of Spoke Type Rotor ............................................................... 28
Figure 2.17. Flux Density Contour of Single Barrier Type Rotor .............................. 29
Figure 2.18. Air-Gap Flux Density of Single Barrier Type Rotor ............................... 30
Figure 2.19. Flux Density Contour of Interior Type Rotor ......................................... 31
xiii
Figure 2.20. Air-Gap Flux Density of Interior Type Rotor ......................................... 32
Figure 2.21. Flux Density Contour of Spoke Type Rotor ............................................ 33
Figure 2.22. Air-Gap Flux Density of Spoke Type Rotor ............................................ 34
Figure 2.23. Torque of Spoke Type Rotor ..................................................................... 35
Figure 2.24. Excitation Current of Spoke Type Rotor ................................................. 36
Figure 2.25. Air Gap and Effective Air Gap ................................................................. 38
Figure 2.26. Slots and Teeth in Traditional BLDC Machine ....................................... 39
Figure 2.27. Geometry of Machine Design with Reduction in Effective Air Gap ..... 41
Figure 2.28. Back EMF of Machine Design with Reduction in Effective Air Gap .... 42
Figure 2.29. Flux Density Contour of Machine Design with Reduction in Effective
Air Gap ..................................................................................................................... 43
Figure 2.30. Air-Gap Flux Density of Machine Design with Reduction in Effective
Air Gap ..................................................................................................................... 44
Figure 2.31. Torque of Machine Design with Reduction in Effective Air Gap .......... 45
Figure 2.32. Excitation Current of Machine Design with Reduction in Effective Air
Gap ............................................................................................................................ 46
Figure 2.33. Flux Density vs Magnetic Field of Soft Magnetic Material ................... 50
Figure 2.34. Flux Density vs Magnetic Field of Permanent Magnet Material .......... 51
Figure 2.35. Phase Inductance vs Electrical Angle of Original Design ...................... 52
Figure 2.36. Phase Inductance vs Electrical Angle of Machine Design with
Reduction in Effective Air Gap ............................................................................... 53
Figure 2.37. Rotor Position with Maximum Phase A Inductance ............................... 54
Figure 2.38. Rotor Position with Minimum Phase A Inductance ............................... 55
xiv
Figure 2.39. Mutual Inductance between Phase A and Other Phases ........................ 56
Figure 2.40. Fixture and Tooling Overview .................................................................. 58
Figure 2.41. Winding Assembling Step 1 ...................................................................... 59
Figure 2.42. Winding Assembling Step 2 ...................................................................... 60
Figure 2.43. Winding Assembling Step 3 ...................................................................... 61
Figure 2.44. Winding Assembling Step 4 ...................................................................... 62
Figure 2.45. Winding Assembling Step 5 ...................................................................... 63
Figure 2.46. Winding Assembling Step 6 ...................................................................... 64
Figure 2.47. Winding Assembling Step 7 ...................................................................... 65
Figure 2.48. Winding Assembling Step 8 ...................................................................... 66
Figure 2.49. Winding Assembling Step 9 ...................................................................... 67
Figure 2.50. Winding Assembling Step 10 .................................................................... 68
Figure 2.51. Winding Assembling Step 11 ..................................................................... 69
Figure 2.52. First Generation Prototype of Slotless Six-Phase BLDC Machine ....... 70
Figure 2.53. Rotor Shaft of Prototype Machine ........................................................... 71
Figure 2.54. Single Conductor of Prototype Machine ................................................. 72
Figure 2.55. Conductor Connections of Prototype Machine ....................................... 73
Figure 2.56. Stator Windings of Prototype Machine ................................................... 74
Figure 2.57. Fixture and Tooling of Prototype Machine.............................................. 75
Figure 2.58. Three-Phase Configuration of Slotless Six-Phase BLDC Machine ....... 76
Figure 2.59. Back EMF in Three-Phase Configuration ............................................... 77
Figure 3.1. Current Back EMF and Torque in Sinusoidal Current Control ............. 81
Figure 3.2. Current, Back EMF and Torque in Trapezoidal Current Control.......... 82
xv
Figure 3.3. Current and Vector Angle Moving Pattern in Conventional Vector
Control (left) and SVC (right) ................................................................................ 83
Figure 3.4. Block Diagram of SVC for BLDC Machine Drive System ...................... 85
Figure 3.5. Equivalent Circuit of BLDC in Commutation Interval ........................... 86
Figure 3.6. Simulation Results of Commutation Torque Ripple................................. 88
Figure 3.7. Ideal Current for Commutation Torque Ripple Minimization ............... 89
Figure 3.8. Simulation Results of SVC .......................................................................... 91
Figure 3.9. Experimental Results of Current with Vector Angle Control in SVC .... 92
Figure 3.10. Experimental Results of Current with both Vector Angle and Vector
Amplitude Control in SVC ...................................................................................... 93
Figure 3.11. Vector Angle and Real Rotor Angle in SVC ............................................ 94
Figure 3.12. Optimal Current Angle Control ............................................................... 97
Figure 3.13. Optimal Current Angle Control with Vector Amplitude Compensation
.................................................................................................................................... 98
Figure 3.14. Simulation Results of Optimal Current Angle Control .......................... 99
Figure 4.1. Typical BLDC Machine FEM Model (1/4) .............................................. 103
Figure 4.2. Phase Inductance Variation ...................................................................... 104
Figure 4.3. Line Inductance Variation ........................................................................ 104
Figure 4.4. Characterizing Current Region ................................................................ 107
Figure 4.5. Typical BLDC Machine System................................................................ 108
Figure 4.6. Flowchart of the Low Speed Sensorless Algorithm .................................112
Figure 4.7. Inductance Measurement Currents in FEM simulation .........................113
Figure 4.8. North Pole Detection Currents in FEM simulation .................................113
xvi
Figure 4.9. Current Variation in Region 0 ...................................................................115
Figure 4.10. BLDC Machine Drive System .................................................................116
Figure 4.11. Inductance Measurement Currents in Experiment ...............................117
Figure 4.12. North Pole Detection Currents in Experiment ......................................118
Figure 4.13. Sensor-based and Sensorless Comparison..............................................119
Figure 4.14. Inductance Measurement Currents ....................................................... 120
Figure 4.15. Extremely Low Speed Operation ........................................................... 121
xvii
CHAPTER 1: INTRODUCTION
Over the past few decades, electrical machines have been a cornerstone of industry
development. Recently, electrical vehicles (EVs) and hybrid electric vehicles (HEVs)
have received much attention due to their high fuel efficiency and low emissions.
However, the electrical machines, the core components of the EV and HEV applications,
should be designed to meet higher standards, such as high torque density, high efficiency,
wide torque-speed capability and high reliability [1-4].
Currently, the interior permanent magnet (IPM) motor and cage induction motor (IM)
are the two most popular choices for EV/HEV traction motors. Due to the rare earth’s
strong magnetic field, this type of IPM motor is able to provide a high torque density,
wide speed-torque range, compact size and high efficiency, while a cage IM has no
external source for a magnetic field. To provide torque, an IM must rely upon its rotor
slip relative to the synchronous speed to generate a rotor current. Therefore, the torque
density of a cage IM is lower and larger than that of an IPM motor. Moreover, dual
mechanical port machines and switched reluctance machines are also proposed and
discussed for EV/HEV applications [5, 6].
Though often used as a variable-speed,
constant-frequency generator for wind power, the doubly-fed induction machine (DFIM)
is proposed as a potential candidate for EV/HEV applications, especially for its much
improved constant torque and constant power operations [7-11].
In order to increase electrical machines’ operation speeds, flux weakening controls
1
are required for IPM, IM and DFIM. When they are working at constant power region, a
negative magnetizing current is needed to demagnetize the permanent magnets in the
IPM flux weakening control. As a result, a reduced magnetizing current is necessary for
IM and DFIM flux weakening controls [12-16]. Current closed loop control is critical for
the implementation of machine control algorithms. In order to increase torque response
and system robustness, current closed loop controls, which depend upon a PI regulator,
can be designed using frequency response, genetic algorithm, poles placement, complex
vector, real-time gain tuning and internal model control method [17-21].
1.1
Slotless BLDC Machine Design
The BLDC machine in high-performance applications requires a very small cogging
torque which can not exceed 2% of the rating torque [22-23]. The cogging torque is
similar to reluctance torque, which is caused by the reluctance variation between
permanent magnets and slot or tooth. When a rotor permanent magnet is approaching or
leaving a slot, the co-energy in the air gap between stator and rotor will change, resulting
in cogging torque. Note that the cogging torque can be minimized by many approaches
[24-29], such as skewing the stator laminations or rotor magnets, varying slot width,
varying magnet width, shifting alternate pair of poles, and notching teeth. The cogging
torque in BLDC machine design can be mitigated most effectively by using slotless stator
core structure [30-35].
1.2
BLDC Machine Commutation Torque Ripple Minimization
2
BLDC and brushless AC (BLAC) machines are widely used in electric vehicles (EVs)
and hybrid electric vehicles (HEVs) applications due to their high power density, high
torque density and high efficiency. Different from BLAC machine with a sinusoidal back
EMF, the BLDC machine is provided with a trapezoidal back EMF. Compared to BLAC
machine, BLDC machine can achieve a higher torque density and a higher power density
for a given size [36]. However, BLDC machine has a significant drawback, which is
commutation torque ripple.
Commutation torque ripple will cause oscillation and
resonance in mechanical components, bringing observable vibration and acoustic noise to
drive systems. The ripple is caused by the currents going through the freewheeling
diodes during commutation intervals, and many studies have been conducted to minimize
this torque ripple.
In [37], a DC bus voltage control method is proposed, but an
additional DC bus voltage controller is required in the method, increasing overall system
cost. In [38] an algorithm based on current slopes control is proposed, in which the
current slopes of the incoming and outgoing phase currents can be controlled in the same
rate of change by adjusting PWM duty ratio. By delaying the turn-off timing instant of
the outgoing switch, an overlap switching algorithm is proposed in [39]. However, these
conventional methods show limited effectiveness in practical applications due to machine
parameter sensitivity and unsatisfactory performance over an entire speed range. An
algorithm based on SVC, which combines the merits of sinusoidal current control and
trapezoidal current control, is proposed to minimize commutation torque ripple.
The trapezoidal current control is a perfect fit for BLDC machine drive because both
high torque production and high efficiency [40, 41] can be achieved. The trapezoidal
current control is usually implemented by hysteresis control, PI control, fuzzy logic
3
control or feed forward control [42-45]. However, in most of the control algorithms
outgoing phase current is without control and its decay rate is only determined by DC bus
voltage and back EMF. The varying decay rate may cause a mismatch between outgoing
current and incoming current, resulting in a commutation torque ripple. In order to
achieve a trapezoidal current control with commutation torque ripple minimization, [4647] are proposed for BLDC motor drive.
To further increase BLDC machine
performance, several torque-enhanced methods are proposed [48-52].
1.3
BLDC Machine Sensorless Control
BLDC machines have been widely used in electric vehicles, servo systems and
appliances due to their high efficiency and high torque density. In high performance
applications, the BLDC machine is driven by an inverter and it requires rotor position
information for current commutations. Usually a group of Hall position sensors provides
commutation signals. In order to reduce cost and enhance mechanical robustness, a
variety of sensorless control algorithms have been studied [53-57]. In three-phase BLDC
machine control algorithms, usually two of the three phases are conducted sequentially
and the other non-conducting phase is called silent phase.
In order to obtain
commutation timings, the back EMF method detects the back EMF zero crossing of the
silent phase and triggers the commutations every 60 degrees [53]; while [54] integrals the
back EMF of the silent phase and compared with a threshold value. It should be pointed
out that these above mentioned methods, as well as other flux linkage based ones [55, 56]
and freewheeling diode conduction methods [57], fail to achieve commutation at zero or
low speed because of the undetectable back EMFs.
4
To overcome the mentioned
drawbacks, a sensorless method based on speed-independent function is proposed in [58],
which can estimate commutation instants from near zero (2% of the rated speed) to high
speed.
However, this method is only applicable to the surface-mounted permanent
magnet BLDC machines.
A BLDC machine sensorless control algorithm based on
inductance variation is proposed in [59]. In this algorithm, a pulse train, including long
and short pulses, is injected into the conducting phases. The long pulses are used for
torque production and the short ones are for inductance measurement. However, a time
interval insertion between the long and the short pulses is required to ensure
measurement accuracy. During the time interval a negative torque is generated, leading
to a degraded torque performance. Other sensorless algorithms for permanent magnet
synchronous machine, including magnetic pole identifications, high frequency injection
and sliding-mode control, have been investigated in [60-64]. However, these methods
based on space vector control are preferred by sinusoidal current drive rather than
trapezoidal current BLDC drive. A sensorless control algorithm for BLDC motors based
on rotor saliency is proposed in [65].
1.4
Chapter Organization
Chapter 2 presents the design process of a 3 kW slotless six-phase BLDC machine,
including electrical and mechanical requirements, stator design, stator winding
connection design, rotor design and air gap design.
Chapter 3 presents a novel control algorithm for BLDC machine. The proposed
control algorithm combines the merits of sinusoidal current control and trapezoidal
current control to minimize commutation torque ripple of BLDC machine.
5
Chapter 4 presents a sensorless BLDC control algorithm based on rotor saliency. A
voltage pulse injection method is used for inductance measurement and the peak
inductance current is measured through the salient phase to increase accuracy. Zero
speed and arbitrary low speed sensorless operations can be achieved with the proposed
algorithm.
Chapter 5 summarizes the research conclusions in this dissertation and the potential
research topics in future works.
6
CHAPTER 2: DESIGN OF SLOTLESS SIX-PHASE BLDC
MACHINE
Design of a slotless six-phase BLDC machine will be studied in this chapter. At first,
a requirement of dimensions, torque, speed, and power is specified, and then stator core,
stator winding connection and rotor are designed sequentially. In the end, a 3 kW slotless
six-phase BLDC machine is designed and verified by finite element analysis (FEA).
The design procedure includes five aspects:
i.
Electrical and Mechanical Requirement
ii.
Stator Design
iii.
Stator Winding Connection Design
iv.
Rotor Design
v.
Air Gap Design
2.1
Electrical and Mechanical Requirement
Based on the operation condition, both electrical and mechanical requirements should
meet the specific requirements which are shown in Table 2.1.
7
Table 2.1. Rating and Parameters of Slotless Six-Phase BLDC Machine
Machine Type
rating output power
rating speed
rating torque
rating DC bus voltage
stator outside diameter
axial length
phase number
pole number
BLDC
3 kW
4000 rpm
7.2 Nm
280 V
120 mm
120 mm
6
8
In mechanical design, the size of the machine is determined by stator outside
diameter and axial length. In electrical design, DC bus voltage is the main limitation
factor of rating speed, and rating torque is proportional to phase current.
2.2
Stator Design
For the BLDC machine in high-performance applications requires a very small
cogging torque which cannot exceed 1% or 2% of the rating torque [22-23]. The cogging
torque is similar to reluctance torque, which is caused by the reluctance variation between
permanent magnets and slot or tooth. When rotor permanent magnet is approaching or
leaving a slot, the co-energy in the air gap between stator and rotor will change, resulting
the cogging torque. Note that the cogging torque can be minimized many ways [24-29],
such as skewing the stator laminations or rotor magnets, varying slot width, varying
magnet width, shifting alternate pair of poles, and notching teeth. The cogging torque in
BLDC machine design can be mitigated most effectively by using slotless stator core
structure [30-35].
8
A rectangular wire rather than a round wire is adopted in this design due to the
advantages in slot-fill factor, increasing the linkage flux and forming the winding
arrangement. Moreover, a slotless stator can possess a higher winding fill factor
compared to a slotted type because of the construction of the toothless stator core.
A distributed winding rather than a concentric winding is adopted in this design due
to better utilization of the winding space and higher magneto motive force. There are 192
virtual slots in this design and the winding distribution factor is calculated by the
following equation,
𝑘𝑑 =
𝑞𝛾
)
2
𝛾
𝑞 sin( )
2
sin(
=
4×7.5°
)
2
°
7.5
sin(
4 sin(
2
= 0.9893
(2.1)
)
where q is the number of slots per pole per phase, the product 𝑞𝛾 represents the total
width of the coil of a phase under one pole.
The distribution of the windings consequently affects the harmonic components of
the MMF and induced EMF. Therefore, the distribution factor for the harmonic of order n
can be derived from the fundamental distribution factor as
𝑘𝑑𝑛 =
𝑞𝛾
)
2
𝛾
𝑞 sin(𝑛 )
2
sin(𝑛
The distribution factors of different order harmonics are shown in Table 2.2.
9
(2.2)
Table 2.2. Distribution Factors of Different Order Harmonics in Six-Phase BLDC
Machine
Harmonic Order Distribution Factor
1
0.9893
3
0.9055
5
0.7498
7
0.5435
9
0.3149
11
0.0945
13
-0.0893
If this six-phase BLDC machine is configured as a three-phase BLDC machine, the
distribution factors of different order harmonics are shown in Table 2.3.
Table 2.3. Distribution Factors of Different Order Harmonics in Three-Phase BLDC
Machine
Harmonic Order Distribution Factor
1
0.9553
3
0.6387
5
0.1910
7
-0.1437
9
-0.2243
11
-0.0915
13
0.0860
The comparison between Table 2.2 and Table 2.3 shows that the fundamental
component increased by 3.6% in six-phase configuration. Besides, 3rd, 5th, 7th and 9th
order harmonics are increased.
To achieve good trapezoidal back EMF, six-phase
configuration is adopted in this design.
10
Winding pitch factor is calculated by following equation,
180°
𝜉
𝑘𝑝 = sin (2) = sin (
2
)=1
(2.3)
where 𝜉 is coil pitch, a fractional pitch coil winding is usually adopted to reduce
harmonics in the induced EMF and reduce the length of the end turns. In BLDC machine
design, a full pitch coil winding is used to achieve trapezoidal back EMF.
Both stator and rotor can be skewed to minimize cogging torque or reduce certain
order harmonics. Skew factor is calculated by
𝑘𝑠𝑘 =
𝜃
sin( 𝑠𝑘 )
2
𝜃𝑠𝑘
2
=1
(2.4)
where 𝜃𝑠𝑘 is the skew angle.
In BLDC machine design, it is unnecessary to skew windings or permanent magnets
since a trapezoidal back EMF is preferred.
As a combined effect of winding distribution factor 𝑘𝑑 , winding pitch factor 𝑘𝑝 and
skew factor 𝑘𝑠𝑘 , the winding factor is given by
𝑘𝑤 = 𝑘𝑑𝑛 × 𝑘𝑝 × 𝑘𝑠𝑘 = 98.93%
(2.5)
In this BLDC machine design, a high winding factor is obtained to achieve a better
utilization of induced back EMF. As a result, double-layer windings are used in the
design. The slotless stator core and stator winding designs are shown as Figure 2.1.
11
Slotless Stator Core
Stator Winding
Figure 2.1. Slotless Stator Core and Stator Winding (1/8)
To summarize, stator core structure, wire type, winding type, winding distribution
factor, winding pitch factor, skew factor and winding layer are designed sequentially.
2.3
Stator Winding Connection Design
A formed stator winding structure is used in the design. The stator winding
connection is shown as Figure 2.2.
12
A
B
C
D
F
E
1
25
5
29
9
33
13
37
17
41
21
45
2
26
6
30
10
34
14
38
18
42
22
46
3
27
7
31
11
35
15
39
19
43
23
47
4
28
8
32
12
36
16
40
20
44
24
48
49
73
53
77
57
81
61
85
65
89
69
93
50
74
54
78
58
82
62
86
66
90
70
94
51
75
55
79
59
83
63
87
67
92
71
95
52
76
56
80
60
84
64
88
68
92
72
96
97
121
101
112
5
105
129
109
133
113
137
117
141
98
122
102
126
106
130
110
134
114
138
118
142
99
123
103
127
107
131
111
135
115
139
119
143
100
124
104
128
108
132
112
136
116
140
120
144
145
169
149
173
153
177
157
181
161
185
165
189
146
170
150
174
154
178
158
182
162
186
166
190
147
171
151
175
155
179
159
183
163
187
167
191
148
172
152
176
156
180
160
184
164
188
168
192
4
172
8
176
12
180
16
184
20
188
24
192
3
171
7
175
11
179
15
183
19
187
23
191
2
170
6
174
10
178
14
182
18
186
22
190
1
169
5
173
9
177
13
181
17
185
21
189
148
124
152
128
156
132
160
136
164
140
168
144
147
123
151
127
155
131
159
135
163
139
167
143
146
122
150
126
154
130
158
134
162
138
166
142
145
121
149
125
153
129
157
133
161
137
165
141
100
76
104
80
108
84
112
88
116
92
120
96
99
75
103
79
107
83
111
87
115
91
119
95
98
74
102
78
106
82
110
86
114
90
118
94
97
73
101
77
105
81
109
85
113
89
117
93
52
28
56
32
60
36
64
40
68
44
72
48
51
27
55
31
59
35
63
39
67
43
71
47
50
26
54
30
58
34
62
38
66
42
70
46
49
25
53
29
57
33
61
37
65
41
69
45
Up
Slot
Down
Slot
Up
Slot
Down
Slot
Up
Slot
Down
Slot
Up
Slot
Down
Slot
Up
Slot
Down
Slot
Up
Slot
Down
Slot
Figure 2.2. Stator Winding Connection
13
Half of a single coil is shown as Figure 2.3,
Figure 2.3. Half of a Single Coil
Two half coils are connected through a form-wound stator structure, as shown in
Figure 2.4.
14
Figure 2.4. Connection between Two Half Coils
15
Phase A winding is shown as Figure 2.5.
Figure 2.5. Phase A Winding
16
For easy assembling puposes, a formed stator winding structure has been utilized in
slotless six-phase BLDC machine design.
Furthermore, the proposed formed stator
winding structure has a shorter end-winding than conventional winding structure.
2.4
Rotor Design
The designed stator core and stator winding provide a rectangular MMF distribution,
the fundamental of which is 27% higher than sinusoidal MMF distribution. There are
three principles in the rotor design of slotless six-phase BLDC machine. The top priority
is performance, referred to as high torque density. Secondly, a trapezoidal back EMF is
required because this is a BLDC type machine. The third principle is to reduce cost by
reducing the usage of permanent magnets.
There are five types of rotor for BLDC machine design and one of them will be
selected based on the three principles; the rotor geometry optimization will be studied
after that. The five types of rotor are surface-mounted, inset, single barrier, interior and
spoke, as shown in Figure 2.6.
17
Surface-mounted
Inset
Interior
Single Barrier
Spoke
Figure 2.6. Five Types of Rotor for BLDC Machine
18
In each type of rotor, geometry and back EMF will be examined by FEA. The
magnitude of back EMF can be considered as an indicator of torque density because
torque is proportional to back EMF when current remains constant. A trapezoidal shape
of back EMF is required for BLDC machine because the current is square shaped. The
permanent magnet area calculated from 2D geometry is used for cost evaluation.
All five rotor candidates are examined by FEA with the same stator. Only 1/8
geometry will be studied in FEA because it is an eight poles machine.
2.4.1
Surface-Mounted Type Rotor
The geometry of surface-mounted type rotor (1/8) is shown as Figure 2.7 and the
permanent magnet area is 157 mm^2.
Figure 2.7. Geometry of Surface-Mounted Type Rotor
19
Based on FEA results, the back EMF of surface-mounted type rotor at 4000 RPM is
shown as Figure 2.8, for shape evaluation purpose only Phase A and Phase C are plotted.
The shape of back EMF is not ideal trapezoidal due to the smooth transition at the
commutation interval.
Figure 2.8. Back EMF of Surface-Mounted Type Rotor
2.4.2
Inset Type Rotor
The geometry of inset type rotor (1/8) is shown as Figure 2.9 and the permanent
magnet area is 157 mm^2.
20
Figure 2.9. Geometry of Inset Type Rotor
Based on FEA results, the back EMF of inset type rotor at 4000 RPM is shown as
Figure 2.10, for shape evaluation purpose only Phase A and Phase C are plotted. The
shape of back EMF is not ideal trapezoidal due to the smooth transition at commutation
interval.
21
Figure 2.10. Back EMF of Inset Type Rotor
2.4.3
Single Barrier Type Rotor
The geometry of single barrier type rotor (1/8) is shown as Figure 2.11 and the
permanent magnet area is 135 mm^2.
22
Figure 2.11. Geometry of Single Barrier Type Rotor
Based on FEA results, the back EMF of single barrier type rotor at 4000 RPM is
shown as Figure 2.12, for shape evaluation purpose only Phase A and Phase C are plotted.
The shape of back EMF is trapezoidal.
23
Figure 2.12. Back EMF of Single Barrier Type Rotor
2.4.4
Interior Type Rotor
The geometry of interior type rotor (1/8) is shown as Figure 2.13 and the permanent
magnet area is 162 mm^2.
24
Figure 2.13. Geometry of Interior Type Rotor
Based on FEA results, the back EMF of single barrier type rotor at 4000 RPM is
shown as Figure 2.14; for shape evaluation purposes, only Phase A and Phase C are
plotted. The shape of back EMF is trapezoidal.
25
Figure 2.14. Back EMF of Interior Type Rotor
2.4.5
Spoke Type Rotor
The geometry of spoke type rotor (1/8) is shown as Figure 2.15 and the permanent
magnet area is 130 mm^2.
26
Figure 2.15. Geometry of Spoke Type Rotor
Based on FEA results, the back EMF of spoke type rotor at 4000 RPM is shown as
Figure 2.16; for shape evaluation purposes, only Phase A and Phase C are plotted. The
shape of back EMF is trapezoidal.
27
Figure 2.16. Back EMF of Spoke Type Rotor
2.4.6
Rotor Comparison Study
Compliant to trapezoidal shape, back EMF principle, single barrier, interior and
spoke type rotors are selected for further study because surface-mounted and inset type
rotor can only provide quasi trapezoidal shape back EMF.
The flux density contour and air-gap flux density of single barrier type rotor are
shown as figures 2.17 and 2.18 respectively.
28
Figure 2.17. Flux Density Contour of Single Barrier Type Rotor
29
Figure 2.18. Air-Gap Flux Density of Single Barrier Type Rotor
The flux density contour and air-gap flux density of interior type rotor are shown as
figures 2.19 and 2.20, respectively.
30
Figure 2.19. Flux Density Contour of Interior Type Rotor
31
Figure 2.20. Air-Gap Flux Density of Interior Type Rotor
The flux density contour and air-gap flux density of spoke type rotor are shown as
figures 2.21 and 2.22, respectively.
32
Figure 2.21. Flux Density Contour of Spoke Type Rotor
33
Figure 2.22. Air-Gap Flux Density of Spoke Type Rotor
Through further comparison, spoke type rotor provides the largest back EMF and
most balanced flux density distribution for a given magnet size.
The torque of spoke type rotor and excitation current are shown as figures 2.23 and
2.24, respectively.
34
Figure 2.23. Torque of Spoke Type Rotor
35
Figure 2.24. Excitation Current of Spoke Type Rotor
As a conclusion, the best candidate is spoke-type interior-magnet rotor that developed
to increase the air-gap flux density by the flux-concentration principle. The spoke-type
interior-magnet rotor was used as an aircraft generator and in servo-motors by Fanuc and
by Pacific Scientific.
2.5
Air Gap Design
Based on the FEA results from above sections, rotor core structure and magnet
dimension decide back EMF shape and torque capability. However, air-gap flux density
is the determinant of back EMF shape and torque capability based on further study,
36
therefore, air gap will be studied in this section.
The difference between air gap and effective air gap are shown as Figure 2.25.
37
Effective Air Gap
Air Gap
Figure 2.25. Air Gap and Effective Air Gap
38
It can be seen that air gap is the physical gap that is much smaller than the effective
air gap. In the traditional BLDC machines, stator core has slots and teeth, shown as
Figure 2.26.
Tooth
Slot
Figure 2.26. Slots and Teeth in Traditional BLDC Machine
The flux density in the teeth are high, while in the slots are low, resulting in the
reduction of average air flux density. The effective air gap is calculated based on the
Carter coefficient,
𝑙𝑒 = 𝐶𝑙𝑔
where 𝐶 is Carter coefficient, 𝑙𝑒 and 𝑙𝑔 are effective air gap and air gap, respectively.
The Carter coefficient is determined by
39
(2.6)
𝑊 +𝑊
𝑠
𝑡
𝐶 = 𝑊 (1−𝜎)+𝑊
=
𝑠
𝑡
1
1−𝜎
(2.7)
𝑊𝑠
𝑊𝑠 +𝑊𝑡
where 𝑊𝑠 and 𝑊𝑡 are slot width and tooth width respectively, 𝜎 is given by
2
𝑊
𝑙𝑔
𝑊
2
𝜎 = 𝜋 {tan−1 2𝑙𝑠 − 𝑊 ln [1 + (2𝑙𝑠 ) ]}
𝑔
𝑠
𝑔
(2.8)
Usually in practical design, the optimal ratio between slot width and tooth width is
one. Therefore, the minimum Carter coefficient can be obtained when 𝜎 is maximized.
The saturation value of 𝜎 can be found close to 0.9 by increasing the ratio between slot
width and air gap.
In slotless machine, slot width is zero and the Carter coefficient is one. However, the
effective air gap is not equal to air gap because the permeability of winding can be
considered as air. As a result, the effective air gap of slotless machine is given by
𝑙𝑒 = 𝑙𝑔 + 𝑊𝑤
(2.9)
where 𝑊𝑤 is winding width.
Since air gap flux density is inversely proportional to effective air gap, a smaller
effective air gap can provide larger back EMF. In other words, it requires less permanent
magnets to obtain the same back EMF. There are several limitations when trying reduce
effective air gap. The air gap reduction is mainly limited by bearing tolerance and
precision, machine manufacturing and installation. The winding width reduction needs to
take into account winding current density, winding heat dissipation and winding
insulation.
With a reduction in effective air gap, with regard to conductor width, conductor
length and insulation, a slotless six-phase BLDC machine is shown in Figure 2.27,
40
Figure 2.27. Geometry of Machine Design with Reduction in Effective Air Gap
Based on FEA results, the back EMF of machine design with reduction in effective
air gap at 4000 RPM is shown as Figure 2.28; for shape evaluation purposes only, Phase
A and Phase C are plotted. The shape of back EMF is trapezoidal.
41
Figure 2.28. Back EMF of Machine Design with Reduction in Effective Air Gap
The flux density contour and air-gap flux density of machine design with reduction in
effective air gap are shown as figures 2.29 and 2.30 respectively.
42
Figure 2.29. Flux Density Contour of Machine Design with Reduction in Effective Air
Gap
43
Figure 2.30. Air-Gap Flux Density of Machine Design with Reduction in Effective Air
Gap
The torque of machine design with reduction in effective air gap and excitation
current are shown as figures 2.31 and 2.32, respectively.
44
Figure 2.31. Torque of Machine Design with Reduction in Effective Air Gap
45
Figure 2.32. Excitation Current of Machine Design with Reduction in Effective Air Gap
The FEA simulation results showed that the machine design with reduction in
effective air gap can achieve the same torque capability, but permanent magnet usage is
dramatically reduced, as shown in Table 2.4.
46
Table 2.4. Effective Air Gap Comparison
Item
Normal Effective Air Gap Reduction
Unit
Stator core OD
120
120
mm
Stator core ID
105
104.5 (decrease)
mm
Rotor core OD
100
101.4 (increase)
mm
Axial length
120
120
mm
Air Gap
0.3
0.3
mm
Effective Air Gap
2.5
1.55 (decrease by 38%)
mm
Insulation thickness
0.2
0.11 (decrease)
mm
Conductor number
384
576 (increase)
conductor
Conductor width
0.8
0.46 (decrease)
mm
Conductor length
1.45
0.93 (decrease)
mm
Conductor area
1.16
0.43 (decrease)
mm^2
Conductor current
7.5
4.6 (decrease)
A
Conductor current density
6.5
10.7 (increase by 65%)
A/( mm^2)
PM width 1
6
3.6 (decrease)
mm
PM width 2
9
5.4 (decrease)
mm
PM length
17.5
17.2 (decrease)
mm
PM area
131
77.4 (decrease)
mm^2
PM residual magnetism
1.2
1.2
T
PM coercive force
910
910
KA/m
Stator core volume
318
327 (increase by 3%)
cm^3
Rotor core volume
272
302 (increase by 11%)
cm^3
Conductor volume
53
30 (decrease by 43%)
cm^3
PM volume
125
74 (decrease by 41%)
cm^3
From the comparison results, machine design with reduction in effective air gap has
the same air gap, but effective air gap is decreased by 38% because of the smaller
conductor and thinner insulation.
The smaller conductor will cause an increase in
conductor current density and the thinner insulation will require a low manufacture
tolerance. As a result, the 65% increase in conductor current density will cause efficiency
drop and bring heat dissipation problems.
In addition, machine design with reduction in effective air gap has the same outside
47
dimensions, with a smaller stator core inner diameter and a larger rotor core outer
diameter. These two changes allow allocating more inductors and generating more torque.
The cost of machine design with reduction in effective air gap will be reduced
because that the PM volume can be decreased by 41% while maintaining the same torque
capability, though stator core volume and rotor core are increased by 3% and 11%
respectively.
In summary, the original design is optimized to achieve a higher efficiency while
machine design with reduction in effective air gap is optimized to use less PM material.
The original design is selected for prototype production because of the high
efficiency and relative ease to manufacture. The machine design with reduction in
effective air gap has advantages in cost and weight and will be manufactured in the next
generation.
2.6
Inductance Calculation and Measurement
From the comparison results above, the air gap flux density of the original design is
slightly higher, but the machine design with reduction in effective air gap has a much
larger back EMF. The root cause is the inductance. In this section, the inductance of sixphase BLDC machine will be studied by different calculation methods and then
inductance will be measured based on FEA simulations.
In electrical machine design, when it refers to inductance calculation, flux linkage is
always required. Therefore, at the beginning, the flux linkage definition will be
introduced as,
𝜓 = 𝐿𝑖
48
(2.10)
where 𝐿 is inductance, 𝑖 is current going through the inductor. Based on Faraday’s law,
𝑣=
𝜕𝜓
(2.11)
𝜕𝑡
flux linkage can also be expressed as the time integration of voltage, then combine the
two equations above,
𝜕𝑖
𝜕𝐿
𝑣 = 𝐿 𝜕𝑡 + 𝑖 𝜕𝑡
(2.12)
the first part in equation 2.12 is overwhelming because the rate of change of inductance
with respect to time is much slower than that of the current. Assuming 𝐿 is constant,
then
𝜕𝑖
𝑣 = 𝐿 𝜕𝑡
(2.13)
thus, inductance can be calculated by the terminal voltage and current.
There is another way to define flux linkage, which is
𝜓 = 𝑁𝜙
(2.14)
where 𝑁 is number of turns, 𝜙 is flux, substitute equation 2.14 into 2.10,
𝐿=
𝑁𝜙
𝑖
(2.15)
the flux can be written as
𝜙 = 𝐹𝑃
(2.16)
where 𝐹 is MMF and 𝑃 is permeance, then inductance can be expressed as
𝐿 = 𝑁2𝑃
(2.17)
From equation 2.17, inductance is proportional to square of number of turns. Hence,
the inductance will be increased significantly by adding number of turns. For example,
the original design has 8 turns while machine design with reduction in effective air has 12
turns. The turns ratio is 2 to 3 and the inductance ratio will be 4 to 9 if permeance is not
49
affected. Theoretically, the back EMF ratio will be 2 to 3 if air gap flux density of both
cases are the same. However, form FEA simulation results, figures 2.16 and 2.28 show
that the back EMF ratio is 2 to 3.2, of which the differences are caused by air gap flux
density. As a result, in order to achieve the same torque capability, 37.5% current can be
reduced for machine design with reduction in effective air.
From equation 2.17, inductance is not only affected by turns ratio but also by
permeance. Magnetic permeability is used to measure the ability of a martial to support
the formation of a magnetic field within itself. Magnetic permeability is defined as,
𝐵
𝜇=𝐻
(2.14)
where 𝐵 is magnetic flux density and 𝐻 is magnetic field, also referred to as magnetic
field strength. For example, stator core and rotor core are soft magnetic material, of
which the magnetic permeability can be calculated based on Figure 2.33.
Figure 2.33. Flux Density vs Magnetic Field of Soft Magnetic Material
50
Magnetic permeability of permanent magnet can be calculated based on Figure 2.34.
Figure 2.34. Flux Density vs Magnetic Field of Permanent Magnet Material
The relative permeability of air and copper is one. Since the spoke type rotor has
salience, the inductance will change periodically according to the position. The
inductance of the original design is shown as Figure 2.35.
51
Figure 2.35. Phase Inductance vs Electrical Angle of Original Design
The inductance of machine design with reduction in effective air gap is shown as Figure
2.36.
52
Figure 2.36. Phase Inductance vs Electrical Angle of Machine Design with Reduction in
Effective Air Gap
Form FEA simulation results Figure 2.35 and 2.36 show that the phase inductance
ratio is 1 to 3.7 because of the turns ratio and permeance. The permeance of original
design is lower than that of machine design with reduction in effective air gap due to the
less effective air gap and thinner permanent magnets.
From Figure 2.35, the phase inductance changes periodically as rotor moves. The
maximum phase A inductance is around 0.197 mH, where rotor position is shown as
Figure 2.37, and minimum phase A inductance is 0.125 mH, where rotor position is
shown as Figure 2.38.
53
Figure 2.37. Rotor Position with Maximum Phase A Inductance
54
Figure 2.38. Rotor Position with Minimum Phase A Inductance
55
In Figure 2.37, most of the flux line does not cross the permanent magnets, resulting
in a high permeance for phase A. On the contrary, in Figure 2.38, most of the flux line
crosses the permanent magnets, resulting in a low permeance.
In original design, mutual inductance between phase A and other phases are shown as
Figure 2.39.
Figure 2.39. Mutual Inductance between Phase A and Other Phases
From Figure 2.39, mutual inductance AB, AD, AE and AF are negative signs because of
the opposite coil direction. Mutual inductance AF is close to zero due to its unique
position, where the number of clockwise flux lines is very close to that of anti-clockwise
56
flux lines.
In this section, the calculation method of inductance has been derived. The influence
of turns number and permeance has been analyzed. Furthermore, phase inductance and
mutual inductance have been measured through the FEA simulations method.
2.7
Winding Resistance Calculation
As the main reason of copper losses, stator winding resistance needs to be designed
appropriately. The resistance calculation of round wire is given as,
𝑅=
4𝜌𝜚𝑛𝑠 𝑙ℎ
(2.15)
𝜋𝑛𝑝 𝑑2
where 𝜌 is resistivity, 𝜚 is number of slots per phase, 𝑛𝑠 is number of wires per slot, 𝑙ℎ is
half length of one single coil, 𝑛𝑝 is number of parallel wires per strand, 𝑑 is diameter of
wire. In slotless six-phase BLDC machine design, rectangular wire is adopted. Thus, the
resistance calculation can be rewritten as,
𝜌𝜚𝑛𝑠 𝑙ℎ
(2.16)
𝑅=𝑛
𝑝 𝑙𝑤 𝑤𝑤
where 𝑙𝑤 is wire length and 𝑤𝑤 is wire width. Particular to this design, 𝜚 is 64 while 𝑛𝑠
and 𝑛𝑝 are both one. The resistance of one phase winding can be calculated as
𝑅=
(1.67×10−8 )×64×1×(162×10−3 )
1×(0.8×10−3 )×(1.45×10−3 )
= 0.15 𝛺
(2.17)
Usually, there is some error between real winding resistance and calculated due to endwinding connections. Winding resistance can be reduced by several methods, such as
parallel wires under different poles, or simply increase the wire cross section. However,
these methods will reduce winding inductance. Therefore, winding resistance cannot be
designed independently; inductance and back EMF should also be considered.
57
2.8
Winding Assembling
The slotless six-phase BLDC machine has two layers of windings and each layer has
192 conductors. Conventional fixture and tooling are no longer suitable for this type of
machine. Therefore, an innovative assembling process is proposed. The fixture and
tooling include six types of parts as shown in Figure 2.40.
A4: OD 98.4 mm
B
A3: OD 100.6 mm
C
A2: OD 102.8 mm
A1: OD 105.0 mm
same as stator ID
Stator Core
1/8 machine model
Figure 2.40. Fixture and Tooling Overview
In Figure 2.40, part A1, A2, A3 and A4 are slots with different outer diameters. Part
B is key and part C is hollow cylinder with multiple slots. Note that outer diameter of
58
part A1 is the same as stator inner diameter. There are eleven steps in the assembling
process.
Step 1: As shown in Figure 2.41, in order to make stator and part C concentric, part
A1s are used to fill the space between stator and part C.
A1: OD 105.0 mm
same as stator ID
C
1/8 machine model
Figure 2.41. Winding Assembling Step 1
Step 2: As shown in Figure 2.42, one of part A1 has been removed, still stator and
part C are concentric.
59
A1: OD 105.0 mm
same as stator ID
C
1/8 machine model
Figure 2.42. Winding Assembling Step 2
Step 3: As shown in Figure 2.43, put one part A3 in the empty place and use part B to
fix A3.
60
Figure 2.43. Winding Assembling Step 3
Step 4: As shown in Figure 2.44, place the first layer winding, including four
conductors, in the space between part A3 and stator. Note that the conductors are
downward. Then potting material is injected into the gaps between the conductors.
61
Figure 2.44. Winding Assembling Step 4
Step 5: As shown in Figure 2.45, replace part A3 with part A2. Part A2 will extrude
conductors and potting material, removing excess potting material.
62
Figure 2.45. Winding Assembling Step 5
Step 6: As shown in Figure 2.46, repeat steps 2, 3, 4 and 5 to install first layer
winding.
63
Figure 2.46. Winding Assembling Step 6
Step 7: As shown in Figure 2.47, replace one part A2 with part A4 and use part B to
fix part A4
64
Figure 2.47. Winding Assembling Step 7
Step 8: As shown in Figure 2.48, place the second layer winding including four
conductors in the space between part A4 and first layer winding.
Note that the
conductors are downward. Then potting material is injected into the gaps between the
conductors.
65
Figure 2.48. Winding Assembling Step 8
Step 9: As shown in Figure 2.49, replace part A4 with part A3. Part A3 will extrude
conductors and potting material, removing excess potting material.
66
Figure 2.49. Winding Assembling Step 9
Step 10: As shown in Figure 2.50, repeat steps 7, 8 and 9 to install second layer
winding.
67
Figure 2.50. Winding Assembling Step 10
Step 11: As shown in Figure 2.51, remove part C and parts A2. Then, a uniform air
gap is obtained. At the meantime, both first layer and second layer windings are
concentric.
68
Figure 2.51. Winding Assembling Step 11
2.9
Prototype
In the previous sections, stator core, stator winding, rotor core and permanent
magnets have been designed and verified by FEA simulations, also the manufacture
fixture and tooling were proposed. The first generation prototype of slotless six-phase
BLDC machine is shown in Figure 2.52.
69
Stator Core
Nonmagnetic Materials
Permanent Magnet (not installed)
Rotor Core
Figure 2.52. First Generation Prototype of Slotless Six-Phase BLDC Machine
From Figure 2.52, the rotor core is different from the original design because of the
mechanical concern. Note that the permanent magnets have not been installed on the
rotor. Both stator core and rotor core are made with lamination stacks. In the center of
rotor core, there is a rotor shaft as shown in Figure 2.53.
70
Figure 2.53. Rotor Shaft of Prototype Machine
From Figure 2.53, rotor shaft is designed to support rating torque. In addition, a
resolver will be mounted on the rotor shaft for rotor position measurement. Stator
windings are made with 384 conductors, single conductor is shown as Figure 2.54.
71
Conductors (total 384)
Figure 2.54. Single Conductor of Prototype Machine
Two conductors are soldered together to form a coil; the conductor connections are
shown as Figure 2.55.
72
Figure 2.55. Conductor Connections of Prototype Machine
73
One phase winding has 32 coils in a series connection. The whole stator windings are
shown in Figure 2.56.
Figure 2.56. Stator Windings of Prototype Machine
74
At last, fixture and tooling for manufacture are shown as Figure 2.57.
Figure 2.57. Fixture and Tooling of Prototype Machine
75
2.10
Configuration
The slotless six-phase BLDC machine can be called a multiphase machine, because
the number of phases is twice that of a three-phase machine. The advantage of this
multiphase machine is that a single inverter can split into smaller inverters. On the other
hand, the slotless six-phase BLDC machine can be configured as a three-phase BLDC
machine as shown in Figure 2.58.
Figure 2.58. Three-Phase Configuration of Slotless Six-Phase BLDC Machine
76
Based on FEA results, the back EMF in three-phase configuration at 4000 RPM is shown
as Figure 2.59.
Figure 2.59. Back EMF in Three-Phase Configuration
The shape of back EMF is not quite trapezoidal. Compare Figure 2.59 with 2.16, the
magnitude of back EMF doubled, but the flat region decreased, making an obvious gap
between two flat back EMF regions.
2.11
Summary
In this chapter, a 3kW slotless six-phase BLDC machine has been designed. The
77
stator core, stator winding connection, rotor core and air gap are optimized by three
principles. The first principle is performance, referring to high torque density. The
second one is trapezoidal back EMF. The third one is to reduce cost by reducing the
usage of permanent magnets. After geometry design and FEA validation, the inductance
and resistance of stator winding is calculated. In the meantime, a winding assembling
method is proposed and a prototype machine has been built. At last, the advantage of sixphase BLDC machine is that a single inverter can split into two smaller power rating
inverters.
78
CHAPTER 3: STEPPING VECTOR CONTROL
In this chapter, a novel control algorithm for slotless six-phase BLDC machine is
proposed. The proposed control algorithm combines the merits of sinusoidal current
control and trapezoidal current control to improve slotless six-phase BLDC machine
performance. The proposed control algorithm is called SVC because the vector angle
changes step by step. With the proposed algorithm, commutation torque ripple will be
minimized by matched incoming and outgoing currents. Furthermore, a torque-enhanced
method based on SVC is proposed.
Essentially, slotless six-phase BLDC machine will be controlled as two slotless threephase BLDC machines. Phases A, C and E are grouped as one slotless three-phase
BLDC machine and phase B, D and F are grouped as another one. The control algorithm
in these machines is identical, the only difference is phase delay. Therefore, SVC is
analyzed and derived based on three-phase BLDC machine at first.
After that, a
commutation torque ripple minimization method based on SVC is proposed and verified.
Finally, an optimized SVC is proposed to increase torque output capability.
3.1
Stepping Vector Control of BLDC Machine
BLDC and brushless AC (BLAC) machines are widely used in electric vehicle (EV)
and hybrid electric vehicle (HEV) applications due to their high power density, high
79
torque density and high efficiency. Different from a BLAC machine with a sinusoidal
back EMF, the BLDC machine is provided with a trapezoidal back EMF. Compared to a
BLAC machine, a BLDC machine can achieve a higher torque density and a higher
power density for a given size [36]. However, a BLDC machine has a significant
drawback, which is commutation torque ripple. Commutation torque ripple will cause
oscillation and resonance in mechanical components, bringing observable vibration and
acoustic noise to drive systems. The ripple is caused by the currents going through the
freewheeling diodes during commutation intervals, and many studies have been
conducted to minimize this torque ripple. In [37], a DC bus voltage control method is
proposed, but an additional DC bus voltage controller is required in the method,
increasing overall system cost. In [38] an algorithm based on current slopes control is
proposed, in which the current slopes of the incoming and outgoing phase currents can be
controlled in the same rate of change by adjusting PWM duty ratio. By delaying the turnoff timing instant of the outgoing switch, an overlap switching algorithm is proposed in
[39].
However, these conventional methods show limited effectiveness in practical
applications due to machine parameter sensitivity and unsatisfactory performance over an
entire speed range. An algorithm based on SVC, which combines the merits of sinusoidal
current control and trapezoidal current control, is proposed to minimize commutation
torque ripple in this chapter.
Sinusoidal current control can be applied to BLDC machine drive but the
performance will be degraded because of the large torque ripple. The torque ripple is
caused by non sinusoidal back EMF.
The sinusoidal current control is usually
implemented by space vector control. The current, back EMF and torque waveforms are
80
shown in Figure 3.1.
I_A
I_B
I_C
BackEMF_A
6
4
2
0
-2
-4
-6
Torque
1.5
1.45
1.4
1.35
1.3
1.25
0.05
0.1
0.15
Time (s)
0.2
0.25
Figure 3.1. Current Back EMF and Torque in Sinusoidal Current Control
The trapezoidal current control is a perfect fit for BLDC machine drive because both
high torque production and high efficiency [40, 41] can be achieved. The trapezoidal
current control is usually implemented by hysteresis control, PI control, fuzzy logic
control or feed forward control [42-45]. However, in most of the control algorithms
81
outgoing phase current is without control and its decay rate is only determined by DC bus
voltage and back EMF. The varying decay rate may cause a mismatch between outgoing
current and incoming current, resulting in a commutation torque ripple. The current,
back EMF and torque waveforms are shown in Figure 3.2.
I_A
I_B
I_C
BackEMF_A
6
4
2
0
-2
-4
-6
Torque
1.3
1.2
1.1
1
0.9
0.1
0.15
0.2
Time (s)
0.25
Figure 3.2. Current, Back EMF and Torque in Trapezoidal Current Control
In order to achieve a trapezoidal current control with commutation torque ripple
82
minimization, a novel vector control algorithm, the SVC, is proposed for BLDC machine
drive. Similar to conventional vector control, vector angle and vector amplitude are the
two control variables in SVC. The main difference lies in the vector angle’s moving
pattern.
As the BLDC machine rotates, the vector angle moves continuously in
conventional vector control, while it moves step by step in SVC. Both moving patterns
are shown in Figure 3.3.
Conventional Vector Control
Ia
Ib
Ic
Stepping Vector Control
(A)
5
0
-5
vector_angle
(degree)
400
300
200
100
0
0.1
0.2
0.3
0.4
Time (s)
Figure 3.3. Current and Vector Angle Moving Pattern in Conventional Vector Control
(left) and SVC (right)
The vector angle move pattern has a direct effect on current shape. In Figure 3.3, the
continuous vector angle leads to a sinusoidal current and the stepping vector angle results
83
in a trapezoidal current with spikes.
Note that in both cases, vector amplitude is kept
constant, when BLDC machine rotates.
In trapezoidal current control, 360 electric degrees are divided into six regions. Only
two phases are conducting (active) in each region, with the other being non-conducting
(inactive). The active phases and inactive phases for each region are listed in Table 3.1.
Table 3.1. Active Phase and Inactive Phase in Six Regions
Electrical Angle Region Active phase Inactive phase Vector Angle
0-60
1
A, C
B
30
60-120
2
B, C
A
90
120-180
3
B, A
C
150
180-240
4
C, A
B
210
240-300
5
C, B
A
270
300-360
6
A, B
C
330
Each of the regions can be represented as one corresponding vector angle. Therefore,
in SVC algorithm, the vector angle is maintained at 30 electric degrees when the rotor
moves in region 1, the resulting phase A current equals minus phase C current, the phase
B current is zero. When the rotor enters region 2, the vector angle will jump to 90
electric degrees in a given commutation interval and keep at 90 electric degrees for the
whole region 2, the resulting phase B current equals minus phase C current, the phase A
current is zero. The same procedure is used for other regions. In this way, the current is
controlled in a trapezoidal shape as expected. The implementation of the proposed SVC
algorithm is shown in the block diagram in Figure 3.4.
84
Figure 3.4. Block Diagram of SVC for BLDC Machine Drive System
In the controller block diagram, vector amplitude is decoupled into magnetizing and
torque components. By default, magnetizing current Id is set to zero in BLDC machine
drive. Then vector amplitude only depends on torque current Iq. Vector angle generation
is the core of SVC.
The position feedback device Hall sensor can provide six
commutation signals to vector angle generation. The details of vector angle generation
will be discussed in the next section.
3.2
Commutation Torque Ripple Minimization of BLDC Machine
In this section, an original idea of SVC algorithm will be proposed for the BLDC
machine drive system, the commutation torque ripple is minimized in this algorithm by
matching the slopes of incoming and outgoing phase currents. After theoretical analysis
and calculation, computer simulations and experimental results will be provided to verify
the proposed SVC algorithm. At last, the length of the ramping region in SVC will be
discussed.
85
3.2.1
BLDC Commutation Torque Ripple Analysis
The commutation torque ripple is caused by the currents going through the
freewheeling diodes during commutation interval. For example, when the machine
commutates from region 1 to region 2, the conducting status of three-phase is shown in
Figure 3.5.
Incoming Current
A
B
C
Equivalent Circuit of
Three Phase BLDC Machine
VA
VDC
VB
VC
R
L
EA
R
L
EB
R
L
EC
VN
Outgoing Current
Figure 3.5. Equivalent Circuit of BLDC in Commutation Interval
The incoming current flows through the upper leg switch of phase B and the outgoing
current flows through the lower leg diode of phase A. Based on the conductions of
switches and diodes, phase voltage equations during commutation intervals can be
expressed as the following,
86
𝑉𝐴 = 0 = 𝑅𝑖𝐴 + 𝐿
𝑑𝑖𝐴
𝑑𝑡
𝑉𝐵 = 𝑉𝐷𝐶 = 𝑅𝑖𝐵 + 𝐿
𝑉𝐶 = 0 = 𝑅𝑖𝐶 + 𝐿
+ 𝐸𝐴 + 𝑉𝑁
𝑑𝑖𝐵
𝑑𝑡
𝑑𝑖𝐶
𝑑𝑡
+ 𝐸𝐵 + 𝑉𝑁
+ 𝐸𝐶 + 𝑉𝑁
(3.1)
(3.2)
(3.3)
the summation of all the currents is given by
𝑖𝐴 + 𝑖𝐵 + 𝑖𝐶 = 0
(3.4)
Then the neutral point voltage can be calculated as
1
𝑉𝑛 = 3 (𝑉𝐷𝐶 − (𝐸𝐴 + 𝐸𝐵 + 𝐸𝐶 ))
(3.5)
Assuming the resistance is very small that can be neglected, the slope of incoming phase
B current can be calculated as
𝑑𝑖𝐵
{𝑑𝑖𝑑𝑡𝐵
𝑑𝑡
=
=
𝑉𝐷𝐶 −𝐸𝐵 −𝑉𝑁
when switch is on
𝐿
−𝐸𝐵 −𝑉𝑁
when switch is off
𝐿
(3.6)
The slope of outgoing phase C current can be calculated as
𝑑𝑖𝐶
𝑑𝑡
=
−𝐸𝐶 −𝑉𝑁
𝐿
(3.7)
When the slopes of incoming current and outgoing current do not match, it will produce a
commutation torque ripple. The simulation waveforms of the incoming current, outgoing
current and commutation torque ripple are shown in Figure 3.6.
87
Ia
Ib
Ic
(A)
20
10
Outgoing Current
Incoming Current
0
-10
-20
toque
(Nm)
Commutation Torque Ripple
35
30
25
20
15
0.204
0.208
Time (s)
0.212
Figure 3.6. Simulation Results of Commutation Torque Ripple
3.2.2
Commutation Torque Ripple Minimization Based on SVC
In the conventional methods of commutation torque ripple reduction, duty ratio has
been controlled to equalize the two mismatched commutation time intervals.
The
limitation of these methods is that only the incoming current is controllable, while the
outgoing current is not because it goes through a freewheeling diode.
In SVC, all three-phase currents are under the control of switching devices. The
incoming and outgoing currents can be manipulated to have matched slopes during the
88
commutation interval. The implementation is based on vector angle control and vector
angle is kept as 30 electric degrees when rotor is rotating in region 1 until Hall sensor
sends a commutation signal. The vector angle will change rapidly from 30 to 90 electric
degrees in a given commutation time and then maintain at 90 when rotor is at region 2.
During commutation interval, three-phase currents are all conducting. The outgoing
current is decreasing to zero while incoming current is increasing from zero, both of them
are with the same rate of change. Though the slopes are matched, spikes still existed in
the commutation interval as in Figure 3.3. In addition, the vector amplitude can be
adjusted during the commutation interval. In order to minimize commutation torque
ripple, vector amplitude will be compensated as a function of vector angle, which can be
written as
𝐴𝑣𝑒𝑐𝑡𝑜𝑟 = sin(60+(𝜃
1
𝑣𝑒𝑐𝑡𝑜𝑟 %60))
(3.8)
where 𝐴𝑣𝑒𝑐𝑡𝑜𝑟 and 𝜃𝑣𝑒𝑐𝑡𝑜𝑟 are vector amplitude and vector angle, respectively.
Ideal trapezoidal current waveforms during commutation interval are shown as Figure
3.7.
Figure 3.7. Ideal Current for Commutation Torque Ripple Minimization
89
Torque equation of BLDC machine is given by,
1
𝑇𝑒 = 𝜔 (𝐸𝐴 𝑖𝐴 + 𝐸𝐵 𝑖𝐵 + 𝐸𝐶 𝑖𝐶 )
𝑚
(3.9)
In region 1, for example, only phase A and phase C are conducting. The currents and
back EMFs of these two phases satisfy
𝑖𝐴 = −𝑖𝐶
(3.10)
𝐸𝐴 = −𝐸𝐶
(3.11)
Torque equation can be simplified as
1
𝑇𝑒 = 𝜔 (𝐸𝐶 𝑖𝐶 + 𝐸𝐶 𝑖𝐶 )
𝑚
(3.12)
During the commutation interval, all three phases are conducting. The currents and back
EMFs of these three phases satisfy
𝑖𝐴 + 𝑖𝐵 = −𝑖𝐶
(3.13)
𝐸𝐴 = 𝐸𝐵 = −𝐸𝐶
(3.14)
Torque equation can be simplified as
1
𝑇𝑒 = 𝜔 (𝐸𝐶 𝑖𝐶 + 𝐸𝐶 𝑖𝐶 )
𝑚
(3.15)
Based equations 3.12 and 3.15, the torque will not change during commutation interval in
the proposed SVC algorithm.
3.2.3
Simulation Verification
A computer model of the BLDC system with proposed SVC algorithm, as shown in
Figure 3.4, has been developed in PSIM simulator. The simulation results are shown in
Figure 3.8.
90
Only with Vector Angle Control
Ia
Ib
Ic
Vector Angle Control with Vector Amplitude Compensation
(A)
20
0
-20
vector_angle (degree)
400
200
0
vector_amplitude (per-unit value)
1.16
1.12
1.08
1.04
1
Id_command
Id_feedback
Iq_command
Iq_feedback
(per-unit value)
0.4
0.2
0
Torque
(Nm)
24
22
20
18
16
0.2
0.22
0.24
0.26
0.28
0.3
Time (s)
Figure 3.8. Simulation Results of SVC
In SVC, with the control of vector angle and vector amplitude, the currents work in a
trapezoidal shape and the slopes of incoming and outgoing phase currents are matched.
As a result, the commutation torque ripple is minimized.
3.2.4
Experimental Verification
To further verify the effectiveness of the proposed SVC algorithm, experimental
91
testing is conducted on an actual BLDC machine system. The parameters of the tested
BLDC machine are given in Table 3.2.
Table 3.2. Rating and Parameters of BLDC Machine
Nominal power
1 hp
Nominal voltage
230 V
Nominal current
2.4 A
Number of pole pairs
2
Base speed
1800 rpm
Stator Resistance
2.9 Ω
Mutual inductance
64 mH
Figure 3.9 shows the current waveform only with vector angle control, thus the
trapezoidal current can be found with spikes during commutation interval.
Figure 3.9. Experimental Results of Current with Vector Angle Control in SVC
92
Figure 3.10 shows the current waveform with both vector angle and vector amplitude
control. Due to vector amplitude compensation, the current spikes are eliminated and the
commutation torque ripple is minimized. The commutation torque ripple is reduced to
less than 20%, which can also be found in Figure 3.8.
Figure 3.10. Experimental Results of Current with both Vector Angle and Vector
Amplitude Control in SVC
3.2.5
Ramping Region of SVC
As shown in Figure 3.11, vector angle includes two types of regions: the flat region
and the ramping region. Most of the time, vector angle stays at the flat region. The flat
region ends when a commutation signal is triggered by the Hall position sensor.
93
Meanwhile vector angle will enter the ramping region, which corresponds to the
commutation interval.
250
vector_angle (degree)
Ramping Region
200
Flat Region
150
Triggered by Controller
100
Triggered by Hall sensor
50
real_rotor_angle (degree)
250
200
150
100
50
0.132
0.136
Time (s)
0.14
Figure 3.11. Vector Angle and Real Rotor Angle in SVC
The ramping region is not terminated by the Hall position sensor, but by a controller.
As a result, the vector angle in the ramping region is an artificial angle, which is
unrelated to the real rotor angle. Therefore, the length of ramping region is controllable.
Usually vector angle is requested to change quickly to achieve a short commutation
94
interval because of the limited overlap between two adjacent flat regions. However, the
current through an inductor cannot change instantaneously. If the commutation interval
is too short, the current cannot follow the vector angle, and vector amplitude commands,
though, that the PI controller is well tuned. Hence, it is easier to implement the optimal
commutation interval at low speeds than at high speeds because real angle moves faster.
The length of ramping region should be chosen as a tradeoff between speed and current
amplitude.
3.3
Enhanced Torque Control of BLDC Machine
In this section, an original idea of enhanced torque control will be proposed for the
BLDC machine drive system, the torque output is enhanced by matching back EMFs and
phase currents. After theoretical analysis and calculation, simulations will be provided to
verify the proposed control algorithm.
3.3.1 Optimal Current in Enhanced Torque Control
In interior permanent magnet machine control, usually maximum torque per ampere
(MTPA) control is adopted to increase torque output. In order to take advantage of
reluctance torque, the MTPA angle varies as current amplitude changes. When current
amplitude stays the same, the MTPA angle will not change.
Different from the concept of MTPA control, optimal current angle in enhanced
torque control is referred to the stator current angle that generate maximum torque when
amplitude of stator current vector does not change.
95
The optimal current angle is
calculated based on back EMFs. For ideal sinusoidal back EMFs, the optimal current
angle is the same as the position angle, which will be verified later in this section. In
practice, back EMFs are non-ideal sinusoidal, therefore, the optimal current angle will
not exactly align with the position angle.
In general, the MTPA angle can be considered as a way to achieve enhanced torque
macroscopically, while the optimal current angle is used to obtain enhanced torque
microscopically.
The reluctance torque is not considered in the following analysis of optimal current
angle in enhanced torque control. In a Y connection type BLDC machine, the threephase currents will satisfy the following equation,
(3.16)
𝑖𝐴 + 𝑖𝐴 + 𝑖𝐶 = 0
either conventional vector control or SVC is applied, the phase angle difference is 120
degrees and phase A current is defined as
(3.17)
𝑖𝐴 = 𝐼 sin(𝜃)
where 𝐼 is current amplitude and 𝜃 is current angle. As a result, phase B and phase C
currents can be expressed as
𝑖𝐵 = 𝐼 𝑠𝑖𝑛(𝜃 − 120°)
(3.18)
𝑖𝐶 = 𝐼 𝑠𝑖𝑛(𝜃 + 120°)
(3.19)
Then, equation 3.9 can be rewritten as
1
𝑇𝑒 = 𝜔 (𝐸𝐴 × 𝐼 sin(𝜃) + 𝐸𝐵 × 𝐼 𝑠𝑖𝑛(𝜃 − 120°) + 𝐸𝐶 × 𝑠𝑖𝑛(𝜃 + 120°))
𝑚
(3.20)
Equation 3.20 can be simplified as
1
1
1
𝑇𝑒 = 𝜔 (𝐼 sin(𝜃) × (𝐸𝐴 − 2 𝐸𝐵 − 2 𝐸𝐶 ) + 𝐼 cos(𝜃) × (−
𝑚
The derivative of equation 3.21 is
96
√3
𝐸
2 𝐵
+
√3
𝐸 ))
2 𝐶
(3.21)
𝑑(𝑇𝑒 )
𝑑(𝜃)
1
1
1
= 𝜔 (𝐼 cos(𝜃) × (𝐸𝐴 − 2 𝐸𝐵 − 2 𝐸𝐶 ) − 𝐼 sin(𝜃) × (−
𝑚
√3
𝐸
2 𝐵
+
√3
𝐸 ))
2 𝐶
(3.22)
The extreme value of torque can be obtained, when 𝜃 satisfies
1
1
0 = cos(𝜃) × (𝐸𝐴 − 2 𝐸𝐵 − 2 𝐸𝐶 ) − sin(𝜃) × (−
√3
𝐸
2 𝐵
+
√3
𝐸 )
2 𝐶
(3.23)
which can also be expressed as
𝜃 = tan−1 (
1
2
1
2
√3
√3
− 𝐸𝐵 + 𝐸𝐶
2
2
𝐸𝐴 − 𝐸𝐵 − 𝐸𝐶
)
(3.24)
From equation 3.24, optimal current angle 𝜃 is calculated based on three-phase back
EMFs. Trapezoidal back EMFs and optimal current angle 𝜃 are shown as Figure 3.12.
Figure 3.12. Optimal Current Angle Control
In figure 3.12, back EFMs are trapezoidal. The optimal current angle 𝜃 is shown
with rotor position angle. The angle difference between optimal current angle and rotor
position angle is less than one degree. The average torque increases by 5.4% from 1.30
Nm in SVC to 1.37 Nm in optimal current angle control. However, there are torque
97
ripples in optimal current angle control.
In order to reduce the torque, vector amplitude will be compensated as a function of
back EMFs, which can be written as
𝐴𝑣𝑒𝑐𝑡𝑜𝑟 =
𝑇𝑟𝑒𝑞𝑢𝑒𝑠𝑡
1
1
1
√3
√3
(𝐼 sin(𝜃)×(𝐸𝐴 − 𝐸𝐵 − 𝐸𝐶 )+𝐼 cos(𝜃)×(− 𝐸𝐵 + 𝐸𝐶 ))
𝜔𝑚
2
2
2
2
(3.25)
where 𝐴𝑣𝑒𝑐𝑡𝑜𝑟 is vector amplitude, 𝑇𝑟𝑒𝑞𝑢𝑒𝑠𝑡 is request torque and 𝜃 is obtained through
equation 3.24. Optimal current angle with vector amplitude compensation is shown as
Figure 3.13.
Figure 3.13. Optimal Current Angle Control with Vector Amplitude Compensation
3.3.2 Simulation Verification
A computer model of the BLDC system with proposed optimal current angle control
algorithm has been developed in PSIM simulator. The simulation results are shown in
Figure 3.14.
In optimal current angle control, with the control of vector angle and vector
98
amplitude, the currents work in a quasi-sinusoid shape and the phase currents and back
EMFs are matched. As a result, the torque output is enhanced and torque ripple is
minimized.
BackEMF_A
BackEMF_B
BackEMF_C (V)
10
0
-10
optimal_current_angle (degree)
400
300
200
100
0
Ia
Ib
Ic (A)
40
20
0
-20
-40
0.4
0.3
0.2
0.1
0
-0.1
25
Id_command
Id_feedback
Iq_command
Iq_feedback (per-unit value)
Torque (Nm)
20
15
10
0.02
0.04
0.06
0.08
Time (s)
0.1
0.12
0.14
Figure 3.14. Simulation Results of Optimal Current Angle Control
3.4
Summary
In this chapter, an original SVC algorithm has been proposed for BLDC machine
drive system; the commutation torque ripple is minimized in this algorithm by matching
99
the slopes of incoming and outgoing phase currents.
Computer simulations and
experimental results are provided to verify the proposed SVC algorithm. Furthermore, an
enhanced torque control of the BLDC machine has been proposed. Based on three-phase
back EMFs, an optimal current angle can be calculated. The optimal current angle
control can provide 5.4% more torque than conventional control, but with a drawback of
torque ripple. At last, the torque ripple in optimal current angle control is minimized by
vector amplitude compensation.
100
CHAPTER 4: SENSORLESS CONTROL OF BLDC MACHINE
In this chapter, a sensorless BLDC control algorithm based on rotor saliency is
proposed. A voltage pulse injection method is used for inductance measurement and the
peak inductance current is measured through the salient phase to increase accuracy. Zero
speed and arbitrary low speed sensorless operations can be achieved with the proposed
algorithm. Finite element analysis method (FEM) simulations and experimental results
are provided to verify the proposed control algorithm.
This chapter is organized as follows: the rotor saliency characteristics are discussed at
the beginning. Then, the principles of the algorithm for the BLDC zero speed starting
and low speed operation are described. Later on, FEM simulations and experimental
testing are conducted and results are presented to verify the effectiveness of the proposed
sensorless control algorithm. A summary is presented as the last section.
4.1
Rotor Saliency Characteristics
BLDC machines have been widely used in electric vehicles, servo systems and
appliances due to their high efficiency and high torque density. In high performance
applications, the BLDC machine is driven by an inverter and it requires rotor position
information for current commutations. Usually a group of Hall position sensors provides
commutation signals. In order to reduce cost and enhance mechanical robustness, a
101
variety of sensorless control algorithms have been studied [53-57]. In three-phase BLDC
machine control algorithms, usually two of the three phases are conducting sequentially
and the other non-conducting phase is called silent phase.
In order to obtain
commutation timings, the back EMF method detects the back EMF zero crossing of the
silent phase and triggers the commutations every 60 degrees [53], while [54] integration
the back EMF of the silent phase compared with a threshold value. It should be pointed
out that these above mentioned methods, as well as other flux linkage based ones [55, 56]
and freewheeling diode conduction methods [57], fail to achieve commutation at zero or
low speed because of the undetectable back EMFs.
To overcome the mentioned
drawbacks, a sensorless method based on speed-independent function is proposed in [58],
which can estimate commutation instants from near zero (2% of the rated speed) to high
speed.
However, this method is only applicable to the surface-mounted permanent
magnet BLDC machines.
A BLDC machine sensorless control algorithm based on
inductance variation is proposed in [59]. In this algorithm, a pulse train, including long
and short pulses, is injected into the conducting phases. The long pulses are used for
torque production and the short ones are for inductance measurement. However, a time
interval insertion between the long and the short pulses is required to ensure
measurement accuracy. During the time interval a negative torque is generated, leading
to a degraded torque performance. Other sensorless algorithms for a permanent magnet
synchronous machine, including magnetic pole identifications, high frequency injection
and sliding-mode control, have been investigated in [60-64]. However, these methods
based on space vector control are preferred by sinusoidal current drive rather than
trapezoidal current BLDC drive.
102
The proposed sensorless control algorithm for BLDC machines is based on rotor
saliency. A voltage pulse injection method is used for inductance measurement and the
peak inductance current is measured to improve rotor detection accuracy. For the speed
ranging from zero to an arbitrarily low speed, sensorless operations of the BLDC can be
achieved with the proposed algorithm.
The saliency characteristics are studied through a typical BLDC model using the
finite element analysis method (FEM) as shown in Figure 4.1.
Stator Core
Winding
Permanent Magnet
Rotor Core
Figure 4.1. Typical BLDC Machine FEM Model (1/4)
By the FEM simulation results, the variation of phase inductance and line inductance
are functions of the BLDC rotor position as presented in figures 4.2 and 4.3, respectively.
For convenience of investigation, one electrical cycle is divided into six regions by
commutation points and each region covers 60 electrical degrees.
103
Region 0
0.16
Region 1 Region 2
Region 3 Region 4
Region 5
0.158
0.156
L(mH)
0.154
A
0.152
B
C
0.15
0.148
0.146
0
30
60
90 120 150 180 210 240 270 300 330 360
Rotor Position (electric degree)
Figure 4.2. Phase Inductance Variation
0.318
Region 0 Region 1
Region 2
Region 3 Region 4
Region 5
0.316
0.314
L(mH)
0.312
AB
0.31
BC
CA
0.308
0.306
0.304
0
30
60
90 120 150 180 210 240 270 300 330 360
Rotor Position (electric degree)
Figure 4.3. Line Inductance Variation
Note that, in both phase inductance and line inductance simulation results, inductance
104
data in deep magnetic saturation conditions are not provided, because in the real situation,
the current for inductance measurement is always less than 20% of the rated current.
Figures 4.2 and 4.3 reveal that both the phase inductance and line inductance vary
with the rotor position in a quasi-sinusoidal manner. For example, across Region 0 where
the rotor position lies within 0 to 60 degrees, the phase inductance of Phase C remains the
smallest among the three, while Phase A inductance keeps increasing and Phase B
decreasing. A similar quasi-sinusoidal manner can also be found in the line inductance,
where, for the same region, AB inductance is the largest, while CA inductance keeps
increasing and BC decreasing. Such kind of manners could provide us not only the
information about which region the rotor lies in, but also a method of detecting
commutation points. In other words, the specific rotor position can be acquired by
knowing phase inductance or line inductance.
4.2
Sensorless Control of BLDC Machine from Zero to Low Speed
As discussed in the last section, it is revealed that the rotor position and the phase and
line inductance are closely inter related, which provides an insight of sensorless control
of a BLDC machine. However, directly measuring the phase or line inductance involves
complicated processes and requires additional circuits in the BLDC system. Therefore, a
more practical method is adopted in this chapter. As is well known, when applying a
voltage across an ideal inductor, the current flowing through the inductor will increase
linearly. The rate of increase is proportional to the inverse of the inductance and the
magnitude of the applied voltage. However, if the voltage, as well as the amount of time
the voltage applied on the inductor, is fixed, the peak current is inversely proportional to
105
the inductance. Therefore, by measuring the inductor peak current, which is simple and
easy to implement, the inductance information can be obtained, as well as the rotor
position. However, BLDC machine winding is not an idealized inductor because of the
resistance.
Therefore, the voltage applying time has to be as short as possible to
minimize the effect of resistance.
As mentioned above, information of both the phase inductance and line inductance
can be utilized as an indicator for the rotor position detection. However, the neutral point
of BLDC machines is usually not available for measurement, making it impossible to
obtain the phase inductance information. Therefore, it is logical that the obtainable line
inductance information is utilized to realize sensorless control of the BLDC machine.
In a BLDC machine system, if DC bus voltage VDC is applied across any two
terminals of the three phases, the voltage equation of the circuit, where the voltage drop
across the resistor is neglected, can be expressed as
𝑉𝐷𝐶 = 𝐿𝑝𝑝 (𝜃)
𝑑𝑖𝑝𝑝
𝑑𝑡
(4.1)
where Lpp (θ) represents the position-dependent line inductance, and ipp is the current
flowing in the corresponding phases. Define the smallest amount of time that the voltage
is applied on stator phases to be one unit of Voltage Applying Period (VAP) 𝑡𝑉𝐴𝑃 , then,
during one VAP, the current variation ∆ipp can be expressed as
∆𝑖𝑝𝑝 =
𝑉𝐷𝐶 ∙𝑡𝑉𝐴𝑃
𝐿𝑝𝑝 (𝜃)
(4.2)
As can be seen, if 𝑡𝑉𝐴𝑃 is kept constant, the current variation is in inverse proportion
with the line inductance. Assuming that there is no current in the corresponding phases
before the voltage is applied, and then only by measuring the peak current at the end of
VAP, the line inductance at arbitrary rotor position can be indirectly obtained.
106
4.2.1 Principles of Initial Rotor Position Estimation Algorithm
As discussed in previous sections, the six regions are marked in Figure 4.3, with each
region characterized by a line inductance being the largest throughout that region. It is
well known that BLDC machines have six operational regions, and each of them requires
specified phase currents, which are shown in Figure 4.4 with arrows.
C+ B-
A+ BRegion 1, iCA_min
Phase A
Phase C
Region 2, iBC_min
Region 0, iAB_min
C+ A-
Region 3, iAB_min
Region 5, iBC_min
A+ C-
Region 4, iCA_min
B+ C-
B+ APhase B
Figure 4.4. Characterizing Current Region
Instead of the characterizing line inductance, the characterizing current is marked for
each region. A typical three-phase BLDC machine drive system is shown in Figure 4.5.
107
IDC
S1
S3
S5
BDCM32
A
VDC
BDCM
BLDC
B
C
S4
S6
S2
Figure 4.5. Typical BLDC Machine System
The implementation is conducted in the following sequences: first, energize A-B
phases for one VAP. At the end of that VAP, sample the DC bus current iAB . Second,
wait until iAB drops to zero. Third, repeat the first two steps to energize B-C phases and
C-A phases in sequence, and sample the DC bus current iBC and iCA . Then, by comparing
the sampled currents, the rotor position could be preliminarily located. For instance, if
iAB is the smallest among the three sampled currents, then the rotor can be considered to
lie in either Region 0 or Region 3 according to figures 4.3 and 4.4.
Further operation has to be adopted to pinpoint the rotor position, and this process is
called the magnet polarity determination, which is based on the core saturation effect.
Forth, a positive voltage is applied to certain phases depending on the rotor’s preliminary
position for eight VAPs, which is sufficient to produce large currents to saturate the core.
108
For example, still assuming that the rotor position is preliminarily located in Region 0 or
Region 3, then Phase A and C are chosen to be energized because voltage VA+C- or VC+Awill produce the most likely flux to saturate BLDC machine. A large current will be
generated and iP will be sampled at the end of the last VAP. Fifth, after iP drops to zero,
apply a negative voltage to the same phases for the same amount of time, 8 VAPs, and
sample iN at the end of 8 VAPs. One of them will produce a flux in alignment with the
rotor flux and saturate the core, hence the current is much larger than the other one. The
comparison procedure is presented in Table 4.1.
Table 4.1. Initial Position Estimation Comparison Procedure
Min(iAB, iBC, iCA)
Polarity Determination Phases
iP , iN Comparison
North Pole Position (Region
Number)
Starting Current
iAB
A-C
iP > iN iP < iN
iBC
B-A
iP > iN iP < iN
iCA
B-C
iP > iN iP < iN
3
0
5
2
4
1
B+ &
A-
A+ &
B-
C+ &
B-
B+ &
C-
C+ &
A-
A+ &
C-
Compared with the initial rotor position estimation method discussed in [66], where
six saturation currents are injected, the proposed algorithm uses five current pulses to
locate the initial rotor position, only two of which are saturation currents. It minimizes
the damage that saturation current might cause and reduces the time of initial rotor
position estimation.
109
4.2.2 Principles of Low Speed Sensorless Algorithm
When the BLDC machine works in low speed operation, the back EMF based
methods are not applicable. The initial rotor position estimation algorithm is also not
applicable because it requires large detection currents and long operation time. The
magnet polarity determination currents are usually greater than rated current, so that the
BLDC machine will suffer from a large torque ripple. In addition, the initial rotor
position estimation algorithm needs a long time interval to complete five current
samplings and the long time interval insertion will bring serious disturbance to normal
operation.
To overcome the drawbacks, a low speed sensorless control of BLDC machine based
on line inductance variation is proposed. Theoretically, all three line inductances can be
used for commutation timing estimation, as shown in Figure 4.3. However, not all of
them are practical to be utilized to trigger a commutation.
The conducting line
inductance is difficult to measure because of the PWM chopping. The feasibility of the
other two line inductances is analyzed as following.
When the BLDC machine is at region 0, Phase A and Phase B are conducting. As
shown in Figure 4.3, B-C line inductance decreases during the first 30 degrees and stays
steady from 30 to 90 degrees, while C-A inductance stays steady at first and increases
later. Assuming that the BLDC machine is moving to region 1, the variation rate of C-A
line inductance is much higher near the commutation point, compared to B-C line
inductance. The line inductance with an obvious variation at commutation point makes
itself a prominent candidate for low speed sensorless control. If the BLDC machine is
110
moving in the opposite direction, B-C line inductance will be chosen for sensorless
control. The sensorless algorithm in other regions will follow the same procedure and the
corresponding injected voltage is given in Table 4.2.
Table 4.2. Rotor Position and Injected Voltage
Region
Clockwise
Motion
Injected
Voltage
Anti-clockwise
Motion
0
1
2
3
4
5
CA
BC
AB
AC
CB
BA
CB
BA
CA
BC
AB
AC
In order to acquire C-A line inductance, C-A current pulses need to be measured.
Assuming the rotor position is in Region 0, where Phase A and B are conducting. When
the PWM is “ON,” the current goes through VDC -S1-Phase A-Phase B-S6-VDC , shown in
Figure 4.5, and IDC is equal to iAB . On the other hand, when the PWM is “OFF,” the
current flows in the loop D4-phase A-phase B-S6-D4, and IDC is zero. If, during OFF
state, Phase C and A are energized by turning on S5 and S4, then the DC current would
be the same when the current goes through C-A phases. In other words, by measuring the
DC current, the C-A inductance could be acquired, and so is the rotor position.
Based on the principle discussed above, the implementation is conducted as follows.
For every N (N could be any number, for instance, 100) DSP interrupt cycles, one voltage
pulse is injected to certain phases for several VAPs and the corresponding current is
sampled at the end of the last VAP. Every time, the sampled current is compared with a
pre-determined value, and if the sampled current drops below this value, a commutation
will be triggered. Figure 4.6 shows the flowchart of the proposed algorithm.
111
Send Pulse
Sample DC Current
Smaller than
Threshold
Current?
No
Yes
Commutation
Figure 4.6. Flowchart of the Low Speed Sensorless Algorithm
4.3
Simulation Verification
Both initial rotor position estimation algorithm and low speed sensorless algorithm
are tested by FEM simulations. In the simulation, the North Pole of the rotor is fixed at
30 degrees, and voltage pulses are applied on A-B, B-C and C-A phases in sequence.
Figure 4.7 shows the FEM results of the sampled DC current.
112
1
iB
0.9
iC
iA
0.8
0.7
0.6
Current (A)0.5
0.4
0.3
0.2
0.1
0
0
0.001
0.002
0.003
0.004
0.005
Time (s)
Figure 4.7. Inductance Measurement Currents in FEM simulation
After that, A-C phases are energized with positive and negative voltages, and the DC
current is shown in Figure 4.8.
2.5
iN
2
iP
1.5
Current (A)
1
0.5
South Pole
0
0
0.001
0.002
North Pole
0.003
0.004
0.005
Time (s)
Figure 4.8. North Pole Detection Currents in FEM simulation
The results that iAB is the smallest and iP is the biggest implies, based on Table 4.1,
113
that the North Pole is located in Region 0, which matches the 30 degrees position. After
the North Pole is identified, the BLDC machine can start rotating from zero speed by
applying A+B- voltage. Further simulation is conducted to illustrate the current variation
as the rotor rotates from 0 to 60 degrees, as shown in Figure 4.9.
114
0.45
0.4
0.35
0.3
0.25
Current (A)
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
50
60
Rotor Position (electric degree)
(a) Current Pulse in AB
0.5
0.45
0.4
0.35
0.3
0.25
Current (A)
0.2
0.15
0.1
0.05
0
0
10
20
30
40
Rotor Position (electric degree)
(b) Current Pulse in BC
0.5
threshold
0.45
0.4
0.35
0.3
0.25
Current (A)
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
Rotor Position (electric degree)
(c) Current Pulse in CA
Figure 4.9. Current Variation in Region 0
115
60
It verifies that C-A current is the most suitable candidate in triggering a commutation
in Region 0. In addition, the threshold trigger is marked in Figure 4.9.
4.4
Experimental Verification
To verify the effectiveness of the proposed control algorithm, an experimental test has
been conducted on a real BLDC machine drive system. Figure 4.10 shows the lab setup
of the BLDC machine system.
Figure 4.10. BLDC Machine Drive System
The machine’s parameters are given in Table 4.3.
Table 4.3. Rating and Parameters of BLDC Machine
Nominal power
1 hp
Nominal voltage
230 V
Nominal current
2.4 A
Number of pole pairs
2
Base speed
1800 rpm
Stator Resistance
2.9 Ω
Mutual inductance
64 mH
Saliency
Yes
116
Figure 4.11 shows the experimental results of the current response after applying
voltage pulses to the standstill BLDC machine.
iA
iB
iC
iB
iC
iA
Figure 4.11. Inductance Measurement Currents in Experiment
The blue trace represents the current as it goes through Phase A, pink is Phase B, and
green is Phase C. The part of the waveforms above the central line can be regarded as the
DC bus current. It is followed by the North Pole detection, and the current responses are
shown in Figure 4.12.
117
|iA |
North Pole
South Pole
iA
Figure 4.12. North Pole Detection Currents in Experiment
The blue trace is the current in Phase A, and the red one is its absolute value, which
can be treated as the DC bus current as well. Figures 4.11 and 4.12 match perfectly with
the simulation results shown in figures 4.7 and 4.8.
The experimental results of a sensor-based operation and the proposed sensorless
operation are compared in figures 4.13.
118
with sensor
sensorless
Figure 4.13. Sensor-based and Sensorless Comparison
The BLDC machine shifts from sensor-based operation to sensorless operation at the
dashed line, the commutation point is detected precisely and the performance under
sensorless operation is as good as it is under sensor-based operation.
Figure 4.14 reveals the detailed sensorless operation within 60 degrees.
119
iA
iB
iC
threshold
Region 0 (0 to 60 electric degrees)
Figure 4.14. Inductance Measurement Currents
From top to bottom are the currents of Phase A, Phase B and Phase C. The center of
the screen, where A-B phases are conducting, corresponds to Region 0 in Figure 4.3. The
sampled DC bus current, which is also the absolute value of the sampled Phase C current,
decreases in this interval. The commutation is conducted when the sampled Phase C
current reaches the threshold. The Phase C current matches with the simulation result
shown in Figure 4.9 (c).
The proposed algorithm is also tested under a low speed operation. Figure 4.15
shows the three phase currents when the BLDC machine is operating at an extremely low
speed, 8.5 RPM, which is less than 0.5% of the rating speed.
120
Figure 4.15. Extremely Low Speed Operation
Given that this algorithm is only position dependent, it can be utilized at an arbitrary
low speed as long as the saliency exists.
4.5
Summary
In this chapter, a sensorless control algorithm for a BLDC machine at zero and low
speed based on rotor saliency is proposed. FEM simulations are conducted on a BLDC
machine to reveal the dependence of the phase inductance and line inductance on the
rotor positions. Algorithms for the detecting rotor position at standstill and extreme low
speed are proposed based on line inductance variation and are verified by both FEM
simulation and experimental testing. The advantages of the proposed control algorithm
121
include the following:

Speed-independent of rotor position detection; with the proposed algorithm, the
BLDC machine can achieve sensorless operation at zero and any arbitrary low
speeds.

Easy to implement; the rotor position detection does not require any real
measurement of inductance, rather than the peak current detection.

Simple and low cost setup; the implementation of the sensorless algorithm uses
only one current sensor.
122
CHAPTER 5: CONCLUSIONS AND FUTURE WORKS
5.1
Conclusions
This dissertation is aimed at developing the next generation high performance BLDC
machine, and advanced motor control algorithms for BLDC machine are proposed.
In chapter two, a 3kW slotless six-phase BLDC machine has been designed. The
stator core, stator winding connection, rotor core and air gap are optimized by three
principles. The first principle is performance, referred to as high torque density. The
second one is trapezoidal back EMF. The third one is to reduce cost by reducing the
usage of permanent magnets. After geometry design and FEA validation, the inductance
and resistance of stator winding is calculated. In the meantime, a winding assembling
method is proposed and a prototype machine has been built. At last, the advantage of a
six-phase BLDC machine is that a single inverter can split into two smaller power rating
inverters.
In chapter three, an original idea of a SVC algorithm has been proposed for BLDC
machine drive system; the commutation torque ripple is minimized in this algorithm by
matching the slopes of incoming and outgoing phase currents. Computer simulations and
experimental results are provided to verify the proposed SVC algorithm. Furthermore, an
enhanced torque control of BLDC machine has been proposed. Based on three-phase
back EMFs, an optimal current angle can be calculated. The optimal current angle
123
control can provide 5.4% more torque than conventional control, but with a drawback of
torque ripple. Finlly, the torque ripple in optimal current angle control is minimized by
vector amplitude compensation.
In chapter four, a sensorless control algorithm for a BLDC machine at zero and low
speed based on rotor saliency is proposed. FEM simulations are conducted on a BLDC
machine to reveal the dependence of the phase inductance and line inductance on the
rotor positions. Algorithms for the detecting rotor position at standstill and extreme low
speed are proposed based on line inductance variation and are verified by both FEM
simulation and experimental testing. The advantages of the proposed control algorithm
include the following:

Speed-independent of rotor position detection; with the proposed algorithm, the
BLDC machine can achieve sensorless operation at zero and any arbitrary low
speeds.

Easy to implement; the rotor position detection does not require any real
measurement of inductance, rather than the peak current detection.

Simple and low cost setup; the implementation of the sensorless algorithm uses
only one current sensor.
Future Works
5.2
Future work will focus on the following:

Optimize slotless six-phase BLDC machine design by reducing effective air gap.

Optimize rotor structure for high speed application.

Investigate the mutual inductance of six-phase BLDC machine.
124

Explore the possibility of extending the proposed SVC algorithm to BLDC flux
weakening control.

Develop SVC algorithm based on discontinuous PWM.

Explore the possibility of extending the proposed optimal current angle control to
an interior permanent magnet machine with utilization of reluctance torque.

Investigate the effects of harmonic currents in optimal current angle control on
motor efficiency.

Develop current close loop control with the proposed sensorless control of BLDC
machine.
125
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