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University of WollongongResearch Online
University of Wollongong Thesis Collection University of Wollongong Thesis Collections
2001
Modelling and field-oriented control of asynchronous reluctance motor with rectangularstator current excitationColin CoatesUniversity of Wollongong
Research Online is the open access institutional repository for theUniversity of Wollongong. For further information contact ManagerRepository Services: [email protected].
Recommended CitationCoates, Colin, Modelling and field-oriented control of a synchronous reluctance motor with rectangular stator current excitation,Doctor of Philosophy thesis, School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, 2001.http://ro.uow.edu.au/theses/1849
MODELLING AND FIELD-ORIENTED CONTROL
OF A SYNCHRONOUS RELUCTANCE MOTOR
WITH RECTANGULAR STATOR CURRENT
EXCITATION
A thesis submitted in fulfilment of the requirements for the award of the degree
DOCTOR OF PHILOSOPHY
from
UNIVERSITY OF WOLLONGONG
by
COLIN COATES, B.MATH-B.E.
School of Electrical, Computer and Telecommunications Engineering
August, 2001
ABSTRACT
The rotor saliency of the axially laminated synchronous reluctance motor (SynRM) produces a
rectangular air-gap flux density distribution. Optimal torque / rms ampere is achieved from the
machine if a rectangular stator current distribution interacts with this flux. The impact of
rectangular stator currents on the design and control of the SynRM are considered.
A design model is developed that assumes rectangular stator currents. The design model is
based on an existing lumped element model of the SynRM magnetic circuit that has been
extended to include saturation effects. All stator and rotor dimensions are included in the
design model. The key dimensions are identified and a simple iterative algorithm is determined
for optimising these values.
A 5.0kW experimental motor is designed and built with an optimal torque / unit mass ratio.
The designed motor has a nine-phase concentrated winding to approximate the ideal rectangular
stator current distribution. Finite element analysis and static tests demonstrate the validity of
the design model.
Generalised voltage and torque expressions are developed for the nine-phase machine. An
orthogonal transformation is obtained to isolate the direct and quadrature, harmonic
components of the stator inductance matrix. This transformation is applied to the standard
stator voltage and torque equations to determine the equivalent d-q harmonic component
equations.
Two field-oriented control strategies are developed for the multiphase SynRM drive. A simple
stator reference frame control strategy is implemented and performance results presented. A
transformed frame vector controller is demonstrated to have theoretically superior performance
to the stator reference frame controller but could not be implemented due to the excessive
computational requirement for this strategy.
DECLARATION
I, Colin Coates, declare that this thesis, submitted in fulfilment of the
requirements for the award of Doctor of Philosophy, in the School of
Electrical, Computer and Telecommunications Engineering, University of
Wollongong, is wholly my own work unless otherwise referenced or
acknowledged. The document has not been submitted for qualifications at
any other academic institution.
Colin Coates
3rd August 2001
ACKNOWLEDG EM ENTS
I would like to thank Don Piatt, Vic Gosbell and Sarath Perera for their guidance, assistance
and encouragement throughout this project.
Particular mention must also go to Brian Webb whose mechanical skills turned my ideas into a
motor, as he does with so many other projects at the University of Wollongong.
Finally, I would like to express my love and gratitude to my wife, Charlene, for her patience,
encouragement and support.
TABLE OF CONTENTS
Abstract
Declaration
Acknowledgements
Table of Contents
List of Figures
List of Symbols
Chapter 1 1.1
Introduction Overview of Electrical Machine Technology
1.1.1 Permanent Magnet Motor
1.1.2 Switched Reluctance Motor
1.1.3 Synchronous Reluctance Motor
1.2 The SynRM: an Historical Perspective
1.2.1 Salient Pole Rotor
1.2.2 Segmented Rotor
1.2.3 Flux Barrier Rotor
1.2.4 Axially Laminated ^isotropic Rotor
1.2.5 Stator Winding Considerations
1.3 Project Overview
1.4 Thesis Outline
IV
vii
1
3
4
5
6
6
8
9
. 10
. 12
. 14
. 16
Chapter 2 Magnetic Circuit Modelling and Design Optimization of the SynRM
2.1. Introduction ... 18
2.2. Design Strategy
2.3. Magnetic Circuit Model
2.4. Saturation Effects
... 19
...22
...25
ii
2.5. Optimization Algorithm ... 29
2.5.1. Key Independent Dimensions ... 30
2.5.2. Dependent Dimensions ...31
2.5.3. Optimization Algorithm ...33
2.6. Optimization Results and Analysis ... 34
2.7. Summary ... 37
Chapter 3 The 5kW Synchronous Reluctance Motor 3.1 Introduction ...39
3.2 5 kW SynRM Construction ... 40
3.3 Results and Analysis ... 46
3.4 Summary ... 51
Chapter 4 Generalized Equations for a Nine Phase SynRM 4.1 Introduction ... 52
4.2 The Stator Inductance Matrix ... 53
4.3 Voltage Equation ... 63
4.4 Torque Equation ... 67
4.5 Summary ... 68
Chapter 5 Field-Oriented Control of the SynRM 5.1 Introduction ...69
5.2 Stator Current Controller ... 70
5.2.1 Stator Current Reference ... 70
5.2.2 Inverter Switching Strategy ... 74
5.2.3 Stator Current Controller Simulation ... 74
5.3 Transformed Frame Vector Controller ... 77
5.3.1 Transformed Frame Current Reference ... 78
5.3.2 Voltage Vector Selection ... 79
5.3.3 Transformed Frame Vector Controller Simulation ... 84
iii
5.4 Summary ... 90
Chapter 6 The Nine Phase Inverter and Controller 6.1 Introduction ... 91
6.2 Inverter Power Circuit ... 92
6.3 DSP Controller ...95
6.4 Controller Interface Circuit ... 97
Chapter 7 The SynRM Drive Software and Performance 7.1 Introduction ... 102
7.2 Control Software ...102
7.2.1 Transformed Frame Vector Controller ... 103
7.2.2 Stator Current Controller ...107
7.3 Performance Results ...111
Chapter 8 Conclusions ... 124
References ... 128
Publications of Work Performed as Part of this Thesis ... 133
Appendix A 5kW SynRM Schematics
Appendix B Inverter Schematics
Appendix C Control Program Listing
Appendix D Numerical Solution to SynRM Model Differential Equation
Appendix E Device Data Sheets
Appendix F Control Simulation Source Files
Appendix G Derivation of Quadrature Axis Reluctance
LIST OF FIGURES
Fig 1.1 Diagrammatic representation of a PMM. 3
Fig 1.2 Diagrammatic representation of a SRM. 4
Fig 1.3 Diagrammatic representation of a SynRM. 5
Fig 1.4 SynRM rotor structures. 7
Fig 2.1 Equivalent magnetic circuit model. 23
Fig 2.2 Typical air-gap flux density distribution in a two-pole SynRM. 24
Fig 2.3 Simplified magnetic circuit of SynRM. 25
Fig 2.4 B-H characteristic assumed for iron. 27
Fig 2.5 Air-gap flux density distributions with iron saturation effects with (a) 28
direct axis excitation, (b) quadrature axis excitation, (c) combined direct
and quadrature axis excitation.
Fig 2.6 Piecewise linear approximation to the air-gap flux density distribution. 29
Fig 2.7 Stator tooth tip detail. 31
Fig 2.8 Block diagram of optimization algorithm. 34
Fig 2.9 Optimum motor dimensions as machine size is varied. 35
Fig 2.10 Sensitivity of machine performance to design parameters. 37
Fig 3.1 Prototype 5kW SynRM. 39
Fig 3.2 5kW SynRM stator lamination. 41
Fig 3.3 5kW SynRM rotor. 45
Fig 3.4 Air-gap flux density distribution in 5kW SynRM. 47
Fig 3.5 Variation of SynRM torque with rotor position. 47
Fig 3.6 Phase winding model. 48
Fig 3.7 Direct axis magnetizing inductance. 49
Fig 3.8 Quadrature axis magnetizing inductance. 49
Fig 3.9 Magnetizing inductance of one phase versus rotor position. 50
Fig 3.10 Mutual inductance between two stator phase windings versus rotor 50
position.
Fig 4.1 Generalized coils on SynRM rotor. 54
Fig 4.2 Air-gap flux density distribution 55
Fig 4.3 Decomposition of air-gap flux density distribution 57
Fig 4.4 Theoretical and measured (a) self inductance for phase 'a' and (b) 59
mutual inductance between phase 'a' and 'e' for the experimental
SynRM.
Fig 5.1
Fig 5.2
Fig 5.3
Fig 5.4
Fig 5.5
Fig 5.6
Fig 5.7
Fig 5.8
Fig 5.9
Fig 5.10
Fig 5.11
Fig 5.12
Fig 5.13
Fig 6.1
Fig 6.2
Fig 6.3
Fig 6.4
Fig 6.5
Compensation for slot effects in the stator current reference
Phase current adjustments for star connected stator.
Typical phase current reference versus rotor position.
Stator current controller simulation block diagram.
Speed controller including approximation to torque control loop.
Step response of torque controller.
S y n R M current reference in transformed rotor current plane.
Voltage vectors from a nine-phase inverter.
Voltage vectors from 0 - 20° sector of fundamental plane.
Voltage vector relationship to inverter switching configuration.
Transformed frame vector controller simulation block diagram.
Step response of dq current components
Response of torque to step change in currents.
Block diagram of the inverter and controller circuit.
Inverter hardware.
D C link power supply.
Circuit diagram for one phase of inverter.
Block diagram of gate drive interface circuit.
71
73
73
75
76
77
78
82
83
84
85
86
88
91
92
93
94
97
VI
Fig 6.6 Shaft encoder outputs. 100
Fig 6.7 Block diagram of shaft encoder interface circuit 100
Fig 7.1 Key control functions necessary to implement the transformed frame 103
vector controller.
Fig 7.2 Step torque response of transformed frame vector controller at 1kHz. 106
Fig 7.3 Stator current controller software block diagram. 108
Fig 7.4 Typical current and voltage waveforms recorded during magnetization 113
test (ID = 1 A, to = 200rpm)
Fig 7.5 Magnetization test results (co = 350rpm) 114
Fig 7.6 Phase current waveforms (a) CO = 80rpm, (b) co = 200 rpm and (c) co = 115
345rpm (inverter bus voltage = 250V)
Fig 7.7 Phase current waveform detail versus position for (a) co = 80rpm, (b) co 116
= 200 rpm and (c) co = 345rpm (inverter bus voltage = 250V)
Fig 7.8 Measured and simulated speed and quadrature current values in 118
response to a step change in speed reference from lOOrpm to 240rpm.
Fig 7.9 Measured and simulated speed and quadrature current values in 119
response to a step change in speed reference from +150rpm to -150rpm.
Fig 7.10 Torque versus quadrature current with S y n R M at very low speed 120
(<5rpm)
Fig 7.11 Torque versus quadrature current for S y n R M with (a) VUNK = 200V, (b) 122
V U N K = 400V and (c) V ^ = 560V.
Fig 7.12 S y n R M phase current (a) Id = 1.8A, L, = IA and (b) L. = 1.8A, Iq = 1.5A. 123
Vll
LIST OF SYMBOLS
Ar/ Average surface area of rotor laminations (m2)
As Air-gap surface area of stator slot pitch (m2)
Bd Air-gap flux density due to direct axis flux (T)
Bg (0) Air-gap flux density (T)
Bq Air-gap flux density due to quadrature axis flux (T)
D Stator slot depth (m)
g Air-gap length (m)
ge Effective air-gap length (m)
H r (0) Rotor magnetic field intensity (A/m)
Hs {&) Stator magnetic field intensity (A/m)
Direct axis component of stator current (A)
n'th harmonic direct axis component of stator current (A)
. Transformed d-q current vector (A)
Quadrature axis component of stator current (A)
n'th harmonic quadrature axis component of stator current (A)
Stator phase current vector (A)
Phase 'x' instantaneous current (A)
Jrmax Maximum stator winding current density (A/m2)
Js (9) Stator current density distribution (A/m)
L Motor axial length (m)
Ld Direct axis inductance (H)
Lda Average direct axis length (m)
ldn
qn
Lfa n'th harmonic component of direct axis inductance (H)
L^ Diagonalized stator inductance matrix (H)
Ldw Scaled difference of direct and quadrature inductance (H)
Lm Stator phase winding magnetising inductance (H)
Lq Quadrature axis inductance (H)
L^ n'th harmonic component of quadrature axis inductance (H)
LT Rotor axial length (m)
Ls Stator phase winding leakage inductance (H)
L^ Stator phase inductance matrix (H)
Lst Stator axial length (m)
I Stator slot pitch (m)
Lsum Scaled sum of direct and quadrature inductance (H)
M^ Mutual inductance between stator coils a and b (H)
N Number of turns / coil in stator phase winding
Ns Number of stator slots
R Air-gap radius (m)
Rc Stator phase winding core loss resistance (Q.)
R Quadrature axis reluctance per metre (A/Wb/m)
Rr Rotor radius (m)
Rs Stator phase winding resistance (Q)
Rst Stator inner radius (m)
S Slot opening (m)
T(a) Transformation matrix
Te Electrical torque (Nm)
IX
TL Rotor iron lamination thickness (m)
trl Ratio of iron : iron + fibre in the rotor n
t^ Ratio of fibre : iron + fibre in the rotor
vd Direct axis component of stator voltage (V)
v^ n'th harmonic direct axis component of stator voltage (V)
vd Transformed d-q voltage vector (V)
vg Quadrature axis component of stator voltage (V)
v n'th harmonic quadrature axis component of stator voltage (V)
Ws Stator slot width (m)
W, Stator tooth width (m)
X Tooth tip thickness (m)
Y Yoke depth (m)
a Angular displacement of rotor axis from coil A axis (rad)
/? Angular displacement between two stator coils (rad)
j3' Angle between axes of adjacent phase windings (rad)
AT Winding temperature rise (°C)
6 Angular displacement from coil A axis around stator (rad)
9p Rotor pole pitch (rad)
As Stator phase flux linkage vector (Wb)
jU0 Permeability of free space, An x 10"7 (H/m)
p Rotor pole pairs
T Rotor torque (Nm)
</> (&) Quadrature axis flux (Wb)
(0 Rotor speed (rad/s)
Introduction 1
CHAPTER 1
Introduction
1.1 Overview of Electrical Machine Technology
The induction machine was invented in the 1880's by Nikola Tesla. Since this time it has gone
on to become the most commonly used electrical machine in industry. Historically, the
induction machine first found use in fixed speed applications where it was supplied directly
from the ac mains (possibly in conjunction with some means of reduced voltage starting to limit
transients at start up). The induction machine enjoyed wide spread acceptance due to its simple,
low cost, low maintenance structure compared to other fixed speed machines.
Over recent decades the use of the induction machine in variable speed applications has
particularly increased. This has been made possible by improvements in variable speed drive
technology. These improvements include the availability of new high-speed power electronic
switching devices as well as more powerful microcontrollers and digital signal processors
(DSP). Speed and torque control matching that of a DC drive is now possible in an induction
machine drive. Thus, DC drives which once dominated in this area are being replaced. The
induction motor offers a significant price advantage over the DC motor and with no brushes is
virtually maintenance free.
The trend is being further driven by a push towards the social and economic goals of energy
efficiency. Many processes that have been traditionally operated with fixed speed machines
(blowers, compressors and air conditioners) are being converted to variable speed operation.
This allows energy savings during low load operating periods that characterize much of the
operating time of these applications.
Since its invention the appearance of the induction machine has changed significantly. This has
been most notable in terms of size reduction due to improved construction techniques and
Introduction 2
materials [47]. However, the fundamental design methodology has not changed from that
originally determined for fixed frequency supplies. One notable exception being the removal of
the double cage or deep bar rotor, which was previously used to improve fixed frequency
starting torque [38].
Given that the design methodology has not changed despite the change in application, the
question arises to the possibility of improving on the performance of the induction machine,
variable speed drive. A starting point might be to define the ideal drive system. One such
description has the ideal drive providing high torque density, with minimal losses while
operating at a high power factor. It has fast speed and torque dynamics, operates over a wide
speed range and has a large peak transient torque density. Finally the rrjachine has a rugged
construction, the controller is simple and the entire system is cost efficient [4].
In terms of the ideal drive the major criticism of the induction machine is its relatively poor
efficiency in variable speed applications. In western society, as much as 70% of all electrical
energy generated is used in motor driven systems [51]. Induction motors form the largest subset
of this group. Typically an induction motor has an efficiency ranging from 75% (small motors,
less than lkW) to 95% (large motors, greater than lOOkW). Any improvement in efficiency
would provide economic benefits to the users of the motors as well as economic and
environmental benefits to society as a whole.
Further, the control of induction motors is relatively complicated. Particularly in high
performance applications it is difficult to accurately control induction motor torque [41].
Torque is proportional to the rotor resistance, which varies with temperature. Some type of
rotor resistance compensation is required for this value making the controller considerably more
complex.
There are three main machines frequently suggested as alternatives to the induction motor in
variable speed applications. These are the permanent magnet, switched reluctance and
synchronous reluctance motors. While they are unsuitable for operating from fixed frequency
Introduction 3
supplies, in the context of variable speed drives, supplied by a power electronic device, they all
have unique advantages and disadvantages that will be briefly considered.
1.1.1 PERMANENT MAGNET MOTOR
Figure 1.1 shows a diagrammatic representation of a brushless permanent magnet motor
(PMM). The PMM has a stator structure similar to that of an induction machine.
However, its rotor contains permanent magnets used to set up the air-gap flux. PMMs are
recognized as offering the highest power density and efficiency of all motors [3, 38].
Recent improvements in permanent magnet technology, leading to the development and
use of neodymium-iron-boron magnetic materials, have allowed the high power density
and efficiency values to be achieved. It is estimated that a PMM has 20-50% more output
power than a comparably sized induction machine [45].
Distributed s winding
rnanent magnets bedded on rotor
Figure 1.1 Diagrammatic representation of a P M M
The main disadvantage associated with this type of motor is the high cost of magnetic
materials. Using permanent magnets is only viable in small machines (less than 20kW),
as the cost quickly becomes excessive in larger frame-sized motors [45]. In addition,
both operating temperature and peak transient torque have to be restricted to avoid
Introduction 4
demagnetization of the magnets. Permanent magnet motor designs generally exhibit
cogging torque, caused by the interaction of the magnet and the stator teeth, which can
lead to output torque ripple, vibration and noise [54]. Nevertheless, despite these
problems the PMM is predicted to receive increased use in the future as oil and energy
prices increase [38].
1.1.2 SWITCHED RELUCTANCE MOTOR
Figure 1.2 shows a diagrammatic representation of the switched reluctance motor (SRM).
The SRM has saliencies on both the rotor and stator, although only the stator contains
windings. The windings associated with the individual stator poles are sequentially
excited causing the rotor to follow in a synchronous fashion. The SRM benefits from a
simple rugged rotor structure, which has a comparatively low inertia. As the rotor
contains no windings it conducts no currents and has no resistive losses. Thus, the
majority of machine losses are on the stator, which is relatively easy to cool. As there are
no permanent magnets in the machine, operating temperatures are less restrictive. The
SRM's power density and efficiency are generally acknowledged as exceeding those of
an induction motor [3,18] but are lower than those of the PMM.
Salient pole stator (with windings)
Salient pole rotor
Figure 1.2 Diagrarnmatic representation of a S R M
Introduction 5
The major problem with the S R M is that it suffers from torque pulsations. It is possible
to reduce torque ripple over narrow speed ranges to levels comparable to induction
motors. However, this level of smoothness cannot be maintained over a large speed
range [45]. The torque pulsations can also produce considerable acoustic noise, which
increases with motor size. Efforts to reduce the torque pulsations and acoustic noise have
led to designs with larger air-gaps, which lowers the achievable power density.
Conversely, in high power density designs there is a cost penalty due to the small, air-gap
tolerance [41]. Other limitations of the SRM include poor utilization of the active
machine iron and copper as well as a transient torque density which is less than that of the
PMM and induction motor [3].
1.1.3 SYNCHRONOUS RELUCTANCE MOTOR
The synchronous reluctance motor (SynRM) combines a stator structure, similar to that of
an induction machine, with a salient pole rotor. This structure is represented in Figure 1.3.
The SynRM shares the advantages of the SRM's rugged rotor construction including an
absence of rotor copper losses and a comparatively low rotor inertia. However, unlike the
SRM, it has a cylindrical stator. This alleviates the problems of torque pulsations and
acoustic noise associated with the SRM.
Distributed winding
Lient pole rotor
Figure 1.3 Diagrammatic representation of a S y n R M
Introduction 6
The S y n R M contains no permanent magnets. As such, it does not suffer from the
demagnetization problems of the PMM, is inherently cheaper and can be operated at
higher temperatures. Further, the SynRM only has copper losses on the stator. The stator
is substantially easier to cool than the rotor. As such, the SynRM can be operated at low
speeds without the need for forced cooling. Induction motors suffer from overheating
under similar conditions.
The advantages of the SynRM suggest it is well suited for general use in inverter fed
variable speed applications. Indeed on this basis the SynRM has attracted significant
recent research interest and is the focus of this thesis. Before proceeding with the specific
goals of this thesis a review of the existing work on the SynRM will be considered.
1.2 The SynRM: an Historical Perspective
The SynRM has a long history. The earliest reference to it is in a paper by Kostko in 1923 [26].
Since then several different rotor structures have been proposed. The earliest structures were
for line start applications and included a starting cage. Recent designs are specifically for
inverter fed applications where the starting cage can be removed. In either case, the
performance of the SynRM is improved by maximizing the ratio of the direct axis inductance to
L. quadrature axis inductance, —— (referred to as the saliency ratio), and the difference Ld — L
(sometimes referred to as the torque index) [1, 2, 41, 53]. The different rotor designs represent
attempts to improve the machine's performance accordingly. Figure 1.4 shows the four-pole
variants of the key rotor structures that have been considered. These will be referred to as the
salient pole rotor, segmented rotor, flux barrier rotor and axially laminated anisotropic rotor,
respectively.
1.2.1 SALIENT POLE ROTOR
The earliest salient pole machines found use in the 1950's and 1960's. They were made
by using special rotor punchings or, more conventionally, by milling away portions of a
Introduction 7
normal induction motor rotor so as to achieve saliency [13, 32]. The motors had the
advantage of providing cheap, robust and reliable synchronous operation, despite
suffering from low power factor and poor torque output. They found application in such
diverse areas as the positioning of control rods in nuclear reactors to use in synthetic fibre
spinning plants [30]. In the latter case, the SynRMs synchronous operation allowed it to
produce better fibres than speed regulated dc or induction motors [38].
O
Salient pole r o t o r S e g m e n t e d r o t o r
Flux barrier r o t o r Axially laminated rotor
Figure 1.4 S y n R M rotor structures
The salient pole machines were being operated from constant frequency supplies. As
such they required starting cages so that induction motor torque brought the rotor up to a
speed where it could synchronize with the stator field. Rotor designs had to balance the
conflicting requirements of high pull-out torque and power factor against the requirement
for high pull-in torque [33]. As such the machines exhibited low saliency ratios in the
range 2 - 3 [12, 46]. Consequently they performed badly in terms of power factor (0.5 -
Introduction
0.55), efficiency (50 - 7 5 % ) and m a x i m u m torque (1.5 times rated value). Additionally
the machines were only capable of producing a fraction of the power (60% - 65%) of
comparably sized induction machines [12, 13,14].
An interesting variation of the salient pole structure was to manufacture the rotor from
solid mild steel [6, 7]. This structure did not require a starting cage in line start
applications. Eddy currents induce a magnetic field in the rotor. Starting torque is
developed by the interaction of the stator and rotor magnetic fields. However, with
reported power factors in the range 0.51 - 0.58 and efficiencies in the range 65 - 75% [7],
the imchine did not offer any significant improvement in synchronous performance over
the conventional design.
1.2.2 SEGMENTED ROTOR
An early alternative to the salient pole machine was the segmented rotor structure. The
segmented rotor consists of isolated poles mounted on a non-magnetic shaft. The
structure was initially proposed in 1962 by Lawrenson [29]. He actually developed two
separate structures. The first was the conventional structure with the poles mounted
direcdy on a non-magnetic shaft. The second had the poles separated from an inner shaft
to reduce the inertia of the rotor [31]. Further work was done to optimize this structure
by Lawrenson [30, 33] and later Ramamoorty [49].
The segmented rotor structure did produce larger torque densities at a better power factor
and efficiency than the salient pole structure. Saliency ratios reported were in the range 3
to 6 [31, 33, 46, 49, 50]. The higher saliency ratios led to better power factor (0.6 - 0.8)
and efficiency (60 - 80%) results for these machines. By comparison the segmented
rotors performed better than the salient pole machines. However, the construction of the
segmented machine was less robust given its greater complexity, due to the necessity for
non-magnetic discs and bolts to secure the poles to the shaft.
Introduction
1.2.3 FLUX BARRIER ROTOR
A second alternative to the salient pole structure was initially considered in the early
1970's. Flux barriers (specially shaped air openings) are introduced into the rotor
structure with the aim of decreasing quadrature axis inductance without reducing direct
axis inductance. A common sub-classification is based on the number of flux barriers
introduced per pole. Some of the structures considered by various researchers were the
double barrier [19, 20, 21, 25], single barrier [6, 7, 44, 53] and essential barrier [14].
Even the segmented rotor can be viewed as a single barrier type rotor but with a very
wide barrier.
The flux barrier rotor also offered improved performance over that of the salient pole
rotor. Saliency ratios were reported in a range comparable to the segmented rotor with
similar performance figures [14, 19, 21]. As these machines were essentially for line-
start applications a key concern was the trade-off between pull out torque and stability.
Honsinger introduced magnetic bridges along the quadrature axis to achieve a
compromise between these goals [21]. The structure made from radial laminations was
inherentiy more robust and easy to build compared to the segmental rotor.
Despite the performance gains achieved by the segmented and flux-barrier rotor
structures, the early SynRMs still did not match the performance of induction machines.
Consequently, interest in the SynRM waned from the mid to late 1970's. This is further
attributed to the emergence of dc drives with accurate speed control and later induction
motor drives with similar speed regulation. However, with the development of field-
oriented control techniques interest in the SynRM has been rekindled. SynRMs
controlled using field-oriented techniques no longer require starting cages, which have
been a major limiting factor in design improvements.
Introduction
1.2.4 AXIALLY LAMINATED ANISOTROPIC ROTOR
With the reemergence of interest in the SynRM a rotor structure that has attracted
considerable focus is the axially laminated anisotropic rotor. The structure can be
thought of as combining characteristics from both the segmented and flux barrier rotors.
Figure 1.4 shows that the rotor laminations are layered axially to act as flux guides for
direct axis flux. They are interleaved with non-magnetic material that acts as a flux
barrier to quadrature axis flux.
Although much of the focus on the axially laminated structure has been recent it does
have a long history. Kostko originally suggested the structure in 1923 highlighting the
importance of anisotropy of the magnetic material with view to reducing the quadrature
inductance without affecting the direct axis inductance [26]. It was not until 1966 that
Cruickshank et. al. proposed their axially laminated structure as a means of implementing
this principle [11]. They along with others optimized the structure, for both line-start and
constant V/f applications, managing to achieve saliencies matching and even exceeding
those of other rotor structures [12, 42, 43, 50]. Typical saliency values obtained were in
the range 4-9. Researchers were restricted from achieving higher values because of the
maintained presence of the starting cage and the knowledge that increasing saliency also
leads to instability at some frequencies [34, 37].
These limitations were overcome with the application of field-oriented control techniques
to the SynRM. This removed the need for a starting cage on the rotor and allows the rotor
structure to be optimized for maximum saliency [1, 2, 53]. Several researchers have
looked at the problem of optimizing the rotor structure under these circumstances [4, 8,
27,28,41,48,53].
Field-oriented controlled axially laminated anisotropic SynRMs have now been reported
as matching and exceeding the performance of equivalent induction motor drives. This
work includes that by Piatt [48] who proposed a rotor structure that utilized the full air-
Introduction 11
gap surface improving upon the stacked "u" or "v" sections originally proposed by
Cruickshank et. al. Although his design was not optimized, he was able to obtain
equivalent torque production to a comparably sized induction rmchine. Staton et. al.,
using a similar rotor structure, also obtained matching performance to an induction
machine [53]. Significantly, in this case if the induction motor was derated for variable
speed inverter operation the SynRM showed a 20% lower kVA requirement and 10 -
15% lower losses.
A key design requirement of high-performance remains achieving a high saliency ratio.
Some research effort has focused specifically on this goal. Matsuo and Lipo calculated
the optimal ratio of rotor insulation width to rotor iron width to be 0.5 [41]. In a 300W
machine based on this, a saliency ratio of 10.4 was obtained. Boldea et. al using a
similar ratio of insulation to fibre, but with thin laminations, demonstrated a saliency ratio
of 16 with high power factor of 0.91 in a 1.5kW machine [4]. Chalmers presents the
performance results for a 7.5kW machine with saliency of 12.5 [8]. The SynRM is
shown to produce 4.3% more output power than that of a comparable induction motor.
However, it is also demonstrated that the SynRM has considerably higher no-load iron
losses due to eddy currents in the rotor laminations. These could be largely reduced by
cutting radial slits in the rotor.
While the development of the axially laminated SynRM is far from complete indications
are that it has the potential to replace the induction motor drive. Its comparative
performance, ability to produce rated torque at low speed and its relatively simple control
algorithms are some of the axially laminated SynRMs key advantages. There are of
course still some issues that need to be resolved with regard to the SynRM. One question
requiring further investigation is that of no-load losses in the rotor iron due to eddy
currents. There are some indications that these can be considerably reduced by cutting
radial slits in the rotor as previously cited. Additionally, there are mechanical issues
associated with the rotor structure. The axially laminated structure is completely different
Introduction
to conventional machine structure and requires new mass manufacturing techniques to be
developed. Also means of maintaining the mechanical integrity of the rotor at high speed
need to be determined and tested.
1.2.5 STATOR WINDING CONSIDERATIONS
The previously cited research has focused on three-phase sinusoidally wound machines
stressing the similarity between the proposed SynRM and induction rnachine stators.
This was necessary for line-start rnachines and was also seen as advantageous to any
potential manufacturing of the SynRM. However, the SynRMs rotor saliency naturally
produces a "rectangular" air-gap flux density distribution. Conventional three-phase
windings produce sinusoidal magnetomotive force (MMF) distributions, which do not
necessarily produce the optimal torque from the machine. Considering that the proposed
field-oriented controlled SynRM drives are supplied from inverters many of the
arguments for a three-phase distributed stator winding are no longer valid. Thus, an
emerging area of research is focusing on the stator winding and excitation.
The advantage of rectangular stator excitation over sinusoidal excitation can be
demonstrated by a simple comparison. Consider a two-pole machine with a rotor pole
pitch of 2 radians. The machine has an air-gap radius, R, and a stack length, L. If the
machine is run at the saturation limit the air-gap flux density, B, will be constant over the
rotor pole face. For a sinusoidal stator current distribution with a peak current density, J,
the torque can be calculated as,
I
T= \BLR2Jcos9d6 _x (LI)
= 1.6S3BLR2J
For a rectangular stator current distribution with the same peak current density the torque
is given by,
Introduction
1
T = \BLR2Jd0 i (i.2)
= 2BLR2J
Although simplistic in its nature the comparison shows a 20% increase in torque in the
latter case. A more realistic comparison would have to account for the fact that the
optimal machine dimensions should be different in each instance as well as include
losses. However, the comparison does highlight the potential gains achievable in using
rectangular stator currents.
Hsu et. al. demonstrate the advantage of adding a third harmonic component to the
fundamental component of MMF in the SynRM [22, 23, 36]. The third harmonic
component was obtained using a dual three-phase machine with isolated windings. The
associated inverter consisted of six single-phase bridges. They show significant increase
in torque per RMS ampere in both a salient pole and segmented rotor machine. Toliyat
et. al. also demonstrate this idea but with a simpler five-phase star connected winding fed
from a voltage source inverter. This proposal had the advantage of reducing the power
electronic requirement of Hsu's system [56, 57, 58]. Toliyat shows a 10% increase in
torque achieved by the addition of a third harmonic component of MMF. Again these
results were obtained with a salient pole rotor but would be expected with any of the
common rotor structures.
Law et. al. consider another variant of the multiphase SynRM coining the term "field
regulated reluctance machine" [5, 27, 28]. In this case the stator is wound with fully-
pitched, concentrated windings. Coils at the rotor pole sides are designated as supplying
the field or direct axis excitation. Coils over the rotor pole face supply the equivalent of
armature current or quadrature axis excitation. The individual phase windings are
isolated from one another and each requires a full bridge inverter. Consequently, the
drive as proposed is expensive in terms of power electronic requirements. However, the
Introduction 14
performance gains were quite substantial with a reported 6 8 % greater force density than
an equivalent induction machine.
Another potential advantage of a higher phase number, in addition to higher torque
density, is increased redundancy in the drive. A phase can fail in the inverter and the
drive will still function albeit with reduced torque output. In applications where
continued operation is critical this is a potential means of increasing drive reliabihty.
At this point in time there has only been hrnited research in the area of multiphase
SynRMs exploiting non-sinusoidal stator excitation, consisting primarily of the references
cited above. There are clear indications of improved performance from the multiphase
drives coming at the cost of increased inverter complexity. As the relative cost of power
electronic devices reduces, the potential for this class of machines becomes more
apparent. A major motivation for this thesis is to investigate the design and field-oriented
control of this class of machine.
1.3 Project Overview
The broad motivation for this thesis is to investigate and develop the potential of the field-
oriented SynRM drive. As seen in the literature review there are indications that the SynRM
offers benefits such as greater torque density, higher efficiency and simpler control algorithms
when compared to the induction machine. The potential advantages associated with realizing
any of these benefits in a practical drive system warrant the additional investigation into the
SynRM.
Particular attention will be given to the class of multiphase axially laminated SynRMs. Axially
laminated machines have emerged from existing research as possessing the highest saliency
ratios when compared to other members of the SynRM family. High saliency ratio is shown to
be associated with greater torque density and efficiency.
Introduction 15
The majority of existing work on axially laminated S y n R M design assumes a standard three-
phase stator with sinusoidally distributed windings. The reason research has focused in this area
is because of the perceived advantage of sharing a stator structure with the induction machrne.
In the context of an inverter fed niachine the need for a certain number of phases disappears and
the stator can have any number of windings. Allowing more than three, non-sinusoidal, phase
windings forces the reevaluation of the questions as to how best design and control the machine.
The design question will be approached assuming a "rectangular" air-gap flux density
distribution, which the rotor saliency of the SynRM naturally produces. Further, a rectangular
stator current distribution will be assumed to interact with this flux. This produces the optimal
output torque per rms ampere from the machine. Implicit in the latter assumption is that the
stator has a multiple-phase winding capable of approximating the assumed current distribution.
The design model will be based on an analytical lumped element model of the machine's
magnetic circuit. Lumped element modelling is chosen over finite-element techniques to allow
fast performance calculations and hence fast design optimization. Further, it is expected that the
analytical techniques will offer better insights into the practical performance limits of the
machine. The design model is validated through the construction and testing of a 5kW
experimental SynRM. This prototype has a nine-phase concentrated stator winding to
approximate the ideal stator current distribution assumed in the design model. The choice of
phase number was made given the rotor dimensions determined through the optimisation
process. Nine was the minimum number of phases necessary to ensure at any time at least one
phase would be dedicated to solely supplying direct axis excitation.
Implementing a field-oriented controller on the multiphase SynRM presents additional
difficulties. To initially approach this problem, the generalized d-q voltage and torque
equations will be determined for the nine-phase SynRM. Similar equations have been
previously determined for the five-phase machine [57]. However, the methods used become
increasingly cumbersome as phase number is increased. A new approach will be considered
Introduction 16
which can be readily generalized to any n-phase SynRM. The equations, once formed, will
allow the simulation of the drive's dynamic performance and perhaps suggest methods for
implementing field-oriented control.
The limited research into multiphase SynRM design means that there is even less research
focused on multiphase SynRM control. Techniques will be considered for implementing field-
oriented control on the experimental SynRM drive. Existing multiphase drives have been
controlled using simple techniques where each phase winding is designated as providing solely
magnetizing flux (direct axis excitation) or torque producing current (quadrature axis excitation)
[27, 36, 58]. This method will be explored more fully along with methods based around current
transformations that recognise the individual windings contribution to both direct and
quadrature axis excitation.
A stator current controller is ultimately implemented in the drive. This controller utilises a
technique similar to that used in the field regulated reluctance machine [27]. Phase windings
are designated as supplying either direct or quadrature axis current depending on their position
relative to the rotor. In the drive control the work of Law et. al. is effectively extended to a
larger phase number machine with a wye connected stator. Importantly the stator connection
significantly reduces the power electronic requirement for the drive and its associated cost.
Performance measures are made on the drive to demonstrate its characteristics.
1.4 Thesis Outline
The remainder of this thesis is organized as follows:
• Chapter 2 develops a magnetic circuit model for the SynRM. This model is based on a
lumped element analysis of the motor's magnetic circuit and includes allowance for
saturation in the machine's iron. The key stator and rotor dimensions relevant to the design
process are identified. An iterative algorithm is determined which optimizes these
parameters.
Introduction
• Chapter 3 presents the construction details for the 5.0kW nine-phase S y n R M designed and
built as part of this project. The results of magnetization and torque tests, carried out on the
machine, are given. They are compared with the theoretical values determined during the
design process.
• Chapter 4 defines the stator inductance matrix for the nine-phase SynRM and consequentiy
develops the generalized d-q equations. These results can be readily extended to any 'n'
phase machine.
• Chapter 5 outlines two field-oriented control strategies for the nine-phase SynRM drive.
The first strategy is based on a simple designation of the stator phase windings as supplying
direct or quadrature excitation. The second is based on the generalized d-q equations and
theory developed in Chapter 4. Simulation results that predict the motor's dynamic
performance are presented.
• Chapter 6 addresses the hardware implementation issues associated with the nine-phase
inverter and DSP controller. The practical hardware setup is described.
• Chapter 7 details the software implementation issues in the drive system as well as
presenting the performance results from it. These results are compared with the simulation
predictions in Chapter 5.
• Chapter 8 is a summary of the relevant conclusions and possible extensions that can be
drawn from the work presented in this thesis.
Magnetic Circuit Modelling and Design Optimization of the SynRM 18
CHAPTER 2
Magnetic Circuit Modelling and Design
Optimization of the SynRM
2.1 Introduction
This chapter develops a magnetic circuit model for the SynRM. The model predicts the air-gap
flux density distribution and torque output from the machine. It is applied in a design
optimization algorithm and criteria are determined to achieve optimal SynRM performance.
Section 2.2 outlines the rationale behind the design strategy. It has been previously noted that
the torque per rms ampere of the SynRM can be increased, with the addition of a third
harmonic component to the spatial MMF waveform [22]. This argument is carried to its logical
conclusion by assuming an ideal "rectangular" stator current distribution. The rotor saliency of
the SynRM naturally produces a "rectangular" air-gap flux density distribution and it follows
that the optimal torque per rms ampere ratio will be obtained with a rectangular stator current
distribution.
Additionally, it is proposed to consider the entire magnetic circuit of the SynRM (stator and
rotor) when optimizing its design. Existing work has focused largely on determining the
Ld optimal rotor dimensions only, in order to maximize the saliency ratio, — [4, 27, 41, 53]. LQ
Saliency ratio is chosen because of its relationship to the torque and power factor produced by
the machine. This approach is flawed as both rotor and stator dimensions can affect the
motor's performance. By focusing solely on the rotor dimensions the best result possible is
only to optimize the rotor dimensions for a given stator and winding configuration. Further, to
achieve a practical machine design, overall dimensions and thermal issues need to also be
Magnetic Circuit Modelling and Design Optimization of the SynRM 19
considered. With this view, saliency ratio is replaced by continuous torque / mass as the
optimization criteria.
The basis of the magnetic circuit model is the existing work carried out by Ciufo [9, 10]. He
uses a lumped element model that includes the majority of SynRM dimensions to determine
expressions for motor inductances and flux densities. Ciufo's work is described in Section 2.3
and extended to include saturation effects in Section 2.4. Saturation effects are critical in any
design optimization, as rated conditions should bring the SynRM to its saturation limit.
Section 2.5 describes the optimization algorithm. Not all of the machine dimensions are
independent. Some sections of the machine carry the same magnetic flux as others. For
example, the stator teeth and rotor iron both carry direct axis flux. Specifying one dimension
automatically sets the requirement for the other. Thus, the various machine dimensions are
classified as either independent or dependent. The key independent dimensions are identified
and an optimization algorithm determined for these. The remaining machine dimensions are
calculated from the key dimensions.
Section 2.6 presents the results of optimization over a range of motor sizes (1 - lOOkW).
Sensitivity of SynRM performance to the key dimensions is also considered. Conclusions are
drawn with regard to optimal SynRM design.
2.2 Design Strategy
With the renewed interest in the SynRM, several researchers have considered aspects of the
design optimization problem. A large portion of work has focused on analysis and comparison
of rotor structures [8, 48, 52, 53]. While this work highlights the potential of the axially
laminated SynRM it stops short of providing optimal machine dimensions. Where effort has
focused on machine dimensions it has been limited to rotor dimensions in sinusoidally excited
machines [4, 41]. The approach has been to maximize the saliency ratio, -j-, or alternatively
Magnetic Circuit Modelling and Design Optimization of the SynRM 20
the "torque index", Ld - Lq, using combinations of finite element analysis, lumped element
modelling and other analytical techniques. Some recent research has moved on to consider
non-sinusoidally excited machines [22, 27, 57]. However, design considerations here have
been limited to the stator winding configuration only. The implications of non-sinusoidal
excitation on the machine dimensions have yet to be explored.
A key focus of this work is to consider the implications of non-sinusoidal stator excitation on
the optimal dimensions of the SynRM. Significantly, the approach to SynRM design
optimization presented is unique in three aspects:
1. It assumes non-sinusoidal stator excitation.
2. It considers all dimensions of the SynRM, both on the stator and rotor.
3. It seeks to optimize the torque / mass ratio for the entire machine rather
than the saliency ratio.
The SynRM does not naturally produce sinusoidal flux waves in the air-gap. The rotor saliency
of the SynRM produces a "rectangular" air-gap flux density distribution. If a rectangular stator
current distribution interacts with this flux the SynRM generates its optimal torque. Further,
the machine will exhibit lower copper losses in comparison to a similarly rated sinusoidal
current machine. These ideas are supported by recent work showing that the addition of a third
harmonic component to the MMF distribution can raise the torque per rms ampere of the
machine [22, 56]. This idea is carried to its logical conclusion by assuming that the motor is
indeed excited by an ideal, rectangular stator current distribution. In practical terms, the ideal
will be approximated by designing machines with non-sinusoidally distributed stator windings
consisting of more than three phases.
To ensure optimal SynRM designs are obtained, as opposed to optimal designs for a given
stator, all rotor and stator dimensions are included in the design model. Existing work on
SynRM design optimization has focused on one or two key rotor dimensions. Stator
dimensions have been largely ignored with prototype rotors designed and built to fit existing
Magnetic Circuit Modelling and Design Optimization of the SynRM 21
induction machine stators, complete with their existing stator winding. The difficulty here is
that rotor dimensions are inherently linked to stator dimensions. By fixing the stator
dimensions, you automatically fix some rotor dimensions. As an example, it is expected that
the iron in the rotor should be matched to the iron in the stator teeth. This is necessary as both
sections of the motor carry similar magnetic flux. Indeed any given rotor or stator dimension
can limit the machine's performance if not chosen correctly. To avoid this pitfall the entire
magnetic circuit of the motor will be considered as a whole.
The most accurate analytical method to account for all the stator and rotor dimensions is that of
finite element analysis. The disadvantage of this approach is that it is computationally
expensive and time consuming. Further, this type of analysis does not necessarily provide
insight into what are the key performance limits and relationships. For these reasons it was
decided to use an analytical approach based on a lumped element approximation to the SynRM
magnetic circuit. Finite element analysis will be used only to validate the final results.
Any optimization requires a goal or performance measure. The goal proposed is to produce the
largest continuous torque / mass ratio for a given frame size. (Mass is defined as the sum of the
rotor and stator iron making up the magnetic circuit plus the stator windings. It does not
include the motor frame or shaft.) Traditionally, the performance measure has been either
saliency ratio or torque index. These values have been used because they determine the
machine's power factor and torque output, respectively. They will not be used in this instance
for two reasons. First, they only reflect the fundamental component of torque and neglect any
contribution from higher harmonics expected in a square current machine. Further, to focus
solely on torque or power factor performance neglects other important elements in a practical
machine design. Most significantly machine size and thermal issues must be considered. The
torque / mass goal obviously addresses the size issue. Thermal issues will be considered
internal to the design optimization, as they will pose limits on some dimensions.
Magnetic Circuit Modelling and Design Optimization of the SynRM 22
2.3 Magnetic Circuit Model
The requirement for the design optimization is an analytical model that is based on the machine
dimensions and includes allowance for saturation. Several researchers have attempted to find
analytical expressions for SynRM torque and fluxes, given the machine dimensions [4, 16, 39,
40]. A common difficulty has been obtaining an accurate representation of quadrature axis
flux. Ciufo offers a significant contribution with this respect [9, 10]. He recognizes two
potential paths for quadrature axis flux. The traditionally acknowledged path is that transverse
to the rotor laminations. Another path can be shown to exist where quadrature axis flux passes
from the rotor to the stator and back again. This "zigzag" flux has been observed by other
researchers using finite element analysis [4, 17, 41] but has not been previously accounted for
in any analytical modelling.
In overview, Ciufo initially determines an expression for quadrature axis reluctance based on
the two flux paths. The expression is obtained from a lumped element approximation to the
machine's magnetic circuit. The elements themselves are detenruned from the relevant rotor
and stator dimensions. Ciufo proceeds to calculate both the air-gap flux density distribution
and quadrature axis flux. However, his analysis contains no consideration for the effects of
magnetic saturation in the machine iron. The requirement that the design model include such
allowance remains. A motor at rated conditions would be expected to be operating with at least
some portion of its iron at the saturation limit. Section 2.4 will extend Ciufo's model to include
saturation effects thus forming a suitable basis for the design model. Before proceeding with
this analysis the original work will be considered in more detail.
Ciufo considers a "snapshot" of the SynRM with its rotor in a random position. The "frozen"
machine's magnetic circuit can be modeled as a network of reluctances associated with the air-
gaps and the non-magnetic laminations in the rotor. The machine iron is assumed to have zero
magnetic reluctance.
Magnetic Circuit Modelling and Design Optimization of the SynRM 23
Figure 2.1(a) shows a typical section from a two-pole S y n R M . The section is taken towards the
centre of the rotor away from the pole edges. The shaded and non-shaded areas do not
represent the magnetic and non-magnetic laminations. Instead, the shaded sections represent
portions of the rotor that allow quadrature axis flux to pass from one side of the stator to the
other. The non-shaded sections represent portions of the rotor located over stator slot openings
that do not facilitate flux being passed from one side of the stator to the other. Thus, both the
traditional and zigzag quadrature axis flux paths can be recognized.
(a) straight q-axis flux path
_ < :
zigzag flux path
X
.)
;)
B
(b)
A
1
B
Air-gap reluctance of zigzag flux path
Represents reluctance of steel / fibre laminations between
A&B
Figure 2.1 Equivalent magnetic circuit model.
Figure 2.1(b) illustrates h o w the lumped element approximation to the quadrature axis channel
is constructed. In particular, the circuit between nodes A and B is developed. The non
magnetic portions of the circuit are represented by reluctances. These reluctances are
determined from the motor dimensions. Once calculated, they can be combined to obtain a
value for the quadrature axis reluctance per metre, Rq, given by [9];
geKoJrl Rq Mo(8eNitl.6RsLs +0.5/T2R2Lstrl)
(2.1)
where, ge = effective air-gap length (m)
Nsi0, = number of stator slots
tH = ratio of fibre : fibre plus iron in the rotor
Magnetic Circuit Modelling and Design Optimization of the SynRM 24
jUo = permeability of free space (4TC X 10"7 H/m)
Rs = stator inner radius (m)
Ls = stator length (m)
This equation is derived fully in Appendix G. Having established the equivalent quadrature
axis reluctance the S y n R M flux distributions can be calculated. The method used is to consider
various M M F loops as well as continuity of flux in the different regions of the machine. One
further simplifying assumption is made. The stator teeth and slots are "smeared" into a
continuous entity. Thus, an ideal stator current distribution is obtained with no stator slot
effects. Ciufo does this analysis and shows that the resulting expressions accurately predict the
average fluxes in the S y n R M [10].
Figure 2.2 shows a typical profile of the air-gap flux density distribution obtained using Ciufo's
model. In this instance, a two-pole machine is assumed with typical levels of direct and
quadrature axis excitation. The distribution can be thought of as an average flux density
produced by the direct axis excitation. Or in other words, the air-gap flux density distribution
with slotting effects removed. At either end of the pole face the flux density rises or falls due
to the flow of quadrature axis flux. Quadrature axis flux is concentrated here as this path offers
lower magnetic reluctance than through the relatively large air-gap at the pole edges.
1.2 -,
1 -
/""""" 0.8 H
0.6-
0.4-
0.2-
. , , , 9-
^
-2 -1.5 -1 -0.5 0 0.5 1 1.5
Angular displacement (rad)
Figure 2.2 Typical air-gap flux density distribution in a two-pole S y n R M
Magnetic Circuit Modelling and Design Optimization of the SynRM 25
2.4 Saturation Effects
For Ciufo's work to be utilized in a design model, allowance needs to be made for saturation
effects. Figure 2.3 shows a simplified representation of a two-pole SynRM. The rotor is
assumed to have a constant width equal to the average direct axis length, L^. The value for L&
can be calculated given the specific rotor dimensions in the corresponding real machine.
Figure 2.3 Simplified magnetic circuit of SynRM.
Quadrature axis flux is confined to a channel through the centre of the rotor. This channel has
reluctance / metre, Rq given by equation (2.1). The remaining portions of the rotor only carry
flux along the direct axis. Further simplifying assumptions made are;
1. The stator has no teeth or slots. Stator currents are assumed to be distributed in a
thin veneer along the inside surface of the stator. The current distribution is
described by Js(0).
Magnetic Circuit Modelling and Design Optimization of the SynRM 26
2. No quadrature axis flux, <Pn, passes from the rotor pole edges.
3. The rotor, H,(G), and stator, Hs(0), magnetic field intensities are functions of
angular position only.
Differential equations that describe the air-gap flux density distribution, Bg(0), and
quadrature axis flux, <j)q (0) , are initially formed. They are derived by considering MMF loops
1 and 3 and continuity of flux in areas 2 and 4 of Figure 2.3. Loop 1 passes from the middle of
the rotor, parallel to the laminations, crossing the air-gap to the stator. It then traverses an
incremental portion of the stator, just inside its surface, before crossing the air-gap once more.
The loop is completed at the middle of the rotor where it passes transverse to the rotor
laminations to reach its starting point. Summing the MMF's around this loop gives;
^Hr(0)-^-Bg(0)-Hs(0)Rsld0 + Js(0)Rstd0 2 Mo
+-^Bg(0 + d0)+^Hr(0 + d0) + 0q(0)Rstd0Rq=O Mo ^
L^difr(^) + g^dg£(g) _ + + = 0
2 d0 }io d0
Area 2 is a small portion of the rotor that spans its width. Summing the fluxes into this region
gives;
Bg {n - 0)LrRrd0 - Bg (0)LrRrd0 + <t>q (0) -0q(0 + d0) = 0
^-^ = RL[Bg <n-&)- Bg (0)] (2.3) d0 8 g
Loop 3 is a path through the entire rotor cross section, across the air-gaps and around the stator,
just inside its inner surface. Summing the MMF's gives;
lj(0)Rd0= ~\Hs(0)Rd0 + ^-[Bg(7T-9) + Bg(0)] 0 e Vo
+ ^[Hr(7i-0) + Hr(0)] (2.4)
Magnetic Circuit Modelling and Design Optimization of the SynRM 27
Area 4 is a small portion of the stator that spans the width of the yoke. Summing the fluxes
into this region gives;
Bg (0)Rstd0 + Bs (0) = Bs(0 + d0)
BA0) = YdBs(0)
R d0
The following boundary condition is required;
v 2 y
(-0A v ^ j
= 0
(2.5)
(2.6)
Symmetry of the system requires;
B(0) = B(TT + 0) (2.7)
Equations (2.2) to (2.7) can be solved numerically to obtain the air-gap flux density distribution
across the rotor pole face and the quadrature axis flux over the width of the rotor. The
numerical technique used to solve the system of differential equations is presented in Appendix
D.
To determine this solution a simple approximation is made to the B-H characteristic for the
motor iron. Figure 2.4 shows the B-H curve assumed. The iron has infinite permeability until
its flux density reaches its saturation level of 1.7T. Past this point the iron flux density rises
only marginally at 5uo H/m.
„4 ^
B i
1.7T
^
k.
-1.7T
r
slope = 5uo
w H
Figure 2.4 B-H characteristic assumed for iron.
Magnetic Circuit Modelling and Design Optimization of the SynRM 28
Figure 2.5 shows a typical air-gap flux density distribution obtained when square current
excitation is applied to the stator. A two-pole machine under similar conditions to those in
Figure 2.2 is assumed. Figure 2.5(a) and 2.5(b) show in isolation the direct and quadrature axis
contributions to air-gap flux density distributions respectively. Significantly, when the
components are combined in Figure 2.5(c), the peak where quadrature axis flux previously
added to direct axis flux is removed. This corresponds to the point where the rotor and stator
iron is first driven into saturation.
(a)
6 n
-2 -1.5
0.9 -] (18-
0.7-0.6-0.5-0.4-
0.3-0.2-0.1-
-1 -0.5 0 0.5 1
Angular displacement (jad)
1.5 2
(b)
e to r~ « -2 -/"
/ /
Q.15-,
0.1 -
0.05 -
•1 -OS oj 1
-0.03
-0.1
J. 15
Angular displacement (rad)
I y. u 2
(c)
p 03
1
-2
r
1
-1.5
1 -,
0.8 -
0.6 -
0.4-
0.2-
n i i U I I
-1 -0.5 0 0.5 1
Angular displacement (rad)
1.5 1
2
Figure 2.5 Air-gap flux density distributions with iron saturation effects with (a) direct axis
excitation, (b) quadrature axis excitation, (c) combined direct and quadrature axis excitation
Magnetic Circuit Modelling and Design Optimization of the SynRM 29
2.5 Optimization Algorithm
To proceed from the SynRM magnetic model to a design optimization algorithm requires
further simplification to the magnetic model. A piecewise linear approximation is applied to
the air-gap flux density distribution predicted by the magnetic model. The approximation
assumes that the direct axis excitation sets up an average flux density across the pole face. At
rated conditions this flux density should place the rotor iron at its saturation limit. All
quadrature axis flux is assumed to flow through the final stator tooth located at the end of the
rotor pole face. Figure 2.6 shows the approximation as applied to a typical model air-gap flux
density distribution. Having established this simple approximation, the torque produced by the
machine can be calculated as the cross product of flux density and current.
p
-2
/T~
-1.5 -1
1 -,
0.8 -
0.6 -
0.4 -
0.2-
-0.5 0 0.5 1
Angular displacement (rad)
1.5 2
Figure 2.6 Piecewise linear approximation to the air-gap flux density distribution
The goal of the design optimization process is to produce the largest torque / unit mass. (Mass
is defined as the sum of the rotor and stator iron that makes up the magnetic circuit plus the
copper that makes the stator windings. It does not include the motor frame or shaft). To this
end, the machine iron should be fully utilized at rated conditions. Considering this latter
requirement, it becomes apparent that some dimensions are independent and can be freely
Magnetic Circuit Modelling and Design Optimization of the SynRM 30
adjusted to optimize the performance parameter. Other dimensions are dependent on the key
variables and require no optimization.
2.5.1 Key Independent Dimensions
The key independent dimensions in the SynRM are rotor pole pitch (0P), rotor radius (Rr),
rotor iron : iron + fibre ratio (r„), air-gap (g), maximum stator winding current density
(Jmax) and stator slot opening (5). These are the values that will be determined in the
optimization algorithm.
There are other dimensions that could be classified as independent. These are not
included in the optimization process as they are better selected on the basis of practical
limitations in either the machine construction or stator phase windings. Specifically,
these dimensions are;
ROTOR IRON LAMINATION THICKNESS (TL)
Thinner rotor laminations lead to smaller effective air-gaps as flux-fringing effects are
reduced. Further benefits of thin rotor laminations are that the increased number of
laminations per pole decreases quadrature axis inductance [53], reduces torque ripple and
possibly reduces losses caused by pulsating fluxes [3, 4]. A practical limit exists to how
thin laminations can be made. As thickness is reduced the number of laminations
required increases as does constructional difficulty. A sensible lower limit to lamination
thickness is 0.3 to 0.5mm. It has been suggested that using standard lamination material,
available in this size range, may contribute to reducing SynRM manufacturing cost [8].
NUMBER OF ROTOR POLE PAIRS (o)
A two-pole SynRM is conceptually simple, yields high saliency, but is difficult to
construct. The major problem is that the rotor structure leaves no space for the rotor
shaft. Four or six pole motors are preferred [8]. Generally, four-pole machines are more
common as they are easier to manufacture when compared to a six-pole machine.
Magnetic Circuit Modelling and Design Optimization of the SynRM 31
N U M B E R O F S T A T O R S L O T S (N.)
The number of stator slots depends largely on the stator winding. Factors that will
influence the number of slots include the number of stator phases, the number of poles
and whether the winding is distributed or concentrated. Commonly used values in A C
motors are 36 and 48.
STATOR TOOTH TIP THICKNESS (X)
Figure 2.7 shows an enlarged view of a stator tooth. The tips of the tooth are assumed to
be triangular. The base of the triangle corresponds to the tooth tip thickness (X). It is
chosen to be approximately half of the triangle height (H). This was considered a good
compromise between providing sufficient mechanical strength to the tooth tip while
limiting the path for stator leakage fluxes.
X = 0.5H
Figure 2.7 Stator tooth tip detail.
2.5.2 Dependent Dimensions
Considering the requirement to fully utilize the machine iron at rated conditions, it
becomes apparent that some dimensions in the SynRM are dependent on others. These
dependent dimensions are;
Magnetic Circuit Modelling and Design Optimization of the SynRM 32
STATOR TOOTH TO SLOT WIDTH RATIO (WT/WS)
In the absence of leakage fluxes, the ratio of the stator tooth width to stator slot width
should be equal to the ratio of rotor iron to fibre. The stator teeth, over the rotor pole
face, carry the same direct axis magnetic flux as the rotor iron. Ideally, the stator tooth
and rotor iron should saturate at the same operating point, otherwise one section of iron
will not be fully utilized. If allowance is made for leakage fluxes then the tooth width is
be raised marginally as only the teeth carry this additional component of flux.
STATOR SLOT DEPTH (D)
Stator slot depth is set given the stator current density and rotor pole pitch. Slot depth is
set to allow sufficient excitation in the stator winding over the rotor pole edges to fully
flux the rotor iron in the direct axis.
Once slot depth is set, an effective direct axis excitation, Jd (A/m), is obtained. The
quadrature axis excitation, Jq, is set to the same value. This provides the maximum
continuous torque without exceeding the winding current density rating.
STATOR YOKE DEPTH (Y)
The stator yoke depth is set to allow sufficient return path for the direct axis flux.
Ideally, the stator yoke over the pole sides, the rotor and stator tooth iron over the pole
face will reach saturation at the same operating point.
MOTOR AXIAL LENGTH (D
The rotor and stator stack lengths are set to the same value. The length is restricted by
the allowable temperature rise in the winding.
The thermal model of the motor assumes the stator winding generates heat through
resistive losses. The heat is primarily dissipated, via natural convection, from the
exposed area of the windings at the ends of the stator according to the equation,
Magnetic Circuit Modelling and Design Optimization of the SynRM 33
Q = hA(T1-T2) (2.8)
where, Q = heat flow (W)
h - heat transfer coefficient (W m"2 K"1)
A = exposed surface area of winding (m2)
Ti = winding temperature (K)
T2 = ambient temperature (K)
The heat transfer coefficient was approximated using measurements from a similarly
sized induction motor stator. The value for acceptable rise in the stator winding's
temperature above ambient was chosen to be 40°C based on the wire insulation
characteristic. In the optimization, a longer motor produces more torque. However,
increasing the length of the machine also increases the winding length along with the
associated conduction losses. As there is a limit to how much heat can be dissipated
from the ends of the winding an equilibrium position must be found that maintains the
winding temperature within acceptable limits. This thermal limit effectively sets the
continuous rating of the machine.
2.5.3 Optimization Algorithm
Figure 2-8 shows in block diagram form the algorithm used to optimize the SynRM
design. This process optimizes the design for a given rotor radius. It consecutively
considers each key independent dimension finding its optimal value in isolation. The
algorithm repetitively cycles through all the key dimensions until the performance index
(torque / unit mass) converges to a maximum value. While optimizing each key
dimension a subroutine is called that sets the dependent dimensions to appropriate
values. The optimization process was repeated using different initial values. In each
case the process yielded the same solution providing confidence that a global and not
local maximum was being found. The entire algorithm is simple enough to be
implemented in any spreadsheet environment that supports macro routines.
Magnetic Circuit Modelling and Design Optimization of the S y n R M 34
f Start )
"
Select rotor radius
II i '
Optimize pole pitch
} '
Optimize steel to fibre ratio
1 '
Optimize air-
gap
} '
Optimize current density
1 '
Optimize slot opening
1
./Has ^\conve
T/m^^
rged? . /
Finish J
(start)
Adjust variable being optimized
Set slot depth to flux direct axis
Set J„ — Jd
Set yoke depth to carry d-axis flux
Set rotor length to satisfy thermal cond.
Compute torque / mass
(^Return J
Figure 2.8 Block diagram of optimization algorithm.
2.6 Optimization Results and Analysis
Four-pole SynRMs were designed for a range of machine sizes (1 - lOOkW). Figure 2.9 shows
the optimum values of the key independent motor dimensions as the machine size was varied.
Of particular note are the values obtained for rotor pole pitch and steel : steel + fibre ratio.
Results indicate advantages associated with large rotor pole pitches (approaching 180 electrical
Magnetic Circuit Modelling and Design Optimization of the SynRM 35
degrees) and steel : steel + fibre ratios between 0.45 - 0.47. These results differ to other
published values which have indicated smaller pole pitches (120 electrical degree) and larger
steel: steel + fibre ratios (0.6 to 0.7) to be desirable [4,41,53].
Power' vs 'Rotor Radius'
60 80 100 120 140
Rotor Radius (mm)
135
Pole Pitch' vs 'Rotor Radius'
40 60 80 100 120
Rotor Radius (mm)
140
'steel: steel + fibre' vs Rotor Radius'
0.475 -i
80 100 120
Rotor Radius (mm)
140
a 7
s 6
^ 5 1 2- 4-
§ 3-Q 2
1 1
'Current Density' vs Rotor Radius'
40 60 80 100 120
Rotor Radius (mm)
140
0.4
f °'3
I- °-2" •3 o.i -
o
'Airgap' vs Rotor Radius'
40 60 80 100 120
Rotor Radius (mm)
'Slot Opening' vs Rotor Radius'
80 100 120
Rotor Radius (mm)
Figure 2.9 Optimum motor dimensions as machine size is varied.
The difference lies in the stator current distributions assumed for the optimization. In a three-
phase machine sinusoidal current distributions are present and the edge regions of large pole
faces are not fully utilized. Under these conditions it is necessary to put more iron in the rotor
to maximize the direct axis flux in the useful central region of the pole face. B y lifting the
restriction of sinusoidal currents it has been possible to utilize the whole pole face creating
better utilization of the machine iron.
Magnetic Circuit Modelling and Design Optimization of the SynRM 36
Also of note is the optimal air-gap, which is relatively small. For the 5 k W motor, discussed in
Chapter 3, the optimal air-gap was determined to be 0.3mm. This is approximately half of that
typically encountered in a similarly sized induction motor. In an induction motor the rotor
heats up due to the currents present in it. As a consequence, allowance for temperature rise is
made in the choice of bearings. Given this restriction on the bearing type a lower limit on the
possible air-gap is set in the induction motor design. Significantly, the SynRM rotor carries no
current and is subject to no internal heating. Thus, the smaller air-gaps proposed are achievable.
Of course, other mechanical factors such as tolerances for cost effective manufacturing and
unbalanced magnetic pull due to rotor eccentricities would also need to be considered if the
motor were to progress beyond the experimental prototype stage.
In a broader sense, the "shape" of the stators designed was encouragingly similar to those of
comparable induction machines. Generally a SynRM of similar rating to an induction machine
is only marginally smaller than the induction machine. However, the SynRM is significantly
lighter due to the reduced iron content in the rotor. The rotors themselves have similar
diameters and lengths. Ratios such as slot depth to yoke depth also remain in proportion.
In Chapter 3 a 5kW machine design is described in detail. For that particular design the
sensitivity of performance relative to the key dimensions was considered. Figure 2.10 shows
graphs of the variation in torque / mass as the individual independent dimensions were varied.
Noting the scales, the most critical design parameters are pole pitch and steel : steel + fibre
ratio. The accuracy of the other dimensions has less significant effect on the machine
performance. In particular the stator slot opening (not shown here) had very small effect on the
SynRM performance as predicted by the design model.
Magnetic Circuit Modelling and Design Optimization of the SynRM 37
3.5 -|
1 6 2.5-Z
i 21
a 1.5-a
I '" ** 0.5 -
1.25 1.3 1.35 1.4
Rotor pole pitch (rad)
1.45 13
3-,
-a 2 « •
1 2.9-z
I 2'85" a 2.8-
f. 2.75 -,3 f- 2.7 -
0.3 0.35 0.4 0.45 0.5
Steel: steel + fibre
0.55 0.6
3-]
-a Z95" i 2'9" S. 2.85 -
1 2-*J « " 5 -
f 2-7_ H 2.65 -
0.15 ' 0.2 ' ' ' 0.25 0.3 0.35
Air-gap (mm)
1 0.4 ' 0.45
2.99 -
~ 2.98 -CO
| 2.97 -
1 2.95 -
o 2-9" "
1 2.93 -*" 2.92 -
/ \
f ^ 1 4.2 4.4 4.6 4.8 5
Current density (A/mm^)
5.2 5.4
Figure 2.10 Sensitivity of Machine Performance to Design Parameters
2.7 Summary
A magnetic circuit model has been developed for the SynRM. This model takes into account
all key stator and rotor dimensions and includes allowance for saturation in the magnetic
circuit. It predicts the average flux densities in the machine and hence the torque output. The
model could be further simplified by applying a piecewise linear approximation to it under the
condition of rated operation. This allows for a very simple rated torque calculation based on
the motor dimensions.
The actual process of designing a machine initially involves examining the relationships
between the various dimensions. The key independent design variables were determined to be
rotor pole pitch, rotor radius, rotor steel: steel + fibre ratio, air-gap, stator current density and
stator slot opening. Other dimensions can be shown to depend on these or on thermal
requirements. Of the design variables the most critical are rotor pole pitch and steel : steel +
fibre ratio.
Magnetic Circuit Modelling and Design Optimization of the SynRM 38
It has been shown that larger pole pitches (approaching 180 electrical degrees) and steel: steel
+ fibre ratios slightly smaller than 0.5 produce the optimal motor performance. These values
are contrary to other published results. The difference is due to the assumed stator current
excitation. Square current excitation has been assumed in this instance because of the greater
torque per rms ampere achievable through it.
The 5 k W Synchronous Reluctance Motor 39
CHAPTER 3
The 5kW Synchronous Reluctance Motor
3.1 Introduction
A prototype 5 k W S y n R M was built based on the design optimization specifications. This
allowed for experimental verification of the design model and a means for validating field-
oriented control techniques at a later stage. Figure 3.1 shows a photograph of the constructed
machine. This chapter outlines the construction methods and performance results of static tests
carried out on the experimental machine.
Figure 3.1 Prototype 5 k W SynRM.
Section 3.2 deals with the motor construction. The "ideal" optimized design is initially
presented. Practical constraints in constructing a one off prototype forced some compromises
in the design dimensions. The construction methods along with the necessary modifications are
The 5kW Synchronous Reluctance Motor 40
presented. The most significant compromise in construction was due to the small stator slot
openings originally specified. The impact of these and solutions to the problems that arose will
be considered.
Section 3.3 presents and analyses the results of tests made on the experimental machine.
Design model predictions for the machine's torque and winding inductance values are
compared with those predicted by finite element analysis and more importantly, the actual
measured values. Only static performance results are presented in this section, dynamic
performance results are contained in Chapter 7.
3.2 5kW SynRM Construction
A four-pole, 5kW SynRM was designed based on the design optimization algorithm. It
achieved a nominal torque / mass ratio of 2.98 Nm/kg which promised significant improvement
over that of a conventional induction motor. Typically, in this size range, induction motors
have torque / mass ratios in the range of 1.2 to 1.8 Nm/kg. Table 3.1 summarizes the key
dimensions of the motor. Appendix A contains detailed mechanical drawings for the motor.
Rotor
Pole Pitch
Steelrsteel + fibre ratio
Radius
Length
Lamination thickness
1.44 rad
0.45
64mm
50mm
0.35mm
Stator
Slots
Outer Diameter
Slot depth
Yoke depth
Length
Slot opening
Tooth tip thickness
36
168mm
22mm
20mm
50mm
0.6mm
1.5mm General
Poles
Air-gap
Phases
Current density
4
0.3mm
9
4.8A/mm2
Current
Voltage
Speed
1.8A
415V
750rpm
Table 3.1 Key 5kW SynRM dimensions
The 5kW Synchronous Reluctance Motor 41
S T A T O R C O N S T R U C T I O N
The SynRM stator dimensions are similarly proportioned to those of a standard induction
machine. Notably, the outer diameter and length of the stator are of the same magnitude as
would be expected in a comparably sized induction machine. Further ratios such as the slot
depths to yoke depth are typical of an induction machine design and a realistic current density
was obtained.
The stator laminations were constructed from 0.5mm Ly-Core 230. Ly-Core 230 is a standard
electrical steel lamination material with a maximum core loss of 2.3W/kg at 50Hz. Figure 3.2
is a photograph of a single stator lamination prior to assembly. The full mechanical details for
the lamination are shown on drawings Al and A2 of Appendix A.
Figure 3.2 5 k W S y n R M stator lamination
The laminations were laser cut. Laser cutting was preferred over punching as it allowed the
stator teeth to be made with a curved face. This ensured that the machine air-gap would be
more uniform. Laser cutting also allowed the stator to be skewed.
The 5kW Synchronous Reluctance Motor 42
The stator was skewed one tooth pitch over its length. A common problem observed in
SynRMs is that of cogging torque. This arises where the stator teeth magnetically "lock" into
the rotor laminations. Physically this can lead to torque pulsations in the motor shaft or in
extreme cases a motor that is difficult to start. Skewing the stator prevents the stator teeth and
rotor laminations aligning exactly. An additional benefit of this arrangement may be a
reduction in the flux pulsations in the rotor laminations leading to lower rotor eddy current
losses.
The very small slot openings (0.6mm) created some problems in the laser cutting process.
Normally it is possible to obtain a clean edge when laser cutting by blowing high-pressure
nitrogen gas onto the cut. However, this process does trap heat in the cut area. The fine detail
around the stator tooth tips meant that nitrogen gas could not be used without causing heat
damage. Consequently the laminations were cut but with burring occurring along the edges.
This burring had to be removed manually and the laminations did not stack as compactly as
originally hoped.
The laminations were secured together by four bolts distributed evenly around the edge of the
stator. These points also doubled as a means of securing the stator to the motor base as can be
seen in Figure 3.1.
STATOR WINDING
The design model assumed an ideal rectangular stator current distribution. The stator was
wound with a nine-phase concentrated winding to approximate this ideal. The physical
configuration of the winding is as shown in drawing A4 of Appendix A.
Consultation with motor rewinders suggested a good "rule of thumb" was that 70% of the
available slot area could be filled with current carrying copper. The remainder of the slot area
is lost due to the gaps formed when bundling the conductors. The design model generated the
slot dimensions based on this rule. Given the stator current distribution, the slot depth was
The 5 k W Synchronous Reluctance Motor 43
increased until 7 0 % of the slot area multiplied by the stator current density gave the current
required over one slot pitch.
To determine the size of the wire and number of turns in the stator winding several factors need
to be considered. These include the width of the slot opening, the maximum voltage available
at the inverter output, the currents required and the speed at which the motor is required to
produce rated torque.
The maximum number of turns in the winding is set by the maximum inverter output voltage
and the speed the motor is required to operate at. It is necessary that the output voltage remains
greater than the speed voltage generated in the winding so that the stator currents can be
controlled. In this instance, this relationship can be quantified as follows. Each phase of the
stator winding consists of four coils connected in series. Assuming negligible resistance the
voltage across the entire winding is approximated by,
v-A—1-dt
-AN^ (3.1) dt
where, y/= flux linkage of one coil (Wb)
N = number of turns / coil
<p= flux in one coil (Wb)
Flux linking the coil will vary as the rotor moves. Assuming that the air-gap flux density
distribution is a rectangular block over the rotor pole face the voltage equation can be modified
to,
d(j) da v~AN—
da dt ~ANBgLRcv
(32)
The 5 k W Synchronous Reluctance Motor 44
where, a = rotor position (rad)
Bg = air-gap flux density (T)
L = motor axial length (m)
R = air-gap radius (m)
co= rotor speed (rad/s)
The motor's rated speed is 1500rpm while fully fluxed (Bg = 0.85T). Substituting into
Equation (3.2) with the speed voltage term limited to 60% of the inverter dc link voltage
(587V) shows that the maximum number of turns in each coil is 206.
The size of the wire is found by dividing the total cross sectional area of copper required in the
slot by the number of turns. This calculation gives a diameter of 0.5mm. Mother "rule of
thumb" is that the maximum wire diameter that can be installed into a slot is half the slot
opening. In the 5kW SynRM the slot openings are 0.6mm wide. It was proposed to use four
0.25mm wires in parallel to obtain the equivalent cross-sectional area of one 0.5mm wire.
Two problems occurred with this approach. First, the wire insulation thickness becomes
significant compared to the copper thickness in small diameter wire. Second, the large numbers
of turns of parallel strands are more difficult to stack in the slot. Both of these factors act to
reduce the percentage of slot area that can be filled with copper. Hence, it was necessary to
reduce the number of turns in the stator coils.
The final winding configuration used four coils of 0.25mm diameter wire in parallel. Each coil
had 170 turns. This meant that only 55% of the available slot area is filled with copper. Thus,
operating the machine at rated torque will involve exceeding the current rating of the stator
winding. This is only possible for short time periods. However, it will still allow experimental
verification of the machine's predicted performance. In hindsight, there is a strong argument
for making the slot openings larger in future machines. This sacrifices only a small fraction of
the machine performance but yields a much more practical machine to construct.
The 5kW Synchronous Reluctance Motor 45
R O T O R C O N S T R U C T I O N
Figure 3.3 is a photograph of the 5.0kW SynRM rotor. A full mechanical schematic is shown
on drawing A5 of Appendix A.
The rotor was constructed on a stainless steel shaft. The rotor laminations were built from
0.48mm sheet steel. Plastic film is used as spacing between the rotor laminations to maintain
the steel: steel + fibre ratio at the designed value of 0.45. The steel laminations were thicker
than those specified in the design model (0.35mm). This was due to availability of material and
will only marginally increase the effective air-gap in the final machine.
The rotor laminations are secured in position by stainless steel screws inserted radially through
the centre of the laminations. The entire structure is bonded in epoxy resin for additional
strength.
Figure 3.3 5.0kW SynRM rotor
The 5 k W Synchronous Reluctance Motor 46
3.3 Results and Analysis
The design model predicted that the prototype SynRM would produce a torque of 36Nm at
rated current. At a speed of 1500rpm this corresponds to a power of 5.65kW.
FINITE ELEMENT ANALYSIS
Prior to construction, finite element analysis was performed on the design to validate the model
predictions. In particular, the air-gap flux density distribution and machine torque were
measured. These values were of interest as they are also generated in the design model
calculations.
For the purpose of the finite element analysis it was assumed that the stator slots over the rotor
pole edges carried rated direct axis current. Similarly, slots over the rotor pole face carried
rated quadrature axis current. Figure 3.4 shows the graphs of air-gap flux density, over the
rotor pole face, as predicted by the finite element analysis and the design model. The flux
density distribution generated in the finite element analysis contains variations due to stator slot
effects. In contrast, the design model prediction represents an average air-gap flux density
value. To enable the two graphs to be compared a moving average was applied to the finite
element analysis results. This moving average operates over one stator tooth pitch. The result
is represented by the third curve in Figure 3.4. The shape of the averaged finite element results
show similar levels of air-gap flux density to those predicted by the design model. The portion
of the air-gap where flux density reduces due to quadrature flux is wider in the finite element
analysis but the reduction is not as large. This last observation is not unexpected as the
approximation made as part of the design model was that all quadrature axis flux flows through
the final stator tooth at the edge of the rotor pole face.
Using finite element analysis the SynRM torque was determined to be 35Nm. With the stator
excitation unchanged the rotor was moved over one stator tooth pitch to see how the torque
output would vary. The motivation for this test was to observe any potential problem with
The 5 k W Synchronous Reluctance Motor 47
cogging torque. This problem has been previously noted in other experimental machines [4,
41]. Figure 3.5 shows the variation in torque as the rotor was moved. In this figure, torque can
be seen to vary by less than 3%, which was considered to be quite acceptable. For this test no
effort was made to modify the stator currents to reduce the torque variation. It may be possible
to reduce the variations further by appropriately adjusting the phase currents with rotor position
if so desired.
Finite Element model
l/\ e ^ A K '5
'r0 i
$ - ^
v f A '
/
If *
-50 -30
1.6-1
1.2 -
-AJGL /-l-/0J^
/I / 0.4
n i u
-10
-0.4 -
Design model /
u f\ 1...
1 I 1
10 30 '
Angular displacement (degrees)
f 50
Figure 3.4 Air-gap flux density distribution in 5 k W SynRM.
Figure 3.5 Variation of S y n R M torque with rotor position.
The 5kW Synchronous Reluctance Motor 48
On the basis of the finite element analysis results the machine was constructed with confidence
in its potential for achieving the design goals. Static tests were performed on the constructed
machine. These tests involved measuring the winding characteristics of the machine.
STATOR WINDING MEASUREMENTS
Figure 3.6 shows the model used to represent a single phase winding on the SynRM. The
winding resistance was measured to be 27.4Q. This resistance is relatively large because of the
poor packing factor achieved in the stator winding due to the problems associated with the
small slot opening. Stator leakage inductance was found by measuring the winding inductance
with the rotor removed. The value was detennined to be 0.18H.
Rs Ls
o VV rv"v"> 1 1 21.AQ. 0.18H
Re p> LM ")
0 ' '
Rs Stator winding resistance
Ls Stator leakage inductance
Rc Core loss resistance
LM Magnetizing inductance
Figure 3.6 Phase winding model
The core loss resistance and magnetizing inductance were found by applying an ac voltage to
the winding. As the stator winding resistance and leakage inductance are known, the other two
model components could be detennined from terminal voltage and current measurements. Core
loss resistance was measured to be 1170& when the direct axis was aligned with the axis of a
coil. The direct axis inductance is a function of current because of iron saturation effects.
Figure 3.7 shows the direct axis magnetizing inductance versus rms phase current curve
measured from the prototype machine.
The 5kW Synchronous Reluctance Motor 49
1.200 n
1.000
g 0.800
1 0.600 u 3 | 0.400
0.200
0.000
0.1 0.2 0.3 0.4 . 0.5
Current (Amps rms)
0.6 0.7 0.8
Figure 3.7 Direct axis magnetizing inductance.
Similarly, core loss resistance was measured to be 27&Q, when the quadrature axis was aligned
with the axis of a coil. Figure 3.8 shows the quadrature axis magnetizing inductance versus rms
phase current curve measured from the prototype machine.
0.2 n 0.18
0.16 0.14
g 0.12 -
I 0.1 | 0.08
£ 0.06 -0.04
0.02
0 0.5 1
Current (Amps rms)
1.5
Figure 3.8 Quadrature axis magnetizing inductance.
Figure 3.9 shows the magnetizing inductance of one phase winding versus rotor position. The
unsaturated saliency ratio is 7. If leakage reactance is included the saliency ratio becomes 3.5 -
4. This is smaller than that reported for other sinusoidal rnachines but is not surprising as the
The 5 k W Synchronous Reluctance Motor 50
design criteria was not to optimise this ratio. Specifically, the contribution of harmonic
components of current compensate for the reduced saliency ratio. Figure 3.10 shows the
mutual inductance between two coils on the stator again plotted as rotor position is varied.
Observe that the inductances do not vary sinusoidally. This is because of the rotor saliency and
concentrated stator winding. These results will be used to establish the validity of the
inductance matrix calculations in Chapter 4.
Figure 3.9 Magnetizing inductance of one phase versus rotor position
Figure 3.10 Mutual inductance between two stator phase windings versus rotor position.
The 5 k W Synchronous Reluctance Motor 51
3.4 Summary
A 5kW four-pole nine-phase SynRM was designed and built. Some compromises were
necessary in the construction. Most significantly the small slot openings led to difficulty
manufacturing the stator laminations and consequently winding the stator. In Chapter 3 it was
noted that the overall machine performance was not very sensitive to slot opening. In
hindsight, this dimension could have been increased without significantly affecting the results.
As the design was compromised the prototype is unable to sustain 5kW-power output
continuously. However, it was possible to confirm this rating using finite-element analysis and
short duration load tests (results presented in Chapter 7).
The final measurements taken were of the winding characteristics. These will be required when
implementing controllers at a later stage. Additionally the results verify inductance versus
position calculations presented in Chapter 4.
Generalized Equations for a Nine Phase SynRM 52
CHAPTER 4
Generalized Equations for a Nine Phase
SynRM
4.1 Introduction
A nine-phase four-pole experimental SynRM has been designed and built. To model and
control the motor's performance requires the determination of appropriate voltage and torque
relationships. This chapter derives these equations specifically for the nine-phase SynRM. The
method used can be readily extended to any "n" phase SynRM.
The generalized d-q equations for the three-phase SynRM are well known. By convention the
direct (d) axis lies along the low reluctance flux path, parallel to the rotor laminations. The
quadrature (q) axis lies along the high reluctance flux path, transverse to the rotor laminations.
Thus, the conventional d-q voltage and torque equations are [41],
Vd=Ld^ + RJd-C0Lqiq (4.1) dt
vq=Lq^ + RJq+C0Ldid (A.2)
T = ^p(Ld-Lq)idiq (4.3)
The aim of this chapter is to develop the analogous equations for the nine-phase machine. This
will allow the SynRM to be modeled and simulated and appropriate control strategies
developed. Chapter 5 will specifically consider methods of implementing field-oriented
control.
Generalized Equations for a Nine Phase SynRM 53
The generalized d-q equations have been previously found for the five-phase machine [57].
The key to this derivation is appropriately defining the stator inductance matrix. It is necessary
to include sufficient harmonic components in the stator frame to be able to deduce a
transformation, to the d-q harmonic reference frame, that is both useful and invertible. The
traditional approach to this problem is to use approximations to the stator winding distribution
and air-gap length as functions of angular displacement around the stator. These are then
combined to produce an expression for inductance. However, this approach becomes
increasingly tedious, as higher harmonics are included in the analysis.
Section 4.2 presents an alternative method for deriving the stator inductance matrix. A
generalized expression is determined for the mutual inductance between two concentrated coils,
positioned arbitrarily on the stator. The approach used is to make an approximation to the air-
gap flux density distribution and hence calculate the flux linkages. The mutual inductance
expression obtained is then used to determine the elements of the stator inductance matrix given
the specific dimensions of the nine-phase machine.
Sections 4.3 and 4.4 derive the generalized voltage and torque equations for the nine-phase
SynRM, respectively. An orthogonal transformation is deduced for the stator inductance
matrix. The transformation is applied to the standard stator voltage and torque equations. This
transforms the equations from the stator reference frame to the synchronous reference frame. In
the synchronous reference frame the direct and quadrature harmonic components of current and
voltage are effectively isolated. This offers potential advantages for the simulation and control
of the drive to be explored in Chapter 5.
4.2 The Stator Inductance Matrix
The stator inductance matrix, Ls(cc), describes the relationship between the stator phase
currents, i , and the stator flux linkages, Xs, in the SynRM such that,
Generalized Equations for a Nine Phase SynRM 54
As=Ls(a)i_s (4.4)
The stator inductance matrix elements are a function of rotor position, a, due to the rotor
saliency. Figure 3.10 showed that the mutual inductance between two phase windings on the
experimental machine varied as a non-sinusoidal function of rotor position. A general
expression describing this variation with rotor position for two arbitrary coils on the stator of
the SynRM can be obtained. This expression can then be used to determine the individual
inductance matrix elements for the nine-phase machine given its relevant dimensions.
Traditionally, approximations are made to the stator winding distribution and air-gap length as
functions of angular displacement around the stator. These expressions are then used to
determine the inductance values including the necessary harmonic components [30, 33, 57].
This approach becomes increasingly cumbersome when higher order harmonics are included in
the analysis. An alternative approach based on first approximating the air-gap flux density
distribution is presented here.
OA'
Figure 4.1 Generalized coils on SynRM stator
Figure 4.1 shows the general case of two fully pitched concentrated coils on the stator of a two-
pole SynRM. The axes of the cods are separated by /? radians. The rotor has a pole pitch of 0P
Generalized Equations for a Nine Phase SynRM 55
radians and is at an angle of a radians to the axis of coil A. The air-gap flux density can be
approximated if the rotor position and dimensions are known.
(a)
(b) n-6„ a>
9. a—
B0
-nn.
Be Bd
S
71/2
a
.71
371/2 Q
Figure 4.2 Air-gap flux density distribution
If current is passed through coil A then a magnetic flux is set up in the machine. Figure 4.2
shows two approximations to the air-gap flux density distribution, around the periphery of the
Generalized Equations for a Nine Phase SynRM 56
rotor. The distribution in Figure 4.2(a) is typical when coil A is positioned over the edges of
the rotor pole. The situation is similar to that represented in Figure 4.1 and is described
n-9p mathematically by the condition a < in a two-pole machine. The full rotor cross-
section is available to carry direct axis flux. This flux is large because of the low reluctance of
the path. It is denoted as producing air-gap flux density Bd in the figure. In contrast, flux
crossing the larger air-gap at the rotor pole edges travels over a high reluctance path.
Consequently, the flux and the resultant flux density are much smaller. This flux is termed
quadrature axis flux and the flux density due to it is labeled Bq.
Figure 4.2(b) shows a second situation where coil A is positioned over the rotor pole face.
Mathematically this corresponds to the condition a > in a two-pole machine. In this
instance, only a reduced portion of the rotor cross-section actually links the two sides of coil A
and is available to carry the direct axis flux. The remainder of the rotor pole face and edges
present a high reluctance path to magnetic flux and as such only carry the smaller quadrature
axis flux.
The air-gap flux density distributions shown represent an approximation to the actual
distributions. The validity of the approximations will be demonstrated by comparing the
calculated inductance values to those measured in Chapter 3. The error introduced by the
approximation is analogous to that obtained when the air-gap is approximated as a rectangular
function as has been done by other researchers [30, 33, 57].
In the interest of simplifying the mathematical analysis, it is advantageous to consider each of
these air-gap flux density distributions as the sum of a direct axis component and a quadrature
axis component. Implicit in this decomposition is the assumption that there is no saturation in
the machine iron. Figure 4.3 shows a typical decomposition. Both cases shown in Figure 4.2
can be decomposed in this way. Note that what is designated solely as direct axis flux in Figure
Generalized Equations for a Nine Phase SynRM 57
4.2 is shown to be a combination of direct and quadrature flux in Figure 4.3. In decomposing
either case the quadrature axis component is identical. Only the shape of the direct axis
component changes dependent on the rotor position.
Bd
-F-
/ B„
1_ J~»
Bd - B„
^ + * zF /
-R
Figure 4.3 Decomposition of air-gap flux density distribution
The direct and quadrature axis air-gap flux density distributions can now be individually
decomposed into their Fourier series components. There are two expressions for the direct axis
flux density distribution depending on the rotor position. Quadrature axis flux density
distribution is independent of rotor position.
r n 0 ^
BAff)J^zM ± sin
V 2 J cos(n(t9 - a)) case (a) ft n=X(odd) n
(4.5)
B-l
A(Bd-Ba) ,A (-1) 2 cos(ncr) , ,n .\ „. Bd(0^ = JLJ. £_ ^ ——I i—/-cos(n(0-a)) case(b)
n n=X{odd) n (4.6)
n-X
ft n=l{odd) n
(4.7)
The flux linking coil B, due to the current in coil A, can be calculated by integrating the air-gap
flux density distribution between the two sides of coil B. Hence,
Generalized Equations for a Nine Phase SynRM 58
r' Wa.=N \Bg(e)LrRd6 { 4 8 )
T *
where, Lr = Rotor length (m)
R = Air-gap radius (m)
N = Number of turns / coil
The mutual inductance values between the coils are now calculated by simply dividing the flux
linkage by current to get;
n-X (n0\ p (-1) 2 sin
S(Bd-BQ)LrRN ^ { 2 , M«w(aO= : ^ r^ -cos(n(a+fi)) case (a) (4.9)
nia n=\{odd) n
S(Bd-Bq)LrRN ~ cos(na) Ma^d(d)= " _, ^cos(n(cr+^)) case(b) (4.10)
ftla n=X(odd) n
SBqLrRN - cos(n^) Mab-q(a)=—
q— __ —Y^- (4.11) ftla n=\(odd) K
where, ia = Phase A current (A)
Figure 4.4 shows graphs of the theoretical self-inductance of phase winding 'a' and the mutual
inductance between phase winding 'a' and 'e' of the experimental machine. These graphs were
formed by using appropriate combinations of equations (4.9) to (4.11). Calculated rninimum
and maximum inductances are used. They are the theoretical equivalent to the measured values
in Figures 3.9 and 3.10. To allow comparison, the measured data points have been included in
Figure 4.4. A close correlation can be observed between the measured and theoretical values.
Generalized Equations for a Nine Phase SynRM 59
(a) Self Inductance vs Rotor Position
0
0 60 120
Rotor position (degrees)
180
(b) Mutual Inductance vs Rotor Position
Rotor position (degrees)
Figure 4.4 Theoretical and measured (a) self inductance for phase 'a' and (b) mutual inductance
between phase 'a' and 'e' for the experimental SynRM.
The impact of the transition from case (a), direct axis excitation to case (b) excitation is
minimal. In the self-inductance curve the effect is to reduce the upper peak of the triangular
waveform. For the mutual inductance curve the effect is barely noticeable. One of the key
characteristics of the designed S y n R M is that it has a large rotor pole pitch that approaches n
radians (electrical). In these circumstances it is reasonable to approximate the mutual
Generalized Equations for a Nine Phase SynRM 60
inductance verses rotor position curve with the triangular wave, obtained using case (b) direct
axis excitation, alone, hi effect we are assuming the rotor pole pitch is n radians (electrical).
Under the assumption that the rotor pole pitch approaches n radians electrical the direct and
quadrature axis inductance expressions can be combined to give a tidy expression for the
mutual inductance between two coils on the stator of a SynRM.
8(Bd-Ba)LrRN - cos(na)cos(n(a+j3)) 8BqLrRN ^ cos(nfi)
Mab(a)= f l_ 1 + — 2_ —ZT~ ft^-a n=\(odd) n ma n=l(odd) n
=± ^ "Wto^4g,tV ± map. (4,2) ft n=X(odd) n ft n=l(odd) n
where! Ld = M S ^ L (4.B)
= phase inductance when d-axis aligned with phase axis
BqLrR7jN ( 4 1 4 )
9
= phase inductance when q-axis aligned with phase axis
This expression can now be used to form the stator inductance matrix given the nine-phase
SynRM dimensions. Consideration must be given to how many spatial harmonic components
from the mutual inductance expression (4.12) should be included in each element of the
inductance matrix. The stator inductance matrix is formed with a view to performing a non-
singular d-q transformation upon it. This goal sets the imnimum number of harmonics required.
An analogy can be drawn to the more familiar three-phase machine where there are two
independent phase currents. A three-phase d-q transformation is based on resolution along the
two quadrature components of the fundamental flux wave. The transformation for a nine-phase
Generalized Equations for a Nine Phase SynRM 61
machine involves eight independent currents. There are not enough degrees of freedom for
them to be associated with the fundamental flux wave alone.
To be able to deduce a transformation which is useful and invertible one needs a model of the
machine incorporating space flux harmonics up to and including the seventh harmonic (odd
only). This provides eight degrees of freedom in the transformed variables. Since the stator is
star connected with no neutral there are only eight independent variables in the original system
and eight degrees of freedom will suffice. Thus the (i,j)'th element of the inductance matrix,
Ls(a), for a machine with p pole pairs, is given by;
M « ) = A - i cos(Mr)/?,) n=l(odd) n
+ L^ _ cos(M2a + 0 + ,--2)^)) (^s)
n=l(odd) K
A where' L^ = — (Ld + Lq) (4.16)
JL
A Ldiff =-j(Ld-Lq) (4.17)
P = ~ h (4-18) P 9
= Angle between adjacent phase axes (radians).
The inductance matrix is symmetrical and a transformation matrix, T(a), can be found such that
the orthogonal transformation T(or) Ls(a) TT(a) yields a diagonal matrix. The transformation
matrix is,
Generalized Equations for a Nine Phase SynRM 62
^il'
"cW sW cM sij
C5(a)
Sij
a$ 57(4 1
.V2
C(a+&5)
S(<rt^
C3(a-^
53(a+&^
C5(a+8^
55(a+8t^
C7(a+&5)
S7(a+&$
1
C(ar-2$
S{a-2$i
da-lfy
53(a-24
C5(a-2t^
S5(a-2c5)
C7(a-2c5)
S7(a-2^
1
C(a+6$
S(a+6^
C3(a+di5
S3(a-^
C5(a-^
S5(a+65)
a{a-^Sj
Sl{a+6$
1
C[a-4S)
S{a-4%
C{a-A$)
S3{a-4^
Cia-A$
S^a-Ad)
C7(a-4$j
Sl{a-A$
1
C(a+4Sj
S(a+4$
C3(a+4J(|
S3(a+45)
C5(a-H^
55(a+4^
Cj{a+4$)
Sl[a+4$
1
C(a-6^
S(a-G5j
C3(a-65S
S3(a-6^
C5(a-6^
S5(a-ci$)
a(a-6^
S7(a-6^
1
C(a+2^
S{a+2Sj
C^eHQSj
Sip+ty
Cia+ty
S5(a+25)
Cl[aY2$
Sl(a+2$ 1
V~2
C(c-&f
S(a-&5)
C3(a-&j)
S3(a-&5)
C5(a-g^
S5(a-84
C7(a-&$
S7(a-&^ 1
(4.19)
where, a = pa
S = * 9
S, C denote sine and cosine functions respectively.
The transformed matrix, L^ = T(a) Ls(or) TT(a), has diagonal elements that are constant, or
independent of rotor position. All other elements in the transformed inductance matrix are
zero. The diagonal elements are representative of the fundamental, third, fifth and seventh
spatial harmonic, direct and quadrature components of stator inductance. They are not the
exact values in a physical sense but a scaled representation produced by the transform. These
elements are,
Ldi
L*
Ld3
^
= -L
- ^
" ^
- ^
L -J--L d5 25K2 d
L —%-L 95 25^ 2 9
Ld1 " A9TT2 d
L. 'ql
36
A9n 2 q
Generalized Equations for a Nine Phase SynRM 63
4.3 Voltage Equation
The stator voltage equation for any machine is;
. d . (4.20)
where in the case of a nine-phase machine,
vs = stator phase voltage vector
= < x vb vty
is = stator phase current vector
= (*« h hf
As = stator flux linkage vector
= (Aa Ab .... Af
rs = stator winding resistance
The stator flux linkage term in equation (4.20) can be replaced by the product of the stator
inductance matrix, Ls(«r), and the stator current vector, is. Applying the product rule to this
term yields an alternative form of the voltage equation expressed in variables that can be
measured at a motors terminals.
dt da
where,
da m- —
dt = rotor speed (rad/s)
Generalized Equations for a Nine Phase SynRM 64
The difficulty in applying equation (4.21) directly is that the terms in the inductance matrix
depend upon rotor position. The orthogonal transformation of Section 4.2 eliininated position
dependence in the transformed inductance matrix. The same transformation can be applied to
the terms of equation (4.21) to yield the d-q voltage equations. Thus,
T(flr)v, = rsT(a)is + T(a)Ls(a)^- + T(a)^^-ajis dt da
Simplifying,
vd9 = rj(a)is +T(a)Ls(a)T\a)T(a)^ + T(a)^^T\a)cM(a)is
« . - r , U + L ^ + {lX-)^r<»-Lj.^r<»^ (4,2,
where,
v^ = transformed d - q voltage vector
= T(a)v,
= (v„, v„ vd3 v?3 vd5 vq5 vdl vql 0?
idq = transformed d - q current vector
= T(af)i,
= (fdX lQX ld3 *,3 ^5 ^5 '<" \l 0)
The bracketed terms in equation (4.22) can be evaluated given the specific inductance matrix
(4.15) and transformation matrix (4.19) for the motor. In the case of the four-pole nine-phase
Generalized Equations for a Nine Phase SynRM 65
experimental machine these matrix identities have been evaluated to obtain identities (4.23) and
(4.24). The L ^ t e r m is as previously defined in equation (4.17).
da
0
18W 0
0
0
0
0
0
0
is*
0
0
0
0
0
0
0
0
0
0
0
6Ldiff
0
0
0
0
0
0
0
6LW
0
0
0
0
0
0
0
0
0
0
0
"W 0
0
0
0
0
0
0
3-6JW
0
0
0
0
0
0
0
0
0
0
0
Z6Lm
0
0
0
0
0
0
0
2-6^
0
0
°1 0
0
0
0 23i
0
0
0
0
and,
dljd)
da T*(o» =
0-2 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
0 0 0 - 6 0 0 0 0 0
0 0 6 0 0 0 0 0 0
0 0 0 0 0 -10 0 0 0
0 0 0 0 10 0 0 0 0
0 0 0 0 0 0 0 -14 0
0 0 0 0 0 0 14 0 0
0 0 0 0 0 0 0 0 0
(4.24)
Substituting the matrix identities (4.23) and (4.24) into equation (4.22) yields the d-q voltage
equations in component form (4.25 to 4.32). Note that the stator winding of the experimental
SynRM is star connected with no neutral. As such there are only eight independent stator phase
currents and no zero sequence component. Only eight transformed variables are required to
describe the system. Equations (4.25 to 4.32) represent the same information as equation
(4.21). However, they are significantly easier to work with because of the reduced couplings
between the windings. Also the inductance terms are constant and do not vary with rotor
position. Essentially the experimental machine has been represented by a simpler set of
Generalized Equations for a Nine Phase SynRM 66
equations without sacrificing any generality. Equations (4.25) and (4.26) when compared to the
standard d-q voltage equations for a three phase machine, (4.1) and (4.2), contain an additional
factor of two in the speed voltage term. This is due to the machine being analysed having four
poles.
Vw, = rsidl +Ldl-^- + 2L„,fljL (4.25) dt
'qX ~ ' J V ' ^gX , "^dX""dX v„ = r±, +L„,-?L- 2L,MA, (4.26)
vd3 = Va +L<*-^- + 6 V*.73 (4'27)
vqi=rJq3+Lq^-6Ld3axd3 (4.28)
vd5 = rJd5+Ld5^ + lOLq5COiq5 (4.29)
vqs=rsiq5+Lq5^-10Ld5COid5 (4-30)
Vdi=rsidl+Ldl^ + lALql0iql (4-31)
^=rJq^Lql^-lALd7aidl (4-32)
Generalized Equations for a Nine Phase SynRM 67
4.4 Torque Equation
To complete the generalized description of the SynRM a torque equation is required. Assurning
that the SynRM can be modeled as a linear magnetic system its co-energy, Wco, will be equal to
the stored magnetic energy;
1 T Wco=-isLs(a)is (4.33)
The electrical torque can be found from the rate of change of the system co-energy with respect
to rotor position;
T = dW-da i's constant
1 .T dh (a). =—i — 1
2's da -s
= ±?X(a)T(a)^^-TT(a)T(a)is 2 da
= \ldq\rW T V ) k
The bracketed term is identical to one that arose in deriving the voltage equations. It has been
previously evaluated to obtain result (4.23), which can now be substituted to yield the d-q
torque equation (4.34).
Te = 2 ( ^ i ~ Lqx)idxiqx +
6(Ld3 ~ Lq3)id3iq3 (4.34)
+10(^5 - Lq5)id5iq5 + 14(Iy7 - Lql)idliql
Note that the torque equation indicates that the fundamental, third, fifth and seventh harmonic
components of current all contribute to torque production within the SynRM. If the higher
harmonic components of current are absent the form of the torque equation reduces to the
3 familiar three-phase result without the — scaling factor, which is a product of the
2
transformation used.
Generalized Equations for a Nine Phase SynRM 68
4.5 Summary
The generalized d-q voltage and torque equations have been derived for the nine-phase SynRM.
These were obtained by applying an orthogonal transformation to the standard stator voltage
and torque equations. The transformed equations are significantly more useful than the
equivalent stator reference frame equations. This is because the transformation effectively
removes the couplings between the stator phase windings. The transformed motor voltages and
currents correspond to the combined direct and quadrature components of these variables.
Further, the transformed inductance values are constant, independent of rotor position.
The simplified mathematical description of the machine opens the door to the possibility of
simulating motor performance as well as the design and implementation of appropriate control
strategies. This forms the focus of the next chapter.
Field-Oriented Control of the SynRM 69
CHAPTER 5
Field-Oriented Control of the SynRM
5.1 Introduction
This chapter considers two methods of implementing field-oriented control in the nine-phase
synchronous reluctance drive. Field-oriented control involves separately controlling the direct
and quadrature axis excitations in the motor. Different control strategies can be used to achieve
such goals as maximum torque, maximum rate of change of torque and maximum power factor
from the drive [2]. In this instance, the methods are discussed from the point of view of
implementing a "constant current in the inductive axis" type controller. Direct axis excitation
is maintained at a constant value to ensure that the machine remains fully fluxed. Quadrature
axis excitation is varied to control the motor's torque. The control methods presented are
essentially means to control the direct and quadrature currents in the SynRM.
Section 5.2 describes what is termed the "stator current controller". If the SynRM rotor
position is known, then a current reference can be generated for each of the stator phase
windings. The portions of the stator winding over the rotor pole sides are designated as
supplying the direct axis excitation. The remainder of the stator winding is designated as
supplying quadrature axis excitation. Thus, a current reference is generated. Law et. al. used a
similar strategy for defining the current references in their field regulated reluctance machine
[5, 27, 28]. The important difference being that the individual phase windings were isolated in
the field regulated machine. Each phase was supplied by a separate full bridge inverter. In this
thesis, the windings are star connected. The motor is supplied from a nine-phase voltage source
inverter eliminating half of the power switches required in the comparable field regulated
machine. Current is controlled by switching the individual phases to the positive or negative
inverter bus depending on the phase current's relationship to its reference.
Field-Oriented Control of the SynRM 70
Section 5.3 explains what is termed the "transformed frame vector controller". In this instance
control is performed in the transformed rotor current space, which is generated by applying the
d-q transformation of Chapter 4 to the stator currents. This method recognizes that the entire
stator winding contributes to both direct and quadrature axis excitation rather than the simple
designation used in the stator current controller. The current reference is generated in the
transformed current space and the optimal voltage vector is selected and applied periodically to
control the position of the current vector.
Both strategies are described and simulation results presented to highlight their relative merits.
Section 5.4 summarizes the key characteristics of the two controllers. The stator current
controller was implemented in the experimental drive system. Practical performance
measurements for this controller are recorded in Chapter 7 to provide validation of the
simulation results.
5.2 Stator Current Controller
The stator current controller designates portions of the stator winding as supplying either direct
or quadrature axis excitation in the SynRM. This assignment is based on the individual phase
winding's position relative to the rotor. Once a phase winding is assigned as supplying either
direct or quadrature axis excitation its current need only be controlled to the appropriate value.
5.2.1 STATOR CURRENT REFERENCE
The idea of splitting the stator into sections, supplying either the direct or quadrature axis
excitation, was introduced in Chapter 2 with application to the design model. There the
effect of stator slotting was ignored. Effectively the stator teeth and slots were assumed
to be "smeared" together so that a continuous current distribution could be obtained
around the stator periphery. In the design model, the area of the stator over the rotor pole
sides carries the current that supplies direct axis excitation. The area of the stator, over
the rotor pole face, carries quadrature axis current.
Field-Oriented Control of the SynRM 71
In a real machine the continuous current distribution of the design model has to be
approximated by the stator winding. Logically the phase windings over the rotor pole
sides carry direct axis current while the phase windings over the pole face carry
quadrature axis current. Thus, the stator phase current reference values can be generated
given knowledge of the rotor's position and its dimensions. On initial inspection the
exercise of generating the stator current reference appears trivial, however, two practical
constraints arise with respect to the stator slot effects and the winding configuration.
In a real machine current is not continuously distributed but is concentrated in the stator
slots. Step changes in the stator current distribution can only be made at a slot opening.
As the rotor moves, individual phase windings at either edge of the rotor pole face must
make a transition from supplying purely direct axis excitation to purely quadrature axis
excitation or vice versa.
7.5° Rotor movement
>
Rotor
Stator
0° 10°
IA,REF '
t
IB,REF i
<
L
"Tv-L ! » ! t
j ; 6
H ! 3.75° 6.25° 8
Figure 5.1 Compensation for slot effects in the stator current reference
Field-Oriented Control of the SynRM 72
Figure 5.1 shows h o w the current references for two adjacent phase windings are
compensated for the stator slot effects. Actual dimensions from the 5kW machine are
used. The rotor is assumed to be moving to the right where 0 is the angle between the
phase A winding and the rotor quadrature axis. While the rotor pole side is over the
phase A slot opening this winding supplies the direct axis excitation. Similarly, phase B
winding supplies direct axis excitation when the pole side is over its slot opening. There
is a transition period where the pole side is entirely over the tooth between the phase A
and phase B winding. In this instance both phase A and B are effectively supplying the
direct axis excitation. Phase A current reference is ramped from the direct axis value to
the quadrature axis value over this interval. Similarly, the phase B current reference is
ramped but in the reverse direction.
The stator phase winding is star connected. Consequently, the individual phase currents
must sum to zero. To aid in achieving this requirement adjacent phase windings on the
stator have their connection polarities reversed. Given the 5kW machine dimensions,
typically one phase supplies the direct axis excitation, while the other eight phases
supply quadrature excitation. The eight quadrature current phases will conveniently sum
to zero. A fraction of the current reference from the ninth phase, that supplies direct axis
excitation, must be subtracted from each of the other eight phases so that all nine phase
currents sum to zero.
Figure 5.2 illustrates the modification made to the stator current reference values. A
situation is assumed where the phase A winding is supplying the entire direct axis
excitation. Phases B to I are positioned over the rotor pole face and carry quadrature axis
current. Adjacent phases have their connection polarities reversed so that their currents
go in opposite directions. The reversed connections ensure that the quadrature phase
currents still physically pass in the same direction through their respective slots. The
first graph plots the individual phase currents in the ideal situation where direct axis
Field-Oriented Control of the SynRM 73
current and quadrature axis current are independent. These currents do not sum to zero.
In the second scenario, an offset equal to one eighth of the direct axis current is
subtracted from each quadrature phase. Thus, the sum of the currents is now zero.
ID
IQ
-IQ
ID
IQ
-lo
A B C D tf T3 G H I
••'I 1 I I
•"-• II II
T 8
Figure 5.2 Phase current adjustments for star connected stator.
•IREF
Figure 5.3 Typical phase current reference versus rotor position.
Field-Oriented Control of the SynRM 74
Figure 5.3 shows a typical current reference for one stator phase of the 5 k W machine.
The current reference is plotted against rotor position. Compensation for both stator
slotting effects and the stator winding connection are included in the current reference.
5.2.2 INVERTER SWITCHING STRATEGY
The inverter is switched at a fixed frequency. During each control cycle, the switching
pattern is generated by comparing each phase current reference with the corresponding
phase current feedback. If the reference is higher than the feedback value then the
respective phase winding is switched to the positive inverter bus. Conversely, if the
reference is lower than the feedback value then the phase is switched to the negative
inverter bus. Clearly, one advantage of the stator current controller is the simplicity of
the switching algorithm.
5.2.3 STATOR CURRENT CONTROLLER SIMULATION
To verify the stator current controller's performance it was initially simulated in
MATLAB® / Simulink®. Figure 5.4 shows a block diagram of the simulated system
Appendix F contains the full set of simulation source files. The simulation can be
divided into two logical components. The controller represents the actual control
algorithm, as would be implemented in a DSP type device. The drive models the inverter
/ motor hardware.
Considering the drive model in more detail, it can be seen that the actual modelling of the
motor is done in the transformed rotor current plane. The input to the drive model is the
inverter-switching pattern, generated by the controller. This is is converted to a voltage
vector, initially in the stator current plane, which is then rotated to form the equivalent
vector in the rotor plane. The voltage equations (4.25 to 4.32) are used to determine the
change in the rotor plane current vector. Instantaneous torque is determined using the
rotor plane torque equation (4.24). Torque is integrated to obtain rotor speed and once
Field-Oriented Control of the SynRM 75
again to obtain rotor position. Thus all electrical and mechanical characteristics of the
motor are represented.
eed«f
Speedy — •
Position
T
CONTROLLER
A •.
Is.»b
S' DRIVE
Position
SpeedVd
Speeds, O-
CONTROLLER DETAIL
Generate stator current reference
Determine inverter switching
-o-ls,0b
Zero order hold
S' O-
Position
— Q —
^
vs
Calculate stator voltage vector
Calculate rotor voltage vector
--o Is,m
Speed
V, f(yr,co)
Calculate current vector
Calculate stator currents
DRIVE DETAIL
Position \co(t)dt
Calculate position
Wr) Torque
\t(t)dt
Calculate torque
Calculate speed
-*Q Speed
Figure 5.4 Stator current controller simulation block diagram
Field-Oriented Control of the SynRM 76
The controller regulates the direct axis component of current to a fixed value appropriate
for fluxing the machine. A PI speed controller generates the quadrature axis component
of the current reference. These references, combined with rotor position, are used to
generate the individual stator phase current references as previously described. The
inverter legs are switched to the positive or negative inverter bus depending on the
relationship between phase current reference and feedback. Thus the inverter switching
configuration is generated. A zero-order hold is included to duplicate the controller's
fixed frequency operation.
(Oref o «* i k
Speed controller
h
G, 7> + l
Current / torque controller
"Cm
' \J r
1 (Of/b
Figure 5.5 Speed controller including approximation to torque control loop
Figure 5.5 shows an approximation to the stator current controller. The model has been
reduced to a speed controller cascaded with a current / torque controller. The torque
controller is approximated by a first order lag element. Figure 5.6 shows the step
response of the torque controller as simulated. The gain of the torque loop is given by
the ratio of motor torque to quadrature axis current when the direct axis is fully fluxed.
_ 12 (Nm) ._._ /A G = — = 12 Nm/A KA)
The time constant will be approximated by the L/R ratio of the quadrature axis circuit.
L g _ 0.15(H)
' R 27.4(0) = 5.5rns
Field-Oriented Control of the SynRM 77
Figure 5.6 Step response of torque controller
The speed controller parameters, Gm and Tm, are chosen in accordance with the
"symmetrical optimum" as is normal practice with transfer functions containing a double
integration [35]. In this case for the unloaded SynRM it was determined that Go, = 0.02
(As/rad) and Tw = 0.035 seconds. This resulted in an optimally damped speed loop
5.3 Transformed Frame Vector Controller
Vector control in the transformed rotor current plane offers potential improvements over the
stator current controller. The stator current controller designates portions of the stator winding
as contributing solely to direct or quadrature axis excitation. In reality, linkages between the
stator phase windings mean that all sections of the stator winding contribute to both direct and
quadrature axis excitation. The stator controller only identifies the dominant contribution of
each phase and neglects any secondary effects. Transforming the stator phase currents into the
rotor current plane isolates the individual harmonic components of direct and quadrature
excitation. A controller based in the rotor current plane has the advantage of being able to
control these components directly. This should lead to more accurate torque control and better
dynamic torque performance from the drive.
Field-Oriented Control of the SynRM 78
5.3.1 TRANSFORMED FRAME CURRENT REFERENCE
The current reference for the transformed frame vector controller is formed as an
approximation to the ideal stator current distribution in the design model. The design
model assumed a rectangular current distribution located in a thin veneer along the
stator's inner surface. The stator current controller generated its reference by
approximating the shape of the current distribution, making the necessary allowances for
stator slot effects and the connection of the winding. For the transformed frame vector
controller the current reference is generated as the harmonic components of the ideal
current distribution. These components are found from the Fourier series decomposition
of the ideal. Figure 5.7 shows the current reference vectors for the transformed frame
vector controller thus formed. Effectively, the reference becomes a set of stationary
vectors in the rotor current plane whose lengths have a simple proportional relationship
to what was designated direct and quadrature axis current in the design model.
0.61 IQ
0.28 ID
Fundamental
Plane
0.31 IQ
0.27 ID >D 0.26 ID
>D
,rd 3 Harmonic
Plane
5th Harmonic
Plane
Q 4
0.16 IQ
0.24 ID >D
7th Harmonic
Plane
Figure 5.7 S y n R M current reference in transformed rotor current plane
The current reference is restricted to containing harmonic components up to and
including the seventh harmonic only. This is to ensure that the current reference vectors
retain a simple proportional relationship to direct and quadrature components of
Field-Oriented Control of the SynRM 79
excitation. Further, the eight-dimensional reference vector matches the degrees of
freedom inherent in a nine-phase star-connected motor.
Interestingly, higher harmonic components can be included in the reference as is the case
in the stator current controller. This is not done by adding extra dimensions to the
current vector reference because of the Umited number of degrees of freedom available.
Instead, the existing vectors require variable components to be added to them to account
for higher order harmonic components. The implication is that the simple proportional
relationship between the current vectors and the direct and quadrature axis excitation is
lost and the generation of the current reference becomes a complex task. This idea has
not been pursued as the additional contribution to torque of higher harmonic components
reduces with the order of harmonic as can be seen in the d-q harmonic torque equation
(4.34). In the torque equation, the third harmonic component potentially contributes an
additional 33% of the maximum fundamental torque to the output. The seventh
harmonic contribution drops to 14% of the maximum fundamental torque. Higher
harmonics if included would contribute less again. It was felt that the benefit of adding
the higher harmonics did not warrant the additional controller complexity.
Once the current reference is generated, the transformed frame vector controller must
ensure that the transforms of the actual currents map to the reference vectors. During
each control cycle the optimal inverter switching configuration (or voltage vector), must
be selected and applied.
5.3.2 VOLTAGE VECTOR SELECTION
Selecting the optimal inverter switching configuration, during each control cycle, is
significantly more difficult in a nine-phase drive than a conventional three-phase drive.
In a three-phase drive motor currents are represented as a two-dimensional current
vector. The controller chooses from 23 = 8 two-dimensional voltage vectors (where 7 are
Field-Oriented Control of the SynRM 80
distinct) to control the position of the current vector and hence the machine. By
extension, to implement vector control in a nine-phase machine leads to attempting to
control an eight-dimensional current vector by choosing from 29 = 512 (511 distinct)
eight-dimensional voltage vectors.
The selection of the voltage vector is further complicated by the different inductances
seen in the direct and quadrature axes as well as the different harmonic planes. This
point is best demonstrated by first considering the voltage vector selection process in a
three-phase induction motor drive. In an induction machine the direct and quadrature
inductances are equal. A vector controller selects the voltage vector that will control the
motor currents closest to the desired current vector. The selection is carried out in the
voltage plane by calculating the ideal voltage vector, v^ai, and comparing it to the
possible voltage vectors, vinv(s) (where s denotes the inverter-switching configuration).
Thus, the optimal voltage vector is found by minimizing the error, v^is) - v^a/. This
process works because the error in the current plane is proportional to the error in the
voltage plane. Performing the comparison in the voltage plane reduces the number of
calculations necessary.
For the nine-phase SynRM drive, where there are different inductances along the direct
and quadrature axes (and indeed in the different harmonic planes), an alternative
approach is required. The method in the three-phase induction motor drive, of
minimizing vinv(s) - vu** applies equal weight to direct and quadrature axis voltage
components. However, when the corresponding events in the current plane are
considered, it can be seen that equal voltage errors in the direct and quadrature axes will
produce different current errors because of the unequal inductances. Consequently, when
minimizing the voltage error the individual components need to be scaled relative to the
associated inductances to ensure the best result is achieved in the current plane. The
scaling function for the voltage error is;
Field-Oriented Control of the SynRM 81
(Vmv W ~ Videal Y = (Vinv (-0 " Videal ) X
¥
r a
0
0
0
0
0
0
0 0
0
1
0
0
0
0
0
0 0
0
0 L0
9-2-
0
0
0
0
0 0
0
0
0
9
0
0
0
0 0
0
0
0
0 La 25-^-Ld 0
0
0 0
0
0
0
0
0
25
0
0 0
0
0
0
0
0
0
49 _L Ld 0 0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
(5.1)
It is possible to greatly reduce the number of voltage vectors necessary to choose from by
using symmetries in the voltage planes. Figure 5.8 shows the d-q harmonic components
of the available voltage vectors in the nine-phase drive. These are generated by applying
the transformation of Chapter 4 to the stator voltages generated given all possible
inverter-switching configurations. In the fundamental plane it can be observed that the
pattern of voltage vectors repeats itself every 20°. The problem of selecting the optimal
voltage vector in this plane can be reduced to selecting the optimal voltage vector in a
20° sector.
Field-Oriented Control of the SynRM 82
Fundamental Plane
•
• 11» ••To
• •
• • • •
« " * • » / • • •
• • • • %<?i&# O i * * * • • • • • • • • «»*,,*•»% • • %
• • • < • •
-4 J
Direct axis
3rd Hannonic Plane
• • • •
2-
• • • '' • • •
3-2-1 1 2 3
• • • • • •
• • • • •2-
• • • •
•3-
1 I r-S-4 a
&
5 th Harmonic Plane
• • •,
• • •
*• •* • • * •
Tf*» • • • < • • *;W«J<
• • % ••*»*« »«?••••# • • • • • • •»•<•• « » • • • •
5";. • • .
-4J
Direct axis
•a •
7th Hannonic Plane
• •
St * • • * • • * •
• •
**>v • • * *• « & f 5 «***••
• • • •V*0*«» • • • .
V*t • • • •
Figure 5.8 Voltage vectors from a nine-phase inverter
Figure 5.9 shows the voltage vectors from the 0 to 20° sector of the fundamental plane
and the associated vectors in the higher harmonic planes. Should a vector be required
from outside this range then it is rotated in steps of 20° until it falls within this sector.
For example, finding the vector that best approximates VZ68°, in the fundamental plane,
would correspond to finding the vector closest to VZ8°. When rotating the voltage
vector in the fundamental plane by 9° the corresponding vector in the third harmonic
plane must be rotated by 39°. Similarly, the vector in the fifth harmonic plane should be
rotated by 59° and so forth.
Field-Oriented Control of the SynRM 83
Fundamental Plane
•
» • •
• • • • • • •
• » *—•-• «>-« •-
Direct axis
•a -4
I
3rd Harmonic Plane
-1 fl) 1 2
• •
• •
•a ,
r a
•3
5th Harmonic Plane
3 i
•
2-
• • •
• •" •
2 -1
• -1 -
•2-
.3 -
-4 -
X •
•
•
•
Direct axis
•
•
'• • 2
•
3 i
1. i.
•
-2
7th Harmonic Plane
2.5-
2 -
•
1-• »
01-•
-1
•0J-
• -1-
• • •
• 1J -
-2 -
•
•
1
•• •
•
•
»
Direct axis
•
2 3
•
4
Figure 5.9 Voltage vectors from 0 - 20° sector of fundamental plane.
Having determined the optimal voltage vector in the 0 to 20° sector it must be converted
back to the appropriate sector and switching configuration. Due to the symmetry of the
machine there is a logical relationship between the switching configuration for a vector
in one 20° sector and the corresponding vector in an adjacent sector. If the inverter
switching state is represented as a 9-bit binary number moving from one 20° sector to the
next in a clockwise direction involves inverting each bit and shifting them one place to
the left. The most significant bit loops around into the least significant bit position.
Figure 5.10 illustrates this concept.
Field-Oriented Control of the SynRM 84
Plane
„.,. 40° .•***"*
20°
V./100 (Switching configuration 111110 010)
D - axis
Figure 5.10 Voltage vector relationship to inverter switching configuration.
The method of dividing into 20° segments reduces the comparison requirement from 512
to 52 vectors. The disadvantage of this approach is that it limits the choice of vectors in
the higher harmonic planes. The optimal region in the fundamental plane is considered
but the corresponding components in the higher harmonic planes may not be in the
desired locations. The impact of this restricted choice will be demonstrated in the
simulation results.
5.3.3 TRANSFORMED FRAME VECTOR CONTROLLER SIMULATION
The transformed frame vector controller was also simulated in MATLAB® / Simulink .
Figure 5.11 shows a block diagram of the simulated system. Appendix F contains the
full set of simulation source files. As expected, the drive model is identical to that used
to simulate the stator current controller. The controller model represents the actual
control algorithm as would be implemented in a DSP type device.
The controller consists of a cascaded speed and current loop. The speed controller is a PI
controller that generates the quadrature current reference to vary torque. The direct
current reference is held constant to maintain machine flux. A set of reference vectors, in
the rotor current plane, are generated as multiples of the nominal direct and quadrature
axis Fundament!
VZ30° (Switching configuration 000 011010)
Field-Oriented Control of the SynRM 85
excitation levels. The d-q harmonic voltage equations (4.25 to 4.32) are used to
determine the ideal voltage that is required to maintain the current reference. This
voltage vector is rotated into the stator voltage plane, compared with the available
voltage vectors and the inverter switching configuration detennined.
Spee<W
Speedm, •
i
Position
'
CONTROLLER
A I
Idq.Ph
S' DRIVE
Speedrcf (y
Speedm, O -
CONTROLLER DETAIL Position
— Q —
Lj,rt
/('„>'„)
Speed controller
Generate rotor current reference
/(/*.*» Vr,d J1-
Calculate ideal rotor voltage
Calculate stator voltage
Zero order hold
f(Y,M)
Select inverter switching
•dq.Cb
Figure 5.11 Transformed frame vector controller simulation block diagram
Three strategies for the voltage vector selection were simulated. These were;
1. Comparing the ideal vector with all 512 possible vectors and selecting the closest
vector. The errors in each harmonic plane are weighted equally.
2. Comparing the ideal vector with all 512 possible vectors but with scaling to allow for
different inductances in different axes and harmonic planes. The errors in each
harmonic plane are weighted according to equation (5.1).
Field-Oriented Control of the SynRM 86
3. Comparing the ideal vector only with vectors from the corresponding 20° sector in
the fundamental plane. Voltage scaling was still employed with this method. The
errors in each harmonic plane are weighted according to equation (5.1).
Figure 5.12 shows a comparison of the step responses in the current components for the
three voltage vector selection strategies. The rotor was simulated as being locked and the
inverter DC bus set to 200V. Direct axis excitation is set to 2A at 0 seconds. Quadrature
axis excitation is stepped from 0 to IA at 0.05 seconds. The controller updated the
voltage vector selection at a 5kHz frequency. In each case the d-q harmonic components
are recorded and graphed separately. Further, Figure 5.13 shows the corresponding
changes in torque when the step change is made in quadrature axis current.
§ 5 2
-0.05
23 i
2-
1.5 -
I -i
Oi
•Oi -
/ 0.03 0.1 0.15
Time (s)
0.2 0.25 0.3
1.5-
1 •
~ -0.05
-03 •
-1
liliiWiiLii.iililJkJilliilJil • P W I i -If::- T i."f-!.l!i! 'hi rf'i'SilM
W^i,^i.iL..^i 1 0.W 1 0.1' 1 0.15 1 ' | 0.2 1 Jo.25 0.3
Timefs)
•i» «»*ii iaiti»»iiMjirt«
Tlme(s)
Figure 5.12a Step response of d-q current components (Case I)
Field-Oriented Control of the SynRM 87
3
-0.05
2-i
1JJ-
1*
IA-
1 2 -
1
OJJ
0.6
04-
02-
•02
j / / ' | 1 0.0S 0.1 0.15
Tax if)
0.2
r
0.25 0J
1J1-
12
1
< 0j3
S Oi
3 0A
02
** -02-
Ik L lllklk k fl lb ill i
HiiiSl 1 0.05 0.1 0.15 0.2 0^3 0 J
Time (s)
i -0.05 cr
l-i
03
-03
-1
-13
-2
o.tts8|
Time (s)
t " r V T P 03
Figure 5.12b Step response of d-q current components (Case IT)
<
2
-0.05
41 33
3-
23
2
13
1 •
03
-03
f i 0.05 0.1 0.15
Time(s)
02 025 03
.tty^uiMiiyVlUi I , . 1 . . ••if hpi!i|'.'.-|'";if V " | m T " .
n^'n'^fPT Tune(s)
Figure 5.12c Step response of d-q current components (Case IH)
Field-Oriented Control of the SynRM
Figure 5.13 Response of torque to step change in currents
Field-Oriented Control of the SynRM 89
The following conclusions can be drawn from the simulation results;
1. In the steady state, the Case I controller (simple comparison of the ideal voltage
vector with all possible vectors, without scaling) gives good current regulation.
However, during changes in current loss of control is evident. Noticeably the third,
fifth and seventh harmonic components of direct axis current go negative on initial
excitation. Similarly, considerable overshoot can be seen in the corresponding
quadrature components. The torque response appears quite good. Most noticeably,
the response is faster, contains no overshoot and maintains low ripple. However, this
is somewhat misleading. The simulation torque calculation assumes constant
inductances. The presence of current transients gives the appearance of fast torque
response where saturation effects would limit the available torque in the real
machine.
2. The introduction of voltage scaling in Case II improves the steady state regulation of
the higher harmonic current components and slightly reduces it in the case of the
fundamental component. This is to be expected as the scaling reduces the
controller's sensitivity to errors in the higher inductance axes. Transient
performance is improved markedly with no negative excursions in the direct axis
currents and reduced overshoot in the quadrature components. The torque response
remains quite good with noticeably less ripple than observed in Case I.
3. Case HI demonstrates the effect of reducing the voltage vector selection to vectors in
a 20° sector in the fundamental plane. The steady state and transient current
regulation nearly matches that of the Case II controller. The most noticeable
difference is a slight increase in ripple, which is also reflected in the steady state
torque regulation. Indications are that this would be an acceptable method of voltage
vector selection. The reduced number of calculations necessary to use this method
makes it the most practical scheme to implement.
Field-Oriented Control of the SynRM 90
Comparing the torque response of the transformed frame vector controllers (Figure 5.13)
to that of the stator current controller (Figure 5.6) shows that the vector controller offers
both improved torque regulation and faster step response. This improvement was as
expected from a vector type controller. One problem, which has been previously alluded
to, is the time necessary to carry out the calculations to implement vector control. This
practical constraint will be examined further in Chapter 7.
5.4 Summary
Two methods of implementing field-oriented control in the nine-phase SynRM have been
presented and simulated.
The stator current controller generates stator phase current references based on rotor position.
A simple hysteresis switching strategy is used to control the phase currents. The main
advantage of this approach is its simplicity to implement. Running the inverter with a relatively
modest control cycle frequency of 5kHz achieved quite acceptable current regulation.
The transformed frame vector controller offers improved performance over the stator current
controller. By controlling the isolated d-q harmonic components of current better current
regulation and faster transient performance are achieved. This is demonstrated in simulations
conducted with the identical control cycle frequency as the simulated stator current controller.
The limitation of the transformed frame vector controller is the time necessary for the
background calculations.
The Nine Phase Inverter and D S P Controller 91
CHAPTER 6
The Nine Phase Inverter and DSP Controller
6.1 Introduction
This chapter describes the inverter and DSP controller used in the project. Figure 6.1 shows a
block diagram of the system hardware. Logically, it can be divided into three main sections.
These are the inverter power circuit, the DSP controller and the controller interface circuit.
Appendix B contains the complete electrical circuit diagrams for the hardware and a full parts
list. Figure 6.2 is a photograph of the assembled inverter power and controller interface
circuits.
3 Phase Supply
INVERTER POWER CIRCUIT r
D C Link Power Supply
Dynamic Brake Circuit
CONTROLLER INTERFACE CIRCUIT
Inverter
Gate Drive Circuit
Motor
/•v
Current Sensing Circuit
Encoder 0
Shaft Encoder Interface
DSP CONTROLLER
Figure 6.1 Block diagram of the inverter and controller circuit.
The Nine Phase Inverter and DSP Controller 92
Figure 6.2 Inverter hardware
6.2 Inverter Power Circuit
The power circuit is that of a typical voltage source inverter. Electrical circuit diagrams Bl and
B2, of Appendix B, show the circuit detail. Figure 6.1 further divides the power circuit into
three logical components. These are the DC link power supply, the dynamic brake circuit and
the inverter proper.
DC LINK POWER SUPPLY
The DC link power supply is an uncontrolled AC to DC converter. Figure 6.3 divides the
power supply into its components. It consists of a three-phase bridge rectifier and DC link
filter.
The rectifier is nominally rated for 1200V / 30A. The DC link filter consists of a 34.4mH
inductor and a lOOOuF electrolytic capacitor (a combination of four electrolytic capacitors are
used to achieve the desired voltage rating). During initial power up a 100Q resistor is
The Nine Phase Inverter and DSP Controller 93
temporarily placed in series with the capacitor to limit inrush current as the capacitor is first
charged. This resistor is bypassed by an external relay after 0.5 seconds.
Three phase 0-415V50Hz Variable supply
Bridge Filter Rectifier
Figure 6.3 DC link power supply
Dependent upon the AC supply voltage, the DC link power supply is capable of supplying up to
30A DC, at a voltage up to 560V DC, with minimum ripple. This represents an oversized
system in terms of its current rating but allows for maximum flexibility with regard to future
work.
DYNAMIC BRAKE CIRCUIT
A diode rectifier is used in the DC link power supply. This means that energy cannot be
transferred from the DC bus back into the AC mains. During braking, the kinetic energy of the
motor is transferred to the DC bus via the anti-parallel diodes in the inverter proper. The
dynamic brake circuit provides the means to dissipate this energy and better regulate voltage of
the DC bus.
The dynamic brake circuit consists of a 94Q resistor and IGBT switch connected in series
across the DC bus. Energy transfer back into the DC link from the motor causes the bus
voltage to rise. The dynamic brake circuit detects this voltage rise and switches the resistor
across the DC bus, dissipating the energy.
The Nine Phase Inverter and DSP Controller 94
The electrical circuit diagram for the dynamic brake control is on drawing B3 of Appendix B.
The voltage level, which the dynamic brake circuit operates at, is adjustable to a value
appropriate to the circuit's input voltage.
INVERTER CIRCUIT
Figure 6.4 shows a schematic diagram of one phase of the inverter proper. A pair of IGBTs
switch the output phase connection to either the positive or negative DC bus. Each of the
IGBTs has an anti-parallel power diode across its collector - emitter terrninals. The diode
provides a path for load currents during IGBT switching.
+VBUS
O v0
'BUS
Figure 6.4 Circuit diagram for one phase of inverter
The power devices used are insulated gate bipolar transistors (IGBTs) and power diodes.
IGBTs were chosen because of their ability to switch high currents and voltages quickly.
Additional benefits were a relatively simple gate drive circuit and a square safe operating area
which would not require snubber circuitry.
The IGBTs and power diodes are nominally rated for 1200V / 8 A. To achieve maximum torque
the motor requires phase currents of 2Apeaic. Again this represents an oversized system in terms
of current rating but allows maximum flexibility with regard to future work.
Thermal considerations normally form an important part of a power circuit design. In this
instance we are operating the power devices at the lower end of their rated operating ranges.
The Nine Phase Inverter and DSP Controller 95
As a consequence no detailed thermal design was done other than taking the usual precautions
of mounting the devices on appropriately sized heatsink. More rigorous thermal calculations
and design would be required if the circuit was to be operated at its maximum electrical rating.
6.3 DSP Controller
The controller software was implemented on an Innovative Integration ADC64 Digital Signal
Processor (DSP) board. This card mounts directly to the PCI bus internal to a computer. From
the computer, source code can be downloaded to the ADC64 via the PCI bus. The ADC64
connects to the outside world via a 100 way SCSI-2 connector. The salient features of this
board are indicated in an excerpt from the device data sheet in Appendix E. With respect to
this project the key features are now summarized.
PROCESSOR
The ADC64 board contains a Texas Instruments TMS320C32 60MHz DSP chip. This device is
capable of performing 32-bit floating-point arithmetic, which again gives maximum flexibility
when implementing control algorithms. The Texas Instruments processor itself was preferred
because of its ready availability and good documentation.
ANALOGUE I/O
The board has 64 analogue inputs. (These are achieved by using 8 independent channels each
connected through an 8-1 multiplexer.). The individual Analog to Digital Converters (ADCs)
have 16-bit resolution with a maximum sampling frequency of 200kHz. The voltage range of
each input can be user selected to a maximum of ±10V. This maximum value was chosen to
limit the impact of any noise in the analog feedback signals.
In addition, the board contains two 16 bit analogue outputs. These were not necessary to
implement the drive system, however, were invaluable when it came to real time monitoring of
internal control software variables during commissioning.
The Nine Phase Inverter and DSP Controller 96
DIGITAL I/O
The ADC64 has provision for 16 bits of TTL compatible digital I/O. The hardware setup of the
ADC64 board restricts the way in which these 16 bits can be configured. They must be
configured as, all outputs, all inputs or a combination of 8 inputs and 8 outputs. This restriction
had further impact on the interface circuitry, where a combination of 9 outputs and some digital
inputs were ideally required. The method used to overcome this problem is detailed in the
following section.
INTERRUPTS
The TMS320C32 has 16 prioritized interrupts from various sources including software,
external pins and internal timers. Interrupts were used in two circumstances.
The control cycle time is fixed by using a timer interrupt to initiate the main control loop. This
method ensures a constant cycle time, which is necessary in implementing control algorithms.
It is preferred over trying to estimate the timing of a piece of code that runs continuously. The
latter approach is subject to errors where the code executes over multiple paths affecting its
cycle time.
An additional external interrupt pin is used in the shaft encoder interface circuitry. The
TMS320C32 has four external interrupt pins. The default ADC64 configuration uses all of
these interrupts for reading and writing from the PCI bus, A/D status and interrupting the DSP
from the host computer. As the control code operates on a fixed cycle time the interrupt for
A/D status could be reconfigured for use in the shaft encoder interface circuitry. This circuitry
is detailed further in the following section.
COUNTERS
The ADC64 has six 16-bit timer/counters independent of the DSP processor chip. Five of these
can be configured for triggering A/D conversions. Most notably one counter is pinned out to
The Nine Phase Inverter and D S P Controller 97
the board's external interface for counting external events up to rates of 1 0 M H z . This counter
is utilized in the shaft encoder interface to count pulses from the shaft encoder.
SOFTWARE
Software can be written for the DSP processor in C or Assembler. The standard Texas
Instruments assembler / linker is used in preparing executable code. The actual control code is
written in C. A listing of the code can be found in Appendix C. The actual code operation is
detailed in Chapter 7.
6.4 Controller Interface Circuit
Interfacing the DSP controller to the power circuit involved correctly matching the DSP I/O
electrical requirements to those of the external hardware. Inherent in this process was dealing
with the issue of voltage isolation between the two systems.
GATE DRIVE CIRCUIT
Figure 6.5 shows an overview of the entire gate drive circuit. It can be divided into three
logical blocks being the gate drive decoder, blanking time circuitry and the gate drive proper.
DSP CONTROLLER
Gatel
Gate 2
Gate 3
Select 1
Select 2
Switch A
Switch B
etc.
Switch A +
Switch A
etc.
Gate Drive Decoder
Blanking Time Circuitry
Gate Drive Circuitry
Figure 6.5 Block diagram of gate drive interface circuit.
The Nine Phase Inverter and DSP Controller 98
The D S P controller has a total of 16 digital I/O points. These can be configured as 16 inputs,
16 outputs or a combination of 8 inputs and 8 outputs. To input data from the shaft encoder
required the use of at least one digital input. Therefore, the number of digital outputs was
restricted to eight, which was insufficient to drive the nine phases of the inverter directly.
The problem is overcome by multiplexing the nine gate drive signals onto only three gate drive
outputs. The gate drive decoder block decodes these three gate and two address signals to
reproduce the original nine gate drive signals. The electrical circuit diagram for the gate drive
decoder is on drawing B6 of Appendix B.
In the power circuit the output phase connection is always switched to either the positive or
negative DC bus. During a transition state, care must be taken to ensure that both the IGBTs in
one phase are not turned on simultaneously, thus avoiding "shoot through" currents and
potential device damage. This is achieved by turning one IGBT off and waiting for a short time
period (termed blanking time) before turning the other IGBT on. The blanking time is
physically achieved using a combination of RC timing circuit and Schmitt trigger. The
blanking time is set to 5ps. Drawing B5 of Appendix B contains the full electrical circuit
diagram of the blanking time circuit.
The gate drive proper provides electrical isolation between the driving logic and the inverter
power circuit. It also provides amplification of the logic signal to a level appropriate for
driving IGBTs. Voltage isolation is achieved by using a 74OL6010 opto-coupler on the logic
signal. Amplification requires a separate supply fed through a transformer, again for isolation
purposes. The output, IGBT switching signal, is a ±15V signal with a series 150Q resistance.
This resistance serves to slow the turn-off time of the IGBT preventing latchup. A full
electrical circuit diagram for the gate drive circuit is shown in drawing B4 of Appendix B.
The Nine Phase Inverter and DSP Controller 99
C U R R E N T S E N S I N G
The electrical circuit diagram of the current sensing circuit can be found on drawing B8 of
Appendix B. In summary, phase currents are measured using LEM LTA50P/SP1 current
transducers. These are Hall effect devices capable of measuring instantaneous currents up to
50A. Other features of the device are its wide frequency range (DC to 100kHz) and large
voltage isolation rating (3kV at 50Hz). As the motor currents are not to exceed 2Apeak the phase
windings are looped five times through the sensors. This allows a greater portion of the current
transducers operating range to be utilized.
The current transducer has both a voltage output (scaled lOOmV/Amp) and current output
(scaled 1mA/Amp). The current output was used with a 500Q. burden resistor to give a scaled
current signal of 4A = 10V.
The DSP controller has 8 ADCs that can each be multiplexed to 8 different inputs to give a
total of 64 analog inputs. For speed, only 8 phases are read to avoid the need for multiplexing.
The ninth phase current is determined because all phase currents must sum to zero.
Finally, the ADCs perform a 16-bit conversion and are scaled to accept a ±10V input. As a
consequence, internal to the DSP, current signals are scaled such that 4A = 32768.
SHAFT ENCODER INTERFACE
The rotor position is measured using a Hewlett-Packard three channel optical encoder. Two
channels, A and B, generate 1000 pulse per revolution signals in quadrature. Rotor position can
be determined by suinming pulses while direction is given by the phase relationship between
the signals. Figure 6.6 demonstrates the phase relationship between channels A and B for
forward and reverse rotation. The third channel, I, gives one index pulse per revolution which
is useful for synchronization.
The Nine Phase Inverter and DSP Controller 100
B
Forward rotation
mfim Reverse rotation
nn
Figure 6.6 Shaft encoder outputs.
The hardware for the shaft encoder interface circuit is shown in drawing B9 of Appendix B.
Figure 6.7 summarizes in block diagram form the circuit's key functions. The three optical
encoder outputs are first fed to a buffer / filter circuit. The filter removes any high frequency
noise in the signals.
A
B
Buffer/ Filter
D
>
Q i
Count
Up / Down
Synch
Figure 6.7 Block diagram of shaft encoder interface circuit.
Channel A is used to clock a counter on the ADC64 DSP board. The counter is set to
continuously count down. The control software adds / subtracts the change in the counter over
one control cycle to an accumulative position variable.
A D flip-flop is used to examine the phase relationship between channel A and channel B
signals. The output from the flip-flop provides indication of forward or reverse operation.
The Nine Phase Inverter and D S P Controller 101
Finally, the synchronization pulse initiates an edge triggered interrupt on the A D C 6 4 processor
board. This interrupt resets the position counter to the value corresponding to the location of
the synchronization pulse.
The SynRM Drive Software and Performance 102
CHAPTER 7
The SynRM Drive Software and Performance
7.1 Introduction
This chapter describes the software implementation of the stator current controller of Chapter 5
with the hardware described in Chapter 6. Performance results for the completed drive are then
presented.
Section 7.2 describes the control software developed to implement the stator current controller
from a block diagram perspective. The full source code is contained in Appendix C for
additional reference. The feasibility of implementing the transformed frame vector controller
in the existing hardware is also considered. This analysis highlights potential means for
implementing the more advanced controller in the future.
Section 7.3 presents the performance results for the drive. Specifically, the drive's current
regulation, speed response and torque response are all demonstrated. These results are
compared with those predicted from the design model in Chapter 2 and the dynamic simulations
of Chapter 5. Appropriate conclusions are then drawn.
7.2 Control Software
The software implementing the stator current controller on the A D C 6 4 D S P development board
will be described here. The full source code (in C programming language) is contained in
Appendix C. Initially, preference was to implement the transformed frame vector controller
because of its superior performance. Unfortunately this was not possible given current
technical constraints and the limits of the existing hardware. Before proceeding with a
description of the stator current controller software the practical constraints preventing
The SynRM Drive Software and Performance 103
implementation of the transformed frame vector controller will be briefly discussed. This also
serves to highlight means for future implementation of the more sophisticated controller.
7.2.1 TRANSFORMED FRAME VECTOR CONTROLLER
In Chapter 5 it was demonstrated through simulation that the transformed frame vector
controller offered significant performance advantages over that of the stator current
controller. Figure 7.1 shows a simplified block diagram of the key controller functions
necessary to implement the transformed frame vector controller. For comparable
operation to the simulation (which had a 5kHz control cycle) the key functions need to be
completed within 200u.s.
1 •
Read stator currents
Transform currents into rotor plane
Calculate the ideal voltage
vector — •
Select the best voltage
vector — •
Set inverter switching
configuration
tv
Figure 7.1 Key control functions necessary to implement the transformed frame vector
controller.
The viability of the transformed frame vector controller can be determined by estimating
the processor time necessary to perform the functions shown in Figure 7.1.
READ STATOR CURRENTS
Reading the stator phase currents requires eight analog-to-digital conversions (the ninth
phase current is dependent on the other eight and can be calculated). The ADC64 is
equipped to read up to eight analog inputs simultaneously with a maximum lOps
conversion time [24]. The outputs from the A/D converters are memory mapped to the
TMS320C32 processor. Thus, reading the stator currents will take a maximum of IOJIS
assuming negligible time to calculate the ninth phase current.
The SynRM Drive Software and Performance 104
TRANSFORM CURRENTS
To transform the currents from the stator reference frame to the rotor d-q reference frame
requires multiplying the 9x1 stator phase current vector by the 9x9 transformation
matrix, T(a). For the TMS320C32 processor a single floating point operation requires
one clock cycle or 33ns [55]. Additionally, the elements in the transformation matrix
contain sine and cosine functions. Each sine / cosine function call typically takes 2.2p,s
to complete. Thus, an approximate figure for the calculation time required for the
transform operation is calculated as;
[81 (multiplications) + 81 (additions)] x 33ns + 81(sin/cos) x 2.2u.s = 184u.s
CALCULATE IDEAL VOLTAGE VECTOR
The ideal voltage vector is calculated using the d-q voltage equations in component form
(4.25 to 4.32). There are eight components in the voltage vector and each component
calculation requires six multiplications and three additions. Thus, the total time
necessary to perform the calculation is;
8 x ^(multiplications) + 3(additions)] x 33ns = 2.4p,s
SELECT VOLTAGE VECTOR
To select the best voltage vector requires the computation of the distance between each
potential vector and the ideal. Further, the individual voltage components need to be
scaled to account for the different inductances seen in the machine axes. Thus, each
vector evaluation requires fifteen additions and sixteen multiplications. If all the
possible vectors are considered the calculation stage of the selection process will take;
512 x [15(additions) + ^(multiplications)] x 33ns = 525u.s
Restricting the selection area to a 20° segment in the fundamental plane reduces the
number of vectors to be considered to 52. The calculation time in this case would be;
The SynRM Drive Software and Performance 105
52 x [15(additions) + ^(multiplications)] x 33ns = 53u.s
The values calculated must be sorted to select the optimal vector. The time required to
perform the sorting function can be estimated as one clock cycle for each voltage vector
considered. Thus, the voltage vector selection process will require 525u.s + 512 x 33ns =
542p.s if all vectors are considered and 53|jis + 52 X 33ns = 55p,s if only a restricted
segment is considered.
SET INVERTER SWITCHING CONFIGURATION
The digital outputs of the ADC64 are capable of switching at 70ns [24]. As nine outputs
are required, and the ADC64 controller only caters for eight, external multiplexing is
needed. The speed that these signals can be multiplexed becomes the limiting factor.
With the present hardware the gate signals are sent as three sets of three with a 10u.s
interval between each set. Thus, a period of 20u.s is required to set the inverter switching
configuration.
The total time necessary to perform the cycle by cycle calculations to implement the
transformed frame vector controller in the existing hardware is,
lOps + 184u.s + 2.4u.s + 525ns + 20u.s = 741u.s
Section 5.3.3 presented simulation results for the transformed frame vector controller
with a 5kHz control cycle. Clearly the software based equivalent cannot be implemented
on the hardware assembled for this project. The main problem areas are the current
transformation and the voltage vector selection portions of the code. One solution is to
run the controller at a slower control frequency. Figure 7.2 shows the simulated torque
response for a controller operating at 1kHz (1ms control period). Comparing this result
with those in Figure 5.3 it can be seen that the stator current controller at 5kHz regulates
The SynRM Drive Software and Performance 106
torque better than the transformed frame vector controller at 1kHz. For this reason the
transformed frame controller was not implemented in hardware.
Figure 7.2 Step torque response of transformed frame vector controller at 1kHz
As a footnote, it may be possible to implement the transformed frame vector controller at
higher control frequencies by,
(a) Modifying the hardware. One potential way of reducing the time necessary for the
current transformation is to do the transformation in hardware external to the DSP
controller. By using a FPGA (field-programmable gate array) or PLD
(programmable logic device) type device and employing look-up tables for the sine /
cosine functions it should be possible to obtain the transformed currents at faster
speeds. This idea has already been successfully demonstrated in a three-phase
controller using discrete logic components [60].
(b) Reducing the voltage vectors considered when selecting the optimal value. The
voltage vector selection problem can be reduced by restricting selection to a 20°
segment in the fundamental plane as described in Chapter 5. This requires
considerably less calculation time and has been shown to sacrifice little in terms of
performance.
Unfortunately time and financial restrictions have prevented these options being fully
explored at this stage.
The SynRM Drive Software and Performance 107
7.2.2 STATOR CURRENT CONTROLLER
The stator current controller requires substantially less background computation than the
transformed frame vector controller does. As such it is easier to implement at higher
control frequencies in the DSP controller. Figure 7.3 shows a block diagram of the stator
current controller software. The corresponding sections of code are similarly labeled in
the source code listing in Appendix C. The functionality of the main blocks will now be
briefly considered.
INITIALIZATION
The initialization block defines the hardware and software configuration of the DSP
controller. Specifically, variables are defined and initialized, the DSP peripherals and
interrupts are configured and all gate drive outputs are set to logic low.
ALIGN POSITION FEEDBACK
The stator current controller requires accurate knowledge of rotor position to function.
Rotor position is tracked by counting pulses from a 1000 pulse / revolution shaft encoder.
The pulse count is aligned to rotor position by monitoring a synchronization pulse
(occurs once per revolution) from the encoder that triggers an external interrupt on the
DSP. The software waits for two synchronization pulses prior to starting. The rotor
shaft has to be rotated manually to obtain these synchronization pulses. Messages
written to the terminal advise of the program status during the alignment operation.
INITIALIZE TIMER INTERRUPT
To ensure the code operates at a fixed control cycle a timer interrupt is used. It is set to a
frequency of 5kHz. Execution of each cycle of the main control loop only proceeds upon
receipt of this interrupt.
The S y n R M Drive Software and Performance
Initialize timer interrupt
NO
Read speed reference
Read position / speed
PI speed controller
Calculate stator current reference
Read phase currents
Switch gate states
Figure 7.3 Stator current controller software block diagram
The SynRM Drive Software and Performance 109
R E C E I V E T I M E R I N T E R R U P T
The software holds itself at this point until the timer interrupt is received. At the end of
executing the main software loop the control returns to this point and waits for the next
interrupt to occur.
READ SPEED REFERENCE
The speed reference is read once per control cycle. The ADC64 can read eight analog
inputs simultaneously. These are all required to read the eight phase currents. As a
consequence the speed reference must be read separately. The value is multiplexed with
one of the phase current inputs. A 3p,s delay is introduced after the speed reference is
read and the channel multiplexed to ensure the system has time to settle before reading
the phase current value later in the code.
The external speed reference is a ±10V signal. The analog to digital conversion process
inverts this so that 10V = -32767. This reference is divided by 160 so that +10V = -205
(which will be shown to correspond to -615rpm).
READ POSITION / SPEED
One of the ADC64 peripheral counters is configured to continuously count down. It is
clocked by pulses from the shaft encoder. The change in this counter over each control
cycle is added or subtracted to a cumulative position variable depending on the motors
direction of rotation. A digital input generated from the shaft encoder interface circuit is
used to indicate forward or reverse direction. There are two variables in software.
Variable "position" counts from 0 to 1000 corresponding to one revolution of the motor.
Variable "modpos" counts from 0 to 180 corresponding to rotor rotation in mechanical
degrees.
The SynRM Drive Software and Performance 110
Speed is represented by the change in the cumulative position variable. The speed value
is updated every 100 control cycles (20ms). As such its value is scaled so that 200 =
600rpm.
PI SPEED CONTROLLER
The quadrature current reference is generated by a PI speed controller. The controller
includes limits on the integrator storage variable to prevent wind-up as well as a limit on
the controller's output. The latter acts as additional protection against exceeding the
inverter and motor ratings. The selection of the proportional and integral gain
components is discussed in Section 5.2.3. When the speed feedback is small the speed
controller is operated as a purely proportional controller to ensure stable operation.
CALCULATE STATOR CURRENT REFERENCE
The nominal direct axis reference is set to a fixed value to flux the SynRM. Once the
rotor position is known and the quadrature reference set the stator phase current
references can be generated. This is done by calling function "curr_ref'. The function
has defined in it the typical phase current reference shape (Figure 5.3). It picks the
appropriate point off the curve as the reference value for each phase current.
READ PHASE CURRENTS
The phase current analog to digital converters are triggered and read once every control
cycle. The analog signals are converted to 16-bit binary values and stored in memory
locations ADC0 to ADC3. Individual phase values are obtained by isolating the
appropriate 16-bits from the memory locations. The ninth phase current is obtained as
the inverted sum of the other eight. The phase current variables are scaled so that IA =
8192. The effect of the analog to digital converters sign change is negated in hardware
by wiring the current transducers backwards.
The SynRM Drive Software and Performance 111
S W I T C H G A T E S T A T E S
The inverter switching configuration required for each phase is found by comparing the
phase current to the reference. The total inverter-switching configuration is stored in the
lowest nine bits of variable "gate_state". These bits are written three at a time to the
output because of the limited number of outputs available. A IOJLXS delay is inserted
between each write to allow time for the external multiplexer circuitry to switch.
The control software was written to operate at 5kHz to match that simulated in Chapter 5.
The actual time that is required for the code to execute one cycle is 140ps. This is
sufficiently small to avoid exceeding the control cycle period of 200us. There remains
some scope for the control cycle frequency to be increased if desired, which would lead
to better current regulation.
The time that elapses between reading the currents and establishing the output switching
configuration is approximately 30u.s. The majority of this time (20u.s) is required to
multiplex the gate drive signals. The time could be significantly reduced by using a DSP
controller with sufficient digital outputs to drive the nine-phases without multiplexing.
However, 30p,s remains small with respect to the entire control cycle and is considered
acceptable.
7.3 Performance Results
This section presents the results of performance tests and measurements made on the completed
drive. In particular, results will be presented from a magnetization test as well as current
regulation, speed response and torque output measurements. These results will be compared
with those predicted from the design model and simulations.
MAGNETIZATION TEST
The machine was run with no load at a fixed speed. The nominal level of direct axis excitation
(ID) was varied and one phase's voltage and current waveforms monitored. By observing the
The SynRM Drive Software and Performance 112
change in the voltage waveform it is possible to detect the start of magnetic saturation within
the machine.
Figure 7.4 shows typical current and voltage waveforms recorded during the magnetization test.
In this instance, Figure 7.4(a) shows one phase current waveform with the motor operating at
200rpm. The nominal level of direct axis excitation is IA. There is minimal quadrature axis
excitation as the machine is being operated unloaded. Figure 7.4(b) shows the voltage
waveform measured on the corresponding phase winding. The voltage waveform was obtained
by applying a moving average to the PWM waveform measured at the motor terminals. While
the phase winding is supplying quadrature excitation, the change in flux linking the coil
produces an average voltage in the winding. Imposed on the average voltage is an oscillation
produced by the changing current reference as the rotor moves.
It is the relationship between the average voltage and the nominal direct axis excitation that is
of particular interest. Figure 7.4(c) shows the voltage waveform again with a moving average
applied over one tooth pitch. This allows the average voltage in a phase winding, while it is
supplying quadrature excitation, to be discerned more clearly. In this instance the direct axis
excitation of IA at a speed of 200rpm is producing an average voltage of approximately 35V.
Figure 7.5 summarizes the measurements made of the average phase voltage as direct axis
excitation is varied. The measurements were obtained with the machine operating at a speed of
350rpm. There is a linear relationship between voltage and current until the iron starts to
saturate. Saturation occurs at approximately 1.7A direct axis current. This compares with the
expected value of 1.6A predicted in the design model (Section 3.2). The measured value is
marginally higher because the design model prediction is based on a linear approximation to the
iron B-H characteristic as opposed to the actual characteristic.
The SynRM Drive Software and Performance 113
(a)
(b)
(c)
0.45
time (s)
Figure 7.4 Typical current and voltage waveforms recorded during magnetization test (ID = 1 A,
co = 200rpm)
The SynRM Drive Software and Performance
• •
114
1.1 1.3 1.5 1.7 1.9 2.1 2.3
direct axis current (A)
Figure 7.5 Magnetization test results (co = 350rpm)
CURRENT REGULATION
Figure 7.6 shows the phase current waveforms recorded with the machine operating at various
speeds. The inverter DC bus voltage was held at a constant value of 250V for each
measurement. The direct axis excitation is set to the rated value of 1.7A. Quadrature excitation
is set by the speed loop to the value necessary to maintain the speed of the unloaded motor.
The direct and quadrature components of current can be clearly recognized along with the
adjustments made for stator slotting and winding connection.
> 80-<u Ml
B O > <u
3 Xi
a.
75 -
70
65
60-1
55
0.9
The SynRM Drive Software and Performance 115
(a)
(b)
(c)
Figure 7.6 Phase current waveforms (a) co = 80rpm, (b) co = 200rpm and (c) co = 345rpm
(inverter bus voltage = 250V)
The SynRM Drive Software and Performance 116
Figure 7.7 Phase current waveform detail versus position for (a) co = 80rpm, (b) co - 200rpm
and (c) co = 345rpm (inverter bus voltage = 250V)
The SynRM Drive Software and Performance 117
As the rotor speed increases, the current waveforms begin to diverge from the shape of the ideal
reference. Figure 7.7 shows an enlarged portion of each of the waveforms presented in Figure
7.6. To allow comparison, the sections of the waveforms corresponding to direct axis
excitation have been shown plotted against rotor position. Clearly, as speed increases the size
of the direct axis current block reduces suggesting an upper speed limit. Beyond a point
reduced direct axis excitation will lower the flux in the machine and reduce the available
torque. This relationship will be examined further in discussion on the torque measurements.
SPEED RESPONSE
The motor was operated with a known moment of inertia (its own rotor and shaft). The drive's
response to step changes in the speed reference were recorded and compared with those from
the dynamic simulations in Chapter 5. Figure 7.8 shows the speed and quadrature current
values recorded in response to a step change in speed reference from 100 rpm to 240 rpm at
time zero. The speed and quadrature current values were obtained by writing the appropriate
variables in the controller to the digital-to-analog converter. A small amount of overshoot with
oscillation can be observed in the measured values. Contributing to the oscillation was an
electrical noise problem noted in the shaft encoder feedback path. Random noise spikes caused
additional pulses to be counted affecting the position and speed feedback values.
Figure 7.8 also shows the simulated speed and quadrature current values in response to the
same step change in speed reference. The rise time of the speed variable in the simulation
matches that obtained in the experimental system. Further, the simulated quadrature current
pulse is of the same order of magnitude as that measured. One notable difference between the
simulated and experimental systems is the steady state quadrature current value. The
simulation does not include mechanical losses, such as friction, so the steady state quadrature
current is shown to be zero amps.
The SynRM Drive Software and Performance 118
(a)
*—\
a e-•a
300 -i
250-
200-
150-
-0.1
50
0.1 0.2
time (s)
measured
- simulated
0.3 0.4
(b)
Figure 7.8 Measured and simulated speed and quadrature current values in response to a step
change in speed reference from lOOrpm to 240rpm.
The performance of the drive while reversing was also measured. Figure 7.9 shows the
measured and simulated speed and quadrature current values. In this instance the speed
reference is changed from +150 rpm to -150 rpm at time zero. Again the time constant of the
speed response and magnitude of quadrature current pulse can be seen as matching in the two
systems.
The SynRM Drive Software and Performance 119
(a)
S Br.
-0.2
• measured
•simulated
time (s)
(b) 0.2
-s/1 -0.2
< cr
J ^ ^
• measured
simulated
time (s)
Figure 7.9 Measured and simulated speed and quadrature current values in response to a step
change in speed reference from +150rpm to -150rpm.
TORQUE MEASUREMENT
The SynRM was coupled to a DC machine to perform torque measurements. The DC machine
was used to set the system speed. With the machines operating at a constant speed the
quadrature current set point for the SynRM was adjusted. The actual shaft torque output from
the machine could be measured using a torque transducer mounted at the coupling between the
machines. Various torque measurements under different conditions were made and will now be
presented.
The SynRM Drive Software and Performance 120
Figure 7.10 shows the torque versus quadrature current measurements made with the motor
turning at very low speed « 5rpm). For this test and subsequent torque tests, the direct axis
excitation was set to the rated value of 1.8A. This result approximates the locked rotor torque
obtainable from the machine. Notice that the torque varies linearly with quadrature axis current
until saturation effects become evident at the extremes of the graph. Included on the graph is
the "ideal" linear torque versus quadrature current curve for a 5kW four-pole SynRM. The
measured and ideal curves align quite well except for the end points. The maximum torque
available was measured to be 27.6Nm compared to the rated value of 31.8Nm. This value is
low for a combination of reasons. Primarily, the original design calculations and finite element
analysis results were based on a machine with straight slots. The experimental machine had
skewed slots to reduce cogging torque. However, skewing also reduces the available torque
from the machine. Adding to the reduction in available torque are the effects of the design
compromises made during construction. Most significantly, the amount of iron that was placed
in the rotor was lower than hoped due to the practical difficulties associated with stacking the
multiple laminations. Consequently the effective air-gap flux density is reduced in the
experimental machine lowering torque output.
Figure 7.10 Torque versus quadrature current with S y n R M at very low speed (< 5rpm)
The SynRM Drive Software and Performance 121
The next series of tests were performed with the motor operating at higher speeds and the
inverter dc link voltage adjusted to different levels. This allowed the dynamic torque
performance of the SynRM to be measured. In addition, the relationship between the dc link
voltage and the effective maximum speed could be examined. Figure 7.11 shows three graphs.
Each graph records the measured torque versus quadrature current results obtained at different
speeds. The first graph is for the case where V^ = 200V DC. The second and third graphs
are for VLINK = 400V and 560V respectively.
(b)
1 3 '
1 "2 i 1
-1.5 -1
40-
30-
20-
10-
n J
-20-
-30-
-4T) J
)
Iq(A)
0.5 1 1.5
200rpm
/Iflfl m m
600rpm
Vlink = 400V
2
The SynRM Drive Software and Performance 122
(c)
Figure 7.11 Torque versus quadrature current for S y n R M with (a) V U N K = 200V, (b) V L INK =
400V and (c) VLINK = 560.
For a given inverter DC link voltage, a linear relationship is maintained between the SynRM
torque output and the quadrature current reference. This matches the low speed characteristic
shown in Figure 7.10. As speed is increased a point is reached where the maximum torque
begins to reduce. Examination of the phase current waveform at this point shows that the
controller is unable to maintain the level of direct axis excitation.
Figure 7.12 demonstrates this last point by showing two phase current waveforms recorded in
the SynRM under different conditions. In Figure 7.12 (a) the direct axis current reference is set
to 1.8A and quadrature axis current reference is set to IA. Both portions of the current
waveform are clearly recognizable. In Figure 7.12 (b) the direct axis current reference is again
set to 1.8A while the quadrature axis current reference is raised to 1.5A. The section of the
current waveform that supplies direct axis excitation fails to reach 1.8A. The controller is no
longer able to control the direct axis portion of the waveform to the desired level. Physically,
the speed voltage term in that phase winding has increased and there is insufficient inverter bus
voltage to drive direct axis excitation to the level required. Consequently, the machine flux
The SynRM Drive Software and Performance 123
falls along with the output torque as can be seen in Figure 7.11 at higher quadrature
reference values.
current
(a)
(b)
Figure 7.12 S y n R M phase current (a) Id = 1.8A, L, = IA and (b) Id = 1.8A, L. = 1.5A.
Figure 7.11 (c) shows that the drive in its present form is unable to produce rated torque at
1500rpm. This problem could be overcome by reducing the number of turns on the stator phase
winding.
Conclusions 124
CHAPTER 8
Conclusions
The broad motivation for this thesis was to investigate and develop the potential of the field-
oriented SynRM drive. This drive offers potential benefits such as greater torque density,
higher efficiency and simpler control algorithms compared to the commonly used induction
machine drive. In particular, the project has focused on axially laminated SynRMs with
rectangular stator current excitation.
Where the majority of existing works on axially laminated SynRM design assume sinusoidal
stator excitation the approach here was to presuppose a "rectangular" stator current distribution.
The rotor saliency of the SynRM naturally produces a rectangular air-gap flux density
distribution. Assuming rectangular stator currents leads to machine designs with a greater
output torque per rms ampere. However, the choice to use a rectangular stator current
distribution changes what are the traditionally recognized optimal machine dimensions.
Further, to produce the current distributions one requires a concentrated, multiphase stator
winding. This necessitates the development of new techniques for field-oriented type current
control.
With regard to the machine design an analytical model, based on a lumped-element
approximation to the machine's magnetic circuit, has been developed for the motor. The model
takes into account all of the motor dimensions and includes allowance for magnetic saturation
in the machine iron. Applying the model to the design process yielded machines featuring large
rotor pole pitches (approaching 180 electrical degrees) and rotor iron : iron +fibre ratios
slightly smaller than 0.5. These values are noted as different to those generally accepted for
sinusoidally excited machines (pole pitches * 120 electrical degrees, iron : iron + fibre « 0.6 to
0.7). The reason for the difference is that the rectangular stator current distribution allows the
Conclusions 125
full rotor pole face to be utilized to carry machine magnetic flux. Sinusoidally excited
machines concentrate the flux in a narrower band and hence exhibit narrower poles with more
rotor iron.
Apart from the rotor pole pitch and iron to fibre ratio, the remaining optimized SynRM
dimensions are similarly proportioned to those of comparably sized induction machines. The
one notable exception is the air-gap width. In induction machines, the rotor carries significant
currents and is subject to heating. As this heat is conducted along the rotor shaft allowance
must be made for it in the tolerance of the bearings chosen. This mechanical allowance
effectively sets the lower limit on the air-gap width in induction machines. The SynRM rotor
carries no current and is not subject to the same heating. Finer tolerance bearings can be
chosen and smaller air-gaps are achievable. This argument of course assumes other mechanical
issues such as maintaining necessary tolerances for cost effective manufacturing and allowing
for unbalanced magnetic pull due to rotor eccentricities can be resolved in a commercial
product. The air-gaps suggested by the design model are generally half of those found in
comparably sized induction machines.
A 5kW four-pole nine-phase experimental SynRM was constructed based on the design model.
Finite element analysis and experimental measurements confirmed the performance of the
prototype machine matched the design expectations.
To control the experimental machine required the development of appropriate field-oriented
control techniques for the multiphase environment. Initially, generalized d-q voltage and torque
equations were derived for the machine. These are significantly more useful than the
equivalent stator reference frame equations because the transformation effectively removes the
coupling between the stator phase windings. Further, the transformed inductances are constant,
independent of rotor position. The generalized equations allowed the motor's performance to
be easily simulated and suggested potential control strategies.
Conclusions 126
T w o methods of implementing field-oriented control in the nine-phase S y n R M were presented.
The first was termed the "stator current controller". Stator phase windings are designated as
supplying purely direct or quadrature axis excitation depending on their position relative to the
rotor pole face. Thus, a set of phase current references is generated and a simple hysteresis
switching strategy can be implemented in an inverter to control the phase currents to these
values. This control strategy was implemented in the experimental drive. Experimental
measurements of the drive's performance were obtained validating the predictions from the
simulated drive.
The second controller was termed the "transformed frame vector controller". The controller
operates on the transformed current variables. By controlling the isolated d-q harmonic
components of current better current regulation and faster transient performance were achieved
in simulation. This controller was not implemented in the experimental drive. The
computational requirement prevented its implementation in the hardware assembled for this
project. However, means are suggested for implementing the higher performance controller in
the future.
In summary, the following points can be made with regard to the experimental drives
advantages / disadvantages and areas needing further research;
(a) The experimental drive demonstrated a high torque density albeit at low speeds. It has been
noted that the speed range could be extended with a more appropriately configured stator
winding. Another alternative is to increase the voltage rating of the inverter, although this
would come at a significant cost penalty.
(b) The multiphase structure offers redundancy, which is advantageous in applications where
the drive must run continuously.
(c) The efficiency of the drive configuration has not been resolved. The initial prototype is
compromised by its stator-winding configuration. This contains long end windings and
Conclusions 127
requires a high current density to achieve rated torque. Ideally a second prototype should
be constructed, using the knowledge obtained with regard to practical machine design
requirements, to allow a more realistic evaluation of the drives efficiency. Included in this
investigation should be consideration of the iron losses in the axially laminated rotor
structure.
(d) The current controller implemented is quite simple but effective. To achieve higher
performance more complicated control strategies are required. The computational
requirement here is prohibitive with existing technology. Further investigation is necessary
into ways in which this problem may be overcome.
(e) The axially laminated rotor structure requires further investigation from a mechanical
viewpoint. In particular questions to be considered include mechanical integrity at high
speed along with methods for economical manufacture given the unusual rotor structure
and the tighter tolerances necessary to support a small air-gap.
(f) Another issue is the cost of the inverter. The experimental drive requires three times the
number of power electronic switches compared to a standard three-phase drive. Clearly
this is more expensive but perhaps not by as much as the three to one ratio suggests. It
must be remembered that the current rating of the individual switches is reduced in the
multiphase case, lowering their cost. Further, over time the cost of semiconductor devices
continues to reduce relative to the cost of the machine itself. If efficiency gains are realised
then drive life cycle costing may even justify the higher initial capital cost.
References 128
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on Power Apparatus an Systems, Volume 90, pages 305-317, 1971.
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Rotor", IEE Proceedings - Part B, Volume 141, Number 4, pages 213-220,1994.
[26] J.K. Kostko, "Polyphase Reaction Synchronous Motor", Journal of ATF.R Volume 42,
pages 1162-1168,1923.
[27] JD Law, A Chertok and T A Lipo, "Design and Performance of Field Regulated
Reluctance Machine", IEEE Transactions on Industry Applications, Volume 30, Number
5, pages 1185-1191, September / October 1994.
[28] JD Law, TJ Busch and T A Lipo, "Magnetic Circuit Modelling of the Field Regulated
Reluctance Machine Part I: Model Development", IEEE Transactions on Energy
Conversion, Volume 11, Number 1, pages 49-55, 1996.
[29] PJ Lawrenson and L A Agu, "A New Unexcited Synchronous Machine", Proceedings
IEE, Volume 110, Number 7, pagel275,1963.
[30] PJ Lawrenson and L A Agu, "Theory and Performance of Polyphase Reluctance
Machines" Proceedings IEE, Volume 111, Number 8, pages 1435-1445, August 1964.
[31] PJ Lawrenson and L A Agu, 'Low Inertia Reluctance Machines", Proceedings IEE,
Volume 111, Number 12, pages 2017-2025, December 1964.
[32] PJ Lawrenson, 'Two-Speed Operation of Salient-Pole Reluctance Machines",
Proceedings IEE, Volume 112, Number 12, pages 2311-2316, 1965.
[33] PJ Lawrenson and S K Gupta, "Developments in the Performance and Theory of
Segmental-Rotor Reluctance Motors" Proceedings IEE, Volume 114 Number 5, pages
645-653, May 1967.
[34] PJ Lawrenson and SR Bowes, "Stability of Reluctance Machines", IEE Proceedings,
Volumell8, pages 356-369, 1971.
[35] W Leonhard, "Control of Electrical Drives", Springer - Verlag, Heidelberg, 1985.
[36] SP Liou, H H Woodson and JS Hsu, "Steady-State Performance of Reluctance Motors
Under Combined Fundamental and Third-Harmonic Excitation Part I: Theoretical
Analysis", IEEE Transactions on Energy Conversion, Volume 7, Number 1, pages 192-
201,1992.
[37] T A Lipo and P C Krause, "Stability Analysis of a Reluctance Synchronous Machine",
IEEE Transactions on Power Apparatus and Systems, Volume 86, pages 825-834, 1967.
[38] T A Lipo, "Novel Reluctance Machine Concepts for Variable Speed Drives", 6
Meditteranean Electrotechnical Conference Proceedings, Volume 1, pages 34-43,1991.
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[39] X Luo, A El-Antably and T A Lipo, "Multiple Coupled Circuit Modeling of Synchronous
Reluctance Machines", Proceedings of IEEE Industry Applications Society Annual
Meeting, Volume 1, pages 281-289,1994.
[40] I Marongiu and A Vagati, "Improved Modelling of a Distributed Anistropy Synchronous
Reluctance Machine", Proceedings of IEEE Industry Applications Society Annual
Meeting, pages 238-243,1991.
[41] T Matsuo and T A Lipo, "Rotor Design Optimization of Synchronous Reluctance
Machine", IEEE Transactions on Energy Conversion, Volume 9, Number 2, pages 359-
365,1994.
[42] R W Menzies, 'Theory and Operation of Reluctance Motors with Magnetically Anistropic
Rotors I - Analysis", IEEE Transactions on Power Apparatus and Systems, Volume 91,
pages 35-41, 1972.
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with Magnetically Anistropic Rotors II - Synchronous Performance", IEEE Transactions
on Power Apparatus and Systems, Volume 91, pages 42-45, 1972.
[44] TJE Miller, A Hutton, C Cossar and D A Staton, "Design of a Synchronous Reluctance
Motor Drive", IEEE Transactions on Industry Applications, Volume 27, Number 4, pages
741-749, 1991.
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293-298,1990.
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Industry Applications, Volume 28, Number 3, pages 652-658,1992.
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Motor Design: A Nonlinear Programming Approach", IEEE Transactions on Power
Apparatus and Systems, Volume 98, pages 527-535,1979.
[50] SC Rao, "Dynamic Performance of Reluctance Motors with Magnetically Anistropic
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1376,1976.
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[51] PE Scheihing, M Rosenberg, M Olszewski, C Cockrill and J Oliver, "United States
Industrial Motor Driven Systems Market Assessment: Charting a Roadmap to Energy
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[52] D A Staton, TJE Miller and SE Wood, "Optimisation of the Synchronous Reluctance
Motor Geometry", Fifth International Conference on Electric Machines and Drives 1991,
pages 156-160.
[53] D A Staton, TJE Miller and SE Wood, "Maximizing the Saliency Ratio of the
Synchronous Reluctance Motor", IEE Proceedings-B, Volume 140, Number 4, pages
249-259, July 1993.
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Permanent Magnet Machines", IEEE Industry Applications Society 32nd Annual Meeting,
Volume 1, pages 42-49,1997.
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1997.
[56] H A Toliyat, L X u and T A Lipo, "A Five Phase Reluctance Motor with High Specific
Torque" IEEE Transactions on Industry Applications, Volume 28, Number 3, pages 659-
667, May/June 1992.
[57] H A Toliyat, M M Rahimian and T A Lipo, "dq Modelling of a Five Phase Synchronous
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Converters for Adjustable Speed Drive Applications", Proceedings of Fifth European
Conference on Power Electronics and Applications, Volume 5, pages 194-199, 1993.
[59] L X u and J Yao, "A Compensated Vector Control Scheme of a Synchronous Reluctance
Motor Including Saturation and Iron Losses", IEEE Transactions on Industry
Applications, Volume 28, Number 6, pages 1330 - 1338, November / December 1992.
133
Publications of Work Performed as Part of
This Thesis
[60] CE Coates and D Piatt, "Field-Oriented Control of a Synchronous Reluctance Motor",
Proceedings of Australian Universities Power Engineering Conference 1994, Adelaide.
[61] C E Coates, D Piatt and VJ Gosbell, "Generalised Equations for a Nine Phase
Synchronous Reluctance Motor", Proceedings of Australian Universities Power
Engineering Conference 1996, Melbourne, Volume 1, pages 43-48.
[62] C E Coates, D Piatt and B S P Perera, "Design Optimisation of an Axially Laminated
Synchronous Reluctance Motor" Proceedings of the IEEE Industry Applications Society
Annual Meeting 1997, Volume 1, pages 279-285.
[63] C E Coates, D Piatt and VJ Gosbell, "Control and Performance of a Nine-Phase
Synchronous Reluctance Drive" Proceedings of Australian Universities Power
Engineering Conference 2000, Brisbane, pages 97-102.
[64] C E Coates, D Piatt and VJ Gosbell, "Performance Evaluation of a Nine-Phase
Synchronous Reluctance Drive", Accepted for inclusion at the IEEE Industry Appications
Society Annual Meeting 2001, Chicago.
APPENDIX A
APPENDIX A
5kW SynRM Schematics
A1 5kW SynRM Stator lamination
A2 5kW SynRM Stator Tooth Detail
A3 5kW SynRM Rotor Cross Section
A4 5kW SynRM Stator Winding Details
A5 5kW SynRM Rotor
FILLETS R5
Z14.62
06.6
Notes: 1. All dimensions are in millimetres. 2. Laminations are to be either 0.35 or 0.5mm Lycore 230 or
similar material. 3. A is the angle between the axis of the tabs and one slot. 4. If 0.35 m m material is used 170 laminations are required for
one stator (this includes spares). For the skewed stator angle A increments by 0.069 degrees between successive laminations.
5. If 0.5mm material is used 120 laminations are required for one stator (this includes spares). For the skewed stator angle A increments by 0.099 degrees between successive laminations.
5kW SynRM Stator Lamination
DRAWN: CEC
DATE: 4/12/95
SCALE: 1:2
Notes:
1. All dimensions are in millimetres. 2. Teeth have parallel sides. 3. Tooth faces are to be (or at least approximate) arcs
of radius 64.29mm. 4. Slot bottoms are to be arcs of radius 87.46mm. Tnis
requirement is less critical than that for the tooth faces.
5kW SynRM Stator Tooth Detai
DRAWN: CEC
DATE: 4/12/95
SCALE: 2:1
Notes: 1. The stator has a 9 phase concentrated winding. 2. One phase winding consists of four coils (numbered
1 to 4 in diagram) connected in series. 3. Each of the four coils consists of four identical coils
in parallel. Each of these has 170 turns of 0.25 m m diameter wire.
5kW SynRM Winding Details
DRAWN: CEC
DATE: 7/2/97
SCALE: 1:2
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APPENDIX B
Inverter Schematics
B1 Power Circuit Diagram (1 of 2)
B2 Power Circuit Diagram (2 of 2)
B3 Dynamic Brake Control Circuit
B4 Gate Drive Circuit
B5 DSP Interface - DSP Cable (1 of 5)
B6 DSP Interface - Gate Decoder I (2 of 5)
B7 DSP Interface - Gate Decoder II (3 of 5)
B8 DSP Interface - Current Feedback (4 of 5)
B9 DSP Interface - Shaft Encoder (5 of 5)
BIO Inverter Gate Drive Board Layout
B11 Inverter Gate Drive Board PCB Artwork
B12 Inverter Parts List
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B12 - INVERTER PARTS LIST
Designation Description
Dwg B1 (Inverter - Power Circuit Diagram - sht 1/2)
DB1
L1 EC1 - EC4
PR1 PR2 - PR3
Tdb
CB1 M T
3 Phase Rectifier 1200V/30A Semikron SKD31/12 Rectifier Heat Sink 1.56 C/W Inductor 34.4mH Capacitor (electrolytic) 1000uF 400VDC Capacitor mounting clips 51 m m dia. Resistor 100R200W Resistor 47R 300W IGBT 1200V/8AGT8Q101 IGBT Heatsink Circuit Breaker 240V AC 2A Main Relay Timer Relay
Dwg B2 (Inverter - Power Circuit Diagram - sht 2/2)
Ta-Ti
Da-Di
IGBT 1200V/8AGT8Q101 IGBT Heatsink Power Diode 1200V / 8A Diode Heatsink
Dwg B3 (Inverter - Dynamic Brake Control Circuit)
IC1 P1 R1 R2
R3, R4 R5, R6 R7 R8
TL071 Op Amp Potentiometer 10k 10 turns Resistor 1M 0.6W Resistor 100k 0.6W Resistor 10k 0.6W Resistor 18k 0.6W Resistor 10M0.6W Resistor 150R0.6W
Dwg B4 (Inverter - Gate Drive Circuit)
BR1 C1.C2 FET1 FET2 IC1 IC2
R1 -R3.R10, R11 R4
R5.R9 R6
R7, R8 Z1 -Z4 Z5.Z6
Transformer 240V to 0-15V,0-15V 6VA W04 bridge rectifier 400V 1.5A Capacitor 330uF 25V IRF9520 - Power MOSFET 100V 6A IRF510 - Power MOSFET 100V 5.6A 74OL6010 - high speed optocoupler LF357N - BiFET high speed op amp Resistor 10k 0.25W Resistor 10R 0.25W Resistor 100k 0.25W Resistor 150R0.25W Resistor 330R 0.5W 15V0.4WZener Diode 15V5WZener Diode Terminals - 2 way Terminals - 3 way
Quantity
1 1 1 4 4 1 2 1 1 1 1 1
18 18 18 18
1 1 1 1 2 2 1 1
1 1 2 1 1 1 1 5 1 2 1 2 4 2 1 2
B12 - INVERTER PARTS LIST
Designation Description
Dwg B5 (Inverter - DSP Interface - DSP Cable - sht 1/5)
Klippon 34 way interface module Ribbon cable 34 way 34 way IDC female socket connector SCSI2 100 way male connector
Dwg B6 (Inverter - DSP Interface - Gate Decoder I - sht 2/5)
74HC139A Dual 1-of-4 Decoder / Demultiplexer MC14013B Dual Type D Flip-Flop Resistor 1k0.6W Capacitor 1nF
Dwg B7 (Inverter - DSP Interface - Gate Decoder II - sht 3/5)
C1.C2 D1.D2 IC1
R1.R2
Capacitor 470pF Diode Hex Schmitt Trigger 40106 Resistor 22k 0.6W
Dwg B8 (Inverter - DSP Interface - Current Feedback - sht 4/5)
CTa - CTi Ra-Ri
Current Transducer Resistor 500R 0.6W
Dwg B9 (Inverter - DSP Interface - Shaft Encoder - sht 5/5)
40106 Hex Inverter MC14013B Dual Type D Flip-Flop Resistor 5k6 0.6W Capacitor 1 nF
Quantity
1
1 1
3 6 9 9
18 18 5 18
9 9
1 1 3 3
APPENDK C C-l
APPENDIX C
Control Program Listing
APPENDDC C C-2
/********************** ******************************************** * *
STACUR Stator Current Controller Program
Version 2 15 / 2 / 2000
* This program implements the stator current controller on * * the ADC64 DSP board. An extended description of code can * * be found in Chapter 7. * * * ******************************************************************/
#include ftinclude #define #define #define #define void void int
"periph.h" "stdio.h" timer_int sync_int P I timer_int() sync_int(); curr_ref();
c_int09 c_int03 50 1
l
II Declare global variables // Set to type volatile so interrupt routines can access them. volatile int timer_int_flag; //flag to indicate 0.2ms interval volatile int sync_int_flag; //flag to indicate sync pulse volatile int position; //rotor position (0-999)
void main() {
/************************************************ * * * INITIALIZATION * * * ************************************************/
// Declare local variabl int count_old; int count_new; int iaref, iafb int ibref, ibfb int icref, icfb int idref, idfb int ieref, iefb int ifref, iffb int igref, igfb int ihref, ihfb int iiref, iifb int id, iq; int modpos; int sampleO; int samplel; int sample2; int sample3; int gate_state; int spdref;
es //Counter value from previous cycle //Counter value from current cycle //Phase A current reference / feedback //Phase B current reference / feedback //Phase C current reference / feedback //Phase D current reference / feedback //Phase E current reference / feedback //Phase F current reference / feedback //Phase G current reference / feedback //Phase H current reference / feedback //Phase I current reference / feedback //Direct / quadrature components of current //Rotor position (degrees electrical) //Temporary storage analog inputs 0 & //Temporary storage analog inputs 2 & //Temporary storage analog inputs 4 & //Temporary storage analog inputs 6 &
1 3 5 7
//Inverter switching config. //Speed reference
(9 bit binary)
APPENDIX C C-3
int int int int int int int
spderr; speed; posold; n; prop ; integral; intold;
//Speed error //Speed feedback //Old position value for speed f/b calc. //Loop counter //PI controller prop. comp. of output //PI controller integral comp. of output //PI controller integrator memory
// Configure ADC64 board MHZ = 60; *DIO_CONFIG = 1; *PIT1_D = 0xb4, *PIT1_C = Oxff; *PIT1_C = Oxff; enable_monitor(); enable_clock(); enable_interrupts()
//set clock speed //d0-d7 outputs, d8-dl5 inputs //set timer/counter 1 chan 2 to mode 2 //load timer/counter 1 chan 2 to // Oxffff (LSB first)
// Initialise variables timer_int_flag = 0 ; // Initialise sync_int_flag = 0 ; // Initialise count_old = Oxffff; // Initialize speed = 0 ; // Initialize n = 0; // Initialize intold = 0 ; // Initialize id = 8000; // Set direct
timer interrupt flag sync pulse interrupt flag count_old speed feedback loop counter integrator memory axis current reference
// Initialise external interrupt install_int_vector(sync_int,3); enable_interrupt(2);
//put sync_int isr at address 3 //sets IE register bit 2
// Initialise analog inputs MADC0); *(ADC1); *(ADC2); *(ADC3) *(INT_MASK) = 0x0 f;
set_mux(0,0) set_gain(0,0) set_gain(l,0) set_gain(2,0) set_gain(3,0) set_gain(4,0) set_gain(5,0) set_gain(6,0) set_gain(7,0) trigger(0,0); timer(0,5000)
set_mux(l,0) set_mux(2,0) set_mux(3,0) set_mux(4,0) set_mux(5,0) set_mux(6,0) set_mux(7,l)
trigger(0,1); trigger(0,2) trigger(0,3!
// Turn all phases off gate_state = 0x00; *DIO = (gate_state | 0x0018) & 0x0007; us (10); *DIO = ((gate_state » 3) | 0x0018) & OxOOOf; us(10); *DIO = ((gate_state » 6) | 0x0018) & 0x0017;
APPENDLK C C-4
,************************************************ * * * ALIGN POSITION FEEDBACK * * * ************************************************/
printf("\n\n Waiting to align position feedback");
// Wait until rotor position calibrated do { } while (sync_int_flag == 0);
sync_int_flag = 0;
do { } while (sync_int_flag == 0) ;
posold =75; // Initialize position memory for speed calc.
printf("\n\n Ready");
/************************************************ * * INITIALIZE TIMER INTERRUPT
* * ************************************************/ timer(6,5000); //set on chip timer 0 to 5kHz install_int_vector(timer_int,9); //put timer_xnt isr at add. 9 enable_interrupt(8); //sets IE register bit 8
// Main loop do {
/************************************************
* * RECEIVE TIMER INTERRUPT?
1***********************************************/ // Cycle at 5kHz do { } while (timer_int_flag ==0);
,************************************************ ' * * * READ SPEED REFERENCE . *
1***********************************************/ sample3 = *ADC3; sample3 = *ADC3; spdref = (sample3 » 16); spdref = spdref/160; set_mux(7,0); us (3); *ADC3=0;
/************************************************ * * * READ POSITION / SPEED * * * *************************************************;
//Read rotor position *PIT1_D = 0x80; count_new = *PITl_C; count_new = ((*PIT1_C « 8) + count_new) & Oxffff;
if (count_new <= countold) {
if ((*DIO & 0x0100) == 0x0100) {
position = position - count_old + count_new; } else {
position = position + count_old - count_new; }
} else {
if ((*DIO & 0x0100) == 0x0100) {
position = position - count_old - Oxffff + count_new;
} else {
position = position + count_old + Oxffff -count_new;
} } if (position > 999)
position = position - 999; if (position < 0)
position = position + 999;
modpos = (position * 360.0 / 1000.0); modpos = modpos % 180;
n = n + 1; if (n=100) {
speed = position - posold; if (speed < -150) speed = speed + 1000; if (speed > 150) speed = speed - 1000; posold = position; n = 0;
}
APPENDIX C C-6
/********************************************* *
* ** *
* PI SPEED CONTROLLER * * * ************************************************,
// Speed controller spderr = spdref - speed; prop = spderr * P; integral = intold + I * spderr; intold = integral; if (intold > 8000) intold = 8000; if (intold < -8000) intold = -8000; iq = prop + integral; if (iq > 8000) iq = 8000; if (iq < -8000) iq = -8000;
/************************************************ * * * CALCULATE STATOR CURRENT REFERENCE * * * ************************************************/
// Calculate the phase current references (scaled IA = 8192) iaref = curr_ref(modpos, id, iq) ; ibref = curr_ref(modpos + 100, id, iq); icref = curr_ref(modpos + 20, id, iq) ; idref = curr_ref(modpos + 120, id, iq) ; ieref = curr_ref(modpos + 40, id, iq); ifref = curr_ref(modpos + 140, id, iq) ; igref = curr_ref(modpos + 60, id, iq) ; ihref = curr_ref(modpos + 160, id, iq) ; iiref = curr_ref(modpos + 80, id, iq) ;
,************************************************ * * * READ PHASE CURRENTS *
* * ************************************************/ // Read phase currents (scaled IA = 8192) sampleO = *ADC0; sampleO = *ADC0; samplel = *ADC1; samplel = *ADC1, sample2 = *ADC2; sample2 = *ADC2, sample3 = *ADC3; sample3 = *ADC3, set_mux(7,1);
iafb = (sampleO « 16) » 16; ibfb = (sampleO » 16); icfb = (samplel « 16) » 16; idfb = (samplel » 16) ; iefb = (sample2 « 16) » 16; iffb = (sample2 » 16); igfb = (sample3 « 16) » 16; ihfb = (sample3 » 16) ; iifb = -(iafb + ibfb + icfb + idfb + iefb + iffb + igfb + ihfb);
APPENDIX C C-7
/***************************************^ * * *
SWITCH GATE STATES
******* * * *
******************** ****************************
II Switch outputs gate_state = 0x000; if (iafb < iaref) if (ibfb < ibref) if (icfb < icref) if (idfb < idref) if (iefb < ieref) if (iffb < ifref) if (igfb < igref) if (ihfb < ihref) if (iifb < iiref)
gate_state gate_state gate_state gate_state gate_state gate_state gate_state gate_state gate_state
*DIO = (gate_state | 0x0018) us(10);
= = — = = = = = =
&
0x001; gate_state gate_state gate_state gate_state gate_state gate_state gate_state gate_state
0x0007;
0x002 0x004 0x008 0x010 0x020 0x040 0x080 0x100
*DIO = ((gate_state » 3) | 0x0018) & OxOOOf; us(10);
*DIO = ((gate_state » 6) | 0x0018) & 0x0017;
timer_int_flag = 0;
} while (1);
curr_ref(offset,id,iq) int int int {
offset; id; iq;
// Define local int ref;
// Rotor position relative to phase winding // Direct axis current reference (IA = 8192) // Quadrature axis current reference (IA = 8192)
function variables // Phase current reference (IA = 8192)
// Make offset modulo 180 offset = offset % 180;
// if if
if if
if if
if if
if
Calculate phase current reference (offset <= 4) ref = id; ((offset > 4) & (offset <= 6)) ref =
interp(offset,4,6,id,iq+id/8) ; ((offset > 6) & (offset <= 14)) ref = iq+id/8; ((offset > 14) & (offset <= 16)) ref =
interp(offset,14,16,iq+id/8,iq-id/8) ; ((offset > 16) & ((offset > 24) &
id/8,iq+id/8); ((offset > 26) & ((offset > 34) &
(offset <= 24)) ref = iq-id/8; (offset <= 26)) ref = interp(offset,24,26,iq-
ref = iq+id/8; ref =
(offset <= 34)) (offset <= 36))
interp(offset,34,36,iq+id/8,iq-id/8) ; ((offset > 36) & (offset <= 44)) ref = iq-id/8;
APPENDIX C C-8
if
if if
if if
if if
if if
if if
if if
if if
if if
if if
if if
if if
if if
if if
if
((offset > 44) & (offset <= 46)) ref = id/8,iq+id/8);
(offset > 46) & (offset <= 54)) ref = (offset > 54) & (offset <= 56)) ref = interp(offset,54,56,iq+id/8,iq-id/8)
interp(offset,44, 46, iq-
iq+id/8;
(offset > 56) & (offset > 64) & id/8,iq+id/8);
(offset > 66) & (offset > 74) &
(offset <= (offset <=
64)) 66))
(offset <= 74)) (offset <= 76))
ref ref
ref ref
iq-id/8; interp(offset,64,66,iq-
mterp (off set, 74, 76, iq+id/8, iq-id/8)
(offset <= 94)) (offset <= 96))
(offset > 76) & (offset <= 84)) (offset > 84) & (offset <= 86)) id/8,-id);
(offset > 86) & (offset > 94) & iq-id/8);
(offset > 96) & (offset <= (offset > 104) & (offset <= iq-id/8,-iq+id/8);
(offset > 106) & (offset <= 114 (offset > 114) & (offset <= 116 iq+id/8,-iq-id/8);
(offset > 116) & (offset <= 124 (offset > 124) & (offset <= 126 iq-id/8,-iq+id/8);
(offset > 126) & (offset <= 134 (offset > 134) & (offset <= 136 iq+id/8,-iq-id/8);
(offset > 136) & (offset <= 144 (offset > 144) & (offset iq-id/8,-iq+id/8);
(offset > 146) & (offset (offset > 154) & (offset <= 156 iq+id/8,-iq-id/8);
(offset > 156) & (offset <= 164 (offset > 164) & (offset <= 166 iq-id/8, -iq+id/8) ,-
(offset > 166) & (offset <= 174 (offset > 174) & (offset <= iq+id/8,id);
((offset > 176) & (offset <=
104) 106
146
154
176
ref = ref =
ref = ref =
ref = ) ref
ref ref
ref ref
ref ref
ref ref
ref ref
ref ref
ref ref
iq+id/8;
l
iq-id/8; interp(offset,84,86,iq-
-id; interp(offset,94,96,-id,
= -iq-id/8; = interp(offset,104,106,
= -iq+id/8; = interp(offset,114,116,
= -iq-id/8; = interp(offset,124,126,
= -iq+id/8; = interp(offset,134,136,-
= -iq-id/8; = interp(offset,144,146, •
= -iq+id/8; = interp(offset,154,156, •
= -iq-id/8; = interp(offset,164,166, -
= -iq+id/8; = interp(offset,174,176,-
180)) ref = id;
// Return phase current reference from function return ref;
}
interp(x,xl,x2,yl,y2) int x,xl,x2,yl,y2; {
int ans ,-ans = ( (y2 - yl) * x + (yl * x2 return ans;
- xl y2; / (x2 - xl);
APPENDIX C
void timer_int(void) {
timer_int_flag = 1; }
void sync_int(void) {
sync_int_flag = 1; position = 75;
}
APPENDED D-l
APPENDIX D
Numerical Solution to SynRM Model
Differential Equations
The air-gap flux density distribution, Bg(0), and quadrature axis flux, 0^0), are described
by equations (2.2) to (2.7), derived in chapter 2. These equations are repeated below for
convenience;
Lda <Mr(0) + 8e_ Sll-RH (0) + RJ(0) + 0 (0)RR =0 (D-l) 2 d9 Mo d0
d(b iff) r l - ^ — = RL[Bg in-0)- Bg (0)\ (D-2)
]j(0)Rd0= ]Hs(0)Rd0 + -^[Bg(7T-0) + Bg(0)] e 0 Mo
+ i*-[ff,(>r-0) + ff,(0)] (D-3)
gK R d0
<t>qfy=WZY') = * v-5)
Bg(-0) = Bg(7t-9) (D-6)
The flux density in the rotor iron, BJ0), is related to the air-gap flux density by;
Br(0) = trxBg(0) (D-7)
where, tr = ratio of iron : iron + fibre in the rotor
APPENDDCD D-2
The iron is assumed to have a B-H characteristic as shown in Figure 2.4. This
characteristic is described mathematically by;
H = 5M0
5A
(B + 1.7)
0
•(B-1.7)
5<-1.7
-1.7<B<1J
B>\.1
(D-8)
In our instance, the rotor iron is in saturation if B^0) > (tr x 1.7). When the iron is in
saturation substituting equation (D-7) into (D-8) and differentiating gives;
dHr(0)= 1 dBg(0)
d0 5/yr d0 (D-9)
-0 0 The system of equations can be solved over the rotor pole arc given by < 0 < — .
Numerical methods were used to solve the differential equations. A state vector was
chosen to be;
x =
Bg(0)
Bs(0)
®q(-0)
Bg(-9)
BA-9)
(D-10)
Effectively, a solution is determined by starting at both ends of the pole face and iterating
towards the centre. This approach was required as the state derivative equations assume
knowledge of both Bg(0) and Bg(-0).
APPENDIX D D-3
The state derivative equations are;
&(9) = RL[BA-0)-B(0)\
B'g(0) = \
-M-{j(0) + q(0)Rq} 8e
l-^^{j(0)^q(9)Rq} WgJr+k da
R Y
B's(0) = -Bg(0)
<&' (-0) = -RL[Bg (0) - Bg (-0)]
B: (-0) =
t^{j(-0)+^ql:-9)Rq} 8e
lOM0trR |J(_^) + 0 ? ( _ ^ j lOgJr+L^
-R
Y B's(-9) = -irBg{-0)
Bg(0)<trx\.l
B(0)>trx\.l
Bg(0)<trxl.l
Bg(0)>trx\.l
(D-ll)
(D-12)
(D-13)
(D-14)
(D-15)
(D-16)
Equation (D-5) gives the initial value for both quadrature flux variables to be 0
0 (d
Substituting 0 = -?- into equation (D-3) determines the relationship between B \ f and
5„ '-0,
to be;
B. f-Q\
\ *- J = f
(0 Yl Br K V *• )
(D-17)
Symmetry requires Bs v 2 v
= -B, f-0\
V 2 J
APPENDIX D D-4
0 Assuming values for both the air-gap and stator yoke flux densities at 0 = -£- forms the
2 initial conditions for the state vector. Thus, the initial state vector becomes;
x, =
0
0 (D-18)
The values for Kj and K2 can be found by iterating until the air-gap and stator yoke flux
densities, found by approaching from either side of the pole face, match at the centre of the
rotor pole face. The solution was determined using MATLAB. The routines used are
included below for reference.
ymam.m
% Outer loop that is used to solve calculation of machine % flux densities when both direct and qaudrature axis % excitation are present. Uses matlabs optimisation routine % in cascaded loops. % Subroutines: ymainsub, ydesol, yde, yexc
% Define global variables global Jd Jq BgO theta sv BsO bgb m;
% Request user defined variables Jd = input('Enter direct axis excitation (A/m) [4000] ' ) ;
if isempty(Jd) Jd = 4000;
end
Jq = input('Enter quadrature axis excitation (A/m) [-2000]
' ) ; if isempty(Jq)
Jq = -2000; end
APPENDDCD D-5
% Initial approximation to air gap and yolk flux density % at -thetap/2 BsO = -1.76; bgb = 0.2;
opt = fzero('ymainsub',BsO);
% Form state and angle matrices State(l:m,1:3) = sv(l:m, 1:3) ; state(m+1:2*m-l,1:3) = flipud(sv(l:m-l, 4:6) ) ; angle (l:m/l) = thetad :m, 1) ; angle(m+l:2*m-l,l) = -flipud (thetad :m-l,l) ) ;
% Plot solution subplot(3,1,1) plot(angle,state(:,1) ) subplot(3,1,2) plot(angle,state(:,2)) subplot(3,1,3) plot(angle,state(:,3))
ymainsub.m
function y2 = ymainsub(BsO)
global bsb bst BsOa bgb sv m;
BsOa = BsO; BgO = bgb;
bgb = fzero('ydesol',BgO);
y2 = sv(m,3)-sv(m,6);
ydesol.m
% This function solves the DE that describes the _ SynRM i % it has both direct and quadrature axis excitation % Saturation is allowed for.
function error = ydesol(BgO)
% Define global variables global theta sv BsOa uO Jd Rs thetap ge W Tnml m;
Bsat = 1.7;
APPENDKD D-6
% Solve DE for given initial state thetaO = -thetap/2; thetaf = 0; Bgb = BgO;
% Determine the starting vector values for the ODE. if BsOa > -Bsat
if Bgb>Tnml*Bsat
Bgt = uO*(Jd*Rs*(pi/2-thetap)-W*(Bgb/Tnml-1.7)/(10* u0)/ge-Bgb;
if Bgt>Tnml*Bsat Bgt = 10*u0*Tnml*(Jd*Rs*(pi/2-thetap)+1.7*W/(5*u0))
/(10*ge*Tnml+W)-Bgb; end
elseif Bgb<-Tnml*Bsat
Bgt = uO*(Jd*Rs*(pi/2-thetap)-W*(Bgb/Tnml+1.7)/(10*u0)) /ge-Bgb;
if Bgt>Tnml*Bsat Bgt = 10*u0*Tnml*Jd*Rs*(pi/2-thetap)/(10*ge*Tnml+W)-
Bgb; end
else
Bgt = uO*Jd*Rs*(pi/2-thetap)/ge-Bgb; if Bgt>Tnml*Bsat
Bgt = 10*u0*Tnml*(Jd*Rs*<pi/2-thetap)+(0.17*W-ge*Bgb) /uO)/(10*ge*Tnml+W);
end
end
else
if Bgb>Tnml*Bsat
Bgt = u0*((Jd+(Bs0a+1.7)/(5*u0))*Rs*(pi/2-thetap)-W*( Bgb / Tnml -1.7) /(10*u0))/ge-Bgb;
if Bgt>Tnml*Bsat Bgt = lO*uO*Tnml*((Jd+(BsOa+1.7)/(5*uO))*Rs*(pi/2-
thetap )+1.7*W/(5*uO))/(10*ge*Tnml+W)-Bgb; end
APPENDDCD D-7
elseif Bgb<-Tnml*Bsat
Bgt = u0*((Jd+(Bs0a+1.7)/(5*u0))*Rs*(pi/2-thetap)-W* (Bgb /Tnml+1.7)/(10*u0))/ge-Bgb;
if Bgt>Tnml*Bsat Bgt = 10*u0*Tnml*(Jd+(Bs0a+1.7)/(5*u0))*Rs*(pi/2-
thetap )/(10*ge*Tnml+W)-Bgb; end
else
Bgt = uO*(Jd+(Bs0a+l.7)/(5*uO))*Rs*(pi/2-thetap)/ge-Bgb;
if Bgt>Tnml*Bsat Bgt = 10*uO*Tnml*((Jd+(BsOa+1.7)/(5*uQ))*Rs*(pi/2-
thetap)+(0.17*W-ge*Bgb)/uO)/(10*ge*Tnml+W); end
end
end
svO = [0 Bgb BsOa 0 Bgt -BsOa]'; tspan = [thetaO thetaf]; [theta,sv] = ode45('yde',tspan,svO);
% Test boundary condition (ie. error at midpoint in airgap % flux density distribution) m = size(theta,1); error = sv(m, 2) -sv(m, 5) ,-
yde.m
% This function defines the state derivative vector defining % the DE that describes the SynRM when it has both direct and % quadrature axis excitation. Saturation is allowed for.
function svdot=yde(theta,sv)
% define global variables global Rr Lr uO Rs Req ge Y Tnml W;
Bsat = 1.7;
svdot = zeros(6,l);
svdot(l)= Rr*Lr*(sv(5)-sv(2));
APPENDDCD D-8
if sv(3) < -Bsat if abs(sv(2)) > Bsat*Tnml
svdot(2)= -10*uO*Rs*Tnml*(yexc(theta)+sv(l) * Req+(sv(3)+1.7) /(5*u0)) /(10*ge*Tnml+W);
else svdot(2)= -uO*Rs*(yexc(theta)+sv(l)*Req+(sv(3)
+1.7)/(5*u0))/ge; end
else if abs(sv(2)) > Bsat*Tnml
svdot(2)= -10*uO*Rs*Tnml*(yexc(theta)+sv(l) *Req) /(10*ge*Tnml+W);
else svdot(2)= -uO*Rs*(yexc(theta)+sv(l)*Req)/ge;
end end
svdot(3)= Rs*sv(2)/Y;
svdot(4)= -Rr*Lr*(sv(2)-sv(5));
if sv(6) > Bsat if abs(sv(5)) > Bsat*Tnml
svdot(5)= 10*uO*Rs*Tnml*(yexc(-theta)+sv(4)*Req-(sv(6)-1.7)/(5*u0))/(10*ge*Tnml+W);
S SSvdot(5)= uO*Rs*(yexc(-theta)+sv(4)*Req-(sv(6) -
1.7)/(5*u0))/ge; end
else if abs(sv(5)) > Bsat*Tnml
10*uO*Rs*Tnml*(yexc( svdot(5)=
theta)+sv(4)*Req)/(10*ge*Tnml+W) ; SSvdot(5)= uO*Rs*(yexc(-theta)+sv(4)*Req)/ge;
end end
svdot(6)= -Rs*sv(5)/Y;
APPENDDCD D-9
yexcm % Define the excitation current on the stator.
function yl=yexc(theta)
global Jq;
% Block current case. yl = Jq;
APPENDIX E
Device Data Sheets
ADC64 DSP Board Technical Specification
GT8Q101 IGBT 1200V / 8A
BY329 Power Diode 1200V / 8A
Sixty-four channel A/D, 32-bit floating-point DSP and PC! bus interface
Features: " 60 M H z TMS320C32 Processor
Eight Multiplexed 200 kH; A/D Input-,
Two D/A Outputs , .,,.,;,:. /
Applications: • Sonar - '' • i'~-
Vibration monitonns
ta logging
Mm 'i* - »; •*"—• °^y^l.Wft^fpw^MMMIWMM
*'.' ;'m.l K-:>0mkAXff!m ^St^iHSHi m vm &wi2mm is "^^jtyRBS^gB
hm-mt&WMs&Mm
••SHAai^m^mFiB^^n j-
IHfiHEHi^S "rr
__K** IIHmBa HUJBft :* -ip|| jPM]w_*gl j ;
BaSs
Overview The A D C 6 4 heralds a n e w era in PC-based data acquisition. Bringing together for the first time a low-cost, high-performance D S P core, a dazzling array of analog and digital I/O with screaming fast 132 Mbyte/sec PCI bus performance, the A D C 6 4 is T H E value platform for next-generation, intelligent data acquisition system designs.
Example Application
Fig. 1 - TheADC64j eight, independent analog input channels are ideal for data logging applications,
aid as this vibration monitoring system.
ftecessor Core TheADC64 features the high-performance Texas Instruments T M S 3 2 0 C 3 2 32-bit floating-point D S P capable of up to 6 0 MFLOPS/30 M I P S . On-chip peripherals include two flexible 32-bit counter/timers, two prioritized D M A controllers, a bidirectional sync serial port, 2 Kbytes of dual-access S R A M and a prioritized interrupt controller.
Memory on the ADC64 may be expanded to include up to 512 Kbytes of zero wait-state S R A M .
On-board Peripherals Hie analog input chain has eight 16-bit, instrumentation-grade A / D converters addressable as pairs by the D S P via four memory mapped locations. Each A / D features an analog input that is simultaneously sampled upon receipt of a D S P software command or an external T T L trigger. Each of the native analog inputs is routed through a differential instrumentation amplifier into a six-pole ( 1 2 0 dB/decade) anti-alias filter. The anti-alias filter circuit has a set of matched resistors to control the filter roll off frequency. Though configured for the maximum Nyquist frequency of 1 0 0 k H z by default, custom cutoff frequencies may be special ordered.
The analog output chain consists of two independent instrumentation-grade 16-bit D / A converters. Writes to specific memory-mapped locations latch data into the selected D / A output roister. Subsequent conversion-triggering of any D / A pair, either via a D S P software command or an external T T L trigger, will update the analog outputs within a conversion period ( < 5 us).
The on-chip timers are augmented by six external channels via two on-board 8 2 C 5 4 s . These timers may be used for pulse stream generation or multichannel timing. M o r e commonly, they are used to multi-rate analog acquisition applications.
A simple high-speed memory-mapped 1 6-bit latch is available to support general-purpose digital I/O. Direction is jumper-configurable in banks of eight bits. The port may be software or externally clocked at rates to 5 M H z and each bit on the port is capable of sourcing or sinking 3 2 m A .
Expansion The A D C 6 4 is compatible with the full range of 3 X B U S cards for I/O expansion including analog I/O Industry Pack modules via the 3 X P A C K and SCSI devices via S C S I 3 X .
Host PC Interface The A D C 6 4 is a half-size card that plugs into a standard 3 2-bit PCI bus slot. The PCI bus interface supports bus mastering, directed by the DSP, capable of bursts of 1 3 2 Mbytes/sec and sustained transfers of 2 0 Mbytes/sec on most host platforms. This provides superior connectivity with transfer rates well above competing C 3 2 offerings featuring awkward, register-based interfaces suitable only for object code downloading. Multiple cards may be installed in systems with full driver support under W i n d o w s 9 5 and N T .
Hardware Option!
Peripherals
SCS!3X
3XPACK
a Options (any combination) •;',
60 MHz/30 MFLOPS
S.E. or Differen!'al
Analog I/O options Breakout Moduie
Fig. 2 • The A D C 6 4 may be equipped with a variety ol options and add-on peripherals to meet
performance and cost goals in O E M applications.
tel (818) 865-6150 • fax (818) 879-1770 » www.innovative-dsp.com_
A. Innovative j O t Integration
I
x > c Cl
k
a
I
Development Tools
The A D C 6 4 is may be programmed in C or Assembler using the tools
available in the Development Package. Components within this package
fully support development of custom D S P applications. The W i n d o w s
device driver and D L L provided in the Z u m a Toolset support host P C
application development in Visual C or Basic, Borland C/Builder/
Delphi and any other environment capable of linking to a standard
Windows DLL. Numerous target and host example programs are
provided as well as support applets for graphic terminal emulation,
object file downloading, etc.
Alternately, the board is compatible with a number of third-party
packages including LabView, Hypersignal RIDE and D A S Y L a b for
users seeking a turnkey data acquisition and analysis solution.
Additionally, the revolutionary Ventura library is available for the
A D C 6 4 to provide full bandwidth access to the extensive hardware
complement of the A D C 6 4 without any D S P programming.
O E M Configurations
The A D C 6 4 can be configured to fit your specific requirements and
provide an optimal mix of performance, cost and features. Contact Innovative Integration with your specific O E M requirements.
Software Options
Development Took
Ventura
Tl C/Assembler
I Code Hammer
*f-* Zuma Toolset
Fig. 3 - Custom software for the ADC64 may be generated using the cross development
tools. Alternatively; a variety of turnkey applications are available.
Ordering information All A D C 6 4 boards include: T M S 3 2 0 C 3 2 processor, 1 2 8 K W 0 w«lt-st«te S R A M , cither four or eight 2 0 0 k H z A / D j each with programmable gain (x 1,2,4,8), six-pole anti-alias filter with
jumperable on/off selection; two independent D / A channels each with smoothing filter; one sync serial port; three 16-bit timers; two 3 2-bit timers with bus mastering PCI host interface with FIFOs;
16-bit digital I/O
ADC6*. Board Options Basic board
80002-0 Basic A D C 6 4 board: 4 0 M H z processor; lour channels muxed 8:1 single-ended
Altemalm ADC64 board configurations
80002-1 A D C 6 4 with 6 0 M H z processor; eight channels muxed 8:1 single-ended
80002-7 A D C 6 4 with 6 0 M H z processor; four channels muxed 4:1 differential
80002-5 A D C 6 4 with 6 0 M H z processor; four channels muxed 8:1 single-ended
80002-6 A D C 6 4 with 6 0 M H z processor; eight channels muxed 4:1 differential
Peripherals 60011-1 SCSI 3X SCSI-2 adapter
80022-1 Screw-terminal breakout module & cable for high-density 100-pin analog I/O
connector
60011-3 3XPACK
Documentation 51001 A D C 6 4 M D C 6 4 hardware manual
51002 ADC64/cADC64 software manual
52001 Texas Instruments TMS320C3x User's Guide
52002 Code Composer software manual
52038 Digital Signal Processing with C and the TMS320C30 textbook with diskette by
Chaussing (details 'C3x signal processing techniques)
Software and Support 53002 Zuma Toolset for ADC64/cADC64
53020 Ventura DLL (or A D C 6 4 M D C 6 4
Hardware-assisted C/Assembler Source Level Debuggers 9 0 0 2 1 -1 Code Hammer with M P S D hardware/Code Composer software - for any "C3x-
based board
8 0 0 2 1 - 1 Code Hammer with M P S D hardware only - for any'C3x-based board
5 4 0 0 3 C o d e Composer software - lor any 'C3x or 'C4x-based board;
Development Package 90002-0 Development Package for ADC64. Indudes all of the following:
54001 Texas Instruments floating-point C compilation system for'C3x/''C4x
80002-1 ADC64 with 60 M H z processor; eight channels muxed 8:1 single-
ended
Screw-temvoal breakout module and cable for high-density 100-pin analog
I/O connector
ADC64/cADC64 hardware manual
ADC64/cADC64 software manual
Texas Instruments TMS320C3x User's Guide
Zuma Toolset for ADC64/cADC64
Code Hammer with MPSD hardware/Code Composer software - for any
C3x-based board
80022-1
51001
51002
52001
53002
90021-1
A Innovative *£& Integration te! (818) 865-6150
ADC64 Technical Specifications
Pnxesor
Men»ry
Flash M e m o r y
FIFO M e m o r y
Debug Port
Host PC Interface
| FIFO Memory
: Disltal I/O
j Timers/Counters
Serial Ports
Power Requirements
Connectors
Physicals
Compatible Add-on Cards Development Languages
Turnkey Software Packages
C/Assy Source Debugger Software Libraries
Texas Instruments T M S 3 2 0 C 3 2 32-bit floating-point DSP Smized instruction set (or DSP
-drip resources: 512 x 3 2 memory,- eight accunulators; hardware muH»Ger, barrel shifter; two D M A controllers; serial port; two 32-bit timers,- 16 prioritized interrupts; 64-word instruction cache DSP speed = 40 or 6 0 M H z
Zero wait-state; 1 28 K x 32
4 Mbit (512 K byte) on-board reprogrammable
I/O mapped on DSP
XDS-510 compatible MPSD port for emulation and scan path testing; Supports C/Assembly source level debugging with Code Hammer
PCI 32-bit; consumes 64 I/O locations, one interrupt
Auto-mappable into PC I/O space by PCI BIOS Supports bidirectional interrupt driven operation - one P C interrupt Multiple cards supported
16 bits TTL input or output, 64 mA sink/ 32 mA source
Two 32-bit timers in DSP clocked at DSP speed/4. Six 1 6-bit timers using independent 10 M H z timebase
One on DSP chip. On-chip: up to 15 Mbaud; 8, 16 or 3 2 formats; synchronous serial interrupt support
+ 5 V DC @ 1.1 A, -12 V @ 9 mA, +12 V @ 300 mA On-board 5W DC-DC converter with short protection for clean analog power, 10 W total power consumption
SCSI-2 100-pin female for analog and digital I/O; DIN 9 6 female for DSP expansion; 2-pin card-to-card synchronizing connectors, I D O 2 male for M P S D debugger port. IDC1 4 for serial port
Half-size PCI card; 7.6 in. long x 4.2 in. high; max component height .75 in. Temp range: 0-7 0 C
SCSI3X SCSI-2 interface; 3XPACK Industry feck adapter
C or Assembler using Tl cross-development tools. Peripheral libraries and Windows drivers via Zuma Toolset
Block-diagram DSP design: Hypersigna! Windows, DSPower, D A S Y U b and LoggerPCI
Code Hammer
Ventura, Zuma Toolset
A/D Converter 8 Channels
Resolution
Update Rate
Settling Time
Analog Input Range
S/H Ratio 88 dB
THD .90 dB
Dynamic Range 90 dB
Cain Error +/-5%
Differential +3/-2LSB Linearity Error Bipolar Zero Error Trimmable
Aperture Delay 40 ns
Aperture Jitter Meets A C specs
Programmable Gain PGA206: 1,2,4,8
Input Impedance 1 Mohm 11 3 PF
Analog Dev,ces, AD976. Each converter hasind. hltenng. Interrupt off conv. complete. Each A/D muxed either 4:1 differential or 8:1 single-ended
16-bit
200 kHz
5 us (no filtering) @ 10 V step settling to .0008%
+/-10 V, +7-2.5 V, 0-10 Y 0-5 V, +/-5 V
Filter Characteristics Conversion Timing Sources
6-pole filter, with user-specifiable roll off -3 dB at 100 kHz Filter may be disabled (Rev H and up)
Software sdect from one of six 16-bit counter/timer sources or DSP memory mapped access or external TTL source
M U X Characteristics D G 4 0 8 for 8:1 single-ended inputs; D G 4 0 9 for 4:1 differential inputs Switch time: 3 0 0 ns
System Scan Rate 64 channels: 25 kHz; 32 channels: 50 kHz; 8 channels: 2 0 0 kHz
D/A Converter
Resolution
Output Range
Slew Rate
Settling Time
Update Rate
S/N Ratio
THD
Bipolar Zero Error Differential Non-Linearity +/-1 LSB max D/A Glitch Impulse Impulse 15 V-ns
Temp Range 0-70 C
Filtering Output smoothing filter - single pole filter, 2 0 0 kHz rolloff (custom with cap/resistor change)
Interface to DSP Memory-mapped
Conversion Software select from one of six 1 6-bit counter/timer Timing Sources sources or DSP memory-mapped access or external
TTL source
Two channels two Burr-Brown D A C 712. Each D/ A channel has independent filtering
16-bit
0-5 V, +/-5V,+ 10 V
15 V/us
1 3 us (no filtering) @ 20 V step,- 2.5 us for 1 LSB step settling to .0008%
200 kHz
.0063% max
.009% max
able
Fig. 4 - ADC64 with 'C3S DSP, 64 channels I/O, ! channels D/A and PCI bus.
jot tel (818) 865-6150 • fax (818) 879-1770 • www.innovative-dsp.com
A\ Innovative Jk^k Integration
TOSHIBA
TOSHIBA INSULATED GATE BIPOLAR TRANSISTOR SILICON N-CHANNEL IGBT
GT8Q101 HIGH POWER SWITCHING APPLICATIONS
MOTOR CONTROL APPLICATIONS
GT8Q101
High Input Impedance
High Speed : tf =0.5/^8 (Max.)
Low Saturation Voltage : VcE(sat)=4-0V (Max.)
i Enhancement-Mode
MAXIMUM RATINGS (Ta = 25°C)
Gate-Emitter Voltage
CHARACTERISTIC
Collector-Emitter Voltage
Collector Current DC
lms
Collector Power Dissipation (Tc=25°C)
SYMBOL
VCES
VGES
ic ICP
PC
RATING
1200
±20
16
100
UNIT
W
Unit in mrp
15.9MAX i3.2+0.2
I
1. GATE 2. COLLECTOR (HEAT SINK) 3. EMITTER
JEDEC
Junction Temperature 150 EIAJ
Storage Temperature Range -55-150 TOSHIBA 2-16C1C
Weight : 4.6g
ELECTRICAL CHARACTERISTICS (Ta = 25°C)
CHARACTERISTIC
Gate Leakage Current
Collector Cut-off Current
Gate-Emitter Cutoff Voltage
Collector-Emitter
Saturation Voltage
Input Capacitance
Switching Time
Rise Time
Turn-on Time
Fall Time
Turn-off Time
SYMBOL
JGES
J-CES
VGE (OFF)
VCE (sat)
Cies
tr
ton
tf
toff
TEST CONDITION
VGE=±20V,VCE = 0
V C E = 1200V, VGE = 0
IC = 8mA, V C E = 5V
IC = 8A, V GE = 15V
V Q E = 10V, VQE=0, f = 1MHz
VOUT
15V r-i 150O | V" 0VJ |p <+ i
_ 1 5 V VCC = 600V
MTN.
—
—
3.0
—
—
—
—
—
—
TYP.
—
—
—
3.0
1100
0.3
0.4
0.3
0.8
MAX.
±500
1.0
6.0
4.0
—
0.6
0.8
0.5
1.5
UNIT
nA
mA V
V
PF
f*
961001EAA2
• TOSHIBA is continually workin, malfunction or fail due to their TOSHIBA prOdUCtS, tO Observe StanoarQS Ml -i' V, '-'<"' '" tfvuii) amoiiuii) in . • , ., .,_•- -r~ ..carl lA/i+hin tntw-ifiorl
of human life, bodily injury or damage to property. In developing, your designs, please ensure that TOSHIBA Pjodu* « • " « « wrth.n specified operating ranges as set forth in the most recent products specifications. Also, please keep in mind the precautions and conditions set tortn in the
• Wfo^^ on.y as a guide for the aPP^^V* r?^ CORPORATION for any infringements of intellectual property or other rights of the third parties A^ch
may result from its use. No license is granted . by implication or otherwise under any intellectual property or other rights of TOSHIBA CORPORATION or others. _* The information contained herein is subject to change without notice.
1997-02-03 1/3
TOSHIBA GT8Q101
lb
12
B
4
n
COMMON EMITTER Tc=25°C
ic -
~-20
^ 1 5
VCE
l
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T 1 t_Pc = 100W _sj
9
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COLLECTOR-EMITTER VOLTAGE VCE (V)
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COMMON EMITTER
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COMMON EMITTER
Te=125'C
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GATE-EMITTER VOLTAGE VQE 00
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GATE-EMITTER VOLTAGE VQE OO
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GATE-EMITTER VOLTAGE VGE OO
20
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GATE CHARGE QG (nQ
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1997-02-03 2/3
TOSHIBA GT8Q101
3
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0.3
0.1
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— H>
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SWITCHING TIME -
IT
' 1 |
- ic
COMMON EMITTER \ 'CC =6
= 16 00\
on,
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= i :15' V
SWITCHING TIME - RQ
5000 3000
1000
500
300
1 2 3 4 6 6 7
COLLECTOR CURRENT Ic (A)
C - VCE
t
COMMON EMITTE
VQE=O f=lMHz Tc=25°C
R
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V
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Co !S
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100
50
30
10
5 0.03 0.1 0.3 1 3 10 30 100
COLLECTOR-EMITTER VOLTAGE VQE 00
SAFE OPERATING AREA
30
10
5
3
1
0.5
0.3
01
58 SINGLE N O N R E P E T I T I V E P U L S E Tc=25''C
CURVES MUST BE DELATED LINEARLY WITH INCREASE IN TEMPERATURE.
.IC MAX.(PULSED)$8 ._
I -IC MAX.
(CONTINUOUS;
i N I nn -DC OPERAT7
uJJL III
' II
III
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2
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83
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BJ
8 Bi
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0.3
0.1
0.03
0.01 10
30
10
3
1
0.3
0.1
0.03
1 3 10 30 100 300 1000 3000
COLLECTOR-EMITTER VOLTAGE VCE OO
0.01
30 100 300 1000 3000
GATE RESISTANCE RQ (fl)
Rth(t) - tw
Tc = 25"<
r
10 - 3 10""1 1
PULSE WIDTH tv (s)
REVERSE BIAS SOA
10
Tj £ 125°C
VGE=±15V
RG=150fl
0 400 800 1200 1600 2000 2400
COLLECTOR-EMITTER VOLTAGE VyE OO
1997-02-03 3/3
philips Semiconductors
Rectifier d i o d e s fast, soft-recovery
Product specification
BY329 series
SYMBOL FEATURES
• Low forward volt drop • Fast switching •Soft recovery characteristic •High thermal cycling performance •Lowthermal resistance
GENERAL DESCRIPTION PINNING
Glass-passivated double diffused rectifier diodes featuring low forward voltage drop, fast reverse recovery and soft recovery characteristic. The devices are intended for use in T V receivers, monitors and switched m o d e power supplies. The BY329 series is supplied in the conventional leaded S O D 5 9 (TO220AC) package.
QUICK REFERENCE DATA
vR = = 800 V/1000 V/1200 V 'F(AV) = 8 A
•FSM 75 A
trr < 135 ns
SOD59 (TO220AC) PIN
1
2
tab
DESCRIPTION
cathode
anode
cathode
LIMITING VALUES Limiting values in accordance with the Absolute Maximum System (IEC 134).
SYMBOL
»RSM
*RRM VRWM
'F(AV)
'F(RMS)
'FRM
'FSM
ft
Ltg I
PARAMETER
Peak non-repetitive reverse voltage Peak repetitive reverse voltage Crest working reverse voltage
Average forward current1
R M S forward current Repetitive peak forward current
Non-repetitive peak forward current.
I2t for fusing Storage temperature
CONDITIONS
BY329
square wave; 8 = 0.5; Tmb<122°C sinusoidal; a = 1.57; Tmb<125'C
t = 25 us; 5 = 0.5; Tmb<122°C t= 10ms t = 8.3 ms sinusoidal; Tj= 150 °C prior to surge; with reapplied VRWMfmax)
t = 10 ms
MIN.
-
-
.
-
-
-
/in
Operating junction temperature I
MAX.
-800 800
800 600
-1000 1000
1000 800 8
7
11 16
75 82
28 1 0 mn
-1200 1200
1200 1000
UNIT
V
V V
A
A
A A
A A
A2s °C °C
1 Neglecting switching and reverse current losses.
Rev 1.200
philips Semiconductors Product specification
Rectifier diodes fast, soft-recovery
B Y 3 2 9 series
THERMAL RESISTANCES SYMBOL
"thj-mb
Rthj-a
PARAMETER
Thermal resistance junction to mounting base Thermal resistance junction to ambient
CONDITIONS
in free air.
MIN. TYP.
60
MAX.
2.0
UNIT
K/W
STATIC CHARACTERISTICS T, = 25 °C unless otherwise stated
SYMBOL
vF
PARAMETER
Forward voltage Reverse current
CONDITIONS
lF = 20 A VR = VRWM;TI=125"C
MIN.
-
TYP.
1.5 0.1
MAX.
1.85 1.0
UNIT
V mA
DYNAMIC CHARACTERISTICS T, = 25 "C unless otherwise stated
SYMBOL
trr
dlf/dt
PARAMETER
Reverse recovery time Reverse recovery charge Maximum slope of the reverse recovery current
CONDITIONS
lF = 1 A; VR > 30 V; ~dlF/dt = 50 A/us lF = 2 A; VR > 30 V; -dlF/dt = 20 A/us lF = 2 A; -dlp/dt = 20 A/us
MIN.
-
TYP.
100 0.5 50
MAX.
135 0.7 60
UNIT
ns uC A/us
2 Rev 1.200
Philips Semiconductors
Rectifier diodes fast, soft-recovery
Fig. 1. Definition of tm Qs and I, m **s « " " inm
20 -
m -
0 -
PF/ w _ ,1. . I.__ IVo=1iSV I ]Bs.0.03C Jhms I
O.I
1 O.z
0.5
Tmb(max) / C
"D=1.0"
H'-h o=\Y
1 —
' r h
u -H T fr- ,' r
1 1 1 1
110
120
130
140
150 12 0 2 4 6 8 10
IF(AV)/A
Fig.2. Maximum forward dissipation, PF = f(lF(AVJ; square wave current waveform; parameter D = duty . cycle = t/T.
Product specification
BY329 series
100
90
80
70
60
50
40
30
20
10
0
1FS
•V-
\
•
(RMS)/A
\
N
_.
]||
u -1 FSM-
4llt h h-
i
T j j j |
1 j j j |
1ms 10ms 0.1s tp/s
1s 10s
Fig.4. Maximum non-repetitive rms forward current. 'F = typ); sinusoidal current waveform; Tj = 150°Cprior
to surge with reapplied VRWM.
20 -
10 -
IF/A
..Ll.Ll.LLU _ 1=150C ! -i _ OR r. 1
typ /
y
i i
; /
' /"
I _ J
i _t
L -L 1 I I Z - it
tj /1 max
77 /
~l i 7 r
\
0 0.5 1 1.5 2 VF/V
Fig.5. Typical and maximum forward characteristic; lF = f(VF); parameter 7,
IE -
10 -
5 -
C
Fig.3. sinus
P F / W Tmb(max)/C
|
£s = 0.03 Ohms L
4
/
/ t 4?
2
r
2
B /
///
I
1.9 d 2 / . / / i/
1 57
) 2 4 6 i IF(AV)/A
Maximum forward dissipation, PF = f( oidal current waveform; parameter a =
factor = IF(RMS/IF(AV)-
120
130
140
150 1
WW' form
10 Qs/uC
0.1
J jjj = 25 C
r
u-- '
^ **" -i
*==—
./
•1
^
" T
-•-'""
-2-4=-
— • * • * »—=
i |-
I F=1C; ufT
10
— r -_ 1_
— 2 -~ 1
A
rr A A
# 14-A
100 10 -dIF/dt (A/us)
F/0.6. Maximum Qs at T,=25°C and 150°C
Rev 1.200
philips Semiconductors Product specification
Rectifier diodes fast, soft-recovery
B Y 3 2 9 series
10O0 trr / ns
100
10
—= > * * c ^
- ^ 0 ~
[Tj = 1 5 0 C —
--*-*::
—
" 1 1 II
'-- ' — •
"^•s|
F = 1 ) A' ---31 • JQb -. "dt < &
10 -dIF/dt (A/us)
100
Fig.7. Maximum t„ measured to 25% of lrrm; Tl = 25°C and 150'C
10
1
0.1
0.01
0.001 1
Fig.S
Transient thermal impedance, Zth j-
lm
m 4™ i iii
i ii T
J i
mil
mb(KAV)
~TTT —
Ein H i - h *~*
1. H. j tr l T
mm 4|||
JS 10us 100us 1ms 10ms 100ms 1s 10s pulse width, tp (s)
. Transient thermal impedance Zlh = f(tp)
100 -1
10 -
1 -
Fig.8. Ty
Cd/ PF
picaljunc
i
--iii
TrUI —U4-"
^ -
10 VR/V 10° 10°°
)tion capacitance Cdatf=1 MHz. Tj = 25°C
September ertsaa. Rev 1.200
APPENDIX F F-l
APPENDIX F
Control Simulation Source Files
The stator current controller simulation files axe:
Fl: Stator Current Controller Simulation
F1.1 Speed Controller Sub-System
Fl .2 Generate Stator Current Reference Sub-System
F1.3 Calculate Rotor Voltage Vector Sub-System
Fl .4 Calculate Current Vector Sub-System
Fl .5 Calculate Torque Sub-System
F1.6 Calculate Speed Sub-System
F1.7 Calculate Position Sub-System
F1.8 Phase Current Calculation Sub-System
The transformed frame vector controller simulation files are:
F2: Transformed Frame Vector Controller Simulation
F2.1 Speed Controller Sub-System (identical to Fl. 1)
F2.2 Generate Current Vector Reference Sub-System
F2.3 Calculate Ideal Rotor Voltage Vector Sub-System
F2.4 Select Optimal Voltage Vector Sub-System
F2.4.a Select from 512 voltage vectors, no scaling
F2.4.b Select from 512 voltage vectors with scaling
F2.4.C Select from 20° sector with scaling
F2.5 Calculate Rotor Voltage Vector Sub-System (identical to Fl.3)
F2.6 Calculate Current Vector Sub-System (identical to Fl .4)
F2.7 Calculate Torque Sub-System (identical to Fl .5)
F2.8 Calculate Speed Sub-System (identical to F1.6)
F2.9 Calculate Position Sub-System (identical to Fl.7)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% F2.4.a Select from 512 voltage vectors, no scaling % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function out = mwsel(in)
global v s scale;
vid = repmat(in1,512,1); err = diag((v-vid)*(v-vid)'); serr = [s err]; sortserr = sortrows(serr,10); out - (sortserr(1:1,1:9))';
% % F2.4.b Select from 512 voltage vectors, with scaling
function out = mwsel(in)
global v s scale;
vid = repmat(in1,512,1); err = diag(((v-vid)*scale)*(v-vid)'); serr = [s err]; sortserr = sortrows(serr,10) ;
out = (sortserr(1:1,1:9))';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
% F2.4.C Select from 20 degree sector, with scaling % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function out = mwselb(in)
global v2 0 s20 scale;
[thl rl] = cart2pol(in(l), in(2)) [th3 r3] = cart2pol(in(3), in(4)) [th5 r5] = cart2pol(in(5), in(6)) [th7 rl] = cart2pol(in{7), in(8))
segment = floor(thl*9/pi);
[svdl, svgl] = pol2cart(thl - segment*pi/9, rl); [svd3, svq3] = pol2cart(th3 - 3*segment*pi/9, r3) ; [svd5, svq5] = pol2cart(th5 - 5*segment*pi/9, r5); [svd7, svq7] = pol2cart(th7 - 7*segment*pi/9, r7) ;
sv = [svdl svql svd3 svq3 svd5 svq5 svd7 svq7 0] ;
vid = repmat(sv,52,1); err = diag(((v20-vid)*scale)* (v20-vid) ' ) ; serr = [s20 err]; sortserr = sortrows(serr, 10) ; swtch = (sortserr(1:1,1:9));
if segment == 0 swtch2 = swtch;
elseif segment > 0 swtch2 = [swtch(10-segment:9) swtch(l:9-segment) ] ;
else swtch2 = [swtch(l-segment:9) swtch(1:-segment)];
end
if round(segment/2)~=(segment12) out = ~swtch2';
else out = swtch2';
end
APPENDIX G G-l
APPENDIX G
Derivation of Quadrature Axis Reluctance
Consider Figure 2.1.
The air-gap reluctance, between a tooth tip and the ends of the rotor laminations, is given
by,
*,=-i- (G-l)
The distance, /;, is the effective air-gap.
h = Se ^
where, ge = effective air-gap (m)
The area, A;, is the portion of the tooth face available for zigzag flux.
27iR,
iy slot
(G-3)
where, Ls = stator length (m)
Rs = stator inner radius (m)
Nsiot = number of stator slots
tml = thickness factor (non-dimensional parameter accounting
for proportion of tooth face that presents a path for
zigzag flux).
Thus, the air-gap reluctance can be calculated to be,
R Se^slo, (G-4) 1 ju,Ls27iRstml
APPENDIX G G-2
The reluctance of the steel / fibre laminations is given by,
*2=i; (G-5) The effective distance, l2, is approximated as half of one "tooth + slot" pitch multiplied by
the ratio of fibre in the rotor.
, 27rRs 1 ^ 2 - T T ^ X - X ^ (G-6)
^ slot *•
where, tri = ratio of fibre : fibre + iron in the rotor
The area, A2, is the average cross-sectional area of the rotor. (Note the rotor radius and
length have been approximated as equal to the stator dimensions. Further, the "width" is
the averaged value over the full rotor pole pitch.)
4 = ^ x 1 . 6 ^ (G-7)
Thus, the reluctance through the rotor can be calculated as,
R ^h. (G-8) ju0Nslot1.6RsLs
The effective quadrature reluctance / metre is now found by,
_(2x(2/?1)||i?2)/ 2itRs
Nslot
Se^slotKl (G-9)
MoiSeNiA-eRA+^Rs^tmO