Modelling and Field-Oriented Control of a Synchronous Reluctance

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2001

Modelling and field-oriented control of asynchronous reluctance motor with rectangularstator current excitationColin CoatesUniversity of Wollongong

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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

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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 îsotropic 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


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


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


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.


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.


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


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


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).


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)


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.


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


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


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


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


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


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.


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;


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,


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


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.


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.


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.


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


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 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


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)


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.


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


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


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.


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.


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


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.


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.


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,


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


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


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


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,


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.


(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


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


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,


îl'

"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$

Sâ-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

CêHQSj

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


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)


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


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


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)


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.


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.


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.


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


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


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.


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


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


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


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.


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


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


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, vâi, 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, vîs) - vâ/. 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;


(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.


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.


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.


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)


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).


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

Wî,î.iL..î 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)


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

.ttyûiMiiyVlUi 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


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.


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


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 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.


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.


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 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 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.


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.


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.


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


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.


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;


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


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.


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


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.


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.


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


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.


(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

3 Xi

a.

75 -

70

65

60-1

55

0.9


(a)

(b)

(c)

Figure 7.6 Phase current waveforms (a) co = 80rpm, (b) co = 200rpm and (c) co = 345rpm

(inverter bus voltage = 250V)


Figure 7.7 Phase current waveform detail versus position for (a) co = 80rpm, (b) co - 200rpm

and (c) co = 345rpm (inverter bus voltage = 250V)


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.


(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.


(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.


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 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


(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


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

REFERENCES

[1] RE Betz, "Control of Synchronous Reluctance Machines", Proceedings of IEEE-IAS

Annual Meeting, Detroit, pages 456-462, September 1991.

[2] R E Betz, "Theoretical Aspects of Control of Synchronous Reluctance Machines", IEE

Proceedings - B, Volume 139, Number 4, pages 355 - 364, July 1992.

[3] I Boldea and SA Nasar, "Emerging Electric Machines with Axially Laminated Anistropic

Rotors: A Review", Electric Machines and Power Systems, Volume 19, pages 673-703,

1991.

[4] I Boldea, Z X Fu and S A Nasar, "Performance Evaluation of Axially - Laminated

Anistropic (ALA) Rotor Reluctance Synchronous Motors", IEEE Transactions on

Industry Applications, Volume 30, Number 4, pages 977-985, July / August 1994.

[5] TJ Busch, JD Law and T A Lipo, "Magnetic Circuit Modelling of the Field Regulated

Reluctance Machine Part II: Saturation Modelling and Results", IEEE Transactions on

Energy Conversion, Volume 11, Number 1, pages 56-61,1996.

[6] BJ Chalmers and A S Mulki, "New Reluctance Motors With Unlaminated Rotors",

Proceedings IEE, Volume 117, Number 12; pages 2271-2272, 1970.

[7] BJ Chalmers and A S Mulki, "Design and Performance of Reluctance Motors with

Unlaminated Structures", IEEE Transactions on Power Apparatus and Systems, Volume

91, pages 1562-1569,1972.

[8] BJ Chalmers and L Musaba, "Design and Field-Weakening Performance of a

Synchronous Reluctance Motor with Axially Laminated Rotor", Proceedings of IEEE

IAS Annual Meeting, pages 271-278, October 1997.

[9] PP Ciufo, D Piatt and BSP Perera, "Magnetic Circuit Modelling of a Synchronous

Reluctance Motor", Australian Universities Power Engineering Conference 1994,

Adelaide, Volume 1, pages 37-42.

[10] PP Ciufo, D Piatt and BSP Perera, "Magnetic Circuit of a Synchronous Reluctance

Motor", Electric Machines and Power Systems, Volume 27, Number 3, pages 253-270,

1999.

[11] A J O Cruickshank, R W Menzies and A F Anderson, "Axially Laminated Anistropic

Rotors for Reluctance Motors", Proceedings of IEE, Volume 113, Number 12, pages

2058-2060, 1966.

References i 129

[12] AJO Cruickshank, A F Anderson and R W Menzies, "Theory and Performance of

Reluctance Motors with Axially Laminated Anistropic Rotors", Proceedings of IEE,

Volume 118, Number 7, pages 887-894,1971.

[13] W Fong, "Change-Speed Reluctance Motors", "Proceedings IEE, Volume 114, Number6,

pages 797-801,1967.

[14] W Fong and JSC Htsui, "A N e w Type of Reluctance Motor", Proceedings IEE, Volume

117, Number 3, pages 545-551,1970.

[15] A Fratta, A Vagati and F Villata, "Control of a Reluctance Synchronous Motor for

Spindle Applications", IPEC Japan 1990.

[16] A Fratta, G P Troglia, A Vagati and F Villata, "Evaluation of Torque Ripple in High

Performance Synchronous Reluctance Machines", Proceedings of IEEE Industry

Applications Society Annual Meeting, Volume 1, pages 163-170,1993.

[17] C L Gu, L R Li, K R Shao and Y Q Xiang, "Anistropic Finite Element Computation of High

Density Axially-Laminated Rotor Reluctance Machine", IEEE Transactions on

Magnetics, Volume 30, Number 5, pages 3679-3682, September 1994.

[18] M R Harris and TJE Miller, "Comparison of Design and Performance Parameters in

Switched Reluctance and Induction Motors", Fourth International Conference on

Electrical Machines and Drives, pages 303-307, 1989.

[19] V B Honsinger, 'The Inductance Ld and Lq of Reluctance Machines", IEEE Transactions

on Power Apparatus and Systems, Volume 90, pages 298-304, 1971.

[20] V B Honsinger, "Steady-State Performance of Reluctance Machines", IEEE Transactions

on Power Apparatus an Systems, Volume 90, pages 305-317, 1971.

[21] V B Honsinger, "Inherently Stable Reluctance Motors Having Improved Performance",

IEEE Transactions on Power Apparatus and Systems, Volume 91, pages 1544-1554,

1972.

[22] JS Hsu (Htsui), SP Liou and H H Woodson, "Peaked-MMF Smooth-Torque Reluctance

Motors", IEEE Transactions on Energy Conversion, Volume 5, Number 1, pages 104-

109, March 1990.

[23] JS Hsu (Htsui), SP Liou and H H Woodson, "Comparison of the Nature of Torque

Production in Reluctance and Induction Motors", IEEE Transactions on Energy

Conversion, Volume 5, Number 2, pages 304-309,1990.

[24] Innovative Integration "ADC64 Hardware Manual" First Edition 1994.

References 130

[25] M J Kamper and A F Volschenk, "Effect of Rotor Dimensions and Cross Magnetisation on

Ld and Lq Inductances of Reluctance Synchronous Machines with Cageless Flux Barrier

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.

References 131

[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.

[43] R W Menzies, R M Mathur and H W Lee, 'Theory and Operation of Reluctance Motors

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.

[45] TJE Miller, "Brushless Permanent-Magnet and Reluctance Motor Drives", Oxford

University Press, 1989.

[46] A L Mohamadein, Y H A Rahim and A S Al-Khalaf, "Steady-state performance of self-

excited reluctance generators", IEE Proceedings, Part B, Volume 137, Number 5, pages

293-298,1990.

[47] E L Owen, "Evolution of Induction Motors - the Ever Shrinking Motor", IEEE Industry

Applications Magazine, Volume 3, Number 1, pages 16-18, January / February 1997.

[48] D, Piatt, "Reluctance Motor with Strong Rotor Anistropy", IEEE Transactions on

Industry Applications, Volume 28, Number 3, pages 652-658,1992.

[49] H Ramamoorty and PJ Rao, "Optimisation of Polyphase Segmented Rotor Reluctance

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

Rotors", IEEE Transactions on Power Apparatus and Systems, Volume 95, pages 1369-

1376,1976.

References 132

[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

Savings for Industry", U S Department of Energy, Motor Challenge Program, 1993.

[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.

[54] C Studer, A Keyhani, T Sebastion and SK Murphy, "Study of Cogging Torque in

Permanent Magnet Machines", IEEE Industry Applications Society 32nd Annual Meeting,

Volume 1, pages 42-49,1997.

[55] Texas instruments 'TMS320C3X User's Guide", Literature number SPRU031E, July

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

Reluctance Machine Including Third Harmonic of Air-Gap M M F ' Conference Record of

the 1991 IEEE Industry Applications Society Annual Meeting Volume 1 pages 231-237.

[58] H A Toliyat, M M Rahimian and T A Lipo, "Analysis and Modelling of Five Phase

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 ^StîHSHi 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

http://www.innovative-dsp.com_

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

http://www.innovative-dsp.com

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

\ S • 5

T 1 t_Pc = 100W _sj

9

8

1 1 VGE=7V

s. v.

0 2 4 6 8 10

COLLECTOR-EMITTER VOLTAGE VCE (V)

CO

u >

I OS Ed

2 Ed

oi

o Ed -J

J O o

16

12

VCE - VQE COMMON EMITTER

Tc= -40"C

\

VlC=16A \ 8 V

4 8 12 16 20

GATE-EMITTER VOLTAGE VQE (V)

>

0

>

16

12

8

4

1)

VCE

COMMON EMITTER

Tc=25"C

OH - 4 ^

VGE

-8 ic= 16A

Ed

>

Ed

I O > ti Ed s Ed

oi O H

o

s o o

12

8

4

n

VCE -

COMMON EMITTER

Te=125'C

1 \ 8

4

VGE

ic= 16A

4 8 12 16 20

GATE-EMITTER VOLTAGE VQE 00

4 8 12 16 20

GATE-EMITTER VOLTAGE VQE OO

$ 0

16

12

8

4

n —*:

Tc=

ic -

19K»f

25s( -4C

^ fc

j

A

A •1 1

1

VGE

H-t

COMMON EMITTER

V( :E=6 V

C 800 VCE, VQE - QG

4 8 12 16

GATE-EMITTER VOLTAGE VGE OO

20

Ed O

> a

§ o > Bi Ed 2

I o o

a o o

600

400

200

20 40 60 80

GATE CHARGE QG (nQ

Ed

O > Ed U

O > Ed

2

Ed

5

1997-02-03 2/3

TOSHIBA GT8Q101

3

1

0.5

0.3

0.1

0,05

— H>

tf

*M

SWITCHING TIME -

IT

' 1 |

- ic

COMMON EMITTER \ 'CC =6

= 16 00\

on,

r,v Tc GG = 2.

= 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

1

c

V

ies

Co !S

r

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

OJ l--\

-jji

"TTT LOO/ia^

: 1ms X

lllllll 50/i

\

•BX

I Ed

2

B o z £

83

10

8

5 o

BJ

8 Bi

o

o u

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


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


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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C o *-< CO o °-

O CO ii> OJ >

n m 4—"

CO cu 1 U O rt O

L.

O CJ C1J > CU nj rt +2 o >

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% 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

Documents

Modelling and Field-Oriented Control of a Synchronous Reluctance