Title
Design, analysis and application of brushless doubly salient
machines
Advisor(s)
Chau, KT
Author(s)
Fan, Ying; 樊英
Citation
Issued Date
URL
Rights
Fan, Y. [樊英]. (2006). Design, analysis and application of
brushless doubly salient machines. (Thesis). University of Hong
Kong, Pokfulam, Hong Kong SAR. Retrieved from
http://dx.doi.org/10.5353/th_b3676285.
2006
http://hdl.handle.net/10722/51508
The author retains all proprietary rights, (such as patent rights)
and the right to use in future works.
Design, Analysis and Application of Brushless Doubly
Salient Machines
by
FAN, Ying
B.Sc.(Eng.), M.Sc.(Eng.)
A thesis submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
at the
Department of Electrical and Electronic Engineering
The University of Hong Kong
April 2006
DECLARATION
I declare that this thesis represents my own work, except where due
acknowledgement is made, and that it has not been previously included in a thesis,
dissertation or report submitted to this University or to any other institution for a degree,
diploma or other qualification.
Signed
________________
FAN, Ying
April 2006
To my parents
and
my husband and son
Abstract of thesis entitled
“Design, Analysis and Application of Brushless Doubly Salient Machines”
submitted by
FAN Ying
for the degree of Doctor of Philosophy
at The University of Hong Kong in April 2006
In response to increasing concern about the environment, research into the
development of electric vehicles (EVs) has accelerated in recent years. To enable
electric vehicles to compete successfully with gasoline vehicles, the goals of motor
drive for electric vehicles are to pursue optimal efficiency over wide operating ranges,
high controllability, wide speed range, high reliability and maintenance-free operation.
In order to pursue these goals, a new class of motor drives is proposed which consists of
two types of stator windings, namely the poly-phase armature winding and dc field
winding. This thesis presents the design, analysis and control of this brushless doublyfed doubly-salient (BDFDS) motor drive.
As a result of the search for alternative forms of energy, there has also been much
interest in the development of wind power generation. The core element of wind power
generation is the electric generator. This thesis first presents a new three-phase 12/8pole DSPM machine for wind power generation, including its design, analysis and
implementation. The corresponding analysis of topological selection is specially
elaborated. A three-phase 12/8-pole BDFDS machine is then developed for wind power
generation, which uniquely offers constant output voltage and efficiency optimization
over a wide range of wind speeds.
The finite element method (FEM) has been used for electromagnetic field analysis
of the proposed BDFDS machines, in which magnetic saturation, armature field and dc
exciting field have been considered. Hence, the static characteristics, being the basis of
analysis, design and control of the BDFDS machine, have been deduced.
The sizing equation of the BDFDS machine has been deduced and design details
have been presented to provide a practical way of making initial calculation of machine
dimensions and parameters. A dynamic model of the BDFDS machine has also been
derived. Numerical simulation been carried out by using Matlab/Simulink revealed that
the proposed three-phase BDFDS machine has the advantage of wide constant power
operation range.
The control strategies of two BDFDS machines, with skewed and unskewed rotors,
have been developed and implemented by a dSPACE-based controller. Sinusoidal
current control is used for the BDFDS machine with skewed rotor, whereas square
current control is applied to the one with unskewed rotor. Moreover, a half-bridge
power converter, which is composed of three IGBT-based power modules, has been
employed to provide bi-directional current operation. It has the advantages of reducing
the number of power switches and providing independent phase current control.
In order to minimize the torque ripple of the four-phase 8/6-pole DSPM motor, a
new two-phase operation mode is proposed and analyzed, in which sinusoidal current
control is proposed. Theoretical analysis, computer simulation, and experimental results
have verified that the operating torque ripple at the rated load can be reduced by about
14% when using the proposed two-phase operation mode.
The results of the numerous experiments conducted not only verify the validity of
the theoretical analysis but also illustrate the good performance of the newly proposed
BDFDS machines for electric vehicles and wind power generation.
ACKNOWLEDGEMENTS
First and foremost I would like to express my sincere gratitude and
appreciation to my supervisor, Dr. K.T. Chau, for his constant and invaluable
guidance, inspiration, encouragement and unceasing support throughout the research
project. I have learnt a lot from my supervisor – his dedication, attitude and devotion
to not only the academic activities but also the way of life.
I also wish to thank my colleagues in the Department of Electrical Engineering,
Southeast University, for their supporting me to pursue this Ph.D. degree. Special
thanks are given to Professor M. Cheng, the head of the Department of Electrical
Engineering, Southeast University, for his discussion and support on construction of
the prototype machine.
I am grateful to Professor J.Z. Jiang for his invaluable advice and discussion in
my research field. I also wish to thank Professor Z.Q. Zhu for his comments and
encouragement.
Many thanks are also given to all the staffs and postgraduate students in our
research group for their support, encouragement and opinions, most notably Mr.
Raymond S.C. Ho, Mr. Sam Y.S. Wong, Dr. Q. Sun, Dr. Y. Gao, Dr. Y. Wang, Miss
S. Ye, Mr. S.W. Chung, Mr. Z. Wang, Mr. C.H. Liu, and Miss S.X. Niu.
Acknowledgements are also due to the CRCG of The University of Hong Kong
for providing a conference grant, and the Hong Kong Research Grants Council for
financial support in part of this work. Two awards which are CLP Fellowship in
Electrical Engineering 2004-2005 and The HongKong Electric Co. Ltd. Electrical
I
Energy Postgraduate Scholarship 2004-05, respectively, and the Postgraduate
Studentship also supported my research work.
I would like to express my deepest appreciation to my parents for their constant
understanding and encouragement as well as genuine support. I am also grateful to
my mother-in-law for her taking care of my son for these years.
Last but not the least, expressions of gratitude and apology are directed to my
husband, Xie Shaojun, and son, Xie Boyuan, who patiently endured the long working
hours dedicated to my study. Without their complete understanding and support, this
work would have been much more difficult.
II
CONTENTS
DECLARATION
ABSTRACT
ACKNOWLEDGMENTS
CONTENTS
CHAPTER 1
I
III
INTRODUCTION
1.1 Introduction....................................................................................................... 1
1.2 Current Status of EV motors.............................................................................. 3
1.3 Current Status of Wind Power Generators ......................................................... 7
1.4 Research Objectives .......................................................................................... 8
1.5 Thesis Outline ................................................................................................... 9
CHAPTER 2
REVIEW OF ADVANCED ELECTRIC MACHINES
2.1 Introduction..................................................................................................... 12
2.2 Switched Reluctance Machines ....................................................................... 12
2.3 Permanent Magnet Brushless Machines........................................................... 15
2.4. Doubly Salient Permanent Magnet Machines ................................................. 18
2.5 Comparison with SR and PMBL Machines ..................................................... 21
2.6 Summary......................................................................................................... 23
CHAPTER 3
PROPOSED TWO-PHASE DSPM MOTORS
3.1 Introduction..................................................................................................... 24
3.2 Motor Configuration ....................................................................................... 25
3.2.1 Four-Phase DSPM Motor ...................................................................... 25
3.2.2 Normal Four-Phase Operation ............................................................... 30
III
3.3 Proposed Two-phase Operation ....................................................................... 32
3.4 Simulation Results........................................................................................... 39
3.5 Experimental Results...................................................................................... 43
3.6 Summary......................................................................................................... 46
CHAPTER 4
PROPOSED
THREE-PHASE
DSPM
WIND
POWER
GENERATORS
4.1 Introduction..................................................................................................... 47
4.2 Proposed Design and Analysis......................................................................... 48
4.2.1 System Configuration and Speed Constraint .......................................... 48
4.2.2 Topological Selection of Machine Design.............................................. 50
4.2.3 Electromagnetic Analysis ...................................................................... 55
4.3 System Operation − Modeling ......................................................................... 58
4.4 System Simulation........................................................................................... 59
4.5 Experimental Verification................................................................................ 61
4.6 Summary......................................................................................................... 66
CHAPTER 5
PROPOSED BDFDS MACHINES – DESIGN AND ANALYSIS
5.1 Introduction..................................................................................................... 67
5.2 Proposed Design Philosophy ........................................................................... 67
5.2.1 Selection of Number of Phases and Poles .............................................. 67
5.2.2 Sizing Equation ..................................................................................... 69
5.2.3 Number of Turns ................................................................................... 74
5.2.4 Design of Prototype Machine................................................................. 75
5.3 Finite Element Analysis................................................................................... 78
5.4 Static Characteristics ....................................................................................... 83
IV
5.4.1 Field Flux Linkage and Back EMF ........................................................ 83
5.4.2 Self Inductance and Mutual Inductance ................................................. 88
5.5 Summary......................................................................................................... 89
CHAPTER 6
PROPOSED BDFDS MACHINES – MODELING, CONTROL
AND SIMULATION
6.1 Introduction..................................................................................................... 90
6.2 Principle of Operation ..................................................................................... 91
6.3 Proposed Control Strategy............................................................................... 95
6.3.1 Converter Topology .............................................................................. 95
6.3.2 Control System Configuration ............................................................. 100
6.3.3 Control Strategy .................................................................................. 105
6.3.3.1 Control of BDFDS Machine with Skewed Rotor ........................ 105
6.3.3.2 Control of BDFDS Machine with Unskewed Rotor .................... 105
6.4 Simulation Model and Results ....................................................................... 108
6.4.1 BDFDS Motor with Skewed Rotor ...................................................... 109
6.4.2 BDFDS Motor with Unskewed Rotor .................................................. 117
6.5 Summary....................................................................................................... 119
CHAPTER 7
PROPOSED
BDFDS
MACHINES
–
EXPERIMENTAL
IMPLEMENTATION
7.1 Introduction................................................................................................... 120
7.2 Experimental Set-up...................................................................................... 120
7.2.1 Power converter .................................................................................. 123
7.2.2 Position Sensor.................................................................................... 125
7.2.3 Current Control ................................................................................... 127
V
7.2.4 Controller − dSPACE .......................................................................... 130
7.2.5 Position Signal Processing................................................................... 132
7.3 Experimental Results..................................................................................... 133
7.3.1 BDFDS Motor with Skewed Rotor ...................................................... 133
7.3.2 BDFDS Motor with Unskewed Rotor .................................................. 143
7.4 Summary....................................................................................................... 146
CHAPTER 8
PROPOSED BDFDS MACHINES – APPLICATION
8.1 Introduction................................................................................................... 147
8.2 Design and Analysis ...................................................................................... 148
8.3 Modeling and Control.................................................................................... 149
8.4 Simulation and Experimentation.................................................................... 150
8.5 Summary....................................................................................................... 154
CHAPTER 9
CONCLUSIONS AND RECOMMENDATIONS
9.1 Conclusions................................................................................................... 155
9.2 Recommendations ......................................................................................... 158
APPENDICES
A1 The characteristics of various power switches................................................ 160
A2 Key parameters of IPM PM75DSA120 .......................................................... 162
A3 Technical details of dSPACE − DS1104 R&D Controller Board.................... 163
NOMENCLATURES
164
LIST OF FIGURES
169
LIST OF TABLES
177
REFERENCES
178
PUBLICATIONS
189
VI
CHAPTER
1
INTRODUCTION
1.1 Introduction
Electric machines have been used in industry for more than one hundred years.
They are the primary workhorse which convert energy between mechanical and
electrical, and underpin the modern industrial civilization. Nowadays, electric machines
are widely used in all walks of our life, including military, aerospace, automobiles,
industrial and domestic applications, etc. In developed countries, electric motor drives
consume 65% of the electrical energy generated [1−2].
There are two main types of electric machines: the dc machines and the ac
machines. The dc machines have been used as variable speed drives for a long time due
to their simple control, smoothness and wide speed range. However, the major
drawbacks are the need to use brushes and commutators and the frequent maintenance
required for their operation restricted their use to high performance applications [2−4].
The ac machines including the induction and synchronous machines, have been the
traditional workhorses for constant speed drive applications due to their ruggedness,
low cost and nearly free of maintenance. Nevertheless, variable speed operation of ac
machine is not attractive due to the complex control and expensive equipment required.
With the development of power electronics, microcontrollers, new control
strategies and the advent of new materials, ac drives are now being used in many
variable-speed areas. Great progresses have been made to operate ac machines to obtain
good reliability, performance, maintenance characteristics and at a low cost [4−6]. With
1
Chapter 1
the progress of machine design theory, the increasing concern of energy conservation as
well as the emerging growth of servo applications with fast transient response, various
brushless ac machines such as switched reluctance motor and permanent magnet
brushless machine have been proposed. Hence, there is an increasing tendency in using
brushless machines with PM excitation for electric vehicles (EVs) and other industrial
applications [7−9].
In a world where environment protection and energy conversation are of growing
concerns, the development of electric vehicle (EV) technology has taken on an
accelerated pace to fulfill these needs. Because EVs provide emission-free from the
users’ point, they can reduce the air pollution in crowded urban area. With the growing
concern for air quality, some cities have set zero-emission zones and have enforced
strict emission regulations to encourage the use of EVs [10]. EVs in America, Europe,
Asia, and most of the world are being developed quickly.
Electric propulsion is to interface electric supply with vehicle wheels, transferring
energy in either direction as required, with high efficiency, under control of the driver at
all times. From the functional point of view, an electric propulsion system can be
divided into two parts − electrical and mechanical. The electrical part includes the motor,
power converter, and electronic controller. The mechanical part consists of the
transmission device and wheels. Sometimes, the transmission device is optional. The
boundary between electrical and mechanical parts is the air-gap of the motor, where
electromechanical energy conversion is taking place. Therefore, the development of EV
motors plays an important role.
2
Introduction
1.2 Current Status of EV motors
Electric motors have been available for over a century. The evolution of motors,
unlike that of electronics and computer science, has been long and slow. Nevertheless,
the development of motors is continually fueled by high-energy permanent magnets
(PMs), sophisticated motor topologies, and powerful computer-aided design (CAD)
techniques. As shown in Fig. 1.1, those motors with dashed frame which are applied to
electric propulsion can be classified as two main groups, namely the motors with
commutators and the motors without commutators.
PMs provide motors with lifelong excitation. The only outlay is the initial cost
which is reflected by the price of motors. Apart from ferrites, alnico, and samarium–
cobalt (Sm-Co), neodymium–iron–boron (Nd-Fe-B) permanent magnet (PMs) have
been introduced. Because of their highest remanence and coercivity as well as
reasonable low cost, Nd-Fe-B PMs have promising applications in motors. In fact,
adopting these “super magnets,” a number of new motor topologies with high power
density and high efficiency have recently been developed [1].
Fig. 1.1 Classification of EV motors.
3
Chapter 1
Traditional dc commutator motors, loosely named as dc motors, have been
prominent in EV propulsion. Their control principle is simple. By replacing the field
winding and pole structure with high-energy PMs, PM dc motors permit a considerable
reduction in stator diameter. Owing to the low permeability of PMs, armature reaction is
usually reduced and commutation is improved. However, the principal problem of dc
motors still arises from their commutators and brushes which make them less reliable
and unsuitable for maintenance-free operation.
Recent technological developments have pushed ac motors to a new era, leading
to definite advantages over dc motors: higher efficiency, higher power density, lower
cost, more reliable, and almost maintenance free. As high reliability and maintenancefree operation are prime considerations in EV propulsion, ac induction motors are
attractive. However, conventional control of induction motors such as variable-voltage
variable-frequency (VVVF) cannot provide the desired performance of EVs. One major
reason is due to the nonlinearity of its dynamic model with coupling between direct and
quadrature axes. With the advent of the microcomputer era, the principle of fieldoriented control (FOC) of induction motors has been accepted. By replacing the field
winding with high-energy PMs, PM synchronous motors can eliminate conventional
brushes, slip-rings, and field copper losses. As these motors are essentially traditional ac
synchronous motors with sinusoidal-distributed windings, they can run from a
sinusoidal or PWM supply without electronic commutation. When PMs are mounted on
the rotor surface, they behave as non-salient synchronous motors because the
permeability of PMs is similar to that of air. On the other hand, by burying PMs inside
the magnetic circuit of the rotor, the saliency causes an additional reluctance torque
which leads to provide a wide speed range at constant power operation [11].
4
Introduction
By inverting the stator and rotor of PM dc motors, rectangular-fed ac motors, socalled PM brushless dc motors, are generated. The most obvious advantage of these
motors is the removal of brushes, leading to the elimination of many problems
associated with brushes. Another advantage is the ability to produce a larger torque at
the same peak current and voltage because of the interaction between rectangular
current and rectangular magnetic field. Moreover, the brushless configuration allows
more cross-sectional area available for the armature winding, thus facilitating the
conduction of heat through the frame and, hence, increasing the electric loading and
power density. Although their configurations are similar to those of PM synchronous
motors, there is a distinct difference in that PM brushless dc motors are fed by
rectangular ac wave, while PM synchronous motors are fed by sinusoidal or PWM ac
wave.
Switched reluctance motors, though the principle of which has been known for
over a century, have seen a revival of interest in recent years. Basically, they are direct
derivatives of single-stack variable-reluctance stepper motors, in which the current
pulses are phased relative to the rotor position to optimize operation in the continuous
rotation mode. Similar to PM brushless dc motors, they usually require shaft position
sensors. However, switched reluctance motors suffer from the same excitation penalty
as induction motors, and cannot attain the efficiency or power density of PM ac motors.
Recently, a research direction has been identified on the development of PM
hybrid motors for EV applications. In principle, there are many PM hybrids in which
three of them have been actively investigated, namely the PM and reluctance hybrid, the
PM and hysteresis hybrid, and the PM and field-winding hybrid. Firstly, by embedding
PMs in the magnetic circuit of rotor, the PM synchronous motor can easily incorporate
5
Chapter 1
both PM torque and synchronous reluctance torque. On the other hand, by incorporating
PMs into the SR structure, another PM and reluctance hybrid is generated which is socalled doubly salient permanent magnet (DSPM) motor [12−13]. Recent development
of this DSPM motor has shown that it is of high efficiency, high power density and
wide speed range [14]. Secondly, another PM hybrid motor, incorporating both PM
torque and hysteresis torque, has been introduced [15]. By inserting PMs into the slots
at the inner surface of the hysteresis ring, this PM hysteresis hybrid motor can offer
unique advantages such as high starting torque as well as smooth and quiet operation for
EV applications. Thirdly, another PM hybrid motor has been developed for EVs, which
comprises of PMs in the rotor and a dc field winding in the inner rotor [7]. By
controlling the direction and magnitude of the dc field current, the air-gap flux of this
motor can be flexibly adjusted, hence the torque speed characteristics can be easily
shaped to meet the special requirements for EV propulsion.
Similar to both the PM brushless DC motor and the SR motor, the DSPM motor
suffers from the problem of torque ripples, causing mechanical vibration and acoustic
noise. In recent years, some methods have been proposed to alleviate this problem. By
using finite element analysis, an optimal skewing angle was designed to reduce the
torque ripple of a PM brushless DC motor [16]. In [17], an optimal control method was
proposed to minimize the torque ripple of modular PM machines. In [18], a direct
torque control method was also proposed to reduce the torque ripple of brushless DC
drives. On the other hand, a conduction angle control method was proposed to minimize
the torque ripple of DSPM motors [19].
In this project, a control approach of two-phase operation is proposed to minimize
torque ripples of the DSPM motor.
6
Introduction
1.3 Current Status of Wind Power Generators
Wind power has been utilized for about three thousand years − the earliest
windmills recorded were used for grinding grain in the seventh century BC. Although
the first wind turbine for electricity generation was built by a Dane in 1891, the use of
wind power was gradually superseded by the more consistent fuel power [20]. Because
of the outbreak of energy crisis in the 1970s, the interest in wind power generation was
rekindled. Starting in the 1990s, due to the ever increasing concerns on our environment,
the development of wind power generation has taken an accelerated pace.
Basically, there are two categories of wind power generation systems: the fixedspeed and the variable-speed generators, respectively. Modern wind power systems are
moving towards the variable speed topology, since it has the merits of higher power
yield, simpler pitch control, and lower power fluctuations [21−22]. Also there are two
major categories of variable speed power generation systems, namely the variable speed
variable frequency (VSVF) and the variable speed constant frequency (VSCF)
generators. The VSVF generators is normally a synchronous machine which can offer
the advantage of mature technology but requires a full rating power converter, whereas
the VSCF one is generally a doubly-fed induction machine, which takes the advantage
of reduced power converter rating but requires complicated slip power control [23-24].
However, both of them suffer from a basic drawback that they need regular maintenance
because of the carbon brushes. Therefore, some viable brushless machines have recently
been proposed for application to wind power generation.
There are mainly two types of brushless VSVF machines: the permanent magnet
(PM) synchronous generator [25−27] and the switched reluctance (SR) generator [28].
The PM synchronous generator has the advantages of high power density and high
7
Chapter 1
efficiency, but it also suffers from the inflexibility of flux control. On the other hand,
the SR generator takes the definite advantages of high robustness and low inertia.
However, it has the drawbacks of lower power density and relatively lower efficiency.
Among those viable brushless VSCF machines, there are the brushless doubly fed
induction generator [29] and the brushless doubly fed reluctance generator [30].
Based on the aforementioned analysis, by incorporating the merits of both the PM
synchronous generators and the SR generators, the doubly salient permanent magnet
generator is proposed to offer advantages of high power density, high efficiency, high
robustness and low inertia.
1.4 Research Objectives
The research objectives of the project, on which this thesis is based, aim at:
To develop a new control strategy and control circuit to minimize the torque
ripple of the DSPM motor which is proposed to run with two-phase operation
of the 8/6-pole DSPM motor.
To design and analyze a new machine which is proposed as a three-phase 12/8pole DSPM machine which is particularly suited for wind power generation.
This DSPM generator can offer higher efficiency, higher power density and
better controllability when compared with induction and SR generators.
To develop theoretical derivation and modeling approaches for the design,
analysis and control of the three phase 12/8-pole BDFDS motor drive, hence
forming a foundation for further development and application of the BDFDS
motor drives.
8
Introduction
To develop a practical three-phase 12/8-pole BDFDS motor drive system
which possesses high efficiency and high operating performance.
To apply the BDFDS machine as a wind power generator to provide constant
output voltage and efficiency optimization for a wide range of wind speeds.
1.5 Thesis Outline
In this thesis, there are nine main chapters. Each chapter consists of several sections.
Some sections may contain several sub-sections. All references quoted within these
chapters are listed in the References while the research outputs of this project are
grouped in the Publications. An outline of all chapters of this thesis is given as follows:
In Chapter 1, an introduction to the current status of motor drives for electric
vehicles and wind power generators, thereby helping to shape the objectives of this
research project.
In Chapter 2, a review is made on the advanced electric machines, including the
switched reluctance motor, permanent magnet brushless ac machines, permanent
magnet brushless dc machines and doubly salient permanent magnet machines.
In Chapter 3, the two-phase operation of the 8/6-pole DSPM motor is proposed.
Basic structure and operating principle of the DSPM motor are described. Modeling and
simulation of the DSPM motors under two operation modes, namely two-phase
operation and four-phase operation, are also discussed. Then, the two-phase operation is
compared with the four-phase operation based on control circuit, control strategy and
torque ripple factor. By using the finite element method (FEM), both the self-
9
Chapter 1
inductances and the PM flux linkages of the two-phase operation of 8/6-pole DSPM
motor with respect to the rotor position are analyzed.
In Chapter 4, a three-phase 12/8-pole DSPM wind generator is proposed. the
system configuration and speed constraint are described. The machine design, including
the topological selection and electromagnetic analysis is presented. The FEM is applied
to analyze the static characteristics of the generator. The system modeling and
simulation are also discussed. Furthermore, the implementation and experimental
verification are given.
In Chapter 5, the three phase 12/8-pole BDFDS motor for electric vehicles is
proposed. The design details of the BDFDS motor, are reported and these details are
providing the designers a practical way to make initial calculation of motor dimensions
and parameters. The design data of the prototype machines are also given. Based on the
finite element analysis, magnetic field distributions at different load conditions are
analyzed and the static characteristics are also deduced. Both magnetic saturation and
the coupling between armature current flux and field current flux are considered in the
study.
In Chapter 6, the principle of operation of the three phase 12/8-pole BDFDS
motor is analyzed. Mathematical models that include the voltage equation and motion
equation are proposed. The control system configuration as well as the control logic and
strategy are also proposed to realize high performance. A PI controller is designed for
speed control and a three-phase half-bridge power converter with winding neutral is
adopted. Based on Matlab/Simulink, simulation of the whole system is performed,
hence the steady state and dynamic performances are given.
10
Introduction
In Chapter 7, an experimental setup, including a three-phase 12/8-pole BDFDS
motor prototype, a power converter which is based on IGBT power model, and a control
circuit which is based on the dSPACE − DS1104 R&D Controller Board, is designed
and implemented. The measured results of the steady-state and dynamic performances
of the BDFDS motor drive are given.
In Chapter 8, application of the BDFDS machine as a wind power generator is
proposed. Modeling, control and simulation of the BDFDS generator are discussed.
Experimentation is given to verify the performance of the BDFDS generator which can
provide constant output voltage and efficiency optimization for a wide range of wind
speeds.
Finally, in Chapter 9, the summary and conclusions of this thesis and the
contributions of this project are highlighted, together with suggestions for possible
future developments in this area.
11
CHAPTER
2
REVIEW OF ADVANCED ELECTRIC MACHINES
2.1 Introduction
With the advent of power electronics, converter-fed machines have been one of
focus in research, development of electrical machines, power electronics and drives.
Some of the converter-fed machines which have attracted extensive interest are
Switched Reluctance Machines (SRM), Permanent Magnet Brushless AC and DC
Machine (PMBLAC and PMBLDC), Doubly Salient Permanent magnet machines
(DSPM), etc. In this chapter, these three brushless machines will be reviewed and
summarized.
2.2 Switched Reluctance Machines
Switched Reluctance Machines (SRMs), or so-called Variable Reluctance
Machines (VRMs), are widely used in ac drives. It was first named by S.A. Nasar and
has two features: (a) switched − the machine must be operated in a continuous switching
mode, and (b) reluctance − both the stator and rotor have variable reluctance magnetic
circuits, inherently, it is a doubly salient machine [31].
Since 1980’s, SRMs have attracted interest in research and development.
Concentrated windings with shorter end are wounded on the stator poles, no windings
or magnets in rotor. Therefore, the machine is easily cooled and capable of very high
speed operation and relatively high torque to inertia ratio [32]. Fig. 2.1 shows a four-
12
Review of Advanced Electric Machines
phase 8/6-pole SR motor, in which only one particular phase winding is sketched.
Because of the doubly salient structure, the inductance of each phase varies with the
rotor position as shown in Fig. 2.2 [33]. The operating principle of the SR motor is
based on the “minimum reluctance” rule. For example, as shown in Fig. 2.1, when the
phase D winding excited, the rotor tends to rotate clockwise to reduce the reluctance of
the flux path until the rotor pole 2 aligns with the stator pole D where the reluctance of
the flux path has a minimum value (the inductance has a maximum value). Then, the
phase D is switched off and the phase A is switched on so that the reluctance torque
tends to make the rotor pole 3 align with the stator pole A. The torque direction is
always towards the nearest aligned position. Hence, by exciting the phase windings in
the sequence of D−A−B−C according to the rotor position feedback from the position
sensor, the rotor keeps rotating clockwise [34].
Fig. 2.1 Four-phase 8/6-pole SR motor.
13
Chapter 2
Fig. 2.2 Variation of inductance, flux linkage, torque and current with rotor position, with ideal
unidirectional current.
(A= aligned position; U= unaligned position; J= start of overlap; K=end of overlap).
A great deal of research has been done on the machine design, modeling,
converter topology, control strategies, simulation and optimization [35−43]. Its simple
and robust rotor structure with concentric winding reduces manufacturing cost. The
unidirectional current in phase windings results in a very simple converter topology.
The SRM is now competing favorably with induction machines, particularly for small
power below a few kilowatts, because of its simple structure, high reliability, high
efficiency over a wide range of speeds and loads, low cost and even fault-tolerance.
However, it has such disadvantages as relatively big torque ripple and considerable
audible noise at low speeds, and for years efforts have been made to solve these
problems [44−47].
14
Review of Advanced Electric Machines
However, there are some limitations in the SR machine, such as
(a)
According to the operating principle of the SR machine, the direction of
torque is only dependent on the sign of dL / dθ − the changing rate of inductance with
rotor position, not on the sign of current. Therefore, each phase can produce a positive
torque only in half of the rotor pole-pitch, the system efficiency and the utilization of
copper and iron materials are relatively poor.
(b)
The stator windings of SR machines must carry not only the excitation
component that magnetizes the iron core, but also the torque-producing component of
the current. Therefore, an increased VA rating of both the power converter and the
motor windings is usually required. This penalty of excitation loss is the price paid for
not using permanent magnets [45].
(c)
Due to the maximum inductance at the aligned position, the rate of falling
current is very low. To prevent the SRM from producing a negative torque, the
commutation angle must precede the aligned position by several degrees and this has to
increase with speed increases in motor. Therefore, the torque producing capability of the
SR machine is limited.
2.3 Permanent Magnet Brushless Machines
With the invention of neodymium-iron-boron (Nd-Fe-B) magnets, the
development of permanent magnet (PM) machines is accelerating. The PM brushless
machine drive is attractive for high-performance applications from servos to traction
drives [48]. The PM brushless machine drives consist of a PM brushless motor, an
inverter, a rotor position sensor and a controller. The motor provide the driving torque,
15
Chapter 2
the inverter and rotor position sensor are needed for electric commutation of the stator
windings. The controller synthesizes the reference signal, feedback signals and control
strategies to produce the switching signals for the inverter.
Based on the back-EMF and the current waveforms, PM brushless machine drives
can be classified as PM brushless AC drives (PMBLAC) and PM brushless DC drives
(PMBLDC) [18], Table 2-1 shows the comparison of PMBLAC and PMBLDC.
Table 2-1 Comparison of PMBLAC and PMBLDC
Items
PMBLAC
PMBLDC
Current
Sinusoidal
Rectangular
Back-EMF
Sinusoidal
Trapezoidal
Rotor position sensor
High resolution
Low resolution
Stator windings
Sinusoidally distributed
Concentrated
According to the rotor geometry, PM brushless motor drives can be classified as:
surface-mounted magnet, inset magnet and interior magnet configurations. The interior
configuration also has two basic types, namely interior radially magnetized and interior
circumferentially magnetized, respectively. As Fig. 2.3(a) shown, thin permanent
magnets are simply mounted on the surface of the rotor iron core by using epoxy
adhesives. Alternating magnetization direction produce radial flux density across the air
-gap. Due to the permeability of virtually unity of the magnet, the motor is essentially
non-salient with a large equivalent air-gap and is commonly used in the brushless dc
motor drive with wide magnet pole arcs and concentrated stator windings [1], [3], [48].
The rotor cross section of an inset PM motor is shown in Fig. 2.3(b). It is similar to
surface-mounted type, but the magnets are inset into the rotor iron in order to make the
outer surface of the rotor cylindrical. As the magnet appears as a large air-gap while the
inter-polar iron presents a small air-gap, the stator currents affect the air-gap flux so
16
Review of Advanced Electric Machines
significantly and the achievable constant power speed range is wider than that of its
surface-mounted counterpart [3].
Two general rotor configurations of interior type motor are shown in Fig. 2.3(c)
and Fig. 2.3(d) with radially and circumferentially magnetized rotors, respectively.
Because the magnets are buried into the rotor iron core, there is small iron-to-iron airgap in the interior magnet motors, with significant armature reaction, which can be used
to realize flux-weakening control at high speeds. The motors are generally used in PM
synchronous motor drives.
(a) Surface-mounted
(b) Inset
17
Chapter 2
(c) Interior radially magnetized
(d) Interior circumferentially magnetized
Fig. 2.3 Typical rotor configurations of PM brushless machines.
2.4 Doubly Salient Permanent Magnet Machines
The DSPM machine essentially adopts the same structure as a SR machine but
with permanent magnets in the stator and it has saliency on both the stator and rotor. It
incorporates the advantages of both the PM brushless machine and the SR machine. The
18
Review of Advanced Electric Machines
DSPM motor drive takes definite merits, such as: high power density, high efficiency,
simple structure and maintenance free, etc.
The development of DSPM machine was renewed in early 90’s, due the new high
performance permanent magnet materials available on the market. In addition to T.A.
Lipo et al [49−54], many researchers have contributed towards the development of the
DSPM motor drive [55−61].
One version of DSPM machine is to incorporate the PMs in the rotor, this
however adversely offsets the merits of mechanical robustness and high speed
capability. Therefore, numerous researchers have focused on the DSPM machine with
stationary PMs. There are some variations in the method of arranging the magnets.
Apart from placing the magnets in the stator yoke radially and making the motor a
football shaped cross section as shown in Fig. 2.4, the arc magnets, for example, may be
used to achieve higher flux concentration and keep the motor a traditional shaped cross
section, as shown in Fig. 2.5 [50]. In this case, sufficient room can be arranged for the
use of ferrite PMs which are much cheaper than rare earth PMs.
Fig. 2.4 Cross-section of a football shaped DSPM machine.
19
Chapter 2
Fig. 2.5 Cross-section of DSPM machine with arc magnets.
Fig. 2.6 Structure of 4/6-pole dual stator DSPM machine.
Fig. 2.7 Cross-section of single phase DSPM machine.
20
Review of Advanced Electric Machines
A two-phase DSPM machine as illustrated in Fig. 2.6 [54]. It is composed of two
sets of 4/6-pole (4 stator poles and 6 rotor poles) single phase DSPM motors, but the
stator (or rotor) of one machine is shifted with respect to the other by 45 degrees so as
to produce starting torque at any rotor positions. In this case when one machine is at its
fully aligned position, the other machine is exactly at its half aligned position.
Electrically the two sets of windings are 90 ° out of phase. Since the frequency of
reluctance torque pulsating is double that of current, the reluctance torques produced by
the two sets are 180 ° out of phase, so that they essentially cancel each other completely.
Therefore the resultant torque is always great than zero so that the machine can start at
any rotor position. In addition, a single phase of DSPM motor as shown in Fig. 2.7 [59]
with a stepped air-gap under the stator poles to produce the starting torque. The air-gaps
are 0.3 mm and 0.6 mm, respectively. Furthermore, the peak static torque is 2.4 Nm
when the phase current is 5 A.
Similar to conventional brushless PM motors, the flux weakening is employed for
the purpose of providing a wide constant power operation range. Hence, some electrical
and mechanical methods [14], [50], [53] for the flux weakening of the DSPM motor
have been proposed.
2.5 Comparison with SR and PMBL Machines
Though the structure of a DSPM motor is similar to that of an SR motor, the
operation principle, especially at low speed, is closer to that of a PM brushless DC
(PMBLDC) motor with 120 ° quasi-square current waveform. The primary difference is
that the two 120 ° conducting current blocks are drawn together in the case of the DSPM
21
Chapter 2
motor. The dominant component of electromagnetic torque produced in both motors is
the torque due to the interaction between the winding current and PM flux, or PM
torque. The energy conversion loop of DSPM motor is limited to the first two quadrants.
In the case of PMBLDC motor, it covers all four quadrants in the flux-MMF plane, as
shown in Fig. 2.8. The DSPM motor has unipolar flux variation and bipolar MMF
variation. The PMBLDC motor has bipolar phase flux and MMF variation, as shown in
Fig. 2.9.
The DSPM motor incorporates the advantages of both the PM brushless machine
and SR machine. The major merits of the DSPM motor are listed below:
The DSPM can produce the torque by applying either a positive current to a
phase winding with its flux linkage increasing or a negative current with its
flux linkage decreasing. Two possible torque producing zones are employed.
Hence the torque density is high.
The armature reaction field energy is small due to the small phase inductance.
Hence, the energy conversion ratio is high.
The PMs are located in the stator and thus can be easily cooled. Therefore, the
problems of irreversible demagnetization and mechanical instability are
alleviated.
The rotor is the similar with that of an SR machine, no windings and PMs on it,
hence it has simple configuration, low inertia, mechanical robustness, and high
speed capability.
The concentrated windings possess shorter overhangs, minimizing the copper
consumption and winding resistance. Therefore, the DSPM motor is of high
efficiency.
22
Review of Advanced Electric Machines
Fig. 2.8 Flux and MMF for three kinds of brushless machines.
Fig. 2.9 The theoretical variation of phase flux and MMF versus the rotor positions for different kinds of
brushless machines.
2.6 Summary
In this chapter, three major converter-fed machines: Switched Reluctance
Machines (SRM), Permanent Magnet Brushless Machine (PMBLAC and PMBLDC),
Doubly Salient Permanent magnet machines (DSPM), have been reviewed and
summarized. DSPM machines are compared with the SR and PMBL machines, the key
merits of DSPM are analyzed.
23
CHAPTER
3
PROPOSED TWO-PHASE DSPM MOTORS
3.1 Introduction
The DSPM motor incorporates the merits of both the PM brushless DC motor and
the switched reluctance (SR) motor. Firstly, the PMs are located in the stator so that the
possibility of irreversible demagnetization under high operating temperature can be
alleviated, and the problem of mechanical instability can be solved. Secondly, the rotor
is the same as that of the SR motor so that the advantages of simple configuration and
mechanical robustness can be retained. Thirdly, because of the nature of concentrated
windings, it can save the overhanging part, hence reducing both copper material and
copper loss. Moreover, it offers the flexibility of split-winding arrangement for fluxweakening operation.
It should be noted that there are prices that one needs to pay in order to realize the
merits of the DSPM motor over the PM brushless DC motor. First, the reduction of
motor torque density is the price to pay for putting the PMs in the stator since only half
of the PM flux produces EMF. Second, the converter cost will be increased if the DSPM
motor adopts a four-phase converter which needs more power devices than a
conventional three-phase inverter.
In this chapter, a new control approach is proposed to minimize torque ripples of
the DSPM motor. Namely, the torque ripple minimization of a four-phase DSPM motor
is performed by using a newly proposed two-phase operation. The basic structure and
operating principle of the four-phase DSPM motor will be described. Then the newly
24
Proposed Two-Phase DSPM Motors
proposed two-phase operation will be discussed. The simulation results, including both
four-phase and two-phase operations will be presented. The implementation and
experimental verification will be given.
3.2 Motor Configuration
3.2.1 Four-Phase DSPM Motor
Fig. 3.1(a) shows the configuration of the four-phase 8/6-pole DSPM motor which
has eight salient poles in the stator ( N s = 8 ), six salient poles in the rotor ( N r = 6 ) and
two pieces of PMs located in the stator. The structure is similar to a SR motor, but with
PMs placed in the stator and no PMs or windings in the rotor. The corresponding
theoretical waveforms of PM flux ψ pm and phase current is with respect to the rotor
position θ are shown in Fig. 3.1(b). Torque production can be achieved by applying a
positive current to the winding when its PM flux is increasing and a negative current
when the PM flux is decreasing.
The system matrix equation describing the four-phase 8/6-pole DSPM motor is
expressed as
V = RI +
dΨ
dt
(3.1)
where the matrix of the applied voltages is
 va 
v 
V =  b
 vc 
 
vd 
(3.2)
25
Chapter 3
(a)
(b)
Fig. 3.1 Four-phase 8/6-pole DSPM motor. (a) Configuration. (b) Operating waveforms.
26
Proposed Two-Phase DSPM Motors
The matrix of winding resistances is
 Ra
0
R =
0

0
0
Rb
0
0
0
0
Rc
0
0
0 
0

Rd 
(3.3)
The matrix of phase currents is
i a 
i 
I =  b
 ic 
 
id 
(3.4)
Ψ = L I + Ψpm
(3.5)
and
with the matrix of phase inductances
 Laa
M
L =  ba
 M ca

 M da
M ab
Lbb
M ac
M bc
M cb
M db
Lcc
M dc
M ad 
M bd 
M cd 

Ldd 
(3.6)
and the matrix of PM fluxes is
Ψ pm
 Ψ pma 
Ψ 
pmb 
=
 Ψ pmc 


Ψ pmd 
(3.7)
When both L and Ψpm are spatially dependent only and independent of the stator
current, it yields
27
Chapter 3
dΨpm
dΨpm
dΨ
dI dL
dI dL
=L
+
I+
=L
+
I ωr +
ωr
dt
dt dt
dt
dt dθ
dθ
(3.8)
where ωr = dθ dt is the rotor speed. Thus, the system equation given by (3.1) can be
rewritten as

dΨpm 

dI
dL 
= − L−1  R +
ωr  I + L−1 V −
ωr 
dt
d
θ
d
θ




(3.9)
The energy stored in the magnetic field W f can be expressed as
W f = W pm + Ww = W pm +
1 T
I LI
2
(3.10)
where W pm is the PM energy and Ww is the winding energy at I . By employing the coenergy method [62], the expression of the total torque T is obtained as
T=
∂ I T Ψ − Wf
(
)
∂θ
∂Ψ ∂W f
= IT
−
∂θ
∂θ
dΨpm 1 T ∂L
dW pm
= IT
+ I
I−
dθ
2 ∂θ
dθ
(3.11)
where I is the solution of (3.9) which is dependent on θ , (1 / 2) I T (∂L / ∂θ) I represents
the reluctance torque component due to the variation of inductances, I T (dΨpm / dθ) is
the PM torque component due to the interaction between the phase current and PM flux,
and dW pm / dθ is the cogging torque due to the variation of the PM energy with respect
to rotor position. Because of the rotor skewing adopted in this motor, the cogging torque
is insignificant and can be omitted. By neglecting the mutual inductances Lxy ( x ≠ y ) of
the motor, (3.11) can be decoupled among phases and the per-phase torque T ph can be
expressed as
28
Proposed Two-Phase DSPM Motors
dΨpm
1 dL
+ is
Tph = is2
2 dθ
dθ
= Tr + Tpm
(3.12)
where L is the self-inductance of each phase winding, Tr is the per-phase reluctance
torque component, and Tpm is the per-phase PM torque component.
The total torque of the DSPM motor can be expressed as the summation of an
average torque component Tav and a periodic torque component T p , namely
T = Tav + T p
(3.13)
where Tav is a constant, and T p is a function of time or position. Hence, the torque
ripple factor k r is defined as
kr =
Tmax − Tmin
× 100%
Tmax + Tmin
(3.14)
where Tmax is the maximum value of the total torque, and Tmin is the minimum value.
According to the operation principle of the DSPM motor, the phase winding
should be turned on or off at specific rotor positions. Hence, the rotor position
information is indispensable for proper operation of the DSPM motor. As shown in Fig.
3.2, the rotor positions are measured by a simple position sensor (PS), which consists of
a slotted disc connected to the rotor shaft and two opto-couplers mounted on the stator
housing. The two opto-couplers S p and S q are located 45° apart from each other along
the circumference of the disc. Because the machine is an 8/6-pole DSPM machine, one
cycle is 60° , according to the four-phase sequence, each phase has 15° phase shift, the
angle between the two opto-couplers Sp and Sq can be separated from each by
(k − 1 ) × 60 ° , in which k is an integer and m is the phase number. Therefore,
m
selecting k=1, they separated from each by 45° . The PS generates a signal edge for
29
Chapter 3
every 15° of mechanical rotation. The transitions of these outputs determine the
specific angles.
Fig. 3.2 Arrangement of position sensor.
3.2.2 Normal Four-Phase Operation
To supply the DSPM motor, a bipolar converter topology is preferred so as to
make bi-directional current operation possible. Thus, there are two converter topologies
in which the phase current can be controlled individually for bi-directional operation,
namely the full-bridge converter and the half-bridge converter with split capacitors. To
avoid voltage imbalance between those power switches in the upper and lower legs of
the converter, the full-bridge converter is adopted as shown in Fig. 3.3(a). The normal
control strategy for four-phase operation is based on chopping control. Fig. 3.3(b)
+
−
shows its typical current waveform. Control angles, namely θon
, θ+off , θon
and θ−off , are
fixed, while the torque control is achieved by changing the current reference. The
corresponding control logic of those power switches is based on the PS feedback signals
as tabulated in the Table 3-1.
30
Proposed Two-Phase DSPM Motors
(a)
(b)
Fig. 3.3 Normal Four-phase operation. (a) System configuration. (b) Controlled current waveform.
Table 3-1 Control logic for four-phase operation
31
Chapter 3
3.3 Proposed Two-Phase Operation
By further reviewing the characteristics and the control logic of the four-phase
8/6-pole DSPM motor drive, it reveals that there is a possibility of the DSPM motor
working as a two-phase motor drive. It can be found that the four PM flux linkages are
lagging each other by 90° . Hence, the back EMF of phase C is of opposite phase to that
of phase A, and the EMF of phase D is of opposite phase to that of phase B. Therefore,
the windings A and C as well as the windings B and D can be reversely connected in
series, respectively, constituting the windings X and Y as depicted in Fig. 3.4(a).
(a)
(b)
Fig. 3.4 Proposed two-phase operation. (a) System configuration. (b) Controlled current waveform.
32
Proposed Two-Phase DSPM Motors
Moreover, the corresponding rotor teeth are purposely skewed by 21° to offer
sinusoidal back EMFs, and the phase current is controlled to synchronize with the phase
back EMF in order to minimize the torque ripple. This value is the simulation result
aiming to make dL sk dθ and dψ sk dθ nearly sinusoidal as shown in Fig. 3.5 and Fig.
3.6, where Lsk and ψ sk are the phase inductance and flux linkage under rotor skewing,
respectively. The ψ sk can be expressed as
1 θ + 2δ
ψ sk = ∫ δ ψ pm (θ)dθ
δ θ− 2
(3.15)
where θ is the rotor angular position. δ is the rotor skewing angle, ψ pm (θ) is the flux
linkage without rotor skewing.
d
sk
d (Wb/rad)
Fig. 3.5 Variation of motor parameters dL sk dθ with the rotor skewing.
Fig. 3.6 Variation of motor parameters dψ sk dθ with the rotor skewing.
33
Chapter 3
And
dψ sk 1 
δ
δ 
= ψ pm (θ + ) − ψ pm (θ − ) 
dθ
δ
2
2 
(3.16)
The Lsk can be expressed as
1 θ+ δ2
Lsk = ∫ δ L(θ)dθ
δ θ− 2
(3.17)
dLsk 1 
δ
δ 
=  L (θ + ) − L (θ − ) 
dθ δ 
2
2 
(3.18)
and
As shown in Fig. 3.4(b), rather than using rectangular current control, the
proposed two-phase operation newly adopts sinusoidal hysteresis current control. The
control angles are generally fixed, while the torque control is achieved by changing the
current reference. For the proposed two-phase 8/6-pole DSPM motor drive, the control
logic can be deduced from the relationship between the position signals and PM flux
linkages as listed in Table 3-2.
Table 3-2 Control logic for 2-phase operation
By using the finite element analysis (FEA), both the self-inductances and PM flux
linkages with respect to the rotor position can be simulated. For two-phase operation,
the corresponding self-inductances Lx and L y are equal to ( Laa + Lcc ) and ( Lbb + Ldd ),
respectively. As shown in Fig. 3.7(a), the calculated Laa and Lcc (solid curves) are very
sinusoidal (dashed curves). Thus, they can be approximately as
34
Proposed Two-Phase DSPM Motors
(a)
(b)
(c)
Fig. 3.7 Calculated waveforms during 2-phase operation. (a)Self-inductances. (b) PM flux linkages. (c)
Back EMF at 600 rpm.
35
Chapter 3
Laa = L0 − Lm cos( N r θ)
Lcc = L0 − Lm cos( N r θ − π)
(3.19)
= L0 + Lm cos( N r θ)
where N r is the number of poles of rotor, L0 is the average value, and Lm is the
maximum value of the sinusoidal variation. Consequently, Lx can be approximately as
Lx = Laa + Lcc = 2 L0
(3.20)
Therefore, the inductances at two-phase operation are constant. Based on (3.12),
the corresponding reluctance torque components are zero. Fig. 3.7(b) shows the
simulated ψ pma , ψ pmb and ψ pmx (solid curves). As expected, they are very sinusoidal
(dashed curves). By differentiating ψ pmx , the simulated back EMF at 600 rpm is shown
in Fig. 3.7(c) which is also very sinusoidal. Thus, it can be expressed as
ex = Em sin( N r θ)
(3.21)
where Em is its maximum value. Since e y lags behind ex by π 2 , it can be expressed
as
π

e y = Em sin  N r θ − 
2

(3.22)
When the sinusoidal currents are properly applied to interact with the sinusoidal
back EMFs, the PM torque components can be obtained as
Tpmx =
Tpmy =
ex ix Em I m
=
sin(N r θ) sin(N r θ − β)
ωr
ωr
eyiy
=
ωr
Em I m
π
π
sin(Nr θ − ) sin(Nr θ − − β)
ωr
2
2
(3.23)
(3.24)
where I m is the maximum value of phase currents, and β is the phase shifting angle
between the back EMF and current. Although a DSPM motor generally incorporates the
36
Proposed Two-Phase DSPM Motors
reluctance torque component, the proposed motor does not include this component since
the corresponding self-inductances no longer have spatial variations.
Since the reluctance torque components are zero, the total torque is given by
T = Tpmx + Tpmy =
Em I m
cos β = Tm cos β
ωr
(3.25)
where Tm = Em I m ωr is the maximum value. When β is purposely set to zero, T is
maximized as a constant value at steady state. To set β to zero experimentally, the first
step is to run the machine as a generator, then adjust the position sensor to synchronize
the position signal with the no-load EMF; the second step is to control the current
synchronizing with the position signal, thus the EMF is synchronize with the current,
therefore β is zero. From (3.25), it can be found that the total torque is independent of
the rotor position. Hence, theoretically, the torque ripples are absent in the proposed
two-phase operation.
Practically, without assuming the sinusoidal variations of both Laa and Lcc , Lx is
no longer a constant value. As shown in Fig. 3.7(a), Lx should be formulated as
Lx = Laa + Lcc
π
1
1

= ( Lx max + Lx min ) + ( Lx max − Lx min ) sin  2 N r θ − 
2
2
2

(3.26)
where Lx max is its maximum value, and Lx min is its minimum value. Notice that the
frequency of variation of Lx is double that of Laa and Lcc . Since L y (θ) = Lx (θ − π 2) ,
Ly is given by
L y = Lbb + Ldd

1
1
π π

= ( Lx max + Lx min ) + ( Lx max − Lx min ) sin  2 N r  θ −  − 
2
2
2 2


(3.27)
37
Chapter 3
Substituting i x = I m sin( N r θ) and i y = I m sin( N r θ − π 2) as well as (3.23) and (3.24) into
(3.12), it yields
T = Trx + Try + Tpmx + Tpmy
=

1 2 2
dL 1
π  dL
π  (3.28)


I m sin ( N r θ) x + I m2 sin 2  N r θ −  y + Tm sin 2 ( N r θ) + sin 2  N r θ − 
2
dθ 2
2  dθ
2 



By substituting (3.26) and (3.27) into (3.28) and setting N r = 6 , the total torque can be
written as
T = Tm +
3 2
I m ∆Lx sin(24θ)
2
(3.29)
where ∆Lx = Lx max − Lx min . It indicates that the total torque varies with the rotor position,
and changes with the frequency four times that of the current. Moreover, by substituting
Tav = Tm = Em I m ωr , Tmax = Tm + (3 2) I m2 ∆Lx and Tmin = Tm − (3 2) I m2 ∆Lx into (3.14), the
torque ripple at the proposed two-phase operation can be analytically derived as
kr =
3I m ∆Lxωr
× 100%
2 Em
(3.30)
It can be found that the torque ripple at steady-state mainly depends on the amplitude of
phase current and the variation of Lx .
It should be noted that the proposed two-phase operation has its disadvantage.
Due to the use of rotor skewing for sinusoidal hysteresis current control, the output
power of the proposed motor is inevitably lower than that of the conventional fourphase operation using unskewed rotor and rectangular current control. Under the same
rms current and flux in the air-gap, it is nearly 10% lower than that on four-phase
operation.
On the other hand, if the four-phase operation also adopts rotor skewing and
sinusoidal current control, the total torque and the associated torque ripple will be
38
Proposed Two-Phase DSPM Motors
similar to that of the proposed two-phase operation. Nevertheless, the two-phase
operation still takes the definite advantages of simpler converter circuitry, lower driving
requirement and lesser current sensors, hence attaining lower cost and higher efficiency.
3.4 Simulation Results
Based on the static characteristics, such as self-inductances, PM flux linkages and
back EMFs shown in Fig. 3.7, obtained from FEA, the motor performances are
simulated using Matlab/Simulink. The use of Matlab/Simulink environment takes the
advantages of easy programming, high flexibility and plentiful toolboxes. The
corresponding power system block is particularly convenient for the simulation of SR
motors and hence DSPM motors [63].
By using Matlab/Simulink simulation, the waveforms of phase current and total
torque of the DSPM motor under four-phase operation are simulated. Fig. 3.8 shows
these waveforms at the rated load of 4.70 Nm. It can be found that the simulated current
waveform shown in Fig. 3.8(a) agrees with the theoretical one shown in Fig. 3.3(b).
Also, from Fig. 3.8(b), it can be observed that the simulated torque waveform swings
between 3.4 Nm and 5.8 Nm. By substituting Tmax =5.8 Nm and Tmin =3.4 Nm into
(3.14), it yields K r =26.1%.
Figure 3.9 shows the simulated average torque and torque ripple factor at the rated
current versus the rotor skewing angle. It can be seen that the rotor skewing angle of
21° is an optimal compromise between the average torque and the torque ripple factor.
Also, Figure 3.10 shows the simulated average torque and torque ripple factor at the
rated current versus the phase shifting angle between the back EMF and current. It can
39
Chapter 3
be seen that 0° is the best choice, which agrees with the theoretical derivation.
Similarly, Fig. 3.11 shows the simulated waveforms of phase current and total
torque of the DSPM motor under the proposed two-phase operation. As expected, the
simulated current waveform shown in Fig. 3.11(a) agrees with the theoretical one
shown in Fig. 3.4(b). Also, Fig. 3.11(b) shows that the simulated torque waveform
(a)
(b)
Fig. 3.8 Simulated waveforms at rated load during four-phase operation. (a)Phase current. (b) Total
torque.
40
Proposed Two-Phase DSPM Motors
swings between 4.1 Nm and 5.2 Nm under the rated load of 4.70 Nm. By substituting
Tmax =5.2 Nm and Tmin =4.1 Nm into (3.14), it results K r =11.8% which is 14.3% lower
than that under four-phase operation. Therefore, the proposed two-phase operation can
significantly reduce the torque ripple occurred at four-phase.
Fig. 3.9 Influence of rotor skewing angle.
Fig. 3.10 Influence of phase shifting angle.
41
Chapter 3
(a)
(b)
Fig. 3.11 Simulated waveforms at rated load during two-phase operation. (a)Phase current. (b) Total
torque.
42
Proposed Two-Phase DSPM Motors
3.5 Experimental Results
An 8/6-pole DSPM motor prototype, with the ratings of 750 W and 600 rpm, is
designed and built for verification. An IGBT based inverter and a microcontroller-based
controller are also implemented to drive the motor. In order to directly measure the
torque ripple, a transient torque transducer is mounted between the motor and the
dynamometer. The stator current is also measured by a Hall effect-current transducer.
Fig. 3.12(a) shows the measured two-phase no-load EMF waveform at 600 rpm
and Fig. 3.12(b) shows the measured phase current of two-phase operation under rated
load. It can be found that they closely agree with the simulated waveform shown in Fig.
3.7(c) and Fig. 3.11(a), respectively. Furthermore, both the phase current and total
torque are measured at the rated load of 4.70 Nm. Fig. 3.13 shows these waveforms
during the traditional four-phase operation and the proposed two-phase operation. It is
obvious that the measured current waveforms shown in Fig. 3.13(a) and Fig. 3.13(b)
closely agree with the simulated current waveforms shown in Fig. 3.8(a) and Fig.
3.11(a), respectively. Also, it can be found that the torque ripples obtained from the
measured torque waveforms are K r =40% during the four-phase operation and K r =26%
during the two-phase operation. It verifies that a significant reduction in the torque
ripple by 14% can be achieved.
It should be noted that the measured torque waveforms are more irregular and
hence the torque ripples are larger than the theoretical ones. This discrepancy is due to
the fact that the simulated torque waveforms in Fig. 3.8(b) and Fig. 3.11(b) take into
account the operating torque ripple only, whereas the measured torque waveforms in
Fig. 3.13(a) and Fig. 3.13(b) consist of all kinds of torque ripples, namely the operating,
43
Chapter 3
(a)
(b)
Fig. 3.12 Measured two-phase waveforms. (a) No-load EMF at 600 rpm (50 V/div, 5 ms/div). (b) Phase
current under rated load (1.65 A/div, 5 ms/div).
practical and manufacturing torque ripples. The practical torque ripple is due to the
system non-idealities such as the cogging effect, while the manufacturing torque ripple
is due to the manufacturing imperfections such as the asymmetry among different
phases. Nevertheless, these practical and manufacturing torque ripples can be roughly
44
Proposed Two-Phase DSPM Motors
(a)
(b)
Fig. 3.13 Measured current and torque waveforms at rated load. (a) 4-phase operation (3.3 A/div, 2.3
Nm/div, 25ms/div). (b) 2-phase operation (3.3 A/div, 2.3 Nm/div, 25 ms/div).
considered as a constant value at a given operating point. By comparing the simulated
K r =26.1% with the measured K r =40% during the four-phase operation, there is a
difference of 13.9% which can be considered as the contributions from both the
practical and manufacturing torque ripples at the rated condition. After subtracting this
45
Chapter 3
13.9% from the measured K r =26% during two-phase operation, the resulting K r of
12.1% (contributed from the operating torque ripple) closely agrees with the simulated
K r =11.8%.
It is interesting to note that the machine imperfection can be inferred from the
EMF waveforms, namely the shape and unequal maxima, as shown in Fig. 3.12.
Detailed analysis of this machine imperfection will be the substance for future research.
Moreover, as depicted in both Fig. 3.11 and Fig. 3.13, the pattern of torque ripples can
be deduced from the reluctance torque first harmonic which is the same as the cogging
torque harmonic.
3.6 Summary
In this chapter, a two-phase operation mode has been newly proposed for DSPM
motors. This two-phase operation can significantly minimize the operating torque ripple
of a four-phase 8/6-pole DSPM motor. The keys are to operate the four-phase windings
as two-phase windings, and to adopt sinusoidal hysteresis current control rather than
rectangular current control. Both computer simulation and experimental results have
confirmed that the operating torque ripple at the rated load can be reduced by about 14%.
46
CHAPTER
4
PROPOSED
THREE-PHASE
DSPM
WIND
POWER
GENERATORS
4.1 Introduction
With ever increasing concerns on energy crisis and environmental protection, the
development of renewable energy resources has taken on an accelerated pace. Wind
power is one of the most viable renewable energy resources. For wind power generation,
the core element is the wind power generator. The conventional generators, such as the
synchronous generator and induction generator, are mainly designed for constant-speed
turbine operation such that they are inefficient or even ill-suited for variable-speed wind
turbine operation. Therefore, an efficient generator particularly for wind power
generation is highly desirable. In [64], the switched reluctance (SR) machine was
proposed for wind power generation because of its advantages of brushless nature, high
robustness and high reliability. In [65], the doubly salient permanent magnet (DSPM)
machine, incorporating the structure of SR machines and the use of PM materials, was
proposed to work as a single-phase generator. Recently, it has been revealed that the
poly-phase DSPM machine can offer higher efficiency, higher power density and better
controllability than its counterparts, including the induction and SR machines [57], [66].
Moreover, compared to induction and SR generators, the DSPM generator can
produce more power from the same geometry, and can offer higher efficiency. By using
sizing equation, it is shown that the DSPM generator has 40% more power production
capability than an induction generator based on the same speed, volume and electric
47
Chapter 4
loading. Furthermore, because of the absence of PM materials in the rotor, the DSPM
generator takes the advantages of higher robustness and higher reliability than other PM
brushless generators [67−70].
In this chapter, a new three-phase 12/8-pole DSPM machine is particularly
proposed for wind power generation. The key is to design a new machine structure, and
to devise the system operation. The system configuration and speed constraint of a 12/8pole DSPM wind generator will be described. The machine design, including the
topological selection and electromagnetic analysis will also be presented. The finite
element method (FEM) is applied to analyze the static characteristics of the generator.
The system modeling and simulation will be discussed. Furthermore, the
implementation and experimental verification will be given to testify the theoretical
analysis.
4.2 Proposed Design and Analysis
4.2.1 System Configuration and Speed Constraint
Fig. 4.1 shows the system configuration, which consists of a wind turbine for
capturing wind power, a three-phase DSPM generator for electromechanical energy
conversion, a three-phase full-bridge rectifier for ac-dc conversion, a buck converter for
dc voltage regulation, a battery for electrical energy storage, and a single-phase or threephase inverter for dc-ac conversion.
48
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.1 System configuration.
The rated speed of the DSPM generator, which dictates the whole size of the
generator, can be determined by the wind energy equation developed by a wind turbine.
The net electrical energy produced by a wind turbine system depends on the speed of
the wind passing through its swept area and the efficiencies of its components. In [26],
for a horizontal-axis wind turbine, the actual mechanical output power Pmech is typically
expressed as
Pmech =
1
C p ρν w3 A
2
(4.1)
where C p is the coefficient of wind power with a typical value of 0.4 or below, ρ is the
air density, νw is the wind velocity and A is the swept area of wind turbine rotor. The
value of C p varies with β , the ratio of the wind turbine’s blade tip speed to the wind
speed
β=
ωR
νw
(4.2)
where R is the radius of blades and ω is the angular speed of the wind turbine shaft.
When β takes the specific value β max , the characteristic of C p has a single maximum
[71]. It is obvious that the shaft speed should change with the wind speed to extract
49
Chapter 4
maximum power from the wind. When the turbine is running at β max , the output power
can be expressed as
Pmech =
1
(C p max πR 2 ρ ) ν 3w
2
(4.3)
The item (C p max πR 2 ρ ) is a constant with a given wind turbine. Thus, the output power
varies with the cubic wind speed, and Pmech can be rewritten as
Pmech
5
1  C p max πR ρ  3
=
ω

2  β 3max

(4.4)
It should be noted that the rotor speed of a small variable-speed direct-drive wind
generator is typically below 1000 rpm.
4.2.2 Topological Selection of Machine Design
There is a wide range of possible combinations of phase number as well as stator
and rotor pole numbers that can be chosen for DSPM generator design. In accordance
with the basic operation principle of the DSPM generator, the general relationship
among N s , N r , and m are given by
 N s = 2mk

 N r = N s ± 2k
(4.5)
where N s and N r are the number of stator and rotor poles, respectively, m is the
number of phases, and k is a positive integer. When the generator runs at the speed n ,
the frequency of no-load EMF is given by
f =
50
Nrn
60
(4.6)
Proposed Three-Phase DSPM Wind Power Generators
To minimize the iron losses in poles and yokes, the number of rotor poles is
usually less than that of stator poles. For example, N s N r =8/6 and 12/8 are possible
configurations of the DSPM generator. Comparing these two types of machines which
run at the same speed, the 12/8-pole machine has the advantages over the 8/6-pole one,
namely smaller number of phases, higher power density, and simpler system
configuration and control.
The DSPM generator is the key of this wind power generating system. Fig. 4.2
shows the cross-section of the proposed three-phase 12/8-pole DSPM generator. It has
twelve salient poles in the stator and eight salient poles in the rotor. There are 4 pieces
of PM material, namely the neodymium-iron-boron (Nd-Fe-B) with a linear
demagnetizing characteristic, placed inside the stator yoke to provide field excitation.
The two coils on the diametrically opposite stator poles are connected in series to form a
winding, and the two relevant windings are also connected in series to form a phase
winding in the stator. Since there are no PMs, no brushes and no windings in the rotor,
it offers simple rotor structure and low rotor inertia.
Fig. 4.2 Three-phase 12/8-pole DSPM generator.
51
Chapter 4
There are two types of rotor for selection: one is the unskewed rotor which
produces square waves of no-load EMF and current, and the other is the skewed rotor
which produces sinusoidal waves of no-load EMF and current. The one offering a
higher power density will be selected for this DSPM generator.
For a machine with sinusoidal waveforms, when its no-load EMF es and phase
current is are in phase, the average power Ps of the machine can be expressed as
Ps =
1 π
1
es (ωt) is (ωt)dωt = Em I m
∫
0
π
2
(4.7)
where Em and I m are the amplitudes of the no-load EMF and current, respectively.
For a machine with trapezoidal waveforms as shown in Fig. 4.3, its no-load EMF
et and phase current it can be expressed as
0
 Etm
( ωt - α 1 )

 k1π
et =  Etm
 − Etm
 k π (ωt - α 2 )
 1
0
(0 ≤ ωt < α1 )
(α1 ≤ ωt < α1 + k1π)
(α1 + k1π ≤ ωt < α1 + (k1 + k 2 )π)
(α1 + (k1 + k 2 )π ≤ ωt < α 2 )
(α 2 ≤ ωt < π)
(4.8)
0
 I tm
( ωt - α 1 )

kπ
 1
it =  I tm
 − I tm
 k π ( ωt - α 2 )
 1
0
(0 ≤ ωt < α1 )
(α1 ≤ ωt < α1 + k1π)
(α1 + k1π ≤ ωt < α1 + (k1 + k 2 )π)
(α1 + (k1 + k 2 )π ≤ ωt < α 2 )
(α 2 ≤ ωt < π)
(4.9)
When et and it are in phase, the average power Pt of this machine is given by
Pt =
52
1 π
1
et (ωt) it (ωt)dωt = (2k1 + 3k 2 ) Etm I tm
∫
0
π
3
(4.10)
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.3 Trapezoidal waveform.
By using (4.7) and (4.10), the power ratio of the sinusoidal to trapezoidal DSPM
generators can be obtained as
  Em I m 
Ps 
3


= 
Pt  4k1 + 6k 2   Etm I tm 
(4.11)
The RMS value of phase current with trapezoidal waveform can be expressed as
I
1 π2
it dωt = tm
∫
0
π
3
It =
6k1 + 3k 2
(4.12)
On the other hand, the RMS value of phase current with sinusoidal waveform is given
by I s = I m
2 . Since I t = I s , the current ratio of the sinusoidal to trapezoidal
waveforms can be obtained as
Im 1
=
12k1 + 6k 2
I tm 3
(4.13)
Similarly, the corresponding air-gap fluxes can be represented by the averaged no-load
EMFs
 π E sin ωtdωt = 2 E
m
 ∫0 m
 π
∫0 et dωt = (k1 + k 2 )πEtm
(4.14)
53
Chapter 4
Hence, the EMF ratio of the sinusoidal to trapezoidal waveforms can be obtained as
Em π
= (k1 + k 2 )
Etm 2
(4.15)
Substituting (4.13) and (4.15) into (4.11), the power ratio can be rewritten as
Ps (k1 + k 2 )π
3
=
Pt
2
4k1 + 6k 2
(4.16)
By taking k1 = 0 , k 2 = 2 3 , α1 = π 6 and α 2 = 5π 6 , the trapezoidal wave
becomes a square wave with a conduction angle of 120° . Table 4-1 compares the power
ratios between the square wave and sinusoidal wave DSPM generators. It can be found
that the square wave generator can produce more power output (namely, additional
10.3%) than the sinusoidal one. Therefore, the unskewed rotor is selected for this wind
generator.
Table 4-1 Power Ratio of Sinusoidal to Square Wave Generators
54
Proposed Three-Phase DSPM Wind Power Generators
4.2.3 Electromagnetic Analysis
By using the FEM, the static characteristics of the proposed DSPM generator are
analyzed. For simplicity, the two-dimensional FEM is adopted. The corresponding
nonlinear partial differential equation is expressed as
∂  ∂Az  ∂  ∂Az
ν
 + ν
∂x  ∂x  ∂y  ∂y

 = −(J z + J pm )

(4.17)
where Az and J z are the z components of vector magnetic potential A and current
density J , respectively, J pm is the equivalent surface current density of PMs, and ν is
the reluctivity. Both the nonlinear characteristics of the iron core and PMs are taken into
account.
The magnetic field distributions of the proposed 12/8-pole DSPM generator under
no-load and full load are shown in Fig. 4.4. It can be seen that the no-load flux
distribution is mainly symmetric with only a minor distortion due to the slot effect. It
can also be found that the flux is mainly concentrated at the overlapping area of the
stator and rotor teeth, and the leakage flux between the PM poles is negligibly small.
Armature reaction does exist because of the bucking feature of the winding currents
with respect to the field created by the PMs. Consequently, it causes voltage drop in the
machine terminal. For the proposed DSPM generator, the armature inductances are low.
The corresponding armature reaction causes only a slight voltage drop. Actually, the
major voltage drop is due to the armature resistance.
Similarly, by using the FEM, the flux linkages and inductances of the proposed
12/8-pole DSPM generator can be obtained. Fig. 4.5 shows the PM flux linkage with
respect to the rotor angle, while Fig. 4.6(a) shows the self-inductance characteristics
with respect to both the armature current and rotor angle.
55
Chapter 4
(a)
(b)
Fig. 4.4 Magnetic field distributions using FEM. (a) No-load. (b) Full load.
Furthermore, the mutual inductance characteristics are shown in Fig. 4.6(b), where
“PM−2A” and “PM+2A” denote the weakening and strengthening actions of the
armature flux with a phase current of 2 A to the PM flux, respectively. It can be found
that the mutual inductance depends not only on the rotor position, but also on the
interaction between the PM flux and the armature flux. When the armature flux
strengthens the PM flux, namely flux strengthening, the corresponding magnitude of the
mutual inductance is smaller than that under flux weakening. It is due to the effect of
magnetic saturation.
56
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.5 PM flux linkage using FEM.
(a)
(b)
Fig. 4.6 Inductance characteristics using FEM. (a) Mutual inductance. (b) Self-inductance.
57
Chapter 4
4.3 System Operation − Modeling
Based on the flux linkages and inductances derived from using the FEM, the
induced EMF e can be calculated by
e=
dψ
= u + Ri
dt
(4.18)
where ψ is the flux linkage, u is the terminal voltage, R is the phase resistance and i is
the phase current. When the current flows from the stator winding to the external load,
the flux linkage ψ is expressed as
(4.19)
ψ = ψ pm − Li
where ψ pm is the PM induced flux linkage, and Li is the flux linkage due to armature
reaction.
Therefore, the three-phase terminal voltages are given by
 dψ pma  
dLaa

  Ra +
dt
dt
v a  
 
v  =  dψ pmb  −  dM ba
 b   dt  
dt
v c   dψ   dM
pmc
ca

 
dt
 dt  
 Laa
−  M ba
 M ca
M ab
Lbb
M cb
dM ab
dt
dL
Rb + bb
dt
dM cb
dt
dM ac 

dt
i a 
dM bc   
 ib
dt
 
dLcc  ic 
Rc +
dt 
 di a 


M ac   dθ a 
di
M bc   b  ω r
 dθ 
Lcc   di b 
 c 
 dθ c 
(4.20)
where u a , u b , u c are the phase voltages, ψ pma , ψ pmb , ψ pmc are the PM flux linkages,
Ra , Rb , Rc are the resistances, Laa , Lbb , Lcc are the self-inductances, M ab , M ac , M ba ,
M bc , M ca , M cb are the mutual inductances, i a , ib , ic are the phase currents, θ a , θ b ,
58
Proposed Three-Phase DSPM Wind Power Generators
θ c are the rotor positions, and ω r is the rotor angular velocity. The rotor positions are
related by
θ b = θ a − α

θ c = θ a − 2α
(4.21)
where α is the position difference between phases as given by:
α=
θr
= 15 °
m
(4.22)
where θ r is the rotor pole pitch. Moreover, the relationships of various variables among
phases are given by
ψ a (θ a ) = ψ b (θ b ) = ψ c (θ c )

i a (θ a ) = ib (θ b ) = ic (θ c )
v (θ ) = v (θ ) = v (θ )
b
b
c
c
 a a
(4.23)
4.4 System Simulation
Making use of the aforementioned system model, computer simulation is conducted
to assess the performance of the DSPM generator. The Matlab/Simulink environment is
adopted, since it takes the advantages of easy programming, high flexibility and
powerful toolboxes. The corresponding power system block toolbox is particularly
useful for simulation of electric machines such as the SR motor and DSPM motor [63].
The no-load EMF at the rated speed of 750 rpm is simulated as shown in Fig. 4.7.
Consequently, the line voltage, line current and DC output voltage under full load at the
rated speed of 750 rpm are simulated as shown in Fig. 4.8, Fig. 4.9 and Fig. 4.10,
respectively.
59
Chapter 4
Fig. 4.7 Simulated no-load EMF waveform.
Fig. 4.8 Simulated line voltage waveform.
Fig. 4.9 Simulated line current waveform.
60
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.10 Simulated DC output voltage waveform.
4.5 Experimental Verification
For exemplification, a low-power experimental setup is established. The proposed
DSPM generator is prototyped, which confirms its high power density and robustness.
The corresponding key data are listed in Table 4-2. The natural wind characteristics are
emulated by real-time controlling a programmable DC dynamometer. Fig. 4.11 shows
the measured no-load EMF waveform of the proposed generator operating at the rated
speed of 750 rpm. Fig. 4.12 shows the measured line voltage and current waveforms
under full load at the rated speed. Fig. 4.13 also shows the measured DC output voltage
waveform under full load at the rated speed. Comparing these experimental results with
the simulated ones from Fig. 4.7 ~ Fig. 4.10 in frequency, amplitude, the tendency of
variation. As expected, these measured waveforms closely agree with the simulation
waveforms.
Through the three-phase rectifier, the variable output voltage of the 12/8-pole
DSPM generator is rectified to a variable DC voltage. Thus, a buck converter is
61
Chapter 4
Table 4-2 Data of Prototype
employed to regulate the DC-link voltage of the inverter. Considering the battery
system voltage of 28 V as the threshold voltage of the DC-link, the wind power
generation directly supplies the inverter and charges the battery when the speed is over
330 rpm. Otherwise, the battery supplies the inverter to produce the desired AC output.
Moreover, Fig. 4.14 shows the measured voltage and current waveforms of the inverter
AC output with the generator operating at the rated speed of 750 rpm and a resistive
load of 250 Ω.
A series of no-load tests are conducted at various rotor speeds. The measured
output line voltage is compared with the simulated one as shown in Fig. 4.15. It can be
seen that they have a good agreement. Also, the measured output voltage is almost
linearly proportional to the rotor speed. Furthermore, the voltage regulations of the
whole system at different load currents and different rotor speeds are assessed as shown
in Fig. 4.16. It is obvious that the simulated and measured results have a good
agreement.
Finally, the system efficiencies at different load currents and rotor speeds are
measured as shown in Fig. 4.17. It can be found that the efficiency can maintain at high
values over a wide range of load currents. Particularly, the efficiency under the full load
of 3 A at the rated speed of 750 rpm is over 82%.
62
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.11 Measured no-load EMF waveform (20 V/div, 1 ms/div).
Fig. 4.12 Measured line voltage and current waveform (50 V/div, 2 A/div, 5 ms /div).
63
Chapter 4
Fig. 4.13 Measured DC output voltage waveform (20 V/div, 5 ms/div).
Fig. 4.14 Measured inverter output voltage and current waveforms (100 V/div, 2 A/div, 5 ms/div).
64
Proposed Three-Phase DSPM Wind Power Generators
Fig. 4.15 Simulated and measured no-load line voltages.
Fig. 4.16 Simulated and measured output voltage regulations.
Fig. 4.17 Measured efficiencies.
65
Chapter 4
4.6 Summary
In this chapter, the design, analysis and implementation of a new three-phase
12/8-pole DSPM generator have been presented. This DSPM generator possesses a new
machine structure which can offer high power density, high robustness and low
manufacturing lost. Also, the proposed generator system can allow for high efficiency
operation over wide ranges of load current and rotor speed. Both computer simulation
and experimental results confirm the validity of the proposed DSPM machine for wind
power generation.
66
CHAPTER
5
PROPOSED
BDFDS
MACHINES
–
DESIGN
AND
ANALYSIS
5.1 Introduction
The objectives of this chapter are to present the design details of the BDFDS
machines, to give equations to make initial calculation of machine dimensions and
parameters. A three-phase 12/8 pole BDFDS machine will be used for exemplification.
By using the finite element method, the static characteristics of the BDFDS machines
will be deduced, including the magnetic field distributions and the flux density
distributions in the air-gap. Moreover, the machine characteristics including the flux
linkage, self-inductance, mutual inductance and no-load EMF will be analyzed.
5.2 Proposed Design Philosophy
5.2.1 Selection of Number of Phases and Poles
The number of phases and poles is usually determined at first in the design of
machines. To make the motor capable of starting by itself in either forward or reverse
direction, the number of phases should be more than or equal to three, from the basic
principles of the BDFDS machines, a higher number of phases are preferable, because it
improves not only the power density but also the torque smoothness of the motor and
system reliability. However, a bigger phase number requires a corresponding number of
converter phase units, their drivers, logic power supplies, and control units.
67
Chapter 5
All these are likely to increase the packaging size and the cost and therefore have to be
considered simultaneously with the design of machine. Thus, three-phase is a preferred
trade off between the performance and the cost for BDFDS machines.
There is a wide range of possible combinations of phase windings, stator and rotor
pole numbers that can be chosen for the design of BDFDS machines. In accordance
with the basic operation principle of the BDFDS machines, the general relationships
among stator pole number N s , rotor pole number N r and phase number m are given by
 N s = 2mk

 N r = N s ± 2k
(5.1)
where k is a positive integer. When the machine runs at the speed of n, the commutating
frequency of any phase is f ph = N r n 60 . To minimize the switching frequency and
hence the loss in power switches as well as the iron losses in poles and yokes, and to
reduce the cost of machine production, the number of rotor poles should be selected as
small as possible. Therefore, the number of rotor poles is usually less than that of stator
poles. Moreover, the number of stator poles should be even times of the phases. Thus,
N s N r = 6 / 4 and 12/8 are possible configurations of the BDFDS machines. As
compared to the three-phase 6/4-pole one, the three-phase 12/8-pole BDFDS machines
is preferable for its shorter flux paths in yoke resulting in less magnetic potential drop
and iron losses. Moreover, because the flux per magnetic pole is halved in the 12/8-pole
machine, the width of both stator yoke and teeth is almost one-half of those of a 6/4pole machine. This allows greater inner stator diameter and hence greater rotor diameter.
Therefore, higher torque density can be achieved. Furthermore, a narrow stator teeth
results in shorter end part of phase windings, leading to less copper consumption and
68
Proposed BDFDS Machines − Design and Analysis
resistance of windings. Hence, higher efficiency can be expected for the 12/8-pole
BDFDS machines.
5.2.2 Sizing Equation
The sizing equations relate the bore diameter, length, speed, magnetic and electric
loading to the output power of the machine. The general purpose sizing equations have
been developed in [72−73]. In general, when the stator leakage inductance and
resistance are neglected, the output power for any electrical machine can be expressed
as
Po = η
m T
e(t )i (t )dt = ηmk p E max I max
T ∫0
(5.2)
where Po is the rated output power, e(t ) and Emax are the phase back EMF and its
maximum, i(t ) and I max are the phase current and its maximum, η is the efficiency of
machine, m is the phase number, and T is the period of one cycle of the back EMF. The
coefficient k p is termed as a electrical power waveform factor and defined as
kp =
1 T e(t )i (t )
1 T
dt = ∫ f e (t ) f i (t )dt
∫
0
T
E max I max
T 0
(5.3)
where f e (t ) = e(t ) Emax and f i (t ) = i (t ) I max are the expressions of normalized back
EMF and current waveforms. The maximum of phase back EMF Emax and e(t ) are
given
Emax = ke NBδ max Di leff
f
p
(5.4)
and
69
Chapter 5
e(t ) =
dψ
f
= Emax f e (t ) = ke NBδ max Dileff
f e (t )
dt
p
(5.5)
where k e is the EMF factor, f e (t ) is the time-variation of back EMF, N is the number
of turns per phase winding, Bδ max is the maximum flux density in the air gap, Di is the
stator inner diameter, leff is the effective stack length, f is the converter frequency, p
is the pole pairs of machine, and ψ is the flux linkage per phase.
To reflect the effect of current waveform, a current waveform factor ki is defined
as
ki =
I max
=
I rms
I max
1 T 2
i (t )dt
T ∫0
(5.6)
where I rms is the rms value of phase current which is related to the electrical loading A,
wherein
I rms
πDi
(5.7)
ki AπDi
2mN
(5.8)
A = 2mN
Then
I max =
Combining (5.2), (5.4) and (5.8), the sizing equation can be expressed as
Po =
π
2
ηke ki k p Bδ max A
f 2
Di leff
p
(5.9)
The trapezoidal waveforms in Table 5-1 are good approximation with the BDFDS
machine, which gives ki =1.389, k p =0.519 and ke = π . From (5.9), the following sizing
equation for BDFDS machines is obtained.
Po = 0.36π 2ηBδ max A
70
f 2
Di leff
p
(5.10)
Proposed BDFDS Machines − Design and Analysis
In most radial air-gap flux machines, the aspect ratio coefficient
leff
λ=
(5.11)
Di
should be chosen based on actual requirement of application, such as 0.25 ~ 1.5. Further
more, the sizing equation can be rewritten as
Po
Di3 =
0.36π 2 ηBδ max A
f
λ
p
(5.12)
When the machine runs at the speed of n , the commutating frequency of any phase is
pn
60
(5.13)
60 Po
0.36π ηBδ max Aλn
(5.14)
f =
Then (5.12) can be rewritten as
Di3 =
2
71
Chapter 5
Table 5-1 Typical Prototype Waveforms
Model
e(t )
i (t )
kp
ki
Sinusoidal
waveform
1
cos φr
2
2
Sinusoidal
waveform
0.5
2
Rectangular
waveform
1
1
Trapezoidal
waveform
0.777
1.134
1
3
3
0.8
1.134
2
3
1.225
Triangular
waveform
Rectangular&
trapezoidal
waveform
Rectangular
waveform
72
Proposed BDFDS Machines − Design and Analysis
Rectangular&
trapezoidal
waveform
0.556
1.389
Trapezoidal
waveform
0.519
1.389
Rectangular&
triangular
waveform
1
3
1.5
Since the BDFDS machine is a new class of machines, there is a shortage of
statistical data on the selection of A. Based on our experience, the range of A is selected
to be 10000~30000 A/m for low power machines. On the other hand, since the air-gap
flux density of the BDFDS machines is usually the same as the tooth flux density, Bδ max
is generally equal to 1.5 T. Therefore, by substituting A=15000 A/m, Bδ max =1.5 T, the
rated speed ns = 1500 rpm and η = 0.82 into (5.14), the main dimensions of the
proposed 750 W 12/8-pole BDFDS machines can be calculated by
Di3 = 4.1604 ×10 -4 m3
(5.15)
Hence, once Di is selected, l eff can be deduced from (5.11). For instance, the main
dimensions of the proposed machine are given by:
 Di = 0.075m

le ff = 0.075m
(5.16)
73
Chapter 5
Once the main dimensions are determined, the other structural dimensions,
namely the stator outer diameter, pole heights etc., can be specified in a similar way of
the SR motors [74].
To minimize the permeance associated with the minimum field flux at the
unaligned rotor position, pole arcs should comply with the following condition
β s + βr <
360°
p
(5.17)
where the β s and β r are stator and rotor pole arcs, respectively. To ensure the current
reversal and self-starting capability of the machine in both directions, the rotor pole arc
should be larger than the stator pole arc
βr > βs
(5.18)
To increase the output power and decrease the torque ripple, the angular
displacement which the flux linkage changes from minimum to maximum should be
increased to make the stator pole arc as large as possible. However, large stator pole arc
means less available space for the armature windings. Hence, the stator pole arc β s is
generally selected to be equal to the half of the stator pole pitch
βs =
360°
2Ns
(5.19)
where N s is the number of stator poles.
5.2.3 Number of Turns
The relationship between rotor and stator pole-arc is discussed as (5.18) shown.
By using (5.7), the number of turns per phase N is calculated for a given current. The
74
Proposed BDFDS Machines − Design and Analysis
conductor size is chosen so that the available winding space will be filled. The resulting
current density is calculated and checked against the maximum permissible value,
which is dependent on the cooling methods employed in the motor. If there is no
restriction on the outside diameter the winding space can be calculated from the number
of turns, the area of cross-section of the conductor, and the insulation thickness. The
height of the stator pole is then derived from the winding space.
From (5.7), for a given specific electric loading A and Di , it can be seen that the
product of N and I rms is a constant. The best values are those that would satisfy the
following mutually contradictory demands: Small current and inductance; Small values
of resistance and inductance of the winding implying a smaller number of turns.
An engineering trade-off has to be made with thermal considerations in
perspective. Again it must be emphasized here that the selection of I rms and N s is also
dependent on the ac supply available for rectification and subsequent input to the
converter to control the BDFDS machines [75].
5.2.4 Design of Prototype Machine
Based on the above design procedure, a prototype of three phase 12/8-pole
BDFDS machine is designed and built. The performance evaluation for the machine is
carried out by using finite element analysis and hence the parameters are finalized. The
main data of prototype machine is listed in Table 5-2. The corresponding cross sections
of prototype machine are shown in Fig. 5.1. In addition, two rotors, namely un-skewing
and skewing rotors, are designed for the proposed machines, respectively, to investigate
the effect of rotor skewing on the performance. The optimum skew angle is 10° which
75
Chapter 5
is calculated by simulation based on FEA results, it is determined by the factors such as
sinusoidal back-EMF, big torque and small torque ripple.
Table 5-2 Design data of the BDFDS machine
Items
Rated power (W)
750
Rated phase voltage (V)
95
Rated phase current (A)
5
Rated field excitation voltage (V)
190
Number of phases
3
Stator pole number
12
Rotor pole number
8
Stator outer diameter (mm)
140
Stator inner diameter (mm)
75
Stack length (mm)
75
Air-gap length (mm)
0.3
Stator pole arc (degree)
15
Stator pole height (mm)
15
Rotor pole arc (degree)
22
Rotor pole height (mm)
9
Rated speed (rpm)
1500
Number of turns/phase
120
Armature winding resistance/ phase (Ω)
76
12/8-pole
0.5692
Proposed BDFDS Machines − Design and Analysis
(a) stator
(b) Rotor
Fig. 5.1 12/8-pole BDFDS machine.
77
Chapter 5
5.3 Finite Element Analysis
One of the key performance characteristics of doubly salient machines, such as
switched reluctance machines, DSPM machines and BDFDS machines, is the static
characteristics, namely back EMF, flux linkage and inductance etc. Equivalent circuits
and lumped parameter models have been the traditional tools to calculate the
performance of the motors. They are simple and provide useful means for developing
control schemes. However, the performances predicted by these models are sensitive to
the parameters. The determination of lumped parameters by analytical method based on
traditional magnetic circuit analysis cannot meet the requirements of high accuracy,
since it cannot accurately calculate the magnetic saturation of iron core and the effects
of teeth and slots, etc. As an effective alternative, numerical calculation methods for the
field analysis have been well developed in recent decades. Among them finite element
method (FEM) is regarded as the most effective and powerful tool. It can greatly
improve the accuracy of the performance prediction and the parameter calculation. With
the rapid improvement of computational speed, this mature technique has become
necessary tool for motor design and analysis [76].
Because of the heavy magnetic saturation of pole tips and the fringe effect of
poles and slots, as well as the cross coupling between the field flux and the armature
current flux, the finite element method (FEM) is used to analyze the magnetic field
distribution of BDFDS machines, and hence to calculate the flux linkage, back EMF,
self-inductance, and mutual inductance. The mathematical model of FEM for the
magnetic field calculation is described.
Since the flux distribution in each cross-section is basically identical and the
leakage flux at two end regions is negligible, the two-dimensional FEM is used to
78
Proposed BDFDS Machines − Design and Analysis
analyze the electromagnetic field. Due to the symmetric motor configuration, the region
of one pair of poles is taken as the interested area. The corresponding Maxwell’s
equation is expressed as
∂ ∂A
 ∂ ∂A
 ∂x (ν ∂x ) + ∂y (ν ∂y ) = −( J z + J f )

A = 0
 S1
(5.20)
r
where A and J z are the z-direction components of vector potential A and current
r
density J , respectively, J f is the equivalent current density of the excitation field. S1
means the Dirichlet boundary, and ν is the reluctivity. The corresponding flux density
r
vector B is expressed as
r
r
B = rot A
(5.21)
Therefore, the corresponding x and y components are expressed as
Bx =
∂A
∂y
By = −
∂A
∂x
(5.22)
(5.23)
The two most popular methods of deriving the finite element equations are the
variational approach and the Galerkin approach which is a special case of the method of
weighted residuals (MWR) [76]. Due to the greater generality of the Galerkin approach,
this method is becoming increasingly popular and is used in here. Substituting an
approximation  for A gives a residual R .
R=
∂ ∂Aˆ
∂ ∂Aˆ
(ν ) + (ν ) + ( J z + J f )
∂x ∂x
∂y ∂y
(5.24)
Multiplying by a weighting function and setting the integral to be zero
79
Chapter 5
∫∫ RWdxdy = 0
(5.25)
Ω
Substituting for R , then it can be obtained
 ∂ ∂Aˆ
∂ ∂Aˆ 
− ∫∫W  (ν ) + (ν ) dxdy = ∫∫W (J z + J f )dxdy
∂y ∂y 
Ω
Ω
 ∂x ∂x
(5.26)
Consider a triangular element depicted in Fig. 5.2, the convention being used is
counter clockwise numbering of the vertices. The vertices are nodes at which the
unknown vector potentials will finally be calculated. The entire planar mesh may
represent the stator, rotor laminations and air-gap of a machine.
Fig. 5.2 Triangular element.
The device being analyzed must be subdivided into elements which may be
rectangular, triangular or any other convenient forms. In electrical machine, it is
convenient to choose triangular elements since they have the advantages of being able
to fit complicated geometry such as teeth and slots of the electric machines. When the
potential varies linearly in the element, the vector potential at any point in the triangle
can be expressed as [76]
Aˆ = a1 + a2 x + a3 y
(5.27)
where a1 , a2 and a3 are constants to be determined. Because the vector potential varies
linearly, the flux density which is the derivative of the potential is constant in the
80
Proposed BDFDS Machines − Design and Analysis
triangle. At the point i , there is x = xi and y = yi . At this vertex  must be equal to Âi ,
so that
Aˆi = a1 + a2 xi + a3 y i
(5.28)
Similar for the nodes j and k , there are
Aˆ j = a1 + a2 x j + a3 y j
(5.29)
Aˆ k = a1 + a2 xk + a3 y k
(5.30)
So
 a1  1 xi
a  = 1 x
j
 2 
 a3  1 xk
yi 
y j 
yk 
−1
 ai Aˆi + a j Aˆ j + ak Aˆ k 
 Aˆi 
ˆ 
1  ˆ
ˆ
ˆ 
 A j  = 2∆  bi Ai + b j Aj + bk Ak 
e 
 Aˆ 
ˆ
ˆ
ˆ 
 k
 ci Ai + c j Aj + ck Ak 
(5.31)
where
ai = x j yk − xk y j , bi = yi − yk , ci = xk − x j
a j = xk yi − xi yk , b j = yk − yi , c j = xi − xk
ak = xi y j − x j yi , bk = yi − y j , ck = x j − xi
1 xi
1
∆e = 1 x j
2
1 xk
(5.32)
yi
1
y j = (bi c j − b j ci )
2
yk
(5.33)
where ∆ e is the area of the triangular element. By substituting (5.31) into (5.28), the
linear interpolating function in terms of values of A at the nodes can be obtained
1
Aˆ =
(ai + bi x + ci y ) Aˆi + (a j + b j x + c j y ) Aˆ j + (ak + bk x + ck y ) Aˆ k
2∆ e
[
]
(5.34)
Therefore, the potential can be expressed as the sum of the shape functions timing
the nodal potential.
Aˆ = N i Aˆi + N j Aˆ j + N i Aˆ k
(5.35)
81
Chapter 5
where N i , N j , N k are the shape functions
Ni =
1
(ai + bi x + ci y )
2∆ e
Nj =
1
(a j + b j x + c j y )
2∆ e
Nk =
1
(ak + bk x + ck y )
2∆ e
(5.36)
In the Galerkin Method, the weighting function is chosen to be the same as the shape
function.
 Ni 
 
W = Nj 
N 
 k
(5.37)
Moreover, the electromagnetic force can be calculated by using the Maxwell
stress tensor method. The force density is then
ft =
Bn Bt
µ0
B 2 − Bt2
fn = n
2µ 0
(5.38)
where f t and f n are the tangential and normal component of the force density,
respectively. Bt and Bn are the tangential and normal component of the flux density,
respectively.
Based on the aforementioned model, electromagnetic field analysis of the
prototype motors is carried out. Due to the periodic motor configuration, the region of
interest for finite element analysis (FEA) is half of the whole machine cross-section for
the 12/8-pole BDFDS machine. The mesh generated for finite element analysis is shown
in Fig. 5.3. The corresponding magnetic-field distributions of the three-phase 12/8–pole
prototype machine are shown in Fig. 5.4. The no-load flux density distribution in air-
82
Proposed BDFDS Machines − Design and Analysis
gap shown in Fig. 5.5(a) indicates the component of the winding excitation field. The
armature only flux density distribution in air-gap is also shown in Fig. 5.5(b). Fig. 5.5(c)
shows the one under the field and armature currents.
5.4 Static Characteristics
5.4.1 Field Flux Linkage and Back EMF
Based on the results of FEA, the characteristics of the BDFDS machine including
the field flux linkage, the back EMF, self-inductance and mutual inductance of the
phase windings can be deduced. This gives the flux linking a coil as
φ = ( A1 − A2 )leff
(5.39)
where A1 and A2 are the vector potentials of two sides in a coil, which can be directly
obtained from the numerical results, and leff is the effective stack length. Hence, the
flux due to field winding excitation linking with a phase winding can be calculated.
Based on the similar method, Fig 5.6 shows the flux linkage versus filed current at
different rotor positions, while the flux versus rotor mechanical angle at different field
currents can be obtained as shown in Fig. 5.7, in which the rotor position angle is
defined as the angle between the center of rotor slot and the center of stator pole. It can
be noted that the magnetic saturation occurs for the cases with large rotor position
angles, namely the stator pole overlapping with rotor pole, when the field current
increases. Fig. 5.8 is a 3-D figure which shows flux linkage with the relation with rotor
positions and field currents.
83
Chapter 5
Fig. 5.3 Mesh generated for finite element analysis.
(a) Field current only
(b) Armature current only
(c) Field and armature current
Fig. 5.4 Magnetic field distributions.
84
Proposed BDFDS Machines − Design and Analysis
(a) Field current only
(b) Armature only
(c) Field and armature current
Fig. 5.5 Flux density distributions in air-gap.
85
Chapter 5
Fig. 5.6 Flux linkage versus field current under different rotor positions.
Fig. 5.7 Flux linkage versus rotor positions under different field currents.
Fig. 5.8 Flux linkage versus rotor positions and field currents.
86
Proposed BDFDS Machines − Design and Analysis
There is one full-pitch phase winding under each pair of poles, so the flux linkage
of each phase winding is given by
ψ = Nφ = N ( A1 − A2 )leff
(5.40)
where N is the number of turns in series of each phase winding. Based on the
Faraday’s Law, the back EMF can be expressed as
e=
dψ dψ 2πn
=
⋅
dt
dθ 60
(5.41)
where n is the rotor speed in rpm, θ is the rotor mechanical angle.
Based on the flux linkage from the FEA result, the theoretical back EMF
waveforms for the BDFDS machine at 1500 rpm which can be deduced by (5.41) are
shown in Fig. 5.9.
(a) Predicted
(b) Meausred
Fig. 5.9 EMF waveforms of a three-phase 12/8-pole machine at 1500 rpm.
87
Chapter 5
5.4.2 Self Inductance and Mutual Inductance
In the calculation of inductance, the cross coupling between the exciting field flux
and the armature flux is considered. Based on the finite element analysis result, the
inductances can be obtained. Fig. 5.10 shows self inductances and mutual inductances
characteristics.
(a) Self inductance.
(b) Mutual inductances.
Fig. 5.10 Inductance characteristics.
88
Proposed BDFDS Machines − Design and Analysis
5.5 Summary
In this chapter, the design details of the BDFDS machines have been discussed.
The equations for initial calculation of machine dimensions and parameters have been
presented. A three-phase 12/8 pole BDFDS machine is used for exemplification. The
finite element analysis is performed to finalize the machine dimensions as well as to
determine the machine parameters and characteristics. The static characteristics of the
BDFDS machine are deduced, including the magnetic field distributions and the flux
density distributions in the air-gap. Moreover, the machine characteristics including the
flux linkage, self-inductance, mutual inductance and back EMF are described.
89
CHAPTER
6
PROPOSED
BDFDS
MACHINES
–
MODELING,
CONTROL AND SIMULATION
6.1 Introduction
In this chapter, the principle operation of three-phase BDFDS machine is
illustrated at first. Then, the dynamic model is developed to be the basis of numerical
analysis. Unlike conventional electric machines, such as a dc and induction machines, a
BDFDS motor can not work from industrial power supply directly. The current in the
phase windings of a BDFDS motor must be switched on and off in accordance with the
rotor position to produce motoring torque. Therefore, a power converter is indispensable
in the BDFDS motor drive. A half-bridge power converter, which is composed of three
IGBT-based power modules, will be employed to make bi-directional current operation
possible, it has the advantages of reducing the number of power switches and being
independent phase current control.
To get as much torque as possible during the conduction interval of each phase,
the phase currents must be controlled carefully. To operate the BDFDS motor properly,
the control strategies of the BDFDS machines with skewed and unskewed rotors will be
developed and implemented in the controller based on dSPACE − DS1104 control
board. The hysteresis current controller has been designed and implemented, in which
the hysteresis band is selected as 0.5 A that is 10% of the rated current. The sinusoidal
current control is used in the BDFDS machine with skewed rotor, and the square current
control is applied in the one with unskewed rotor. A PI controller using
90
Proposed BDFDS Machines − Modeling, Control and Simulation
conditional integration combining with bang-bang control has been designed to control
speed. To measure rotor position, a simple position sensor consisting of a slotted disc
which has eight slits − producing eight pulse per rotation and three opto-couplers is
adopted in the BDFDS machine with skewed rotor, and an incremental encoder is
coupled with the BDFDS machine which has unskewed rotor.
Based on the dynamic model and using the Matlab/Simulink, the BDFDS motor
drives system is simulated, and the corresponding results will be presented in this
chapter. The control strategy and simulation of the BDFDS motor drives in this chapter
as well as its implementation in the next chapter will be focused on the three-phase
BDFDS motor with skewed rotor.
6.2 Principle of Operation
A three-phase 12/8-pole BDFDS machine is shown in Fig. 6.1, which consists of
two types of stator windings, one is dc field winding and the other is three-phase
concentrated armature winding. It has the same structure as a SR motor with twelve
salient poles in the stator and eight salient poles in the rotor. Since there are no PMs, no
brushes and no windings in the rotor, it offers very simple rotor structure and the
capability to run at high speed. Because the dc current flowing through the field
winding can be independently controlled, this BDFDS machine will not only solve the
fundamental problem of the DSPM motor, but also offer the possibility to optimize the
efficiency on-line.
The operating waveforms of field flux linkage ψ and phase current i s with respect
to the rotor position θ are shown in Fig. 6.2. When the rotor pole is entering the zone of
91
Chapter 6
a conductive phase, the flux of the phase winding is increasing. By applying positive
current to the winding, a positive torque will be produced. When the rotor pole is
leaving the stator pole from the aligned position, the flux is decreasing. The positive
torque is also produced by applying negative current to the winding. Therefore, the two
possible torque producing zones are fully utilized.
Fig. 6.1 Cross section of three-phase 12/8-pole BDFDS machine.
Fig. 6.2 Theoretical waveforms of flux linkage and current.
Based on the parameters calculated from the FEA results in chapter 5, the system
matrix equations describing the three-phase 12/8-pole BDFDS machine is expressed as
V = RI +
where the matrix of the applied voltages is
92
dΨ
dt
(6.1)
Proposed BDFDS Machines − Modeling, Control and Simulation
 va 
v 
b
V = 
 vc 
 
v f 
(6.2)
where v a , vb , v c are the phase voltages and v f is the field voltage.
The matrix of resistances is
 Ra
0
R =
0

 0
0
Rb
0
0
0
0
Rc
0
0
0 
0

R f 
(6.3)
where Ra , Rb , Rc are the armature winding resistances and R f is the field winding
resistance.
The matrix of applied currents is
 ia 
i 
b
I = 
 ic 
 
i f 
(6.4)
where i a , ib , ic are the phase currents and i f is the field current.
And the matrix of flux linkages is
Ψ = LI
(6.5)
with the matrix of inductances given as
 Laa
M
ba
L =
 M ca

 M fa
M ab
M ac
Lbb
M bc
M cb
M fb
Lcc
M fc
M af 
M bf 
M cf 

L ff 
(6.6)
where Laa , Lbb , Lcc are the self-inductances of armature winding and L ff is the selfinductances of field winding. M ab , Mba , M ac , Mca , Mbc , Mcb are the mutual inductances
93
Chapter 6
between the armature windings, and M af , M fa , M bf , M fb , M cf , M fc are the mutual
inductances between the armature windings and field winding, respectively. Therefore,
dΨ dt = L (dI dt ) + (dL dt ) I
(6.7)
Thus, the system equation (6.7) can be rewritten in terms of currents as
dI
dL
= L −1V − L −1 ( R +
ωr ) I
dt
dθ
(6.8)
where the ωr is the angular speed of rotor, θ is the rotor position which is a mechanical
angle.
The energy stored in the magnetic field under current I can be expressed as
Wf = I T LI 2
(6.9)
When the iron loss is neglected, the input power of the machine can be described
as
dI
dL
I
+IT
dt
dt
1 dL
d 1
I + ( I T LI )
= I T RI + I T
2
dt
dt 2
1
d
L
d 1
Iωr + ( I T L I )
= I T RI + I T
2
dθ
dt 2
I TV = I T R I + I T L
(6.10)
Equation (6.10) can be rewritten as
Pin = Pcu + Tωr + dW f dt
(6.11)
Therefore, the electromagnetic torque of the motor can be calculated by
T=
1 T dL
I
I
2
dθ
(6.12)
In the dynamic simulation, based on the derived electromagnetic torque, the motion
equation of the BDFDS motor can be expressed as
94
Proposed BDFDS Machines − Modeling, Control and Simulation
T=J
dω
+ k v ωr + Tl
dt
(6.13)
dωr 1
= (T − Tl − k v ωr )
dt
J
(6.14)
where Tl is the torque of load, k v is the viscous damping coefficient.
Combining (6.8) and (6.14) results in the state equation of three-phase BDFDS machine
as (6.15) shown.
 ia   Laa
i  
M ba
b
d   
 ic  =  M ca
dt   
 i f   M fa
ωr   0
 
 Laa
M
 ba
−  M ca

 M fa
 0
M ab
Lbb
M cb
M fb
0
M ac
M bc
Lcc
M fc
0
M ab
Lbb
M cb
M fb
M ac
M bc
Lcc
M fc
M af
M bf
M cf
L ff
0
0
0
where cij =
dLij
dθ
M af
M bf
M cf
L ff
0
0
0 
0

0
J 
−1
0
0 
0

0
J 
−1
 va 
 v 
 b 
 vc 


 vf 
T − Tl 
c12
 Ra + c11
 c
c22 + Rb
 21
 c31
c32

c42
 c41
 0
0
c13
c23
c33 + Rc
c14
c24
c34
c43
0
c44 + R f
0
0   ia 
0   ib 
 
0   ic 

0   i f 
k v  ωr 
(6.15)
ωr , i = 1 ~ 4, j = 1 ~ 4 .
6.3 Proposed Control Strategy
6.3.1 Converter Topology
To supply the BDFDS machine, a bipolar converter topology is preferred so as to
make bi-directional current operation possible. Three-phase converters are commonly
used to supply three-phase motors. It is possible to supply three-phase armature
windings by means of three separate single-phase converters, where each converter
produces an output displaced by 120 degree (of the fundamental frequency) with each
95
Chapter 6
other. Though this method maybe preferable under independent control requirement of
each phase, actually, such topology is generally not available. Furthermore, it requires
twelve switches. The three phase converters of three legs are most frequently utilized,
with one leg for each phase. Thus, there are two converter topologies in which the phase
current can be controlled individually for bi-directional operation, namely the halfbridge converter with split capacitors and the full-bridge converter.
Supplied by the half-bridge converter and full-bridge converter as shown in Fig.
6.3 and Fig. 6.6, the BDFDS machines are simulated under two kinds of rotor − skewed
rotor and unskewed rotor. Comparing the simulated results as shown in Fig. 6.4 − Fig.
6.5 and Fig. 6.7 − Fig. 6.8, it can be found that the torque ripple is smaller and the
current waveform is better when the half-bridge converter is used. Moreover, as shown
in Fig. 6.3, the half-bridge converter minimizes the number of power devices and each
phase current can be independently controlled. The connection between the midpoint of
the split capacitors and the neutral of motor windings, is usually necessary to
accommodate the additional current during the commutation period. Hence, the halfbridge converter is adopted.
Fig. 6.3 Half-bridge converter.
96
Proposed BDFDS Machines − Modeling, Control and Simulation
(a) Total toque and reluctance torque
(b) Phase current
Fig. 6.4 Simulated results based on half-bridge converter of BDFDS machine with skewed rotor.
(a) Total toque and reluctance torque
97
Chapter 6
(b) Phase current
Fig. 6.5 Simulated results based on half-bridge converter of BDFDS machine with unskewed rotor.
Fig. 6.6 Full-bridge converter.
(a)
98
Proposed BDFDS Machines − Modeling, Control and Simulation
(b)
Fig. 6.7 Simulated results based on full-bridge converter of BDFDS machine with skewed rotor.
(a)
(b)
Fig. 6.8 Simulated results based on full-bridge converter of BDFDS machine with unskewed rotor.
99
Chapter 6
6.3.2 Control System Configuration
Fig. 6.9 Functional block diagram of the control system.
Fig 6.9 shows the functional block diagram of the control system. The speed of the
BDFDS motor drive is controlled by a PI controller whose output is the torque reference.
The key of the control system is the dSPACE control board, it estimates the rotor speed
and position based on the position signals which are generated by rotor position sensors.
The command speed is compared with the feedback speed, according to the speed offset,
the torque reference is obtained. With the developed control strategies, command
current and turn on and off angles can be calculated. The hysteresis current controller
generates gating signals to drive the power switches of inverter. By controlling the on
and off state of power switches, the BDFDS motor is supplied, and phase current can be
controlled. Because torque is generally propotional to current, hence, the torque can be
controlled. Torque control is important in electric vehicles, where pedal pressure
represents a torque demand signal and the driver compares the desired speed with the
100
Proposed BDFDS Machines − Modeling, Control and Simulation
actual speed indicated by the speedometer. Due to the current changing, the torque can
usually be changed rapidly, therefore, by tuning the current, the torque can be controlled.
In motor drive control, the PI controller is often used. It consists of a proportional
gain an integral gain. The proportional term controls the loop gain of the system. The
integral term increases the order of the system in order to reduce the steady state error.
Most motor control is now implemented in digital electronics, the digital controllers has
the feature of being more accurate, less susceptible to noise and more flexible in
programming.
A typical digital PI algorithm is
k
T (k ) = k p e(k ) + ki ∑ e( j ) = Tp (k ) + Ti (k )
(6.16)
j =0
where k p and k i are the proportional and integral gains, respectively. To minimize the
computation time, the integral term can be written as [75]:
Ti (k ) = Ti (k − 1) + k i e(k )
(6.17)
To reduce the speed oscillations, a small dead zone of speed is deliberately
introduced into the controller. When the speed error is less than ε1 , the output of the
controller T (k ) takes the previous value T (k − 1) without corrective actions.
To speed up the dynamic response of the system, bang-bang control is combined
with PI control. When the absolute value of the speed offset is larger than a given value
ε 2 , the bang-bang control is adopted, otherwise, PI control is performed
 e(k) > ε 2

 e(k) ≤ ε 2
bang − bang control
PI control
(6.18)
In bang-bang control, when the speed offset is positive and the speed is increasing,
the output of the controller is directly set to be the maximum. Otherwise, it is directly
101
Chapter 6
set to zero. The structure of the developed PI controller for the BDFDS motor drive is
shown in Fig. 6.10.
Inspecting the controller, it can be found that there are two adjustable parameters,
namely proportional gain k p and integral gain k i . With these two gains, one can adjust
the PI actions and hence the performance of the overall system. The selection of the
controller means finding a compromise between the requirement for fast control and the
need for stable control. In this study, the PI controller is tuned by trial and error method
based on both simulation and experiment.
Based on the rotor position signal, the power switches can be controlled on and
off to supply the phase windings. The control logic of the three phase converter is
shown in Table 6-1.
Table 6-1 Control logic of the three phase converter
SASBSC
Phase A
Phase B
Phase C
102
S1
S2
S3
S4
S5
S6
001
0
0
0
1
1
0
010
0
1
1
0
0
0
011
0
1
0
0
1
0
100
1
0
0
0
0
1
101
1
0
0
1
0
0
110
0
0
1
0
0
1
Proposed BDFDS Machines − Modeling, Control and Simulation
Fig. 6.10 Structure of the digital PI controller.
103
Chapter 6
The flowchart of the control program is shown in Fig. 6.11.
Fig. 6.11 Flowchart of the control program.
104
Proposed BDFDS Machines − Modeling, Control and Simulation
6.3.3 Control Strategy
6.3.3.1 Control of BDFDS Machine with Skewed Rotor
In order to minimize the torque ripple, the rotor of BDFDS machine is specially
skewed to make the back EMF sinusoidal. The skewed angle is selected at 10 ° , this
value is the simulation result aiming to make the back EMF nearly sinusoidal, and the
reduction of the torque is about 10% of the rated torque under this skewed angle is
acceptable. Based on the skewed rotor structure, the sinusoidal current is adopted in
such a way that the phase current is controlled to synchronize with the phase back EMF.
Based on the rotor position signal as shown in Fig. 6.12(a), according to the
control logic of the three phase converter shown in Table 6-1, the phase current can be
controlled to synchronize with the phase back EMF as shown in Fig. 6.12(b).
6.3.3.2 Control of BDFDS Machine with Unskewed Rotor
For BDFDS machine with unskewed rotor, the control is different from the
aforementioned one with skewed rotor. Because the back EMF is trapezoidal, to
produce maximum output and increase the system efficiency, the turn on angle is
specially chosen to assure that the phase current is the maximum at the point when the
phase flux linkage starts to increase. The turn off angle is selected to get the maximum
viable torque. According to the flux linkage profiles of each phase shown as the upper
traces ( ψ a , ψ b , ψ c ) in Fig. 6.13, the control logic for each switch in the converter is
portrayed as the lower traces ( S1 , S 2 , S 3 , S 4 , S 5 , S 6 ) in Fig. 6.13. At any instant in time
two phases are energized and one phase is off. The command currents in each phase are
105
Chapter 6
described as Fig. 6.14, in which θ e is the electrical angle and the relation between the
electrical angle and mechanical angle is θ e = N r θ .
(a) Position signals.
(b) Back EMFs and phase currents.
Fig. 6.12 Theoretical Waveforms of BDFDS machine with skewed rotor.
106
Proposed BDFDS Machines − Modeling, Control and Simulation
Fig. 6.13 Flux linkages of three-phase windings and control logic of the BDFDS machine with unskewed rotor.
Fig. 6.14 Three-phase command currents.
107
Chapter 6
6.4 Simulation model and results
Simulink is a toolbox extension of the Matlab program, which is a program for
simulating dynamic systems. The first step to use the Simulink is to define a
mathematical model of the research project, then select a suitable integration method,
and set up the running conditions, such as initial conditions and running time.
Based on the static characteristics, such as flux linkages, self-inductances and
mutual inductances as shown in Fig. 5.6 − Fig. 5.8 and Fig. 5.10, obtained from FEA,
the motor performances are simulated using Matlab/Simulink. The use of
Matlab/Simulink environment takes advantages of easy programming, high flexibility
and plentiful toolboxes. The corresponding SimPowerSystems block is used to simulate
the three phase inverter and BDFDS machine together. The Matlab/Simulink model of
BDFDS machine system is shown in Fig. 6.15, Fig. 6.16 shows the block of phase A,
and block of generating pulses for power switches is shown as Fig. 6.17. Moreover,
block related with mechanic subsystem is also as Fig. 6.18 described.
In simulation, the currents are solved by (6.8) after the voltages are determined by
the rotor position and switching mode. The instantaneous torque can be calculated by
(6.12) when the currents have been worked out. The control strategy for three-phase
BDFDS machine is based on the aforementioned analysis, while the torque control is
achieved by changing the current reference. The corresponding control logic of those
power switches is based on the rotor position signals.
108
Proposed BDFDS Machines − Modeling, Control and Simulation
6.4.1 BDFDS Motor with Skewed Rotor
For the BDFDS machine with skewed rotor, the system simulation is performed.
The simulation results are shown in Fig. 6.19 − Fig. 6.24. At first, the no-load back
EMF is simulated, Fig. 6.19 is the simulated three-phase no-load back EMF at If=1 A
and 1500 rpm, it can be noted that the back EMF is very sinusoidal. Moreover, the
simulated phase back EMF under three different field current at 1500 rpm is shown in
Fig. 6.20, in which the upper line is under If=1.5 A, the middle line is under If=1.0 A,
and the lower line is under If=0.5 A. It is seen that the amplitude of back EMF increases
with the field current increasing. Fig. 6.21 shows the simulated phase back EMF and
related command maximum and minimum currents at 1500 rpm, it can be seen that the
current is synchronized with the phase back EMF. The simulated phase current, related
maximum and minimum command phase currents at 1500 rpm are shown in Fig. 6.22,
the phase current can be theoretically controlled in the hysteresis loop. Furthermore, Fig.
6.23 shows the simulated phase current (upper line) and phase voltage (lower line)
under If=1 A and 1500 rpm, in which the phase voltage swings from the maximum of
the rated power supply to the minimum one corresponding to the results of on and off
operation of power switches. Finally, the simulated instantaneous torque (upper line)
and phase current (lower line) under If=1 A and 1500 rpm are shown in Fig. 6.24, it can
be found that the torque ripple is very small under the sinusoidal current.
109
110
Chapter 6
Fig. 6.15 Matlab/Simulink model of BDFDS machine system
Proposed BDFDS Machines − Modeling, Control and Simulation
Fig. 6.16 Block of phase A.
Fig. 6.17 Block of generating pulses for power switches.
Fig. 6.18 Block to mechanic subsystem.
111
Chapter 6
Fig. 6.19 Simulated three-phase no-load back EMF at If=1 A and 1500 rpm.
Fig. 6.20 Simulated phase back EMF under three different field current at 1500 rpm.
(The upper line is at If=1.5 A, the middle line is at If=1.0 A, and the lower line is at If=0.5 A).
112
Proposed BDFDS Machines − Modeling, Control and Simulation
Fig. 6.21 Simulated phase back EMF, command maximum and minimum currents at 1500 rpm.
Fig. 6.22 Simulated phase current, related maximum and minimum command phase currents at 1500 rpm.
113
Chapter 6
Fig. 6.23 Simulated phase current (upper line) and phase voltage (lower line) under If=1 A and 1500 rpm.
Fig. 6.24 Simulated instantaneous torque (upper line) and phase current (lower line) under If=1 A and
1500 rpm.
114
Proposed BDFDS Machines − Modeling, Control and Simulation
The torque speed characteristic is simulated as shown in Fig. 6.25. It can be found
that the BDFDS motor drives provide the constant torque when it is running below the
rated speed. On the other hand, it keeps constant power above the rated speed.
Furthermore, reducing the field current to realize the flux weakening, the constant
power range is extended. Fig. 6.26 shows the comparison of the constant power range at
I f = 1 A and I f = 0.5 A , it is easy to find that the constant power range is larger at
small field current. Moreover, the system efficiency is calculated as Fig. 6. 27 shows,
the efficiency is keeping about 72% in a wide load range, only below 60% when the
load is small. Fig 6.28 shows the system dynamic response from standstill to the rated
speed.
6
5
4
3
2
1
0
0
500
1000 1500 2000
Speed (rpm)
2500
3000
Fig. 6.25 Torque speed characteristic.
Fig. 6.26 Comparison of constant power range at different field currents.
115
Chapter 6
Fig. 6.27 The simulated efficiency at 1500 rpm.
(a) Speed
(b) Phase current
Fig. 6.28 The simulated dynamic response ( Tl =0.6 Nm, K p = 0.02 , K i = 0.003 ).
116
Proposed BDFDS Machines − Modeling, Control and Simulation
6.4.2 BDFDS Motor with Unskewed Rotor
Based on the aforementioned static characteristics in Chapter 5 which are
obtained from FEA, the motor performances are simulated using Matlab/Simulink. The
control strategy for three-phase BDFDS motor with unskewed rotor is based on the
above analysis, while the torque control is achieved by changing the current reference.
The current is controlled to be a square wave to maximize the torque production. The
positive turn on angle is selected as 15° 4 as well as the positive off angle is 75° 4 . On
the other hand, the negative turn on angle is 105° 4 and the negative off angle is
165° 4 . In determining the turn on and turn off angle, the optimum angles are the
simulation results in which the maximum torque is obtained. The parameters used in the
simulation are from the FEM results. The corresponding control logic of those power
switches is based on the rotor position signals as Fig. 6.13 shows.
The waveforms of total average torque Tav , the instantaneous torque Tinst , the
phase current ia , and the flux φ a under steady state are simulated. Fig. 6.29 shows these
waveforms when the BDFDS machine is operated under the rated load of 4.70 Nm at
speed of 600 rpm, it can be found the Tav keeps constant and the current amplitude as
well as waveform are effectively controlled. Fig. 6.30 shows these waveforms at high
speed of 1800 rpm, it can be seen Tav is reduced to realize the constant power operation.
117
Chapter 6
Fig. 6.29 Simulated results of the BDFDS motor with unskewed rotor under rated load at 600 rpm.
Fig. 6.30 Simulated results of the BDFDS motor with unskewed rotor at the speed of 1800 rpm.
118
Proposed BDFDS Machines − Modeling, Control and Simulation
6.5 Summary
In this chapter, the principle operation of three-phase BDFDS machine has been
illustrated at first. The dynamic model has been developed to be the basis of numerical
analysis. A half-bridge power converter, which is composed of three IGBT-based power
modules, has been employed to make bi-directional current operation possible, it has the
advantages of reducing the number of power switches and independent phase current
control.
To operate the BDFDS motor properly, the control strategies of the BDFDS
machines with skewed and unskewed rotors have been developed and implemented in
the controller based on dSPACE − DS1104 control board. A PI controller using
conditional integration combining with bang-bang control has been designed to control
the speed. Based on the dynamic model and using the Matlab/Simulink, the BDFDS
motor drives system has been simulated. The simulation results have shown that the
BDFDS motor with skewed rotor has the advantage of less torque ripple than the
BDFDS motor with unskewed rotor. Furthermore, it has wider constant power range.
119
CHAPTER
7
PROPOSED BDFDS MACHINES – EXPERIMENTAL
IMPLEMENTATION
7.1 Introduction
The purpose of implementation is to maximize the software flexibility as well as to
minimize the hardware. The system hardware includes three-phase power converter,
gate drive circuit of power switches, current and position detecting circuit, and digital
controller.
In this chapter, implementation of the hardware is described in detail and the key
circuits are presented. In software implementation, the emphasis is given to the
description of the program flow and key routines. Moreover, a series of experiments on
two type of rotor structure of the BDFDS motor will be carried out. The experimental
results will be presented to verify the simulation.
7.2 Experimental Set-up
The experimental set-up of the prototype is composed of a BDFDS machine, a
dSPACE-based controller, three IGBT intelligent power modules, a torque sensor and a
dc dynamometer as shown in Fig. 7.1. The prototype of BDFDS machine is coupled to
the dc dynamometer. When the prototype of BDFDS machine as shown in Fig. 7.2 is
120
Proposed BDFDS Machines − Experimental Implementation
controlled to be a motor, the load of the tested machine is provided by a dc
dynamometer. The operating point of the tested BDFDS machine can be changed by
regulating the field current and the electronic load of the dc dynamometer. The
electronic load can be easily set as constant resistance, constant current or constant
power loads. The dc dynamometer can be used as a motor or generator, therefore all
experiments can be done in one test-bed.
Fig. 7.1 The configuration of experimental test-bed.
The input power and current of the BDFDS motor drive are measured by a digital
power analyzer. The voltage and current are measured and recorded by a multiplechannel digital oscilloscope. Furthermore, the torque is tested by a torque transducer,
and the dynamic torque waveform can be shown on the oscilloscope. The experimental
set-up and its subsystems are shown in Fig. 7.3 and Fig. 7.4. All the instruments
involved in the experimental set-up are listed in Table 7-1.
Fig. 7.2 The prototype of BDFDS machine.
121
Chapter 7
Fig. 7.3 The power converter, gating drive circuit, current sensor, dSPACE connector/led panel and
BDFDS machine in the experimental set-up.
Fig. 7.4 The power converter and dSPACE connector/led panel.
122
Proposed BDFDS Machines − Experimental Implementation
Table 7-1 Types and features of the instruments involved in experimental set-up
Name
Type
Features
20 Arms
Power analyzer
PA2200
650 Vrms
1000 Vpk
Torque transducer
T34FN
Torque transducer amplifier
MGC/IGC with AB12
Oscilloscope
LeCroy WaveRunner
6050A
20 Nm
40000 rpm
500 MHz
50 Ω − 5 Vrms
1 MΩ − 250 Vpk
1000 W
Electronic load
PLZ1003WH
5~500 V
0~50 A
Differential Probe
LeCroy ADP300
1000 Vrms
1400 Vpk
2300 W
dc dynamometer
230 V
10 A
RCL meter
FLUKE PM6360
dc power supply
KIKUSUI
dc~1 MHz
0~110V
10 A
7.2.1 Power converter
To verify the performance of the motor, the hysteresis current control circuit and
three-phase half-bridge converter shown in Fig. 7.3 were built and used in the
experimental drive. Nowadays many power semiconductor devices are available in the
market. Power devices can be classified into three groups according to their degree of
controllability: diodes, thyristors and controllable switches. The controllable switches
123
Chapter 7
are required in the power converter for the BDFDS motor drive, which include four
types of devices, namely bipolar junction transistors (BJTs), metal-oxide-semiconductor
field effect transistors (MOSFETs), gate turn-off (GTO) thyristors and insulated gate
bipolar transistors (IGBT). The characteristics of various power switches are shown in
Table A1-1.
The IGBT is a hybrid power device that combines the advantages of BJT (low
conduction losses) and MOSFET (fast switching and low drive power). It is suitable for
the high voltage, medium and low power applications, and thus has been widely
accepted for motor control applications.
Considering the advantages of IGBTs over other type of power switches and the
ratings of the prototype BDFDS motors, the IGBTs are adopted in the power converter.
In this research, three intelligent power modules from Mitsubishi Inc. are adopted,
Mitsubishi Intelligent Power Modules are isolated base modules designed for power
switching applications operating at frequencies up to 20kHz. The built-in control
circuits can provide optimum gate drive and protection for the IGBT and free-wheel
diode power devices. The IPM has the features such as complete output power circuit,
gate drive circuit, short circuit protection, over current protection, under voltage
protection and over temperature protection. Also, it is flexible enough to construct
different converter topologies for the BDFDS motor without more changes.
Fig. 7.5 shows a real physical intelligent power module. Circuit diagram of the
intelligent power module is shown in Fig. 7.6. Its key parameters are listed in Table A21, Table A2-2 shows the Key parameters of the control sector in IPM PM75DSA120.
124
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.5 A real physical intelligent power module − PM75DSA120.
Fig. 7.6 Circuit diagram of the intelligent power module − PM75DSA120.
7.2.2 Position Sensor
As described in Chapter 6, rotor position is the essential parameter for BDFDS
motor drive. Based on the rotor position, the power converter turns on and off the phase
windings of the BDFDS motor and drives the motor. The rotor position sensor is
implemented and its circuit is shown in Fig. 7.7. It consists of a slotted disc connected
to the rotor shaft and three opto-couplers mounted to the stator housing. The three opto-
125
Chapter 7
couplers are located 120 ° apart from each other along the circumference of the slotted
disc. As shown in Fig. 7.8, the part of on the right side of the dashed line is the signal
regulating circuit which is installed in the controller circuits, whereas the part on the left
side of the dashed line is the opto-coupler. In order to minimize the influence of
electrical interference, the position signal output is designed to be 0 ~ 15 V by
supplying the position sensor with 15 V. The output signals of the opto-couplers are not
ideal square waves and need to be conditioned by the circuit shown in Fig. 7.8 before
feeding into dSPACE control board.
Because the switches of power converter need to turn on and off the phase
windings at specific rotor positions, there should be a proper relationship between the
phase windings and rotor position sensor. The rotor position sensor is located by
comparing the waveforms of phase A back EMF and the position signal SP, the slotted
disc of the rotor position sensor is firstly fixed in the shaft, then the location of the optocouplers is finely modified until the rising edge of SP is aligned with cross-zero point
which the back EMF change from negative to positive.
Fig. 7.7 The rotor position sensor of three-phase BDFDS machine.
126
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.8 Position signal regulating circuit.
7.2.3 Current Control
To perform the hysteretic current control, the phase current of the BDFDS motor
must be detected instantaneously. Hence, a current sensor should be provided for each
phase. The current sensor being used is the LEM module (LA25-NP) which is based on
the hall-effect. It measures bi-directional currents up to 25 A rms from dc to 150 kHz,
furthermore, it can be mounted on the circuit board and the current ranges can be
selected.
Based on the control commands, the feedback current and rotor position, the
controller produces the driving signals which are transmitted to the gate drivers of the
converter.
To simplify the current comparing, the bipolar phase current of BDFDS motor
should be converted to unipolar one. Hence, an absolute value amplifier is adopted for
each phase as shown in Fig 7.9, in which fast recovery diodes are used in the circuit,
where Ia is the output of the current sensor, and I12 is proportional to the absolute value
of Ia.
127
Chapter 7
Fig. 7.9 Absolute value amplifier of phase current.
The hysteretic current control is implemented by a circuit that includes two
comparators and a flip-flop in each phase as shown in Fig. 7.10. The output of the
absolute value amplifier is compared with the maximum and minimum command
currents of each phase which is the D/A output signal from the dSpace control board,
and is latched by the flip-flop. The results are given in Table 7-2, where IC12=1
corresponds to turn-on the power switch of phase A and vice versa. Furthermore,
IC34=1 and IC56=1 related to turn-on the power switch of phase B and C and vice
versa, respectively.
To minimize the torque ripple, the sinusoidal current of each phase is required and
needs to be synchronized with back EMF waveform as analyzed in Chapter 3. Because
there are different command currents of each phase at one rotor position, independent
current references are provided as shown in Fig 7.10. According to the rotor position,
the model based on Matlab/Simulink generates the related maximum and minimum
command currents of each phase, which are converted to analog signals through D/A
channels of dSpace control board.
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Proposed BDFDS Machines − Experimental Implementation
Fig. 7.10 Three phase hysteretic current control circuits.
129
Chapter 7
Table 7-2 Results of hysteretic current control circuit
Conditions
CD
SD
Q (IC12)
I12<Iamin
0
1
1
I12>Iamax
1
0
0
Iamin<I12<Iamax
1
1
keeping
7.2.4 Controller − dSPACE
In order to implement the control algorithm so as to control the BDFDS machine,
a proper controller is needed. While MATLAB and the SIMULINK block diagram
environment are useful for control design and analysis, the dSPACE DS1104 R&D
Controller Board provides the means for acquiring system identification data and
implementing a discrete-time controller for analog plants. It is a piece of hardware that
upgrades PC to a powerful development system for rapid control prototyping.
The dSPACE system consists of three components: the DS1104 R&D Controller
Board as shown in Fig. 7.11 that can be plugged into a PCI slot of a PC, a connector/led
panel which provides easy-to-use connections between the DS1104 R&D Controller
Board and devices to be connected to it, and software tools for operating the DS1104
R&D Controller Board through the SIMULINK block diagram environment. Fig. 7.12
shows a block diagram of the DS1104 R&D Controller Board.
Rapid control prototyping is used to develop and optimize new control concepts
on a real system. Design tools such as MATLAB/Simulink enable different users to
130
Proposed BDFDS Machines − Experimental Implementation
design their own controllers directly in the block diagram. Real-time code is generated
from the block diagram and automatically implemented on the flexible prototyping
hardware. In the closed loop, users can change parameters online, record time histories
in real time, and run through automation scripts in a development phase which the costs
for corrections are still minimal, and this greatly reduces the development and
prototyping time for a variety of drive systems.
Fig. 7.11 DS1104 R&D Controller Board
Users program their control algorithms using MATLAB/Simulink. And after
compiling, these algorithms will be downloaded to the DS1104 R&D Controller Board
by means of a real-time workshop. Once the algorithm has been downloaded, the
DS1104 will handle the control of its targets such as the BDFDS machine in this project,
as well as communication with host PC. At the same time, users can use software
ControlDesk to tune the control parameters such as PID parameters online, supervise
experimental results online and record data online as well.
Its technical details are shown in Table A3-1.
131
Chapter 7
Fig. 7.12 A block diagram of the DS1104 R&D Controller Board.
7.2.5 Position Signal Processing
Three position signals are connected to the three I/O interfaces of dSPACE LED
connector. Both the rising and falling edge of the position signal trigger the speed
calculation subsystem, and then the time at each transition can be recorded. According
to the time interval between the two successive transitions, which are related with 15°
mechanical degrees, the motor speed can be measured for being used subsequently in
speed feedback. Based on the position signals, the rotor position can be achieved to be
applied in the control strategy.
132
Proposed BDFDS Machines − Experimental Implementation
7.3 Experimental Results
7.3.1 BDFDS Motor with Skewed Rotor
For the BDFDS motor which has a skewed rotor, it adopts the sinusoidal
hysteresis current control. The control angles are generally fixed, while the torque
control is achieved by changing the current reference. For the three-phase 12/8-pole
BDFDS motor with skewed rotor drive, the control logic has been deduced in Chapter 6
from the relationship between the position signals and back EMF as shown in Fig. 6.11.
The corresponding measured no-load back EMF at 1500 rpm is shown in Fig.
7.13. It can be found that the waveform is very sinusoidal. Moreover, Fig. 7.14 shows
the measured no-load phase back EMF waveforms at three field currents: If=1.5 A,
If=1.0 A, and If=0.5 A under rated speed. Fig. 7.15 also shows the measured three phase
no-load back EMF. To evaluate the synchronization of the phase current and phase back
EMF, both of these two waveforms are measured and shown in Fig.7.16.
Fig. 7.13 Mearsured no-load phase back EMF waveform at 1500 rpm and If=1 A (20 V/div, 500 µs/div).
133
Chapter 7
Fig. 7.14 Measured no-load phase back EMF waveforms at 1500 rpm with different field currents (25
V/div, 25 V/div, 25 V/div, 1 ms/div).
(Upper trace: If=1.5 A, middle trace: If=1.0 A, lower trace: If=0.5 A).
Fig. 7.15 Measured no-load three-phase back EMF waveforms at 1500 rpm and If=1 A (20 V/div, 20
V/div, 20 V/div, 1 ms/div).
(Upper trace − e A , middle trace −
134
eB , lower trace − eC ).
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.16 Measured phase back EMF (bipolar trace), maximum (upper positive trace) and minimum
(lower positive trace) command currents at 120 rpm and If=1 A (7.6 V/div, 2.5 A/div, 2.5 A/div, 25
ms/div).
To provide an accurate rotor position to start and run the BDFDS motor, the
position signals are measured as shown in Fig. 7.17 and Fig.7.18. It can be noted that
the phase back EMFs are synchronized with the related position signal. Hence, by
measuring the position signal, the rotor position can be calculated. Based on this
calculated rotor position, the motor can be effectively controlled. Fig. 7.19 shows the
measured phase current at 1500 rpm and If=1 A. it can be found that the phase current is
very sinusoidal, and there is a good agreement between the simulated and experimental
current waveform. The phase current synchronized with the position signal is verified
by Fig. 7.20. Hence the phase current is synchronized with the phase back EMF,
because the phase back EMF is synchronized with the position signal.
In order to verify the hysteresis current controller, the phase current is compared
with the related maximum and minimum reference current as shown in Fig. 7.21. It is
135
Chapter 7
noted that the phase current is effectively controlled in the hysteresis loop. Moreover, to
reflect the current chopping effect, Fig.7.22 shows the measured phase current and the
phase voltage.
To evaluate the dynamic performance of the BDFDS motor drive, the speed and
current response are measured. Fig. 7.23 shows the measured speed and current
responses of the BDFDS motor starting from standstill to rated speed. It can be found
that the motor drive responds quickly and takes only 0.8 second to reach the rated speed
without overshoot and steady-state error. Furthermore, Fig. 7.24 − Fig. 7.25 shows the
dynamic characteristics under a sudden change of load torque from 3.2 Nm to 0.6 Nm
and vice versa at the rated speed. The speed regulation is very good and the
instantaneous drop is small. Finally, the system characteristics including the transient
torque, phase current, speed and phase voltage are measured as shown in Fig.7.26.
Due to the rotor inertia of the dc dynamometer unable to measure accurately, no
simulated dynamic responses at the same conditions are included for comparison with
Fig. 7.24 − Fig. 7.25.
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Proposed BDFDS Machines − Experimental Implementation
Fig. 7.17 Measured phase back EMFs and related position signals waveforms.
Square waveforms for position signal A (upper) and C (lower) (2 V/div, 5 ms/div).
Sinusoidal waveforms for phase A (upper) and C (lower) back EMF (10 V/div, 5 ms/div).
Fig. 7.18 Measured position signals of three position sensors (2 V/div, 2 V/div, 2 V/div, 5 ms/div).
137
Chapter 7
Fig. 7.19 Measured phase current at 1500 rpm and If=1 A (2.5 A/div, 1 ms/div).
Fig. 7.20 Measured phase current (upper) and position signal (lower) waveforms at 1500 rpm and If=1 A
(2.5 A/div, 2 V/div, 2 ms/div).
138
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.21 Measured phase current (bipolar trace), related maximum (upper positive trace) and minimum
(lower positive trace) command current waveforms at 1500 rpm and If=1 A (2.5 A/div, 1 ms/div).
Fig. 7.22 Measured phase current (upper) and phase voltage (lower) waveforms at 1500 rpm and If=1 A
(2.5 A/div, 50 V/div, 2 ms/div).
139
Chapter 7
Fig. 7.23 Measured speed (upper) and current (lower) responses of the BDFDS machine starting from
standstill to rated speed − 1500 rpm (400 rpm/div, 2.5 A/div, 1 S/div).
Fig. 7.24 Measured current (upper) and speed (lower) responses of the BDFDS machine under a sudden
change of load from 3.2 Nm to 0.6 Nm at 1500 rpm and If=1 A (5 A/div, 600 rpm/div, 1 S/div).
140
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.25 Measured current (upper) and speed (lower) responses of the BDFDS machine under a sudden
change of load from 0.6 Nm to 3.2 Nm at 1500 rpm and If=1 A (2.5 A/div, 400 rpm/div, 1 S/div).
Fig. 7.26 Measured characteristics of the BDFDS machines at 1500 rpm and If=1 A.
Trace 1: Transient torque waveform (1 Nm/div, 20 ms/div).
Trace 2: Phase current waveform (2.5 A/div, 20 ms/div).
Trace 3: Speed waveform (400 rpm/div, 20 ms/div).
Trace 4: Phase voltage waveform (50 V/div, 20 ms/div).
141
Chapter 7
Fig. 7.27 Measured efficiency at If=1 A.
(a) Measured efficiency
(b) Simulated and measured efficiency
Fig. 7.28 System efficiency.
142
Proposed BDFDS Machines − Experimental Implementation
7.3.2 BDFDS Motor with Unskewed Rotor
For verification, based on the similar control circuit and power inverter in the
BDFDS motor with skewed rotor, the experiments of BDFDS motor with unskewed
rotor are performed. Only the control strategy is different, which the current is
controlled as square wave and the turn on and off angle can be regulated. Moreover, the
incremental encoder is adopted as the position sensor.
Fig. 7.29 shows the measured no-load EMF waveform at 1500 rpm, it can be
found that they closely agree with the simulated waveform shown in Fig. 5.9. Under the
rated load of 4.70 Nm and at the speed of 600 rpm, the phase current, phase voltage and
line to line voltages are measured. Fig. 7.30 shows the measured phase current and
phase voltage of the hysteresis control operation, respectively. The line to line voltage
between two phases is shown in Fig. 7.31. Furthermore, both the phase current and total
torque are measured at the same condition, the torque is tested by a torque sensor
T34FN under the steady state. Fig. 7.32 shows these waveforms. Also, it can be
calculated from Fig. 7.32 that the torque ripple obtained from the measured torque
waveforms is about 6%. It is very small, because in the steady state at low speed, the
current amplitude is controlled to keep constant.
The phase current and the related gating signals of switches are also measured
and as shown in Fig. 7.33 and Fig. 7.34. It is obvious that the measured current
waveforms closely agree with the simulated current waveforms shown in Fig. 6.28, and
it can also be found that the new machine has better turn on and turn off performances
as predicted by the simulation.
143
Chapter 7
Fig. 7.29 Measured no-load EMF waveform at rated speed − 1500rpm (50 V/div, 2 ms/div).
Fig. 7.30 Measured phase current (upper)and phase voltage (lower) waveforms under rated load (4.5
A/div, 50 V/div, 5 ms/div).
Fig. 7.31 Measured line to line voltage waveform under rated load (50 V/div, 5 ms/div).
144
Proposed BDFDS Machines − Experimental Implementation
Fig. 7.32 Measured phase current (upper) and totoal torque (lower) waveforms under rated load (4.5
A/div, 2.8 Nm/div, 5 ms/div).
Fig. 7.33 Measured phase current (upper) and gating signal of the upper switch (lower) waveforms (4.5
A/div, 2 V/div, 5 ms/div).
Fig. 7.34 Measured phase current (upper) and gating signal of the lower switch (lower) waveforms (4.5
A/div, 2 V/div, 5 ms/div).
145
Chapter 7
7.4 Summary
In this chapter, the hardware and software implementations of the control system
of the BDFDS motor drive has been presented. The IGBT based power converter has
been designed, and the gate drive device as well as its application circuit has been
described. The dSPACE − DS1104 based controller for the BDFDS motor drive has
been developed. The key circuits in the controller, such as current chopping circuit,
position signal conditioning circuit, and so forth, have been given. In software
implementation, the emphasis has been focused on describing the program flow and key
routines. The experiments on two BDFDS motors with different rotor structures have
been performed, and the experimental results closely agree with the simulated ones.
146
Proposed BDFDS Machines − Experimental Implementation
147
CHAPTER
8
PROPOSED BDFDS MACHINES – APPLICATION
8.1 Introduction
With ever increasing concerns on energy crisis and environmental protection, the
development of renewable energy resources has taken on an accelerated pace. Wind
power is one of the most viable renewable energy resources, and its core element is the
electric machine − the generator.
Conventional generators, such as the synchronous and induction ones, are mainly
designed for constant-speed turbine operation. Therefore, they are inefficient or even illsuited for variable-speed wind turbine operation. In [78], the doubly-salient permanent
magnet (DSPM) machine, incorporating the structure of a switched reluctance (SR)
machine and the use of PM material, was proposed for wind power generation.
Although this DSPM generator offers the advantages of high power density and high
robustness, it suffers from the drawbacks of high PM cost and uncontrollable flux. In
[79], with the replacement of PMs in the DSPM motor by a dc field winding, the
brushless doubly-fed doubly-salient (BDFDS) motor was proposed for electric vehicles
(EVs). By using dc field current control, this motor offers the definite advantage that it
can provide wide-range constant-power operation for EV cruising at which the input
voltage is fixed at the rated value.
The purpose of this chapter is to reverse and further extend this idea. Namely,
with the use of dc field current control, the generator can provide constant output
voltage and efficiency optimization for a wide range of wind speeds.
147
Chapter 7
8.2 Design and Analysis
Fig. 8.1 shows the configuration of the proposed BDFDS machine system for wind
power generation. It mainly consists of a wind turbine for capturing wind power, a
three-phase BDFDS generator for electromechanical energy conversion, a diode
rectifier for ac-dc conversion, and a three-phase inverter for dc-ac conversion.
First of all, the rated speed of the proposed BDFDS machine needs to be identified
since it affects the sizing of the whole system. For a horizontal-axis wind turbine, the
mechanical output power Pmech is typically expressed as [26]
Pmech =
1
C p ρν w3 A
2
(8.1)
where C p is the coefficient of wind power, ρ is the air density, νw is the wind speed
and A is the swept area of wind turbine rotor. Taking the mean annual wind speed to be
7.1 m/s, the nominal speed of the wind turbine is selected as 150 rpm. Further selecting
fixed gearing with the ratio of 1:10, the rated speed of the BDFDS generator becomes
1500 rpm.
Fig. 8.1 System configuration.
The cross-section of the applied three-phase 12/8-pole (12 stator poles and 8 rotor
poles) BDFDS machine is shown in Fig. 6.1. It adopts the same structure as a SR
machine, namely saliency on both the stator and rotor. There are no windings or PMs on
the rotor, whereas there are two types of windings on the stator − a poly-phase armature
148
Proposed BDFDS Machines − Application
winding and a dc field winding. Since the dc current flowing through the field winding
can be independently controlled, this arrangement can solve the problem of
uncontrollable PM flux. Based on the aforementioned design philosophy described in
Chapter 5, the three-phase BDFDS machine can be used as wind power generator.
By using the finite element analysis (FEA), the static characteristics of the BDFDS
machine are deduced. Fig. 5.4 shows the magnetic field distributions due to the field
current only, the armature current only and both the field current and the armature
current, respectively. Based on these distributions, the machine dimensions and
parameters can be fine tuned. Moreover, the machine characteristics, including the flux
linkage, self-inductance, mutual inductance and no-load EMF, can be obtained. The
corresponding flux linkages which vary with both the rotor angle and field current are
shown in the Fig. 5.6 − Fig. 5.8. The characteristics of self-inductance and mutual
inductances are also shown in Fig. 5.10.
8.3 Modeling and Control
Based on the parameters obtained from the FEA, the model of the BDFDS machine
can be formulated as
  Laa

d   M ba

dt   M ca
  M fa

M ab
M ac
Lbb
M bc
M cb
Lcc
M fb
M fc
M af   ia    v a   Ra

M bf   ib    vb   0
=
+
M cf   ic    vc   0
     
L ff  i f   v f   0
0
0
Rb
0
0
Rc
0
0
0   ia 
0   ib 
0   ic 
 
R f  i f 
(8.4)
where Laa , Lbb , Lcc are the phase self-inductances, L ff is the field self-inductance,
M ab , M bc , …, M fc are the mutual inductances, ia , ib , ic are the phase currents, i f is the
149
Chapter 7
field current, va , vb , vc are the phase voltages, v f is the field voltage, Ra , Rb , Rc are the
armature winding resistances, and R f is the field winding resistance.
With the use of this machine model, system control can be performed. As shown in
Fig. 8.1, the core of system control is the field controller. On one hand, it measures the
input wind speed and hence deduces the mechanical power using (8.1). On the other
hand, it measures the generated output voltage and power of the BDFDS machine.
Consequently, this controller performs two tasks: First, if the generated output voltage
deviates from the pre-set value due to the variation of wind speeds, the field controller
will tune the DC field current to achieve constant output voltage. Second, based on the
measured mechanical input power and electrical output power, the DC field current is
fine tuned to maximize the system efficiency.
8.4 Simulation and Experimentation
Computer simulation using MATLAB is based on the machine model as given by
(8.4). Experimentation is based on the designed machine with specifications as listed in
Table 5-2. The natural wind characteristics are emulated by real-time controlling a
programmable DC dynamometer.
Fig. 5.9 shows the simulated and measured no-load EMF waveforms at the rated
speed. As expected, the agreement is very good. Moreover, Fig. 8.2 shows the simulated
waveforms of the machine line voltage and phase current as well as the rectified DC
output voltage at the rated conditions with the field current of 1 A, whereas Fig. 8.3 and
Fig. 8.4 show the measured counterparts. It can be found that these operating
waveforms are closely matched.
150
Proposed BDFDS Machines − Application
Fig. 8.2 Simulated waveforms of line voltage, phase current and DC output voltage.
Fig. 8.3 Measured line voltage and phase current waveform (100 V/div, 5 A/div, 2.5 ms/div).
151
Chapter 7
Fig. 8.4 Measured DC output voltage waveform (20 V/div, 2.5 ms/div).
In order to assess the validity of the field controller, the no-load EMF characteristic
at various field currents is measured as shown in Fig. 8.5. It can be seen that the EMF
can be linearly controlled over a wide range of field currents. Moreover, Fig. 8.6 shows
line to line voltage at various speed and field currents, it can be noted that the line to
line voltage increase linearly with I f when it bellows 0.75A under the same speed, and
the saturation mode is shown clearly when I f is 1.25 A (the dot line below I f =0.75 A),
the related value is smaller than that one in I f =1 A. Hence, by online adjusting the field
current, the DC output voltage shown in Fig. 8.7 can be controlled to remain constant
over a wide range of rotor speeds or wind speeds. Fig. 8.8 shows the measured DC
output voltages at different loads and speeds. It can be seen that the voltage can be
constant in a wide load range. Furthermore, the machine efficiency characteristic at
various field currents is measured as shown in Fig. 8.9. It confirms that the efficiency
can be optimized by fine tuning the field current.
152
Proposed BDFDS Machines − Application
Fig. 8.5 Measured no load EMF characteristic at various field currents.
DC output voltage (V)
Fig. 8.6 Measured no load line to line voltage characteristic at various speeds and field currents.
Fig. 8.7 Measured DC output voltage characteristic at various speeds.
153
Chapter 7
Fig. 8.8 Measured DC output voltage characteristic at various speed and load currents.
Fig. 8.9 Measured efficiency characteristic at various field currents at rated speed and load.
8.5 Summary
In this chapter, a new three-phase 12/8-pole BDFDS machine system has been
applied as wind power generator. Based on the electromagnetic field analysis in Chapter
5, theoretical derivation, system modeling and field current control have been discussed.
Both computer simulation and experimental results have been given to verify the
validity of the proposed system, particularly the constant voltage output by field
regulation and efficiency optimization.
154
CHAPTER
9
CONCLUSIONS AND RECOMMENDATIONS
9.1 Conclusions
The objectives of this project have been successfully accomplished. A new threephase brushless doubly-fed doubly-salient motor drive has been developed. The
approaches of design, analysis and control strategy for the BDFDS motor drive have
been established and verified by the experimental results of the prototype machines. The
new three-phase 12/8-pole BDFDS motor drive not only possesses wide constant power
operation range, simple control, fast dynamic response and maintenance free, but also
offers the merits of series dc motor drives such as high starting torque and wide
adjustable speed range for constant power operation.
Based on the aforementioned design and finite element analysis of the three-phase
BDFDS machine, its new application for wind power generation is proposed. The
system model is formulated and applied for computer simulation. Moreover, field
current control has been discussed. Both computer simulation and experimental results
have been given to verify the validity of the proposed system, particularly the constant
voltage regulation and efficiency optimization.
A new three-phase 12/8-pole doubly salient permanent magnet (DSPM) machine
for application to wind power generation has been proposed. The design, analysis and
simulation of the proposed DSPM generator have been presented. Moreover, the
topological selection is supported by analytical analysis of the DSPM machine.
Experimental results have confirmed that this DSPM generator possesses high power
155
Chapter 9
density, high robustness and high efficiency.
To minimize the torque ripple of four-phase 8/6-pole DSPM motor, a new twophase operation mode is proposed and analyzed, in which the sinusoidal current control
is proposed. The analytical model of torque generation has been derived. Theoretical
analysis, computer simulation, and experimental results have verified that the operating
torque ripple at the rated load can be reduced by about 14% by using the proposed twophase operation mode.
The research output of this project is fruitful and some of the work has been
consolidated as publications [J.1]-[J.5], [C.1]-[C.6]. The key achievements of the
project on BDFDS machine can be summarized as follows:
Firstly, the finite element method (FEM) has been used to analyze the magnetic
field of the BDFDS machines, in which the magnetic saturation, the interaction between
the armature field and the dc exciting field has been considered. Based on the FEM, the
static characteristics, being the basis of analysis, design and control of the BDFDS
machine, have been deduced.
Secondly, the sizing equation of the BDFDS machine has been deduced and design
details have been presented to provide a practical way of making initial calculation of
motor dimensions and parameters. The dynamic modeling of the BDFDS machine has
also been described. Two different prototype machines with skewed and unskewed
rotors have been designed and built. Furthermore, based on the dynamic model,
numerical simulation has been carried out by using Matlab/Simulink, revealing that the
proposed three-phase BDFDS machine offers the definite advantages of wide constant
power operation range.
156
Conclusions and Recommendations
Thirdly, the control strategies of the BDFDS machines with skewed and unskewed
rotors have been developed and implemented in the controller based on dSPACE −
DS1104 control board. The hysteresis current controller has been designed and
implemented. The sinusoidal current control is used in the BDFDS machine with a
skewed rotor, whereas the square current control is applied to the one with unskewed
rotor. A PI controller using conditional integration and bang-bang control has been
designed to control the speed. To measure rotor position, a simple position sensor
consisting of a slotted disc and two opto-couplers is adopted in the BDFDS machine
with skewed rotor, whereas an incremental encoder is used for the BDFDS machine
with unskewed rotor. Moreover, a half-bridge power converter, which is composed of
three IGBT-based power modules, has been employed to provide bi-directional current
operation. It has the advantages of reducing the number of power switches and
independent phase current control.
Finally, the experimental implementation has been carried out. The steady-state and
dynamic operation performances as well as the effectiveness of flux weakening on
extension of the speed range have been experimentally investigated. It has shown that
the measured and theoretical results are in good agreements.
In short, the major contributions of this project are:
♦
A sizing equation and design procedure of the BDFDS machine, providing a
practical way to making initial selections of the main motor dimensions and
parameters.
♦
A sinusoidal hysteresis current control strategy for the BDFDS machine with
skewed rotor, hence reducing the torque ripple and make the control simple.
157
Chapter 9
♦ An accurate rotor position measurement to make the phase current synchronize with
the phase back EMF.
♦ A field winding to realize flux weakening and to extend the constant power
operation range.
♦ A two-phase operation mode of the 8/6-pole DSPM motor to minimize the torque
ripple, a two-phase inverter with the relevant control circuit to reduce the number of
power switches, and an analytical analysis of torque ripples.
♦ A new three-phase 12/8-pole DSPM machine topology for wind power generation
to provide high power density, high robustness, and low manufacturing cost and an
analytical analysis of this machine for topological selection.
♦ Application of the three-phase 12/8-pole BDFDS machine for wind power
generation to provide constant voltage and efficiency optimization for a wide range
of wind speeds.
9.2 Recommendations
As a new class of brushless motor drives, the development of the BDFDS
machine is still increasing. This research has focused mainly on the analysis approaches
and the basic control scheme and its implementation. There are a lot of unexplored
research areas. Even in the areas involved in this study, some aspects, such as
experimentation at high speeds of the BDFDS motor with unskewed rotor, has not yet
been fully explored due to time limitation. Some of the suggested further work may
include the following:
158
Conclusions and Recommendations
Due to the existence of reluctance torque component, the torque ripple of the
proposed motor drive is more serious than that of conventional induction and dc
motor drives. Therefore, the torque ripple minimization method is an important
research subject for future work.
The system simulation and experiment of the three-phase DSPM motor drive was
not carried out in this thesis due to the limitation of time. It should be performed in
future to compare with the three-phase BDFDS motor drive.
Since the position sensor increases both complexity and cost of the BDFDS motor
drive [80 − 84], it should be an important trend to develop its sensorless control.
A new type of wind power generator, which incorporates the merits of DSPM
machine and BDFDS machine, should be designed and analyzed in next research
project. For example, the permanent magnet hybrid machine topology can be taken
into account.
Study on the efficiency change of the generator when the wind speed is fluctuating
widely.
159
APPENDICES
A1
The characteristics of various power switches
Table A1-1 The characteristics of various power switches
Devices
Characteristic
♦ Current-controlled bipolar device
♦ Can not be reverse biased
♦ On-state voltage: 1-2 V
♦ Long storage time during turn-off transition
♦ Low current gain
BJT
♦ Switching speed in the range of 0.5-5 micro seconds
♦ Blocking voltage: 1500 V
♦ Conducting current: 200-300 A
♦ Switching frequency applications: 1-10 kHz
♦ Sensitive to temperature
♦ Secondary breakdown effect
Voltage-controlled device
Can not be reverse biased
On-state resistance RDS(ON), limits the power handling
capability of MOSFET. High losses especially for high
MOSFET
voltage device due to RDS(ON)。
Switching speed in the range of 10-300 nano seconds
Blocking voltage: 300-400 V
Conducting current: 20-100 A
Switching frequency applications: 30-500 kHz
Less sensitive to temperature
160
Appendices
Current-controlled device
Switching speed in the range of 5-25 micro seconds
Blocking voltage: 4.5 kV
Conducting current: 3 kA
Switching frequency applications: 100 Hz-10 kHz.
Gate drive design is very difficult. Need very large reverse
gate current to turn off. Often custom-tailored to specific
GTO
application.
Bilateral voltage block capability
Current triggered latch on
Can be turned off by applying a negative gate-cathode voltage
On-state voltage: 2-3 V
Low dv/dt, must be protected by turn-off snubber for
inductive load.
Voltage-controlled device
Large current handling capability
Reduced temperature coefficient
Lower forward conduction voltage drop
Smaller reverse transfer capacitance
Less gate charge
IGBT is especially suitable in applications of medium
frequency (20 kHz) medium power (1 to 100 kW) PWM
IGBT
inverters and motor drives.
Motor control: Frequency <20kHz, short circuit/in-rush limit
protection.
Uninterruptible power supply (UPS): Constant load, typically
low frequency.
Welding: High average current, low frequency (<50kHz),
ZVS circuitry.
Low-power lighting: Low frequency (<100kHz)
161
Appendices
A2
Key parameters of IPM PM75DSA120
Table A2-1 Key parameters of the IGBTs in IPM PM75DSA120
Collector-emitter voltage
VCES
(max)
1200 V
Collector-emitter saturation voltage
VCE(sat)
(typ)
2.3 V
Collector current (TC = 25°C)
IC
(max)
75 A
Peak collector current (TC = 25°C)
ICP
(max)
150 A
Supply voltage (applied between C1-E2)
VCC
(max)
900 V
Supply voltage surge(applied between C1-E2)
VCC(surge) (max)
1000 V
Collector dissipation(TC = 25°C)
PC
(max)
460 W
Power device junction temperature
Tj
(max)
-20 to 150 °C
Table A2-2 Key parameters of the control sector in IPM PM75DSA120
Input ON voltage (applied between CP1VPC, CN1-VNC)
VCIN(on)
(typ)
0 ~ 0.8 V
Input OFF voltage (applied between CP1VPC, CN1-VNC)
VCIN(off)
(typ)
4.0 ~ 5.1
Supply voltage (applied between VP1-VPC,
VN1-VNC)
VD
(max)
20 V
PWM input frequency
fPWM
(typ)
5 ~ 20 kHz
Fault output supply voltage (applied
between FPO-VPC and FNO-VNC)
VFO
(max)
20 V
Fault output current (sink current at FPO,
FNO terminal)
IFO
(max)
20 mA
162
Appendices
A3
Technical details of dSPACE − DS1104 R&D Controller Board
Table A3-1 Technical details of dSPACE − DS1104 R&D Controller Board
Processor
Power PC 603e running at 250 MHz
8 MB boot fl ash for applications
32 MB SDRAM global memory Comprehensive
8 A/D channels
8 D/A channels
20 bits of digital I/O (bit-selectable)
Incremental encoder interface (2 digital inputs)
Serial interface (UART)
Digital signal processor for three-phase PWM
Memory
Comprehensive
I/O interfaces
Interfaces
163
NOMENCLATURES
A
Electrical loading/Swept area of wind turbine rotor
r
A
Vector potential
A1 , A2
Vector potentials of two sides in a coil
Bδ max
Maximum flux density in the air gap
r
B
Flux density vector
Bt
Tangential component of the flux density
Bn
Normal component of the flux density
Cp
Coefficient of wind power
Di
Stator inner diameter
Em
Maximum value of phase back EMF
e(t )
Back EMF, a function of time
es (t )
Phase back EMF with sinusoidal waveform
et (t )
Phase back EMF with trapezoidal waveform
f ph
Commutating frequency of any phase
fn
Normal component of the force density
ft
Tangential component of the force density
is
Phase current with sinusoidal waveform
ia , ib , ic , id
Phase currents
if
Field current
164
Nomenclatures
Im
Maximum value of phase currents
it
Phase current with trapezoidal waveform
It
RMS of Phase current with trapezoidal waveform
Is
RMS of Phase current with sinusoidal waveform
J
The moment of inertia
J pm
Equivalent surface current density of PMs
r
J
Current density
Jf
Equivalent current density of the excitation field
ke
EMF waveform factor
ki
Current waveform factor
kp
Electrical power waveform factor
kr
Torque ripple factor
kv
Viscous damping coefficient
leff
Effective stack length
Laa , Lbb , Lcc , Ldd
Phase self-inductances
Lsk
Phase inductance under skewing rotor
Lx , L y
Two-phase inductance under skewing rotor
L ff
Self-inductance of field winding
m
Phase number
M ij ( i ≠ j )
Mutual inductances ( i = a, b, c, d / f , j = a, b, c, d / f )
N
Number of turns per phase winding
165
Nomenclatures
Ns
Stator pole number
Nr
Rotor pole number
Ni , N j , Nk
Shape functions
n
Rotor speed in rpm
ns
Rated speed in rpm
p
Machine pole pairs
Pmech
Mechanical output power of windmill
Ps
Average power of the machine with sinusoidal back EMF
and current
Pt
Average power of the machine with trapezoidal back EMF
and current
Po
Rated output power of motor
R
Radius of blades
Ra , Rb , Rc , Rd
Phase winding resistances
Rf
Field winding resistance
T ph
Per-phase torque
Tr
Per-phase reluctance torque component
Tpm
Per-phase permanent magnet torque component
Tav
Average torque component
Tp
Periodic torque component
Tmax
Maximum torque
Tmin
Minimum torque
166
Nomenclatures
Tl
Torque of load
Tinst
Instantaneous torque
va , vb , vc , vd
Phase voltages
νw
Wind velocity
vf
Field voltage
Wf
Energy stored in the magnetic field
W pm
Permanent magnet energy
Ww
Winding energy
ψ pm
Permanent magnet flux linkage
ψ pma , ψ pmb , ψ pmc , ψ pmd
Phase permanent magnet flux linkages
ψ sk
Flux linkage under skewing rotor
α
Position difference between phases
β
Phase shifting angle between the back EMF and current
βr
Rotor pole arc
βs
Stator pole arc
θ
Rotor position
θe
Electrical angle
θr
Rotor pole pitch
+
θ on
Switch-on angle in the positive stroke
+
θ off
Switch-off angle in the positive stroke
−
θ on
Switch-on angle in the negative stroke
167
Nomenclatures
−
θoff
Switch-off angle in the negative stroke
δ
Rotor skewing angle
ωr
Rotor angular speed
ρ
Air density
ν
Reluctivity
η
Efficiency of machine
168
LIST OF FIGURES
Fig. 1.1 Classification of EV motors. ........................................................................... 3
Fig. 2.1 Four-phase 8/6-pole SR motor....................................................................... 13
Fig. 2.2 Variation of inductance, flux linkage, torque and current with rotor position,
with ideal unidirectional current. ................................................................. 14
Fig. 2.3 Typical rotor configurations of PM brushless machines................................. 18
Fig. 2.4 Cross-section of a football shaped DSPM machine........................................ 19
Fig. 2.5 Cross-section of DSPM machine with arc magnets........................................ 20
Fig. 2.6 Structure of 4/6-pole dual stator DSPM machine........................................... 20
Fig. 2.7 Cross-section of single phase DSPM machine. .............................................. 20
Fig. 2.8 Flux and MMF for three kinds of brushless machines.................................... 23
Fig. 2.9 The theoretical variation of phase flux and MMF versus the rotor positions for
different kinds of brushless machines............................................................ 23
Fig. 3.1 Four-phase 8/6-pole DSPM motor. (a) Configuration. (b) Operating waveforms.
..................................................................................................................... 26
Fig. 3.2 Arrangement of position sensor..................................................................... 30
Fig. 3.3 Normal Four-phase operation. (a) System configuration. (b) Controlled current
waveform...................................................................................................... 31
Fig. 3.4 Proposed two-phase operation. (a) System configuration. (b) Controlled current
waveform...................................................................................................... 32
Fig. 3.5 Variation of motor parameters dLsk dθ with the rotor skewing. ..................... 33
Fig. 3.6 Variation of motor parameters dψ sk dθ with the rotor skewing. ..................... 33
169
List of Figures
Fig. 3.7 Calculated waveforms during 2-phase operation. (a)Self-inductances. (b) PM
flux linkages. (c) Back EMF at 600 rpm. ..................................................... 35
Fig. 3.8 Simulated waveforms at rated load during four-phase operation. (a)Phase
current. (b) Total torque............................................................................... 40
Fig. 3.9 Influence of rotor skewing angle. .................................................................. 41
Fig. 3.10 Influence of phase shifting angle. ................................................................ 41
Fig. 3.11 Simulated waveforms at rated load during two-phase operation. (a)Phase
current. (b) Total torque. ............................................................................ 42
Fig. 3.12 Measured two-phase waveforms. (a) No-load EMF at 600 rpm (50 V/div, 5
ms/div). (b) Phase current under rated load (1.65 A/div, 5 ms/div). ............ 44
Fig. 3.13 Measured current and torque waveforms at rated load. (a) 4-phase operation
(3.3 A/div, 2.3 Nm/div, 25ms/div). (b) 2-phase operation (3.3 A/div, 2.3
Nm/div, 25 ms/div).................................................................................... 45
Fig. 4.1 System configuration..................................................................................... 49
Fig. 4.2 Three-phase 12/8-pole DSPM generator. ....................................................... 51
Fig. 4.3 Trapezoidal waveform................................................................................... 53
Fig. 4.4 Magnetic field distributions using FEM. (a) No-load. (b) Full load................ 56
Fig. 4.5 PM flux linkage using FEM. ......................................................................... 57
Fig. 4.6
Inductance characteristics using FEM. (a) Mutual inductance. (b) Selfinductance. ................................................................................................ 57
Fig. 4.7 Simulated no-load EMF waveform. ............................................................... 60
Fig. 4.8 Simulated line voltage waveform. ................................................................. 60
Fig. 4.9 Simulated line current waveform. .................................................................. 60
Fig. 4.10 Simulated DC output voltage waveform. ..................................................... 61
170
List of Figures
Fig. 4.11 Measured no-load EMF waveform (20 V/div, 1 ms/div).............................. 63
Fig. 4.12 Measured line voltage and current waveform (50 V/div, 2 A/div, 5 ms /div).
.................................................................................................................. 63
Fig. 4.13 Measured DC output voltage waveform (20 V/div, 5 ms/div). ..................... 64
Fig. 4.14 Measured inverter output voltage and current waveforms (100 V/div, 2 A/div,
5 ms/div). .................................................................................................... 64
Fig. 4.15 Simulated and measured no-load line voltages. ........................................... 65
Fig. 4.16 Simulated and measured output voltage regulations..................................... 65
Fig. 4.17 Measured efficiencies.................................................................................. 65
Fig. 5.1 12/8-pole BDFDS machine. .......................................................................... 77
Fig. 5.2 Triangular element. ....................................................................................... 80
Fig. 5.3 Mesh generated for finite element analysis. ................................................... 84
Fig. 5.4 Magnetic field distributions........................................................................... 84
Fig. 5.5 Flux density distributions in air-gap. ............................................................. 85
Fig. 5.6 Flux linkage versus field current under different rotor positions. ................... 86
Fig. 5.7 Flux linkage versus rotor positions under different field currents................... 86
Fig. 5.8 Flux linkage versus rotor positions and field currents. ................................... 86
Fig. 5.9 EMF waveforms of a three-phase 12/8-pole machine at 1500 rpm................. 87
Fig. 5.10 Inductance characteristics............................................................................ 88
Fig. 6.1 Cross section of three-phase 12/8-pole BDFDS machine. .............................. 92
Fig. 6.2 Theoretical waveforms of flux linkage and current. ....................................... 92
Fig. 6.3 Half-bridge converter. ................................................................................... 96
Fig. 6.4 Simulated results based on half-bridge converter of BDFDS machine with
skewed rotor................................................................................................ 97
171
List of Figures
Fig. 6.5 Simulated results based on half-bridge converter of BDFDS machine with
unskewed rotor. ........................................................................................... 98
Fig. 6.6 Full-bridge converter..................................................................................... 98
Fig. 6.7 Simulated results based on full-bridge converter of BDFDS machine with
skewed rotor. ............................................................................................... 99
Fig. 6.8 Simulated results based on full-bridge converter of BDFDS machine with
unskewed rotor. ........................................................................................... 99
Fig. 6.9 Functional block diagram of the control system........................................... 100
Fig. 6.10 Structure of the digital PI controller........................................................... 103
Fig. 6.11 Flowchart of the control program. ............................................................. 104
Fig. 6.12 Theoretical Waveforms of BDFDS machine with skewed rotor. ................ 106
Fig. 6.13 Flux linkages of three-phase windings and control logic of the BDFDS
machine with un-skewed rotor. ................................................................ 107
Fig. 6.14 Three-phase command currents. ................................................................ 107
Fig. 6.15 Matlab/Simulink model of BDFDS machine system.................................. 110
Fig. 6.16 Block of phase A. ...................................................................................... 111
Fig. 6.17 Block of generating pulses for power switches. ......................................... 111
Fig. 6.18 Block to mechanic subsystem.................................................................... 111
Fig. 6.19 Simulated three-phase no-load back EMF at If=1 A and 1500 rpm. ........... 112
Fig. 6.20 Simulated phase back EMF under three different field current at 1500 rpm.
................................................................................................................... 112
Fig. 6.21 Simulated phase back EMF, command maximum and minimum currents at
1500 rpm. ................................................................................................ 113
172
List of Figures
Fig. 6.22 Simulated phase current, related maximum and minimum command phase
currents at 1500 rpm. ............................................................................... 113
Fig. 6.23 Simulated phase current (upper line) and phase voltage (lower line) under
If=1 A and 1500 rpm. .............................................................................. 114
Fig. 6.24 Simulated instantaneous torque (upper line) and phase current (lower line)
under If=1 A and 1500 rpm. .................................................................... 114
Fig. 6.25 Torque speed characteristic. ...................................................................... 115
Fig. 6.26 Comparison of constant power range at different field currents. ................ 115
Fig. 6.27 The simulated efficiency at 1500 rpm........................................................ 116
Fig. 6.28 The simulated dynamic response ( Tl =0.6 Nm, K p = 0.02 , K i = 0.003 ).... 116
Fig. 6.29 Simulated results of the BDFDS motor with unskewed rotor under rated load
at 600 rpm. ................................................................................................ 118
Fig. 6.30 Simulated results of the BDFDS motor with unskewed rotor at the speed of
1800 rpm. ................................................................................................ 118
Fig. 7.1 The configuration of experimental test-bed. ................................................ 121
Fig. 7.2 The prototype of BDFDS machine. ............................................................. 121
Fig. 7.3
The power converter, gating drive circuit, current sensor, dSPACE
connector/led panel and BDFDS machine in the experimental set-up. ............... 122
Fig. 7.4 The power converter and dSPACE connector/led panel............................... 122
Fig. 7.5 A real physical intelligent power module − PM75DSA120.......................... 125
Fig. 7.6 Circuit diagram of the intelligent power module − PM75DSA120............... 125
Fig. 7.7 The rotor position sensor of three-phase BDFDS machine........................... 126
Fig. 7.8 Position signal regulating circuit. ................................................................ 127
Fig. 7.9 Absolute value amplifier of phase current. .................................................. 128
173
List of Figures
Fig. 7.10 Three phase hysteretic current control circuits. .......................................... 129
Fig. 7.11 DS1104 R&D Controller Board................................................................. 131
Fig. 7.12 A block diagram of the DS1104 R&D Controller Board. ........................... 132
Fig. 7.13 Mearsured no-load phase back EMF waveform at 1500 rpm and If=1 A (20
V/div, 500 µs/div). ............................................................................................ 133
Fig. 7.14 Measured no-load phase back EMF waveforms at 1500 rpm with different
field currents (25 V/div, 25 V/div, 25 V/div, 1 ms/div). ..................................... 134
Fig. 7.15 Measured no-load three-phase back EMF waveforms at 1500 rpm and If=1 A
(20 V/div, 20 V/div, 20 V/div, 1 ms/div). .......................................................... 134
Fig. 7.16 Measured phase back EMF (bipolar trace), maximum (upper positive trace)
and minimum (lower positive trace) command currents at 120 rpm and If=1 A (7.6
V/div, 2.5 A/div, 2.5 A/div, 25 ms/div).............................................................. 135
Fig. 7.17 Measured phase back EMFs and related position signals waveforms. ........ 137
Fig. 7.18 Measured position signals of three position sensors (2 V/div, 2 V/div, 2 V/div,
5 ms/div). .......................................................................................................... 137
Fig. 7.19 Measured phase current at 1500 rpm and If=1 A (2.5 A/div, 1 ms/div). ..... 138
Fig. 7.20 Measured phase current (upper) and position signal (lower) waveforms at
1500 rpm and If=1 A (2.5 A/div, 2 V/div, 2 ms/div). ......................................... 138
Fig. 7.21 Measured phase current (bipolar trace), related maximum (upper positive
trace) and minimum (lower positive trace) command current waveforms at 1500
rpm and If=1 A (2.5 A/div, 1 ms/div). ............................................................... 139
Fig. 7.22 Measured phase current (upper) and phase voltage (lower) waveforms at 1500
rpm and If=1 A (2.5 A/div, 50 V/div, 2 ms/div)................................................. 139
174
List of Figures
Fig. 7.23
Measured speed (upper) and current (lower) responses of the BDFDS
machine starting from standstill to rated speed − 1500 rpm (400 rpm/div, 2.5 A/div,
1 S/div). ............................................................................................................ 140
Fig. 7.24
Measured current (upper) and speed (lower) responses of the BDFDS
machine under a sudden change of load from 3.2 Nm to 0.6 Nm at 1500 rpm and
If=1 A (5 A/div, 600 rpm/div, 1 S/div). ............................................................. 140
Fig. 7.25
Measured current (upper) and speed (lower) responses of the BDFDS
machine under a sudden change of load from 0.6 Nm to 3.2 Nm at 1500 rpm and
If=1 A (2.5 A/div, 400 rpm/div, 1 S/div). .......................................................... 141
Fig. 7.26 Measured characteristics of the BDFDS machines at 1500 rpm and If=1 A.
......................................................................................................................... 141
Fig. 7.27 Measured efficiency at If=1 A. .................................................................. 142
Fig. 7.28 System efficiency...................................................................................... 142
Fig. 7.29 Measured no-load EMF waveform at rated speed − 1500rpm (50 V/div, 2
ms/div).............................................................................................................. 144
Fig. 7.30 Measured phase current (upper)and phase voltage (lower) waveforms under
rated load (4.5 A/div, 50 V/div, 5 ms/div). ........................................................ 144
Fig. 7.31 Measured line to line voltage waveform under rated load (50 V/div, 5 ms/div).
......................................................................................................................... 144
Fig. 7.32 Measured phase current (upper) and totoal torque (lower) waveforms under
rated load (4.5 A/div, 2.8 Nm/div, 5 ms/div). .................................................... 145
Fig. 7.33 Measured phase current (upper) and gating signal of the upper switch (lower)
waveforms (4.5 A/div, 2 V/div, 5 ms/div).......................................................... 145
175
List of Figures
Fig. 7.34 Measured phase current (upper) and gating signal of the lower switch (lower)
waveforms (4.5 A/div, 2 V/div, 5 ms/div). ............................................... 145
Fig. 8.1 System configuration................................................................................... 148
Fig. 8.2 Simulated waveforms of line voltage, phase current and DC output voltage. 151
Fig. 8.3 Measured line voltage and phase current waveform (100 V/div, 5 A/div, 2.5
ms/div). ..................................................................................................... 151
Fig. 8.4 Measured DC output voltage waveform (20 V/div, 2.5 ms/div). .................. 152
Fig. 8.5 Measured no load EMF characteristic at various field currents. ................... 153
Fig. 8.6 Measured no load line to line voltage characteristic at various speeds and field
currents...................................................................................................... 153
Fig. 8.7 Measured DC output voltage characteristic at various speeds. ..................... 153
Fig. 8.8 Measured DC output voltage characteristic at various speed and load currents.
................................................................................................................ 154
Fig. 8.9 Measured efficiency characteristic at various field currents at rated speed and
load. .......................................................................................................... 154
176
LIST OF TABLES
Table 2-1 Comparison of PMBLAC and PMBLDC ................................................... 16
Table 3-1 Control logic for four-phase operation........................................................ 31
Table 3-2 Control logic for 2-phase operation ............................................................ 34
Table 4-1 Power Ratio of Sinusoidal to Square Wave Generators............................... 54
Table 4-2 Data of Prototype ....................................................................................... 62
Table 5-1 Typical Prototype Waveforms.................................................................... 72
Table 5- 2 Design data of the BDFDS machine .......................................................... 76
Table 6-1 Control logic of the three phase converter ................................................ 102
Table 7-1 Types and features of the instruments involved in experimental set-up..... 123
Table 7-2 Results of hysteretic current control circuit .............................................. 130
Table A1-1 The characteristics of various power switches ....................................... 160
Table A2-1 Key parameters of the IGBTs in IPM PM75DSA120............................. 162
Table A2-2 Key parameters of the control sector in IPM PM75DSA120 .................. 162
Table A3-1 Technical details of dSPACE − DS1104 R&D Controller Board ........... 163
177
REFERENCES
[1]
T.J.E. Miller, Brushless Permanent Magnet and Reluctance Motor Drives.
Clarendon Press, Oxford, 1989.
[2]
B.K. Bose, “Power electronics and motion control–technology status and recent
trends,” IEEE Transactions on Industry Applications, Vol. 29, No. 5, pp. 902-909,
September/October,1993.
[3]
G.R. Slemon, “Electrical machines for variable-frequency drives,” Proceedings of
IEEE, Vol. 82, No. 8, pp. 1123-1139, Aug. 1994.
[4]
P.C. Sen, “Electric motor drives and control–past, present and future,” IEEE
Transactions on Industrial Electronics, Vol. 37, No. 6, pp. 562-575, 1990.
[5]
B.K. Bose, Power Electronics and Variable Frequency Drives–Technology and
Applications, IEEE Press, 1997.
[6]
T.A. Lipo, “Recent progress in the development of solid-state AC motor drives,”
IEEE Transactions on Power Electronics, Vol. 3, No. 2, pp. 102-117, 1988.
[7]
C.C. Chan, K.T. Chau, J.Z. Jiang, W. Xia, M. Zhu, and R. Zhang, “Novel
permanent magnet motor drives for electric vehicles,” IEEE Transactions on
Industrial Electronics, Vol. 43, No. 2, pp. 331-339, April 1996.
[8]
R. Deodhar, S. Anderson, I. Boldea, and T.J.E. Miller, “The flux-reversal machine:
a new brushless doubly-salient permanent magnet machine,” IEEE Transactions
on Industry Applications, Vol. 33, No. 4, pp. 925-934, 1997.
[9]
Y.S. Chen, Z.Q. Zhu, and D. Howe, “Slotless brushless permanent magnet
machines: influence of design parameters”, IEEE Transactions on Energy
Conversion, Vol. 14, No. 3, pp. 686-691, 1999.
178
References
[10] C. C. Chan, and K. T. Chau, “An overview of power electronics in electric
vehicles,” IEEE Transactions on Industrial Electronics, Vol. 44, No. 1, pp. 3–13,
1997.
[11] C. C. Chan, and K. T. Chau, “An advanced permanent magnet motor drive system
for battery-powered electric vehicles,” IEEE Transactions on Vehicular
Technology, Vol. 45, No.1, pp. 180–188, 1996.
[12] Y. Liao, F. Liang, and T. A. Lipo, “A novel permanent magnet motor with doubly
salient structure,” IEEE Transactions on Industry Applications, Vol. 31, No.7, pp.
1069–1078, 1995.
[13] M. Cheng, K.T. Chau, C.C. Chan, E. Zhou and X., Huang, “Nonlinear varyingnetwork magnetic circuit analysis for doubly salient permanent magnet motors,”
IEEE Transactions on Magnetics, Vol. 36, No. 1, 339–348, 2000.
[14] M. Cheng, K.T. Chau, and C.C. Chan, “New split-winding doubly salient
permanent magnet motor drive,” IEEE Transactions on Aerospace and Electronic
Systems, Vol. 39, No. 1, pp. 202–210, 2003.
[15] M. A. Rahman, and R. F. Qin, “A permanent magnet hysteresis hybrid
synchronous motor for electric vehicles,” IEEE Transactions on Industrial
Electronics, Vol. 44, No. 1, pp. 46–53, 1997.
[16] M. Dai, A. Keyhani, and T. Sebastian, “Torque ripple analysis of a PM brushless
DC motor using finite element method,” IEEE Transactions on Energy
Conversion, Vol. 19, No. 1, pp. 40-45, 2004.
[17] K. Atallah, J. Wang, and D. Howe, “Torque-ripple minimization in modular
permanent-magnet brushless machines,” IEEE Transactions on Industry
Applications, Vol. 39, No. 6, pp. 1689-1695, 2003.
179
References
[18] Y. Liu, Z.Q. Zhu, and D. Howe, “Direct torque control of brushless DC drives
with reduced torque ripple,” IEEE Transactions on Industry Applications, Vol. 41,
No. 2, pp. 599-608, 2005.
[19] K.T. Chau, Q. Sun, Y. Fan, and M. Cheng, “Torque ripple minimization of doubly
salient permanent-magnet motors,” IEEE Transactions on Energy Conversion,
Vol. 20, No. 2, pp. 352-358, 2005.
[20] T. Ackermann and L. Söder, “An overview of wind energy-status 2002,”
Renewable and Sustainable Energy Reviews, Vol. 6, No. 1-2, pp. 67-127, 2002.
[21] X. Zhao and P. Maißer, “A novel power splitting drive train for variable speed
wind power generators,” Renewable Energy, Vol. 28, No. 13, pp. 2001-2011,
2003.
[22] L. Holdsworth, X.G. Wu, J.B. Ekanayake, and N. Jenkins, “Comparison of fixed
speed and doubly-fed induction wind turbines during power system disturbances,”
IEE Proceedings-Generation, Transmission and Distribution, Vol. 150, No. 3, pp.
343-352, 2003
[23] S. Müller, M. Deicke, and R.W. De Doncker, “Doubly fed induction generator
systems for wind turbines,” Industry Applications Magazine, IEEE, Vol. 8, No. 3,
pp. 26-33. 2002.
[24] R. Datta and V.T. Ranganathan, “Variable-speed wind power generation using
doubly fed wound rotor induction machine-a comparison with alternative
schemes,” IEEE Transactions on Energy Conversion, Vol. 17, No. 3, pp. 414-421,
2002.
180
References
[25] B.J. Chalmers and E. Spooner, “An axial-flux permanent-magnet generator for a
gearless wind energy system,” IEEE Transactions on Energy Conversion, Vol. 14,
No. 2, pp. 251-257, 1999.
[26] J. Chen, C.V. Nayar, and L. Xu, “Design and finite-element analysis of an outerrotor permanent-magnet generator for directly coupled wind turbines,” IEEE
Transactions on Magnetics, Vol. 36, No. 5, pp. 3802-3809, 2000.
[27] E. Muljadi, C.P. Butterfield, and Y. H. Wan, “Axial-flux modular permanentmagnet generator with a toroidal winding for wind-turbine applications,” IEEE
Transactions on Industry Applications, Vol. 35, No. 4, pp. 831-836, 1999.
[28] H. Chen, T. Su, F. Xiao, and Y. Zhu, “A switched reluctance wind power
generator with the excitation of low voltage,” 2002 IEEE International
Conference on Systems, Man and Cybernetics, Vol. 6, No. WA2I4, pp. 1-5, 2002.
[29] S. Bhowmik, R. Spee, and J.H.R. Enslin, “Performance optimization for doubly
fed wind power generation systems,” IEEE Transactions on Industry Applications,
Vol. 35, No. 4, pp.949-958. 1999.
[30] M.G. Jovanović, R.E. Betz, and J. Yu, “The use of doubly fed reluctance
machines for large pumps and wind turbines,” IEEE Transactions on Industry
Applications, Vol. 38, No. 6, pp.1508-1516, 2002.
[31] S.A. Nasar, I. Boldea and L.E. Unnewehr, Permanent Magnet, Reluctance, and
Self-synchronous Motors, CRC Press, 1993.
[32] T.A. Lipo, “Recent progress in the development of solid-state ac motor drives,”
IEEE Trans. on Power Electronics, Vol. 3, No. 2, pp. 102-117, 1988.
[33] T.J.E. Miller, Electronic Control of Switched Reluctance Machines, Oxford:
Newnes, 2001.
181
References
[34] C.C. Chan and K.T. Chau, Modern Electric Vehicle Technology, Oxford
University Press, 2001.
[35] P.J. Lawrenson, J.M. Stephenson, P.T. Blenkinsop, J. Corda and N.N. Fulton,
“Variable-speed switched reluctance motors”, IEE Proceedings B, Vol. 127, No.
4, pp. 253-265, 1980.
[36] M.R. Harris, J.W. Finch, J.A. Malick, T.J.E. Miller, “A Review of the Integral
Horsepower Switched Reluctance Drives,” IEEE Trans. on Industry Applications,
Vol. 22, No. 4, pp. 716-721, 1986.
[37] M.F. Momen and I. Husain, “Design and Performance Analysis of a Switched
Reluctance Motor for Low Duty Cycle Operation,” IEEE Trans. on Industry
Applications, Vol. 41, No. 6, pp. 1612-1618, 2005.
[38] K.M. Rahman and S.E. Schulz, “Design of high-efficiency and high-torquedensity switched reluctance motor for vehicle propulsion,” IEEE Trans. on
Industry Applications, Vol. 38, No. 6, pp. 1500-1507, 2002.
[39] K.M. Rahman, B. Fahimi, G. Suresh, A.V. Rajarathnam and M. Ehsani,
“Advantages of switched reluctance motor applications to EV and HEV: design
and control issues,” IEEE Trans. on Industry Applications, Vol. 36, No.1, pp. 111121, 2000.
[40] A.M. Michaelides and C. Pollock, “Modeling and design of switched reluctance
motors with two phases simultaneously excited,” Electric Power Applications,
IEE Proceedings, Vol. 143, No. 5, pp. 361-370, 1996.
[41] M.S. Islam, M.N. Anwar and I. Husain, “Design and control of switched
reluctance motors for wide-speed-range operation,” Electric Power Applications,
IEE Proceedings, Vol. 150, No. 4, pp. 425-430, 2003.
182
References
[42] T.J.E. Miller, “Optimal design of switched reluctance motors,” IEEE Trans. on
Industrial Electronics, Vol. 49, No. 1, pp. 15-27, 2002.
[43] T.A. Lipo and J.C. Moreira, “Simulation of a Four Phase Switched Reluctance
Motor Including the Effects of Mutual Coupling,” Electric Machines and Power
System, Vol. 16, pp.281-299, 1989.
[44] N.C. Sahoo, J.X. Xu and S.K. Panda, “Low torque ripple control of switched
reluctance motors using iterative learning,” IEEE Trans. On Energy Conversion,
Vol. 16, No. 4, pp. 318-326, 2001.
[45] N.T. Shaked and R. Rabinovici, “New procedures for minimizing the torque
ripple in switched reluctance motors by optimizing the phase-current profile,”
IEEE Trans. on Magnetics, Vol. 41, No. 3, pp. 1184-1192, 2005.
[46] M.S. Islam and J. Husain, “Torque-ripple minimization with indirect position and
speed sensing for switched reluctance motors,” IEEE Trans. on Industrial
Electronics, Vol. 47, No. 5, pp. 1126-1133, 2000.
[47] L. Venkatesha and V. Ramanarayanan, “Comparative study of pre-computed,
current methods for torque ripple minimization in switched reluctance motor,”
IEEE IAS Annual Meeting, Vol. 1, pp.119-125, 2000.
[48] T.M. Jahns, "Motion control with permanent magnet AC machines," Proceedings
of the IEEE, Vol. 82, No. 8, pp.1241-1252, 1994.
[49] Y. Liao and T.A. Lipo, “A new doubly salient permanent magnet motor for
adjustable speed drives”, Electric Machines and Power Systems, Vol. 22, No. 1,
pp. 259-270, 1994.
183
References
[50] Y. Li and T.A. Lipo, “A doubly salient permanent magnet motor capable of field
weakening”, Proceedings of IEEE Power Electronic Specialist Conference,
Atlanta, USA, pp. 565-571, June 18-22, 1995.
[51] T.A. Lipo, Y. Li, X. Luo, and B. Sarlioglu, “Doubly salient permanent magnet
machines – A progress report”, Proceedings of the IEEE/KTH Stockholm Power
Tech Conference, Stockholm, Sweden, pp. 81-86, June 18-22, 1995.
[52] F. Leonardi, T. Matsuo, Y. Li, T.A. Lipo, and P. McCleer, “Design consideration
and test results for a doubly salient PM motor with flux control”, Proceedings of
the 31st IEEE IAS Annual Meeting, San Diego, USA, pp. 458-463, Oct. 6-10, 1996.
[53] A. Shakal, Y. Liao, and T.A. Lipo, “A permanent magnet AC machine structure
with true field weakening capability”, Electric Machines and Power Systems, Vol.
24, No. 5, pp. 497-509, 1996.
[54] X. Luo, D. Qin, and T.A. Lipo, “A novel two phase doubly salient permanent
magnet motor”, Conference Record of the 31st IEEE IAS Annual Meeting, San
Diego, USA, pp. 808-815, Oct. 6-10, 1996.
[55] F. Blaabjerg, L. Christensen, P.O. Rasmussen, L. Oestergaard, and P. Pedersen,
“New advanced control methods for doubly salient permanent magnet motor”,
Conference Record of the 30th IEEE IAS Annual Meeting, Orlando, USA, pp. 222230, Oct. 8-12, 1995.
[56] M.M. Radulescu, C. Martis, and K. Biro, “A new electrically-commutated
doubly-salient permanent-magnet small motor”, Proceedings of the 7th
International Conference on Electrical Machines and Drives, Durham, UK, pp.
213-216, Sept. 11-13, 1995.
184
References
[57] M. Cheng, K.T. Chau, and C.C. Chan, “Static characteristics of a new doubly
salient permanent magnet motor”, IEEE Transactions on Energy Conversion, Vol.
16, No. 1, pp. 20-25, 2001.
[58] C. Martis, M.M. Radulescu, and Biro K., “On the dynamic model of a doublysalient permanent magnet motor”, Proceedings of Mediterranean Electrotechnical
Conference, Tel-Aviv, Israel, pp. 410-414, May 18-20, 1998.
[59] D.X. Bian and Q.H. Zhan, “A novel single phase doubly salient permanent
magnet motor,” Proceedings of IEEE International Conference on Power
Electronics and Drive Systems, Hong Kong, pp. 725-729, July 27-29, 1999.
[60] K.T. Chau, M. Cheng and C.C. Chan, “Performance analysis of 8/6-pole doubly
salient permanent magnet motor,” Electric Machines and Power Systems, Vol. 27,
No. 10, pp. 1055-1067, 1999.
[61] M. Cheng, K.T. Chau and C.C. Chan, “Design and analysis of a new doubly
salient permanent magnet motor,” IEEE Transactions on Magnetics, Vol. 37,
No.4, pp. 3012-3020, 2001.
[62] J.R. Hendershot Jr. and T.J.E. Miller, Design of Brushless Permanent-Magnet
Motors. Oxford University Press, 1994.
[63] F. Soares and P.J. Costa Cranco, “Simulation of a 6/4 switched reluctance motor
based on Matlab/Simulink environment,” IEEE Transactions on Aerospace and
Electronic Systems, vol. 37, No. 3, pp. 989-1009, 2001.
[64] H. Chen, C. Zhang, and X.C. Zhao, “Research on the switched reluctance wind
generator system,” IEEE International Conference on Systems, Man, and
Cybernetics, 2001, pp. 1936–1941.
185
References
[65] B. Sarlioglu, Y.F. Zhao, and T.A. Lipo, “A novel doubly salient single phase
permanent magnet generator,” IEEE Industry Applications Society Annual
Meeting, 1994, pp. 9–15.
[66] M. Cheng, K.T. Chau, C.C. Chan, and Q. Sun, “Control and operation of a new
8/6-pole doubly salient permanent magnet motor drive,” IEEE Trans. Ind. Appl.,
vol. 39, no. 5, 2003, pp. 1363–1371.
[67] B. Sarlioglu and T.A. Lipo, “Comparison of power production capability between
doubly salient permanent magnet and variable reluctance type generators,”
International Aegean Conference on Electrical Machines and Power Electronics,
1995, pp. 1–8.
[68] B. Sarlioglu and T.A. Lipo, “Nonlinear analysis and experimental result of doubly
salient PM generator,” International Conference of Electrical Machines and
Power Electronics, 2001, pp. 1–6.
[69] B. Sarlioglu and T.A. Lipo, “Assessment of power generation capability of
doubly-salient PM generator,” IEEE International Electric Machines and Drive
Conference, 1999, pp. 549–552.
[70] B. Sarlioglu and T.A. Lipo, “Nonlinear modeling and simulation of single phase
doubly salient permanent magnet generator,” IEEE Industry Applications Society
Annual Meeting, 1998, pp. 18–26.
[71] M.R. Patel, Wind and Solar Power Systems. CRC Press, 1999.
[72] S. Huang, J. Luo, F.Leonardi, and T. A. Lipo, “A general Approach to Sizing and
Power Density Equations for Comparison of Electrical Machines,” IEEE Trans.
on Industry Applications, Vol. 34, No. 1, pp. 92-97, 1998.
186
References
[73] S. Huang J. Luo, F. Leonardi, and T. A. Lipo, “Comparison of Power Density for
Axial Flux Machines Based on General Purpose Sizing Equations,” IEEE Trans.
on Energy Conversion. Vol. 14, No. 2, pp. 185-192, 1999.
[74] R. Krishnan, Switched Reluctance Motor Drives, CRC press, 2001.
[75] R. Krishnan, R. Arumugan and J.F. Lindsay, “Design procedure for switchedreluctance motors,” IEEE Trans. on Industry Applications, Vol. 24, No. 3,
pp.:456-461, 1988.
[76] S.J. Salon, Finite Element Analysis of Electrical Machines. Kluwer Academic
Publishers, 1995.
[77] K.J. Astrom and T. Hagglund, PID Controllers: Theory, Design and Tuning,
Research Triangle Park, N.C.: Instrument Society of American, 1995.
[78] Y. Fan, K.T. Chau, and M. Cheng, “A new three-phase doubly salient permanent
magnet machine for wind power generation,” IEEE Transactions on Industry
Applications, Vol. 42, No. 1, pp. 53-60, January/February 2006.
[79] Y. Fan and K.T. Chau, “Design, modeling and analysis of a brushless doubly-fed
doubly-salient machine for electric vehicles,” Industry Applications Conference,
40th IAS Annual Meeting. Conference Record of the 2005 IEEE, Hong Kong,
China, pp. 2712-2719, 2-6 Oct., 2005,
[80] C.G. Kim, J.H. Lee, , H.W. Kim, and M.J. Youn, “Study on maximum torque
generation for sensorless controlled brushless DC motor with trapezoidal back
EMF,” IEE Proceedings – Electric Power Applications, Vol. 152, No. 2, pp. 277291, March 2005.
187
References
[81] G.J. Su and J.W. McKeever, “Low-cost sensorless control of brushless DC motors
with improved speed range,” IEEE Transactions on Power Electronics, Vol. 19,
No. 2, pp. 296-302, 2004.
[82] D.H. Jung, and I.J. Ha, “Low-cost sensorless control of brushless DC motors
using a frequency-independent phase shifter”, IEEE Transactions on Power
Electronics, Vol. 15, No. 4, pp. 744-752, 2000.
[83] N. Kasa and H. Watanabe, “A mechanical sensorless control system for salientpole brushless DC motor with autocalibration of estimated position angles”, IEEE
Transactions on Industrial Electronics, Vol. 47, No. 2, pp. 389-395, April 2000.
[84] I.W. Wang and Y.S. Kim, “Rotor speed and position sensorless control of a
switched reluctance motor using the binary observer”, IEE Proceedings – Electric
Power Applications, Vol. 147, No. 3, pp. 220-226, May 2000.
188
PUBLICATIONS
International Journal Papers:
[J.1] Ying Fan, K.T. Chau, and Ming Cheng, “A new three-phase doubly salient
permanent magnet machine for wind power generation,” IEEE Transactions on
Industry Applications, Vol. 42, No. 1, pp. 53-60, January/February 2006.
[J.2] Ying Fan, K.T. Chau, “Torque ripple minimization of four-phase doubly salient
permanent magnet motors using two-phase operation,” Electric Power
Components and Systems, Vol. 34, No. 4, pp. 401-415, April 2006.
[J.3] Ying Fan, K.T. Chau, “Development of doubly salient permanent magnet motors
for electric vehicles,” Journal of Asian Electric Vehicles, Vol. 3, No. 1, pp. 689695, June 2005.
[J.4] Ming Cheng, Ying Fan, and K.T. Chau, “Design and analysis of a novel statordoubly-fed doubly salient motor for electric vehicles,” Journal of Applied Physics,
Vol. 97, No. 5, pp. May 2005.
[J.5] K. T. Chau, Qiang Sun, Ying Fan, and Ming Cheng, “Torque ripple minimization
of doubly salient permanent magnet motors,” IEEE Transactions on Energy
Conversion, Vol. 20, No. 2, pp. 352-358, June 2005.
[J.6] Ying Fan and K. T. Chau, “Design, modeling and analysis of a brushless doublyfed doubly-salient machine for electric vehicles,” IEEE Transactions on Industry
Applications, submitted.
[J.7] Ying Fan and K. T. Chau, “Development of a new brushless doubly-fed doublysalient machine for wind power generation,” IEEE Transactions on Magnetics,
under revised.
189
Publications
International Conference Papers:
[C.1] K.T. Chau, Ying Fan, and Ming Cheng, “A novel three-phase doubly salient
permanent magnet machine for wind power generation,” Industry Applications
Conference, 39th IAS Annual Meeting. Conference Record of the 2004 IEEE,
Seattle, USA, 3-7 Oct. 2004, pp. 366-372.
[C.2] Ying Fan and K. T. Chau, “Design, modeling and analysis of a brushless doublyfed doubly-salient machine for electric vehicles,” Industry Applications
Conference, 40th IAS Annual Meeting. Conference Record of the 2005 IEEE,
Hong Kong, China, 2-6 Oct., 2005, pp. 2712-2719.
[C.3] Ying Fan and K. T. Chau, “Development of a new brushless doubly-fed doublysalient machine for wind power generation,” Proceedings of IEEE International
Magnetics Conference (Intermag), San Diego, California, USA, May 8 to 12,
2006. No. HU-04, p. 1
[C.4] Ying Fan and K. T. Chau, “Design and analysis of a novel torque-ripple-free
doubly salient permanent magnet motor,” 49th Annual Conference on Magnetism
& Magnetic Materials, Jacksonville, USA, 2004, No. GQ-12, p. 1.
[C.5] Ming Cheng, Ying Fan and K.T. Chau, “Design and analysis of a novel statordoubly-fed doubly salient motor for electric vehicles,” 49th Annual Conference on
Magnetism & Magnetic Materials, Jacksonville, USA, 2004, No. GQ-03, p. 1.
[C.6] Ying Fan, K.T. Chau, and Ming Cheng, “Control of doubly salient permanent
magnet motor drives,” Proceedings of the International Conference on Electrical
Engineering (ICEE2003), Hong Kong, China, 6-10 July, 2003, No. ICEE-315, p.
1.
190