DIRECT CONTROLLED INDUCTION MACHINES FOR INTEGRATED / SYSTEM

Jun Zhang

A thesis submitted for the degree of Doctor of Philosophy

School of Electrical Engineering and Telecommunications The University of New South Wales

August 2006 CERTIFICATE OF ORIGINALITY

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.

Signed …………………………….

Jun Zhang

ii

Dedicated to the memory of my grandmother

iii ACKNOWLEDGMENTS

I would like to express my sincere acknowledgments to my supervisor, Professor M. Fazlur Rahman, for his guidance and support during my PhD study. I would also like to sincerely thank Professor Yuwen Hu for his kind help and encouragement during my study.

I thank all my colleagues of the Energy Systems Research Group in the School of Electrical Engineering and Telecommunications at University of New South Wales. Special thanks are given to Dr. Lixin Tang and Dr. Zhuang Xu for their valuable suggestions and help for my research.

I would like to express my deepest appreciation to my wife, my parents, my parents in law and my younger brother for their love, patience and support.

iv ABSTRACT

An integrated starter/alternator (ISA) has been proposed for the future 42 V PowerNet, which combines both starter and alternator functions into a single electrical machine with bidirectional power flow ability. This thesis presents analysis, design, modeling and experimental results of the direct torque controlled ISA system based on a low induction machine.

The classical direct torque controlled ISA based on switching-table is systematically for an ISA evaluated in this thesis. The simulation and experimental results show that the (DTC) concept can be successfully extended to the ISA application.

An improved DTC of the ISA based on direct flux vector is presented to reduce the drawbacks of high torque and flux ripples of the classical DTC. Robust design of the controller ensures the system is not sensitive to the variation of resistance. By controlling the electromagnetic torque of the induction machine quickly, the required dc bus voltage can be well regulated within the 42 V PowerNet specifications. Another improved DTC of the ISA with direct torque and flux control is also studied. Compared to the direct flux scheme, the calculation of the commanded voltage vector in this scheme only requires the derivative of the stator flux magnitude, which is a dc quantity. In addition, both torque and flux are regulated directly with two independent closed-loops. This scheme is relatively insensitive to the noise.

The thesis proposed compensation methods to reduce the effects of switch voltage drops and dead-time on the estimation of the stator flux. Experimental results confirm that the estimation error is reduced with compensation for both motoring and generating modes of the ISA.

A closed-loop type of sliding mode flux observer is proposed to reduce the estimation error of the stator flux. Both Simulation and experimental results confirm that the proposed sliding mode observer is insensitive to the stator resistance variation and sensor offsets.

v A loss minimized scheme with power factor control for the ISA is proposed in this thesis. It provides a simple solution for the efficiency improvement of the induction machine without requiring any speed or load information.

The effectiveness of the direct torque controlled induction machine for an integrated starter/alternator system has thus been confirmed and well supported by the studies presented in this thesis.

vi CONTENTS

CERTIFICATE OF ORIGINALITY...... II

ACKNOWLEDGMENTS ...... IV

ABSTRACT ...... V

CONTENTS ...... VII

LIST OF FIGURES ...... XI

LIST OF TABLES ...... XVI

LIST OF SYMBOLS...... XVII

CHAPTER 1 INTRODUCTION...... 1

1.1 42-VOLT POWERNET ...... 1 1.2 INTEGRATED STARTER ALTERNATOR - ISA...... 5 1.2.1 Electrical specification ...... 7 1.2.2 Machine technologies ...... 8 1.2.3 Electrical System configuration and Power converter topology...... 13 1.2.4 Machine controller- control of generator ...... 17 1.3 SCOPE OF THE THESIS...... 20 1.4 OUTLINE OF THE THESIS...... 21

CHAPTER 2 AN INDUCTION MACHINE BASED INTEGRATED STARTER/ALTERNATOR USING ROTOR FIELD ORIENTED CONTROL WITH SPACE VECTOR MODULATION...... 22

2.1 INTRODUCTION ...... 22 2.2 INDUCTION MACHINE MODEL...... 22 2.3 ROTOR FLUX ORIENTED CONTROLLED ISA ...... 24 2.4 EXPERIMENTAL SETUP ...... 27 2.5 EXPERIMENTAL RESULTS ...... 28 2.5.1 Starting mode...... 28 2.5.2 Generating mode - steady state...... 31 2.5.3 Generating mode - dynamic response...... 32 2.5.4 High speed operation...... 39 2.6 CONCLUSION ...... 39

vii CHAPTER 3 CLASSICAL DIRECT TORQUE CONTROLLED INTEGRATED STARTER/ALTERNATOR...... 41

3.1 INTRODUCTION ...... 41 3.2 CLASSICAL DIRECT TORQUE CONTROL PRINCIPLE ...... 42 3.3 ISA WITH CLASSICAL DTC ...... 45 3.4 SIMULATION RESULTS...... 46 3.4.1 Starting mode...... 47 3.4.2 Generating mode- steady state...... 48 3.4.3 Generating mode - dynamic response...... 50 3.5 EXPERIMENTAL RESULTS ...... 53 3.5.1 DTC-ST with constant switching frequency...... 53 3.5.2 Generating mode- steady state...... 54 3.6 CONCLUSION ...... 56

CHAPTER 4 DIRECT FLUX VECTOR CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SPACE VECTOR MODULATION ...... 57

4.1 INTRODUCTION ...... 57 4.2 DIRECT FLUX VECTOR CONTROL ...... 58 4.2.1 Direct flux vector control scheme ...... 62 4.2.2 Design of the PI controller for torque regulation ...... 64 4.2.3 Design of the PI controller with control delay...... 66 4.2.4 Modeling results...... 71 4.2.5 Experimental results ...... 80 4.3 DIRECT FLUX VECTOR CONTROLLED INDUCTION GENERATOR FOR AN ISA...... 85 4.3.1 Induction generator with DFC...... 85 4.3.2 Experimental results ...... 88 4.4 CONCLUSION ...... 94

CHAPTER 5 DIRECT TORQUE AND FLUX CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SPACE VECTOR MODULATION ...... 96

5.1 INTRODUCTION ...... 96 5.2 DIRECT TORQUE AND FLUX CONTROL PRINCIPLE ...... 97 5.3 DIRECT TORQUE AND FLUX CONTROLLED INDUCTION GENERATOR FOR AN ISA...... 101 5.4 EXPERIMENTAL RESULTS ...... 102 5.4.1 Starting mode...... 102 5.4.2 Generating mode - steady state...... 104 5.4.3 Generating mode - dynamic response...... 105 5.4.4 Performance High speed operation ...... 108 5.5 CONCLUSION ...... 109

viii CHAPTER 6 NON-LINEAR BEHAVIOUR OF THE DC-AC CONVERTER AND ITS COMPENSATION...... 110

6.1 INTRODUCTION ...... 110 6.2 EFFECT OF DEAD-TIME ...... 111 6.3 EFFECT OF VOLTAGE DROP ON THE POWER DEVICE...... 115 6.4 COMPENSATION ALGORITHM ...... 117 6.4.1 Backward compensation ...... 117 6.4.2 Forward compensation ...... 118 6.5 EXPERIMENTAL RESULTS ...... 119 6.5.1 Motoring mode...... 119 6.5.2 Generating mode...... 130 6.6 CONCLUSION ...... 134

CHAPTER 7 AN IMPROVED STATOR FLUX ESTIMATION OF DIRECT TORQUE CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SLIDING MODE OBSERVER ...... 136

7.1 INTRODUCTION ...... 136 7.2 DYNAMIC MODEL OF INDUCTION MACHINES ...... 137 7.3 SLIDING MODE STATOR FLUX OBSERVER...... 139 7.4 SIMULATION RESULTS ...... 142 7.5 EXPERIMENTAL RESULTS ...... 146 7.5.1 Stator flux and torque estimation in motoring mode...... 146 7.5.2 Stator flux and torque estimation in generating mode ...... 153 7.6 CONCLUSION ...... 158

CHAPTER 8 EFFICIENCY IMPROVEMENT FOR INTEGRATED STARTER/ALTERNATOR WITH POWER FACTOR CONTROL...... 159

8.1 INTRODUCTION ...... 159 8.2 INDUCTION MACHINE LOSS MODEL ...... 160 8.3 PRINCIPLE OF POWER FACTOR CONTROL...... 161 8.4 MODELING RESULTS...... 163 8.5 EXPERIMENTAL RESULTS ...... 166 8.5.1 Motoring mode...... 167 8.5.2 Generating mode...... 168 8.6 CONCLUSION ...... 169

CHAPTER 9 CONCLUSIONS ...... 170

9.1 SUGGESTIONS FOR FUTURE WORK...... 175 9.1.1 Machine ...... 175 9.1.2 Power converter...... 176

ix 9.1.3 Direct torque controlled ISA based on permanent synchronous machine...... 176

REFERENCES ...... 177

APPENDIX A LIST OF PUBLICATIONS...... 187

APPENDIX B MODELLING OF THE DIRECT FLUX VECTOR CONTROL ...... 189

APPENDIX C MODELLING OF THE DIRECT TORQUE AND FLUX CONTROL ...... 197

x LIST OF FIGURES

FIG. 1.1 ELECTRICAL AND ELECTRICS COMPONENTS IN AUTOMOBILES [2, 3] ...... 1 FIG. 1.2 MORE EXTENSIVE ELECTRONICS IN MODERN VEHICLES [4] ...... 2 FIG. 1.3 GENERATOR PEAK POWER DEMAND OF AVERAGE PASSENGER VEHICLE [9] ...... 3 FIG. 1.4 VOLTAGE REGULATION OF 42 V ELECTRICAL SYSTEM [13] ...... 3 FIG. 1.5 CONVENTIONAL 14V DC DISTRIBUTION SYSTEM ARCHITECTURE [1] ...... 4 FIG. 1.6 ADVANCED MULTIPLEXED AUTOMOTIVE POWER SYSTEM ARCHITECTURES OF THE FUTURE WITH

POWER AND COMMUNICATION BUSES [1] ...... 4 FIG. 1.7 CRANKSHAFT MOUNTED STARTER ALTERNATOR [34]...... 5 FIG. 1.8 STARTING WITH ISA AND DC MOTOR [8] ...... 6 FIG. 1.9 STARTER/ALTERNATOR STARTING AND APPROXIMATE GENERATING TORQUE REQUIREMENT (*)

AND THE TORQUE/SPEED CHARACTERISTIC (LINE) [15]...... 7 FIG. 1.10 DC BUS VOLTAGE DYNAMIC REQUIREMENT [6] ...... 8 FIG. 1.11 ROTOR STRUCTURE OF IPM MOTORS ...... 10 FIG. 1.12 COST COMPARISON OF THREE MACHINE SYSTEMS FOR A 6KW DIRECT-DRIVE

STARTER/ALTERNATOR APPLICATION [15] ...... 12 FIG. 1.13 HIGH VOLTAGE BUS CONFIGURATION ...... 14 FIG. 1.14 HIGH VOLTAGE BUS CONFIGURATION WITH ULTRACAPACITOR...... 14 FIG. 1.15 BLOCK DIAGRAM OF THE OVERALL SUPERVISORY CONTROL SCHEME [60] ...... 15 FIG. 1.16 DUAL VOLTAGE (14V AND 42V) AUTOMOTIVE ELECTRICAL SYSTEM [59]...... 16 FIG. 1.17 PROPOSED ISA ELECTRICAL SYSTEM CONFIGURATION ...... 16 FIG. 1.18 DTC OF ...... 18 FIG. 1.19 DTC OF INDUCTION GENERATOR ...... 19

ee e e FIG. 2.1 DYNAMIC dq− EQUIVALENT CIRCUITS OF MACHINE (A) q AXIS CIRCUIT, (B) d AXIS

CIRCUIT...... 24 FIG. 2.2 ROTOR FLUX ORIENTED CONTROLLED ISA WITH SVM...... 25 FIG. 2.3 FLUX MODEL IN THE ROTOR-FLUX-ORIENTED REFERENCE FRAME [75]...... 26 FIG. 2.4 VECTOR DIAGRAM OF THE INDUCTION MACHINE ...... 26 FIG. 2.5 EXPERIMENTAL SETUP ...... 28

e e FIG. 2.6 STARTING OF ISA WITH RFOC: (A) TORQUE, SPEED AND STATOR FLUX (B) TORQUE id AND iq 30

FIG. 2.7 ISA GENERATING WITH FULL LOAD ...... 31 FIG. 2.8 SPECTRUM ANALYSIS OF THE STATOR CURRENT OF ISA WHILE OPERATING AS GENERATOR IN THE STEADY-STATE...... 32

FIG. 2.9 LOAD DUMP OF ISA WITHOUT BATTERY CONNECTED: (A) BUS VOLTAGE, TORQUE, STATOR FLUX

e e AND STATOR CURRENT (B) TORQUE, id AND iq ...... 34

xi FIG. 2.10 LOAD DUMP OF ISA WITH BATTERY CONNECTED: (A) BUS VOLTAGE, TORQUE, STATOR FLUX AND

e e STATOR CURRENT (B) TORQUE, id AND iq ...... 35

FIG. 2.11 ISA PERFORMANCE AT ACCELERATION: (A) BUS VOLTAGE, SPEED, STATOR FLUX AND STATOR

e e CURRENT (B) SPEED, id AND iq ...... 37

FIG. 2.12 ISA PERFORMANCE AT DECELERATION: (A) BUS VOLTAGE, SPEED, STATOR FLUX AND STATOR

e e CURRENT (B) SPEED, id AND iq ...... 38

FIG. 2.13 ISA WITH FIELD WEAKENING AT HIGH SPEED...... 39 FIG. 3.1 EIGHT SWITCHING STATES AND THE VOLTAGE SPACE VECTORS ...... 43 FIG. 3.2 MOVEMENT OF STATOR FLUX VECTOR BY SELECTION DIFFERENT VOLTAGE SPACE VECTORS ...... 43 FIG. 3.3 STRUCTURE OF CLASSICAL DIRECT TORQUE CONTROL...... 44 FIG. 3.4 STATOR AND ROTOR FLUX VECTOR AT MOTORING AND GENERATION STATES ...... 45 FIG. 3.5 CLASSIC DTC SCHEME FOR ISA ...... 46

FIG. 3.6 STARTING PROCESS OF ISA (A) TS =150 μs (B) TS =50 μs ...... 48

FIG. 3.7 ISA GENERATING WITH FULL LOAD (A) TS =150 μs (B) TS =50 μs ...... 49

FIG. 3.8 SPECTRUM ANALYSIS OF THE STATOR CURRENT WITH FFT (A) TS =150 μs (B) TS =50 μs ...... 50

FIG. 3.9 LOAD DUMPING PERFORMANCE OF ISA (A) TS =150 μs (B) TS =50 μs ...... 51

FIG. 3.10 ISA PERFORMANCE AT SPEED RAMP (TS =50 μs ) (A) ACCELERATING (B) DECELERATION ...... 53

FIG. 3.11 ANALOG (A) AND DISCRETE (B) HYSTERESIS COMPARATOR [64]...... 54 FIG. 3.12 ISA GENERATING WITH DTC-ST ...... 55 FIG. 3.13 STATOR FLUX VECTOR DIAGRAM ...... 55 FIG. 4.1 EQUIVALENT SYSTEM MODEL OF THE TORQUE LOOP...... 62 FIG.4.2 PI CONTROL OF THE EQUIVALENT SYSTEM...... 62 FIG.4.3 DIRECT FLUX VECTOR CONTROL SCHEME FOR INDUCTION MACHINE ...... 64 FIG.4.4 PI CONTROL OF EQUIVALENT SYSTEM WITH PRE-FILTER...... 66 FIG.4.5 PI CONTROL OF EQUIVALENT TORQUE LOOP ...... 67 FIG.4.6 PI CONTROL OF EQUIVALENT SYSTEM WITH PRE-FILTER...... 71 FIG.4.7 TORQUE DYNAMIC PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH ROTOR RESISTANCE VARIATION OF 50% AND 100% ...... 72 FIG.4.8 PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH SPEED LOOP ...... 73 FIG.4.9 TORQUE DYNAMIC PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH AND WITHOUT PRE- FILTER...... 75 FIG.4.10 TORQUE DYNAMIC PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH ROTOR RESISTANCE

VARIATION OF 50% AND 100% (PRE-FILTER ADDED) ...... 75 FIG.4.11 PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH SPEED LOOP – NO PRE-FILTER ADDED.. 76 FIG.4.12 PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH SPEED LOOP –PRE-FILTER ADDED...... 77 FIG.4.13 TORQUE DYNAMIC RESPONSE OF RFOC ...... 78 FIG.4.14 ROTOR FLUX ORIENTED CONTROL SCHEME WITH SVM ...... 78

xii FIG.4.15 TORQUE DYNAMIC PERFORMANCE OF ROTOR FLUX ORIENTED CONTROL WITH VARIED ROTOR RESISTANCE ...... 79 FIG. 4.16 THE EXPERIMENT SETUP OF THE SYSTEM ...... 80 FIG.4.17 TORQUE DYNAMIC PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH DIRECT SYNTHESIS OF

PI CONTROLLER ...... 80 FIG.4.18 PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH SPEED LOOP ...... 81 FIG.4.19 TORQUE DYNAMIC PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH PRE-FILTER ...... 81 FIG.4.20 PERFORMANCE OF DIRECT FLUX VECTOR CONTROL WITH SPEED LOOP ...... 82 FIG.4.21 STEADY STATE PERFORMANCE WITH SPEED-LOOP...... 83 FIG.4.22 SPECTRUM ANALYSIS OF THE STATOR CURRENT ...... 83 FIG. 4.23 DFC SCHEME FOR ISA...... 84 FIG. 4.24 REFERENCE SPACE VOLTAGE VECTOR...... 86 FIG. 4.25 STARTING PROCESS OF ISA...... 88 FIG. 4.26 ISA GENERATING WITH FULL LOAD ...... 89 FIG. 4.27 SPECTRUM ANALYSIS OF THE STATOR CURRENT OF ISA ...... 89 FIG. 4.28 LOAD DUMP OF ISA WITHOUT BATTERY CONNECTED ...... 90 FIG. 4.29 LOAD DUMP OF ISA WITH BATTERY CONNECTED...... 91 FIG. 4.30 ISA PERFORMANCE AT ACCELERATION...... 92 FIG. 4.31 ISA PERFORMANCE AT DECELERATION...... 92 FIG. 4.32 ISA WITH FIELD WEAKENING AT HIGH SPEED...... 93 FIG. 5.1 VECTOR DIAGRAM OF THE INDUCTION MACHINE ...... 96 FIG. 5.2 DIRECT TORQUE AND FLUX CONTROLLED INDUCTION GENERATOR FOR ISA ...... 100 FIG. 5.3 STARTING PROCESS OF ISA...... 102 FIG. 5.4 ISA GENERATING WITH FULL LOAD ...... 103 FIG. 5.5 SPECTRUM ANALYSIS OF THE STATOR CURRENT OF ISA ...... 104 FIG. 5.6 LOAD DUMP OF ISA WITHOUT BATTERY CONNECTED ...... 105 FIG. 5.7 LOAD DUMP OF ISA WITH BATTERY CONNECTED...... 105 FIG. 5.8 ISA PERFORMANCE AT ACCELERATION...... 106 FIG. 5.9 ISA PERFORMANCE AT DECELERATION...... 107 FIG. 5.10 ISA WITH FIELD WEAKENING AT HIGH SPEED...... 108 FIG. 6.1 ONE LEG OF THE CONVERTER ...... 110

FIG. 6.2（A） IDEAL GATE SIGNAL （B）PRACTICAL GATE SIGNAL WITH DEAD-TIME （C）VaN WITH

DEAD-TIME EFFECT ONLY（D）CONSIDERING ton AND toff OF THE POWER DEVICE...... 111

FIG. 6.3 SWITCHING STATE OF VSI (A) AND SPACE VOLTAGE VECTORS (B)...... 111 FIG. 6.4 GATE SIGNAL WITHOUT DEAD-TIME...... 112 FIG. 6.5 GATE SIGNAL WITH DEAD-TIME ...... 113 FIG. 6.6 ANALYSIS OF THE VOLTAGE DROP ON THE POWER DEVICE ...... 114 FIG. 6.7 GATE SIGNAL WITH VOLTAGE DROP...... 115 FIG. 6.8 BACKWARD COMPENSATION STRUCTURE ...... 116

xiii FIG. 6.9 FORWARD COMPENSATION STRUCTURE ...... 117 FIG. 6.10 THE WITH VOLTAGE DROP AND DEAD-TIME COMPENSATION...... 118 FIG. 6.11 CURRENT MODE STATOR FLUX AND TORQUE ESTIMATOR ...... 119 FIG. 6.12 VOLTAGE MODE STATOR FLUX AND TORQUE ESTIMATOR ...... 120

FIG. 6.13 ROTOR SPEED, STATOR CURRENT, AND ESTIMATED TORQUE AND FLUX AT NO-LOAD -WITHOUT COMPENSATION...... 121 FIG. 6.14 ESTIMATION ERRORS OF THE STATOR FLUX- WITHOUT COMPENSATION...... 122 FIG. 6.15 ROTOR SPEED, STATOR CURRENT, AND ESTIMATED TORQUE AT NO-LOAD - WITH BACKWARD

COMPENSATION...... 123 FIG. 6.16 ESTIMATION ERRORS OF THE STATOR FLUX- WITH BACKWARD COMPENSATION ...... 123 FIG. 6.17 REFERENCE AND ERROR VOLTAGES - WITH BACKWARD COMPENSATION ...... 124 FIG. 6.18 ROTOR SPEED, STATOR CURRENT, AND ESTIMATED TORQUE AT NO-LOAD - WITH FORWARD

COMPENSATION...... 125 FIG. 6.19 ESTIMATION ERRORS OF THE STATOR FLUX- WITH FORWARD COMPENSATION...... 125 FIG. 6.20 REFERENCE VOLTAGES AND ERROR VOLTAGES - WITH FORWARD COMPENSATION ...... 126 FIG. 6.21 FLUX ESTIMATION ERRORS COMPARISON FOR WITH AND WITHOUT COMPENSATION...... 127

FIG. 6.22 DYNAMICS OF THE TORQUE AND FLUX FOR THE DTC-SVM WITH AND WITHOUT COMPENSATION ...... 129 FIG. 6.23 PERFORMANCE COMPARISON WITH AND WITHOUT COMPENSATION WHILE ISA IS GENERATING AT 1500 RPM WITH NO-LOAD...... 131

FIG. 6.24 PERFORMANCE COMPARISON WITH AND WITHOUT COMPENSATION DURING LOAD DUMP AT 1500 RPM...... 133 FIG. 7.1 THE OVERALL STRUCTURE OF THE DIRECT TORQUE CONTROLLED INDUCTION MACHINE WITH SLIDING MODE OBSERVER ...... 140

FIG. 7.2 OPEN-LOOP STATOR FLUX ESTIMATION WITH 50% ERROR IN Rs ...... 141

FIG. 7.3 SLIDING MODE FLUX OBSERVER WITH 50% ERROR IN Rs ...... 142

FIG. 7.4 OPEN-LOOP STATOR FLUX ESTIMATION WITH 3A DC CURRENT OFFSET...... 143 FIG. 7.5 SLIDING MODE FLUX OBSERVER WITH 3A DC CURRENT OFFSET ...... 143

FIG. 7.6 DIRECT TORQUE CONTROLLED INDUCTION MACHINE WITH OPEN-LOOP STATOR FLUX ESTIMATOR ...... 144 FIG. 7.7 DIRECT TORQUE CONTROLLED INDUCTION MACHINE WITH SLIDING MODE FLUX OBSERVER...... 144 FIG. 7.8 ROTOR SPEED, STATOR CURRENT, AND ESTIMATED TORQUE AND FLUX AT NO-LOAD WITH OPEN-

LOOP STATOR FLUX ESTIMATION...... 145 FIG. 7.9 ROTOR SPEED, STATOR CURRENT, AND ESTIMATED TORQUE AND FLUX AT NO-LOAD WITH SLIDING MODE FLUX OBSERVER...... 146

FIG. 7.10 OPEN-LOOP STATOR FLUX ESTIMATION WITH 50% Rs ERROR...... 147

FIG. 7.11 SLIDING MODE FLUX OBSERVER WITH 50% Rs ERROR...... 147

FIG. 7.12 OPEN-LOOP STATOR FLUX ESTIMATION WITH 3A DC CURRENT OFFSET...... 148

xiv FIG. 7.13 SLIDING MODE FLUX OBSERVER WITH 3A DC CURRENT OFFSET ...... 149 FIG. 7.14 DYNAMIC PERFORMANCE WITH OPEN-LOOP STATOR FLUX ESTIMATION ...... 150 FIG. 7.15 ESTIMATION ERRORS WITH OPEN-LOOP STATOR FLUX ESTIMATION ...... 150 FIG. 7.16 DYNAMIC PERFORMANCE WITH SLIDING MODE FLUX OBSERVER ...... 151 FIG. 7.17 ESTIMATION ERRORS WITH SLIDING MODE FLUX OBSERVER ...... 151 FIG. 7.18 CURRENT ESTIMATION WITH SLIDING MODE FLUX OBSERVER...... 152 FIG. 7.19 PERFORMANCE COMPARISON WITHOUT AND WITH COMPENSATION, AND SMO WHILE ISA IS GENERATING AT 1500 RPM...... 155

FIG. 7.20 PERFORMANCE COMPARISON WITH/WITHOUT COMPENSATION AND WITH SMO DURING LOAD DUMP AT 1500 RPM ...... 156 FIG. 8.1 THE OVERALL STRUCTURE OF THE DIRECT TORQUE CONTROLLED INTEGRATED STARTER/ALTERNATOR ...... 161 FIG. 8.2 POWER FACTOR CONTROLLER...... 162 FIG. 8.3 POWER FACTOR OF THE INDUCTION UNDER DIFFERENT LOADS ...... 163 FIG. 8.4 STATOR VOLTAGE, STATOR AND ROTOR CURRENTS WITH 30% RATED LOAD ...... 163 FIG. 8.5 CORE LOSS PERCENTAGE WITH AND WITHOUT POWER FACTOR CONTROL ...... 164 FIG. 8.6 COPPER LOSS PERCENTAGE WITH AND WITHOUT POWER FACTOR CONTROL...... 165 FIG. 8.7 EFFICIENCY COMPARISON OF THE INDUCTION MACHINE WITH AND WITHOUT POWER FACTOR CONTROL IN MOTORING MODE AT 1200 RPM AND 1500 RPM...... 166 FIG. 8.8 TRANSIENTS OF THE REGULATION OF THE POWER FACTOR CONTROLLER...... 167

FIG. 8.9 EFFICIENCY COMPARISON OF THE INDUCTION MACHINE WITH AND WITHOUT POWER FACTOR CONTROL IN GENERATING MODE AT 1500 RPM AND 2100 RPM ...... 168 FIG. B.1 EQUIVALENT SYSTEM MODEL OF THE TORQUE LOOP ...... 194 FIG.B.2 PI CONTROL OF THE EQUIVALENT SYSTEM ...... 194 FIG. C.1 VECTOR DIAGRAM OF THE INDUCTION MACHINE...... 196

xv LIST OF TABLES

TABLE 2.1 PARAMETERS OF THE INDUCTION MACHINE ...... 27 TABLE 3.1 SWITCHING TABLE OF INVERTER VECTORS ...... 44 TABLE 4.1 PARAMETERS OF THE INDUCTION MACHINE ...... 71 TABLE 4.2 PARAMETERS OF THE CONTROL SCHEME...... 77

TABLE 6.1 DEAD-TIME EFFECT ANALYSIS ( ia > 0 ; ib > 0 ; ic < 0 ) ...... 113

TABLE 6.2 ERROR VOLTAGE VECTORS UNDER DIFFERENT CURRENT POLARITIES ...... 114 TABLE 6.3 ERROR VOLTAGE VECTORS UNDER DIFFERENT CURRENT POLARITIES ...... 116 TABLE 9.1 COMPARISON OF DIFFERENT CONTROL SCHEMES FOR THE ISA...... 172

xvi LIST OF SYMBOLS

α−β stationary reference frame

dq− stator flux reference frame

dqee− rotor reference frame ia, ib, ic stator phase currents, A

Ic collector current of a power device, A id, iq d and q axis stator currents, A

Is amplitude of the stator current, A is stator current vector, A isα, isβ α and β axis stator currents, A p derivative

P number of pole pairs

Rs stator resistance of the induction machine

Ls stator inductance

Lr rotor winding self-inductance

Lm mutual inductance

Lls stator leakage inductance

Llr rotor leakage inductance G Ψs Stator flux vector G Ψr rotor flux vector

Te electromagnetic torque, Nm

TL load torque

xvii Test, Tˆ estimated electromagnetic torque, Nm td dead-time in the inverter, μs toff turn off delay of the power device, μs ton turn on delay of the power device, μs

Tref reference torque, Nm

Ts, Δt sampling interval, μs

Vce collector-emitter voltage, V

γ angle between the rotor and stator flux linkage vector, rad or degree

Superscripts

* reference value

^ estimated value

Subscripts est estimated value act actual value ref reference value k, k-1 kth and k-1 sampling interval

Abbreviation ac, AC dc, DC

DSP digital signal processor

DTC direct torque control

DTFC direct torque and flux control

DFC direct flux vector control

EKF extended emf electromagnetic force

xviii FOC field oriented control

RFOC rotor field oriented control

FVD forward voltage drop

FW field weakening

IGBT insulated gate bipolar transistor

IPM interior permanent magnet

IPMSM interior permanent magnet

PI proportional and integral

PID proportional, integral and derivative

PM permanent magnet

PMSM permanent magnet synchronous motor

PWM pulse width modulation

SVM space vector modulation

SM sliding mode

THD total harmonic distortion

VC vector control

ISA integrated starter alternator

ISG integrated starter generator

VSI voltage source inverter

SPM surface permanent magnet machine

VRM variable reluctance machine

ICE internal combustion engine rms root mean square.

xix CHAPTER 1 INTRODUCTION

1.1 42-Volt PowerNet

The electrical power demand in automobiles keeps increasing in recent years with proliferation electrical systems installed in More Electric Cars (MEC) [1]. The electrical systems in a MEC perform more duties other than conventional purposes of lighting, cranking, and battery charging. The electric machines play an important role in current and future automotive electrical system for propulsion, power steering, pumps, fans, air conditioners, electrically active suspension, electric brakes electromechanical engine valve, and so on [2]. Fig. 1.1 summarized partially current electrical and electric applications and future products under development in automobiles.

Fig. 1.1 Electrical and Electrics components in automobiles [2, 3]

Chapter 1 Introduction 1 In addition, the automotive electronic systems are also kept growing. As shown in Fig. 1.2, many electric networks will be equipped in modern vehicles such as CAN (controller area network), GPS (global positioning system), GSM (global system for mobile communications), LIN (local interconnect network) and MOST (media-oriented systems transport).

Fig. 1.2 more extensive electronics in modern vehicles [4]

As a result, the electrical power load on the alternator is expected to increase to 4 - 6 kW [5] and even to about 20 kW in the next decades [2]. The trend of power demand in vehicles is shown in Fig. 1.3. This dramatic increase requires substantial changes in automotive electrical generation and distribution systems. The present 14 V system cannot meet the enhanced power requirements. Therefore, the electrical bus voltage of automobiles is proposed to be increased from 14 V to 42 V, which is known as the 42 V PowerNet [6-8].

Chapter 1 Introduction 2

Fig. 1.3 Generator peak power demand of average passenger vehicle [9]

Higher voltage system offers a lot of benefits, which includes:

• Saving in weight and improving in fuel efficiency. The current of 42 V systems will be reduced by three times with same power output. Thus, the overall efficiency of the system is improved with less copper loss. Furthermore, the wiring resistance can be increased while retaining the same power loss over a given length of wire. A lighter wiring harness can be achieved with a reduction in the bundle diameter. Therefore, the duct arrangement becomes easier in the limited space of automobiles.

• Reduction in the cost of semiconductor devices. The standard of the 42 V electrical system is proposed [10], which stipulate a much tighter voltage regulation than the current 14 V standard as shown in Fig. 1.4. The maximum voltage is 58 V including transient voltages, whereas some auto manufacturers allows 80 V [11] or even 100 V [12]. Therefore, the semiconductor devices can be rated as lower voltage rating. Besides lower current rating, the lower voltage rating results in significant reduction of the cost of semiconductor devices.

Fig. 1.4 Voltage regulation of 42 V electrical system [13]

Chapter 1 Introduction 3 • Flexibility in distribution of load and electrical system. The conventional 14 V electrical system use point-to-point distribution architecture shown in Fig. 1.5. The wiring and harness is heavy and complex. The 14 V system cannot handle future higher power in MECs due to expensive cost and low efficiency [1]. The electrical system can change from point-to-point architecture to multiplexed architecture in 42 V system. As shown in Fig. 1.6, the loads are controlled by intelligent remote modules. Power Management System can be realized by interconnection between remote modules. The 42 V or a similar high voltage bus for distributed application is inevitable in automobiles.

Fig. 1.5 Conventional 14V dc distribution system architecture [1]

Fig. 1.6 Advanced multiplexed automotive power system architectures of the future with power and communication buses [1]

Chapter 1 Introduction 4 1.2 Integrated Starter Alternator - ISA

The existing Lundell alternator is not able to meet the requirements of high power, efficiency and voltage transients. The maximum output power of Lundell alternator is only 2 kW under force cooling [14]. New type of the alternator has to be used for high power generation. With the introduction of 42 V PowerNet, an integrated starter alternator (ISA) system has been proposed [2, 15-30], which is also named as integrated starter generator [31-33] (ISG). In conventional system of automobiles, the dc starter motor for cranking and the alternator for generation are separate as two units. The ISA combines both starter and alternator functions into a single electrical machine with bi- directional power flow. The ISA has attracted more and more research interest around the world as an alternative to the current unsatisfactory generating system in automobiles. The ISA provides a number of advantages listed as follows.

• The ISA can save space and reduce the cost and weight of the electrical system with multifunctional integration, including starting, generating and reduction of engine torque pulsations.

• The ISA can be mounted directly on the crankshaft of the engine and replaces the flywheel. Fig. 1.7 shows crankshaft mounted starter alternator, which is so called “Flywheel-starter-alternator”.

Fig. 1.7 Crankshaft mounted starter alternator [34]

Chapter 1 Introduction 5 • The ISA offers geater generating capacity and a start-stop facility that improves fuel economy and reduces harmful gaseous emissions. Improved fuel efficiency is obtained through implementation of start/stop cycles. With a conventional dc starter, fuel is supplied shortly after engine cranking begins, but the engine does not fire until about 500 ms later as shown in Fig. 1.8 because its torque decreases as motor speed increases. In contrast, the ISA can start the engine within about 250 ms [8] by producing torque without regard to speed. Therefore, only the fuel necessary to maintain idle is supplied. Fuel saving and reduction of hydrocarbon emissions are both achieved.

1000 Integrated DC starter starter/alternator Motor 800

600

400 Engine speed (rpm) 200

0

0 200 400 600 800 1000

Starting time (ms)

Fig. 1.8 Starting with ISA and DC motor [8]

• The ISA provides additional braking ability by converting kinetic energy to electrical energy.

• The ISA also offers possibility of a soft hybrid configuration for acceleration boost at low engine speeds. This feature allows the use of smaller internal combustion engines.

Several important issues should be considered for the design of ISA system. They are: electrical specification, selection of the machine, the power converter topology and the control scheme.

Chapter 1 Introduction 6 1.2.1 Electrical specification

ISA operates on both starting mode and generation mode. For starting mode, The MIT/industry consortium on automobiles recommended that the engine starting torque requirement to be set at 150 Nm from standstill up to 100 rpm engine speed [15]. For generation mode, the power level of the ISA is about 4 kW at 600 rpm engine (idle condition) and it rises to 6 kW at 6000 rpm. The specification of the power level reveals its high requirement over wide speed range. Due to the future fuel efficiency consideration, the alternator system efficiency requirement was set to 75% for rated base load for the combined electrical machine and converter. Fig. 1.9 shows the resulting starting and generating torque requirements as a function of speed for the ISA.

Fig. 1.9 Starter/alternator starting and approximate generating torque requirement (*) and the torque/speed characteristic (line) [15].

Although no decided specification of the dynamic performance of ISA is presented, some general ideas are described in literatures. For example, the starting time of ISA is accepted to 0.2 to 0.5 seconds. Faster starting characteristics ensures low emission and fuel saving. On the other hand, the smooth transition from starting mode to generation mode is also important for an ISA. In generation mode, the voltage regulation ability for rated load and load dump plays an essential role to evaluate an ISA system. Finally, cost and reliability determines whether certain ISA system can be applied in automobiles.

Chapter 1 Introduction 7 As shown in Fig. 1.4, the standard of the 42 V electrical system is proposed [10]. The voltage transient is also defined for the worst case when full load is suddenly disconnected from dc bus [6, 10]. This is known as the load dump condition [35-37]. The peak voltage of the 42 V is required to limits below 1.4 times (58 V) of rated voltage during load dump. As shown in Fig. 1.10, the transient voltage of the 42 V electrical system is required to be limited in 400 ms duration and magnitude lower than 58 V. in addition, the voltage has to be regulated back to 46.2 V within 430 ms since the load dump happens.

Fig. 1.10 dc bus voltage dynamic requirement [6]

The above voltage transient specifications require the generation system of automobiles has good dynamic regulation ability. This ability is determined by the controller of the generator. The scalar control (V/f) scheme is not able to satisfy these requirements. The advanced control scheme with field oriented control or vector control is thus adopted for the existing ISA system [16, 20, 24-26, 38]. Another advanced control scheme with direct torque control is explored in this thesis for the control of a generator for the ISA application.

1.2.2 Machine technologies

For the application of ISA system, the selection of machine which determines the performance of ISA system is very important. Although the DC machine has inherent flexibility in control and capability of operation in both motor and generator, the makes it is impossible to be used in an ISA application due to the

Chapter 1 Introduction 8 limitation of speed and reliability. The conventional synchronous machine used in today’s has severe limitation due to its size and efficiency scaling characteristics [22, 28, 38]. Therefore, the existing literatures on machine topologies for ISA discuss and compare four alternative brushless machines. They are induction machine (IM), surface permanent magnet machine (SPM), interior permanent magnet machine (IPM), and variable (switched) reluctance machines (VRM or SRM).

1.2.2.1 Induction Machine (IM)

The induction machine is one of the most serious candidates for the starter/alternator application because of its attractive characteristics such as robust rotor structure and mature manufacturing technology. A primary advantage of the induction machine is the simplicity and reliability. Since the power is transformed from the stator to the rotor through transformer action, no commutators, brushes, or slip rings are required. Therefore, the machine requires less maintenance, which makes it attractable in automotive application. In addition, induction machines have very good efficiency, smooth torque and wide speed range which match the specification of ISA application. Control technologies for induction machines have been well studied over several decades. These technologies are now quite mature.

In paper [16], the authors present the comparison results of using induction and variable reluctance machines as the starter-alternator in a hybrid electric vehicle. Permanent magnet machines are not considered due to the rotor heating under the dense packaging. When both machines are compared against specified engine cranking and continuous alternator output power requirements, they found that the induction machine has higher average thermal duty cycle and benefits from the ability to use a simpler incremental encoder for control. The variable reluctance machine has significant benefits for in- vehicle packaging and low rotor inertia but suffered more in thermal performance and its need for a high resolution encoder.

Researchers at Delphi describe their design of belt-driven starter-generator with induction machine [39]. As mentioned in the paper, they considered PM machine as the most expensive solution in this case because the inverter rating must handle the large voltage range produced by the (10:1 from idle to 6000 rpm). As for switched reluctance machine, noise and vibrations would be the problem. And it is still an emerging technology, which may complicate practical developments. By contrast, the

Chapter 1 Introduction 9 induction machine is an established technology with good efficiency and smooth torque. Therefore, induction machine was selected for their project.

A integrated starter-alternator system was introduced by Visteon Automotive Systems [18]. They also selected induction machine as the best machine for ISA application. They consider that the induction machines have wide speed range, have a better failure mode and are more reliable in the case of a winding short circuit; have high performance at lowest possible cost.

1.2.2.2 Surface Permanent Magnet Machine (SPM)

The surface permanent magnet synchronous machine employs surface-mounted rotor magnets to achieve high torque and power densities. Such characteristics make the SPM well suited for delivering the high starting torque required in the starter/alternator application. Unfortunately, the SPM has difficulty achieving wide constant-power speed ranges because its back-EMF rises linearly with speed, and its phase inductances are typically too low for effective flux weakening [15]. To overcome this obstacle, additional DC-DC converter is required [15, 28] to regulate the voltage of the bus which has a negative impact on the system cost.

1.2.2.3 Interior Permanent Magnet Machine (IPM)

S S

N N

N S S N N S S N

N N

S S

(a) IPMSM-I (b) IPMSM-II Fig. 1.11 Rotor structure of IPM motors

As shown in Fig. 1.11, the magnets are buried inside the rotor of IPM. As a result, the IPM is inherently a ‘hybrid’ machine with torque contributions from both the magnets

Chapter 1 Introduction 10 and the iron saliency produced by the magnet cavities. Interior permanent magnet (IPM) synchronous motors offer many advantages over induction motors, such as higher overall efficiency, effective use of reluctance torque, smaller losses and compact motor size. Moreover, the use of flux weakening control based on pole saliency supports a wider range of speeds. In particular, proper balancing of the magnet strength and the rotor saliency makes it possible to achieve very wide speed ranges of constant-power operation. This is a major advantage over the SPM discussed above, further accentuated by the IPM’s need for significantly less magnet material to deliver the same torque [15].

The benefits provided by IPM come with some disadvantages. Since the motor magnetic field cannot be shut off, even with the stator winding disconnected from the drive, the rotor will always create an induced voltage in the winding. In the event of a winding failure or fault, the rotor will continue to pump fault current into the failed region, even after the inverter trips the motor off line. This has the potential to do considerable damage to motor components other than just the winding making repair more costly. Moreover, the PM motor may have limited overload or peak torque capability and can be demagnetized when the overload limit is exceeded. Overloads limits for a PM motor may be as low as 120% of rated load. PM motors may have to be oversized for applications that require overloads. In contrast, induction motors designed for variable-speed application typically have a minimum of 250% overload capability and have been applied for overloads as high as 600% [40]. In addition, IPM has the thermal problem which is very harmful for practical application. Moreover, the relative complexity of the IPM’s rotor structure represents an important technical risk in comparison to the mature induction machine structure. The presence of the embedded magnets contributes cost and manufacturing complications associated with the installation and magnetization process. Relatively higher cost of the IPM high efficiency magnetic material holds back its application.

1.2.2.4 Variable Reluctance Machine (VRM)

The variable (or switched) reluctance machine offers some attractive characteristics for the integrated starter/alternator application including its robust rotor construction and a torque-speed characteristic.

However, variable reluctance machines are excited with non-sinusoidal waveforms that make it difficult to simultaneously minimize torque ripple while maximizing

Chapter 1 Introduction 11 torque/power density. In addition, it is still an emerging technology, which may complicate the practical development.

From the literatures, it is found that the researches on the starter-alternator system with switched reluctance machine are mainly for the aircraft application [41-46]. Only a few papers discuss the SRM for automotive application [47-49].

Paper [48] concluded that thermal management of any permanent magnet machine seems to be problematic due to the close distance from the engine. They announce that the performance comparison of induction machine and SRM will be different with that described in the paper [16] due to current intensive scenario (42 V,7.2 kW). Therefore, a switched reluctance machine based ISA system was proposed by them. However, they also concluded that there exists limitation on the performance of SRM in ISA which depends on the development of ultra-fast DSP based processors and semiconductor.

Fig. 1.12 Cost comparison of three machine systems for a 6kW direct-drive starter/alternator application [15]

Paper [15] estimated the cost of ISA system. The authors used cost estimation algorithms into each of the analysis models in order to permit the cost of each individual machine design to be estimated together with the cost of its accompanying converter. The result of the cost optimization process for each of the four candidate machine types is presented as a cost bar chart in Fig. 1.12. It can be observed from the bar diagram that the induction and IPM are more attractive for the ISA application on the basis of projected system cost compared to the surface PM and variable reluctance machines.

Chapter 1 Introduction 12 Their completed results of the trade-off study indicated that the induction machine and IPM are both serious candidates for the direct-drive starter/alternator application.

1.2.2.5 Summary

As discussed in last sections, both induction machine (IM) and interior permanent magnet machine (IPM) are suitable for of ISA application. Permanent-magnet machine and induction machine based ISA systems have been proposed for automotive applications by many researchers [16, 20, 24-26, 38, 50].

In comparison, IM has lower efficiency than that of IPM due to the loss in the rotor. However, IM has higher reliability than IPM because of easing of thermal problem. Compared with the permanent-magnet machine, the induction machine has robust structure, low cost, mature technology and low maintenance requirement. Moreover, the induction machine dose not retain magnetization, unlike a permanent-magnet machine, when the system is turned off under fault condition. Therefore, the induction machine is a viable option for ISA system design. The induction machine based integrated starter/alternator systems have been reported in [16, 18-22, 24-26, 29, 34, 51-55]. Based on the mature technology of previous research work, higher reliability can be achieved. Therefore, induction machine is selected in this study.

1.2.3 Electrical System configuration and Power converter topology

Among several publications on induction generator for ISA [16, 20, 24-26, 38] and stand-alone application [56, 57] to date, the Pulse Width Modulation (PWM) voltage source converter is the most attractive hardware structure due to its excellent dynamic performance.

Both high voltage [16, 20, 26] and low voltage [50, 58, 59] bus system of the ISA were developed. Basically, high voltage electrical system has two stages of the power converter as DC-DC-AC and low voltage electrical system has one stage of the power converter as DC-AC.

Chapter 1 Introduction 13 1.2.3.1 High bus voltage with battery

Fig. 1.13 High voltage bus configuration

In paper [16], the authors presented a parallel hybrid structure with starter-alternator. High voltage batteries (Pb-Acid) are used to provide about 300V bus voltage directly to the inverter. In this kind of configuration, the machine acting as starter-alternator should be high voltage machine and no boost converter is required between bus and machine. The inverter is actually a bi-direction converter which transfers power flow between dc bus and starter-alternator. However, DC-DC converters are needed to step-down the high voltage for the supplying the low voltage electrical load of automobiles.

With this configuration, the bi-direction function is easy to fulfill by a simple full- bridge without voltage-boasting part. But the cost of high voltage batteries may be the problem for commercial application.

1.2.3.2 High bus voltage with ultracapacitor

Fig. 1.14 High voltage bus configuration with ultracapacitor

Visteon developed an integrated starter-alternator (V-ISA) system [20]. The V-ISA system includes induction motor, inverter, DC-DC converters (boost and buck pattern), ultracapacitors on the high voltage side and 42 Volt Battery. Therefore, this configuration has high bus voltage. The ultracapacitor has a number of very attractive features, offering high power density and extremely high cycling capability. The boost converter powered by the 42 volt battery can charge capacitors up to 300 Volts in a few

Chapter 1 Introduction 14 seconds even during cold start. Fully charged capacitors can start the engine consecutively before next recharge. Depending on battery’s state of charge, the regenerative action charges the 42 volt battery, 12 volt battery and capacitors, respectively. The main energy source during the start is from high voltage ultracapacitors. Adding ultracapacitors to the system significantly reduces weight and space by elimination high voltage batteries and also it makes braking regeneration possible since capacitors and ideal for absorbing high inrush current.

A similar system configuration was proposed in paper [26], which is shown in Fig. 1.15. Two DC-DC converters were applied in their scheme to realize the bi-direction power flowing. The low-power DC-DC converter is enabled in start-up mode to provide energy for engine cranking. And the high-power DC-DC converter transfers generation power from inverter to the battery and loads. This function is achieved by a single bi- direction DC-DC converter in paper [20], which required better tradeoff design for the bi-directional converter.

Fig. 1.15 Block diagram of the overall supervisory control scheme [26]

1.2.3.3 Low bus voltage

Besides high bus voltage, a low bus with 42V is also adopted by some researchers [50, 58]. With low bus voltage, the DC-DC converter between the battery and inverter can be removed when low voltage machine is used. Figure 2.7 shows a dual voltage (14V

Chapter 1 Introduction 15 and 42V) automotive electrical system with low voltage bus. In this system, the bi- directional converter has no boost pattern with low voltage starter/alternator [59].

Fig. 1.16 Dual voltage (14V and 42V) automotive electrical system [59]

1.2.3.4 Summary

Single-stage bidirectional three phase DC-AC converter is selected in this study. In comparison, the two-stage converter topology has a negative impact on the system cost and raises special packaging issues in order to adequately protect humans from exposure to the high voltages.

In the single-stage scheme, bi-directional DC-AC converter connects battery and the machine. Single-stage scheme has higher power efficiency than the two-stage scheme and is easier to control without considering the independent control of the two converters. Moreover, isolation is not required in low voltage system.

Fig. 1.17 Proposed ISA electrical system configuration

Chapter 1 Introduction 16 1.2.4 Machine controller- control of generator

1.2.4.1 Field Oriented Control

The ISA requires sophisticated control that must monitor power demand and power flow in and out of the motor/generator and batteries in all operating modes of automobiles, whether the vehicle is cruising, braking, or accelerating. In the publications related to ISA development, Field Oriented Control (FOC) of AC machines [16, 20, 24-26, 38, 60] appears to have drawn much interest. Field oriented control has been used in induction motor control for a long time and it was natural to extend it to induction generator application [57, 61, 62]. Although field oriented control is an advanced scheme, it has several disadvantages such as high computational requirement for the co-ordinate transformation and high parameters dependency [63, 64]. In addition, the rotor speed signal is essential for co-ordinate transformation in field oriented control. Therefore, encoder based speed sensing or speed observer is needed for both generation and motoring with field oriented control [20, 24-26, 38, 57, 61, 62, 65]. To avoid these drawbacks, efforts have gone into sensorless field oriented controllers in the past two decades.

1.2.4.2 Direct torque control

Direct torque control (DTC) was introduced in 1980’s [66, 67]. Compared with field oriented control, direct torque control is a very simple control scheme with low computational requirement. Current regulator and co-ordinate transformation are not required with DTC [63, 64]. The DTC and some of its variations have the merits like inherent sensorless operation and reduced parameter sensitivity. DTC is increasingly gaining wide acceptance in motor drives application from both academia and industry, but has not yet been considered for ISA application. In generation application, the speed of the machine is already determined by the prime mover or engine. No speed control loop is thus needed for the controller. The speed sensorless controller is thus a natural choice for ISA application. For starting mode, ISA system only requires large starting torque and short starting time without concerning about the speed characteristics. Therefore, the poor performance of DTC in low speed range is not a significant problem in this application. For the application of ISA, the AC machine mostly operates in

Chapter 1 Introduction 17 generation state after the engine is started and runs above the idling speed. The DTC scheme is thus more suitable than FOC scheme for ISA application.

This thesis is primarily concerned with the application of direct torque controlled induction machines for the control of the ISA in both motoring (i.e. starting) and generating modes.

By neglecting the loss of AC machine and the converter, the electromagnetic power of generator should be balanced with the absorbing power of the load. In other words, the following equation should be satisfied at any time.

TVIedcdcω = (1-1)

where ω is the speed of AC machine, which is determined by the engine. Te is the torque of AC machine; V,Idc dc are the output voltage and current on the dc side.

Fig. 1.18 shows the structure of basic DTC scheme for induction motor. The electromagnetic torque can be regulated as follows:

⎧u a JG G ⎧Vdc ⎪ ⎨⎨→→→Ψ→uVbse T (1-2) ⎩Switching Signal ⎪ ⎩uc

By producing different voltage vector through the voltage source inverter (VSI), DTC scheme restricts the flux and torque errors within respective flux and torque hysteresis bands.

Vdc

Fig. 1.18 DTC of induction motor

Chapter 1 Introduction 18 The concept of DTC for can be mirrored to generator mode of operation directly. In motoring state, the desired voltage vector for torque control is produced by VSI with certain switching signal. In other words, the dc bus voltage and voltage vector are uniquely determined through the switching signals of the VSI inverter. Their relationship depends on the switching signals that have been selected. In generating state, this corresponding relationship still exists and it determines which switching signal should be applied. On the other hand, the switching signal is also restricted by the flux-linkage which is determined by desired electromagnetic torque. Based on above analysis, DTC scheme of induction generator can be built as the structure shown in Fig. 1.19. The torque reference is given by voltage regulator. The dc bus voltage can be regulated as follows:

⎧ua JG G ⎪ ⎪ub VT→Ψs →edc →⎨ → V (1-3) ⎪uc ⎩⎪Switching Signal

Udc

Fig. 1.19 DTC of induction generator

A few papers have studied the classic switching table based DTC control with schemes for the generator [68-71]. Switching table based DTC for integrated starter/alternator is also reported in [72]. However, the switching table based classic DTC has some drawbacks such as large torque and flux ripples, and variable switching frequency. Faster sampling frequency has to be used to minimize the torque and flux ripples for digital implementation of hysteresis controllers [63, 73].

Chapter 1 Introduction 19 The problems associated with the classic DTC can be solved by Proportional-Integral (PI) controller plus Space Vector Modulation (SVM). This improved DTC scheme can achieve better performance with reduced torque ripple and constant switching frequency. This thesis proposed two improved DTC based control with space vector modulation schemes for the integrated starter/alternator [29, 55]. Several papers arising from this thesis have been published in proceeding and journal, which can be found in the Appendix A. A DTC control scheme of a permanent magnet-assisted reluctance synchronous machine (PM-RSM) with SVM for ISA application were reported [30]. This paper indicates further the potential of DTC for ISA application and also shows the acceptance this idea in academia.

1.3 Scope of the thesis

The purpose of the thesis is to extend the application of direct torque control and its variations in ISA system for the future 42 V PowerNet. This thesis presents the modeling, design as well as experimental results of the direct torque controlled ISA system, which includes

• Evaluation of the classical direct torque controlled integrated starter/alternator

• Study of improved direct torque control schemes for integrated starter/alternator with space vector modulation

• Compensation of the non-linearity of the DC-AC converter due to dead-time and voltage-drop of the power devices

• Design of an sliding mode observer for improvements on stator flux estimation

• Efficiency improvement of the integrated starter/alternator with power factor control

The objective of this project is to develop a direct torque controlled induction machine driven ISA meeting the strengthen requirements of the 42 V PowerNet. The solution carried out in thesis in the above areas have proved the suitability of direct torque controlled induction machine driven ISA, as is reported in Chapters 2-8.

Chapter 1 Introduction 20 1.4 Outline of the thesis

Chapter 1 gives a brief introduction of the Integrated Starter/Alternator (ISA). This chapter also reviews the state-of-the-art for integrated starter/alternator and discusses the machine selection, power converter topology and advance control schemes.

Chapter 2 presents a rotor field oriented controlled integrated starter/alternator with space vector modulation in order to compare with the proposed DTC schemes.

Chapter 3 presents the analysis and implementation of the classical direct torque controlled integrated starter/alternator.

Chapter 4 and Chapter 5 present two different direct torque control schemes for integrated starter/alternator with space vector modulation. They have one-PI and two-PI structures. Their controllers are analyzed and the design procedures are developed.

Chapter 6 analyzes the non-linear characteristics of the inverter and develops their compensations. The compensation methods will be used in the control schemes in the following chapters.

Chapter 7 presents a sliding observer to estimate the stator flux linkage based on the motor current model. Compared to the open-loop estimator, the observer has exhibited better dynamic behaviour, disturbance resistance and high accuracy estimation ability. The experimental results show that the proposed observer is able to deliver more accurate estimation than open-loop integrator estimator both in the steady state and during transients.

Chapter 8 investigates an efficiency improvement method of the ISA with power factor controller. The modeling and experimental results shows the efficiency of the induction machine is improved with proposed method.

Chapter 9 gives the conclusions and suggestions for future research.

Chapter 1 Introduction 21

CHAPTER 2 AN INDUCTION MACHINE BASED INTEGRATED STARTER/ALTERNATOR USING ROTOR FIELD ORIENTED CONTROL WITH SPACE VECTOR MODULATION

2.1 Introduction

As discussed in 1.2.4.1, rotor flux oriented control scheme has been used recently in a few ISA designs [16, 20, 24-26, 38]. In order to compare the direct torque control with rotor flux oriented control, the chapter presents a study of rotor flux oriented controlled ISA. The structure of the rotor flux oriented controlled ISA is presented first, followed by experimental results of an implemented ISA. Subsequent chapters present direct torque controlled ISA solutions.

This chapter is organized as follows. Section 2.2 presents the dynamic model of the induction machine. Section 2.3 proposes the rotor flux oriented controller for ISA. Experimental results are shown in 2.4. At last, conclusion is drawn in Section 2.6.

2.2 Induction machine model

In the synchronously rotating reference frame ( dqee− ), the dynamic of the induction machine can be expressed as

Chapter 2 An induction machine based ISA using RFOC with SVM 22 ⎧ dψ vRi=+sα −ωψ ⎪ sd s sddt e sq ⎪ dψ ⎪vRi=+sq +ωψ ⎪ sq s sqdt e sd ⎨ (2-1) dψ ⎪vRi= +−ω−ωψrd () ⎪ rd r rddt e r rq ⎪ dψ ⎪vRi= ++ω−ωψrq () ⎩ rq r rqdt e r rd where

vsd and vsq are the stator voltages;

ωe and ωr are synchronous and rotor rotating frequency;

isd , isq , ird and irq are stator and rotor currents in d- and q-axis;

ψsd , ψsq , ψrd and ψrq are the stator and rotor flux linkages in d- and q-axis;

Rs and Rr are the stator and rotor resistances.

The dynamic equivalent circuits of the induction machine are shown in Fig. 2.1. According to Fig. 2.1, the flux linkage can be expressed in term of the currents as follows:

⎧ψ=sdssdmrdLi + L i ⎪ ⎪ψ=sqssqmrqLi + L i ⎨ (2-2) ⎪ψ=rdLi m sd + Li r rd ⎪ ⎩ψ=rqLi m sq + Li r rq

where Ls , Lr and Lm are the stator self, rotor self and mutual inductances, respectively.

Chapter 2 An induction machine based ISA using RFOC with SVM 23 i L = LL− L = LL− i sq ωψ ls s m lr r m rq esd (ωerrd− ωψ) R Rs r

L m Vrq Vsq ψ sq ψ rq

(a)

i L = LL− L = LL− i sd ω ψ ls s m lr r m rd esq (ωerrq− ωψ) R Rs r

L m Vrd Vsd ψ sd ψ rd

(b)

Fig. 2.1 Dynamic dqee− equivalent circuits of machine (a) qe axis circuit, (b) d e axis circuit

2.3 Rotor flux oriented controlled ISA

The structure of ISA with rotor flux oriented control is shown in Fig. 2.2. There are two control loops in this structure.

The outer-loop determines the torque and flux references for the inner-loop. In the starting mode, the torque reference is the pre-determined starting torque Tstarting . In the generating mode, torque reference is connected to the output of the dc bus by the Staring/Generating switch when the engine is started. A negative gain is used for the dc bus voltage controller because the torque should be negative in generation state. The flux reference is obtained from the output of the flux reference block in Fig. 2.2 for both starting and generating modes. The flux reference is weakened

Chapter 2 An induction machine based ISA using RFOC with SVM 24 in proportional to 1 ωr when the rotor speed is above the base speed of the induction machine.

The two inner-loops implement the effective control of the torque and flux of the induction machine for both starting and generating modes. The torque and flux are independently regulated by the decoupled d and q axis current controllers. The q-axis current reference is calculated by (2-3) and the d-axis current reference is the output of the rotor flux PI controller to maintain the rotor flux level according to the flux reference block. In this scheme, the angle and the amplitude of the rotor flux is estimated by a conventional current mode estimator as shown in Fig. 2.3. The speed signal and stator current are used as the inputs of the flux estimator. The outputs of the d and q axis current controllers are the voltage references in the rotating frame ( dqee− ), which are transformed to the stationary frame ( α −β) by dqee− to α−β block by (2- 4). Finally, the PWM signal is generated by the SVM unit according the voltage reference in the stationary frame ( α −β).

* Vdc Tstarting + Vdc −

T * * + isq Vsq ee KT PI dq− G VVα , β ∗ * − Ψr i SVM IM sd Vsd PI PI α − β ω b − G ωr ∠Ψr i i sq G sd Current Model Estimator Ψr

ωr Encorder

Fig. 2.2 Rotor flux oriented controlled ISA with SVM

22 LT∗ i ∗ = re (2-3) sq 3 pL ψ mrest

Chapter 2 An induction machine based ISA using RFOC with SVM 25 G i i ψr sA isα sd 1 isB Lm −θj r 1+ Ts isβ isq r isC e

Tr θ r θr ÷ + ∫

ωr

Fig. 2.3 flux model in the rotor-flux-oriented reference frame [74]

⎡VV⎤⎡⎤⎡⎤cosθ− sin θ α = eed (2-4) ⎢VV⎥⎢⎥⎢⎥ ⎣ β ⎦⎣⎦⎣⎦sinθθee cos q

ee where θe is the angle between the rotor flux frame ( dq− ) and stationary frame ( α−β), i.e. the angle of rotor flux linkage vector as shown in Fig. 2.4

β ωe

qe e G d G Is Ψr

isd isq

θe α

Fig. 2.4 Vector diagram of the induction machine

The ISA using a rotor flux oriented induction machine was extensively studied by mathematical modeling and experiments. The simulation results were fully in agreement with experimental results. In view of the fact that induction machine based ISA using RFOC has been developed and tested by other researchers [16, 20, 24-26, 38, 60], simulation results are not being included here. Only the experimental results of a fully tuned RFOC for an ISA system are included in this chapter. These results are presented

Chapter 2 An induction machine based ISA using RFOC with SVM 26 in this chapter to serve as benchmarks for ISA using DTC which are described in Chapters 3-8.

2.4 Experimental setup

The ISA using a rotor flux oriented induction machine, as shown in Fig. 2.2, was implemented in the laboratory.

As mentioned in Chapter 1, a squirrel-cage induction machine was chosen in this study to demonstrate the proposed control scheme of the ISA. The induction machine is rewound with a 22 V 4-poles winding to work with the 42 V dc voltage bus. The parameters of the induction machine are given in Table 2.1.

Table 2.1 Parameters of the Induction Machine

Rated output power(W) 1000 Rated Voltage (Volt) 22 Rated frequency (Hz) 50 Poles number p 4

Stator resistance Rs ( mΩ ) 25.1

Rotor resistance Rr ( mΩ ) 18.2 Mutual inductance (mH) 1.8

Stator leakage inductance Lls (mH) 0.07618

Rotor leakage inductance Llr (mH) 0.07618 Inertia (Kg.m²) 0.00824 The rated line to line voltage of the induction machine is chosen as 22 V (rms) by considering (2-5) in a boost type three-phase PWM converter.

⎛⎞23 ⎛ 2 ⎞ 3 VmVll− ≤⋅⎜⎟ dc ⋅ =0.7855 × ⎜ × 42 ⎟ × = 25.7 V (2-5) ⎝⎠ππ22 ⎝ ⎠

where m (=0.7855) is the modulation factor with sinusoidal PWM [75], Vdc is the dc bus voltage (with 42 V rating).

An ISA system based on the induction machine was implemented with the experimental platform shown in Fig. 2.5. A DC machine is mechanically coupled with the induction

Chapter 2 An induction machine based ISA using RFOC with SVM 27 machine to simulate the engine during both starting and generation modes of operation. The power converter for the experiment is a three-phase DC-AC voltage source bidirectional converter, which is supplied with three 12 V batteries in series giving 36 V.

Fig. 2.5 Experimental setup

The control software is developed on a dSPACE DS1104 Controller Board with slave a built-in Digital Signal Processor (TMS320F240). The rotor position and speed were obtained from an incremental encoder with 5000 pulses per revolution. Voltage and current sensors are used to detect the dc bus voltage and stator currents of the induction machine, respectively. The signals of dc bus voltage and two stator currents are read by the DSP through A/D (Analog to Digital) converter. The control algorithm is embedded in the DS1104 from dSPACE and the PWM (SVPWM) that gates the power converter is generated through the slave DSP.

2.5 Experimental results

2.5.1 Starting mode

During the starting period, the induction machine produces full torque to drive the DC machine which simulates the engine. In this experimental setup, the starting torque is set as 6 Nm and the engine starting speed is 500 rpm to reflect the idle speed of the engine.

Chapter 2 An induction machine based ISA using RFOC with SVM 28 After DC machine simulated engine is started, both the DC machine and induction machine are accelerated from 500 rpm (see A in (a) of Fig. 2.6) to 1200 rpm (see B in (b) Fig. 2.6). For the study in this thesis, 1200 rpm was chosen as the simulated ISA generating speed because of the limitation of the DC machine simulating the engine.

As shown in Fig. 2.6, the induction machine torque runs the whole set from 0 to 1200 rpm. After the speed reaches 1200 rpm, the DC machine simulated engine sets its speed reference to 1500 rpm and regulated by its own controller. In this study, 1500 rpm is the base speed of the induction machine. This speed is consequence of the 4-poles induction machine chosen for the ISA. For a practical ISA, 10-12 poles machine should be more appropriate. At the same time, the reference of the induction machine is switched from torque to voltage to reflect the transition from motoring to generating. The induction machine begins to act as a generator and provide power to the battery and the dc load. The torque of the induction machine is thus changed from 6 Nm to -6 Nm as (i) in Fig. 2.6. The rotor flux [(iii) in Fig. 2.6] of the machine is kept constant by the rotor flux control in Fig. 2.2. The decouple control of the torque and rotor flux is achieved by rotor flux oriented control scheme. The part (b) of Fig. 2.6 shows the d and q axis currents during starting and generating period. As discussed in Section 2.3, the d and q axis currents control the flux and torque of the induction machine, respectively. Therefore, the d axis current is fixed to maintain the rotor flux, and q axis current is regulated according to the operation modes of the machine.

Chapter 2 An induction machine based ISA using RFOC with SVM 29

(a)

(b)

e e Fig. 2.6 Starting of ISA with RFOC: (a) torque, speed and stator flux (b) torque id and iq

Chapter 2 An induction machine based ISA using RFOC with SVM 30 2.5.2 Generating mode - steady state

The steady state performance with full load of the induction machine is shown in Fig. 2.7. With voltage regulator the dc voltage of the ISA system is kept as 42 V when the induction machine provides full torque to the load. And the stator flux of the induction machine is still constant. The stator current waveform is captured by a digital oscilloscope (LeCroy LT364L) and the data is analysed by FFT algorithm. It indicates in Fig. 2.8 that the DC-AC converter of the ISA system runs at constant frequency 6.67 kHz, which is corresponding to the sampling time 150 μs .

Fig. 2.7 ISA generating with full load

Chapter 2 An induction machine based ISA using RFOC with SVM 31

Fig. 2.8 Spectrum analysis of the stator current of ISA while operating as generator in the steady-state

2.5.3 Generating mode - dynamic response.

The dynamic performance of the ISA also studied in this section. The performance of the ISA system under load dumping and engine speed acceleration or deceleration is presented as follows.

2.5.3.1 Performance during load dump

The dc load of the ISA is removed suddenly at the generating state when the speed is 1500 rpm. Two conditions are considered for the load dump of the ISA. They are load dump without battery connected and load dump with battery connected as shown in Fig. 2.9 and Fig. 2.10, respectively

As shown in Fig. 2.9, the peak dc bus voltage of the ISA is well controlled below the limitation of the 42 V PowerNet standard (58 V) [6] when the dc load is dumped. The settling time of the dc bus voltage is about 150 ms. The induction machine’s torque is

Chapter 2 An induction machine based ISA using RFOC with SVM 32 e changed from -5 Nm to about -1 Nm during load dumping. The id is constant in Fig. 2.9 (b) to maintain the rotor flux. Consequently, the stator flux of in Fig. 2.9 (a) is kept constant.

(a)

Chapter 2 An induction machine based ISA using RFOC with SVM 33

(b)

Fig. 2.9 Load dump of ISA without battery connected: (a) bus voltage, torque, stator flux and

e e stator current (b) torque, id and iq

As shown in Fig. 2.10, the dc bus voltage of the ISA is also below the limitation of the 42 V PowerNet standard (58 V) [6] when the dc load is dumped. The torque of the induction machine varies slower than last case because of the charging of the batteries.

Chapter 2 An induction machine based ISA using RFOC with SVM 34

(a)

(b)

Fig. 2.10 Load dump of ISA with battery connected: (a) bus voltage, torque, stator flux and

e e stator current (b) torque, id and iq

Chapter 2 An induction machine based ISA using RFOC with SVM 35 2.5.3.2 Performance acceleration/deceleration

In normal operation, the engine speed may change quiet rapidly and frequently. The ISA should cope with this and maintain the dc bus voltage to the 42 V PowerNet specifications.

In this test, the DC machine’s speed reference is increased suddenly from 1500 rpm to 3000 rpm, while the induction machine is generating with full dc load. As shown in Fig. 2.11, the dc bus voltage of the ISA is well controlled as 42 V during speed acceleration. Fig. 2.11 (a)-(iii) shows the flux of the machine is weakened when the speed is above base speed (1500 rpm). Part (b) of Fig. 2.11 shows the d and q axis currents during accelerating of the ISA.

(a)

Chapter 2 An induction machine based ISA using RFOC with SVM 36

(b)

Fig. 2.11 ISA performance at acceleration: (a) bus voltage, speed, stator flux and stator current

e e (b) speed, id and iq

The deceleration of the ISA is also tested by dropping the speed suddenly from 3000 rpm to 1500 rpm, while the induction machine is generating with full dc load. As shown in Fig. 2.12, the dc bus voltage of the ISA varies a little within the limitation of 42 V specifications [6] during speed deceleration. Fig. 2.12 (a)-(iii) shows the flux of the machine is increased when the speed returns to base speed (1500 rpm). Part (b) of Fig. 2.12 shows the d and q axis currents during decelerating of the ISA.

Chapter 2 An induction machine based ISA using RFOC with SVM 37

(a)

(b)

Fig. 2.12 ISA performance at deceleration: (a) bus voltage, speed, rotor flux and stator current

e e (b) speed, id and iq

Chapter 2 An induction machine based ISA using RFOC with SVM 38 2.5.4 High speed operation

The operation of proposed ISA system in high speed range is also tested. When the speed of the induction machine exceeds the base speed (1500 rpm), the stator flux reference is weaken by the inverse proportional with the rotor speed. Fig. 2.13 shows the ISA performance at 4000 rpm with full load. The induction machine’s torque is less than 6 Nm due to the high speed operation. The flux of the induction machine is reduced for field weakening.

In this thesis, it is possible to run the ISA only up to 4000 rpm due to limitation of the experimental setup in the laboratory.

Fig. 2.13 ISA with field weakening at high speed

2.6 Conclusion

This chapter presents a rotor flux oriented control scheme of the integrated starter/alternator. Extensive experimental results show its effectiveness in ISA application. However, the current decoupling and co-ordinate transformation make the

Chapter 2 An induction machine based ISA using RFOC with SVM 39 control structure quite complex. Due to existence of current control loop, at least three PI controllers have to be used for the torque and flux control of the induction machine. In practice, these PI controllers’ gains are not easy to design and tune. Moreover, the rotor flux estimation is sensitive to the variation of the induction machine’s parameters, especially the rotor resistance. A mechanical speed sensor is also necessary for the torque and flux control. This sensor requirement is a major disadvantage of the RROC based ISA.

Because the above limitations of the flux oriented control, direct torque controlled ISA is proposed in this thesis. Three different control structures based on direct torque control concept are discussed in the following chapters under same conditions. Subsequent chapters deal with a direct torque controlled ISA, starting with the simple switching-table based DTC described in Chapter 3.

Chapter 2 An induction machine based ISA using RFOC with SVM 40

CHAPTER 3 CLASSICAL DIRECT TORQUE CONTROLLED INTEGRATED STARTER/ALTERNATOR

3.1 Introduction

As stated in Chapter 1, classical direct torque control (DTC) for induction motors was first introduced in 1980’s [66, 67]. Classical direct torque control is a very simple control scheme with low computational requirement. A switching table is adopted to select one of eight basic voltage space vectors determined by the torque and flux errors and position of the stator flux vector. This classical direct torque control is a DTC with a Switching-Table (DTC-ST). The torque and flux are estimated by a voltage mode estimator in the stationary frame. Only stator resistance is involved in the calculation and no axis transformation is required for DTC-ST. In addition, there is no rotor velocity or position sensor required for the torque and flux control.

Since late 1980’s, DTC-ST has gained wide acceptance in motor drives application from both academia [63, 76-80] and industry [73]. DTC-ST controlled generators has attracted research interests in aircraft application [71], grid application [68, 69], wind power generation [70] and ISA application [72] as well.

This chapter describes the principle of the classical direct torque control and the classical direct torque controlled scheme for ISA. Both simulation and experimental results are provided to confirm the feasibility of DTC-ST for ISA operation of the induction machine. This chapter is organized as follows. Section 3.2 presents the principle of classical direct torque control. The ISA control scheme with classic DTC is developed in Section 3.3. Simulation results of ISA are given in Section 3.4. Section 3.5 provides the experimental results. Due to the limitation of hardware, only steady state of

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 41

the classic DTC controlled induction generator with 150 μs (sampling time) is tested in this chapter.

3.2 Classical direct torque control principle

In stationary frame, the dynamic behaviour of induction machine can be described as following equations: G JJG G dΨ VRI=+s (3-1) sssdt G G dΨ G 0 = RI+−ωΨr j (3-2) rrdt m r G G G ⎪⎧Ψ=s LIss + L mr I ⎨ G G G (3-3) ⎩⎪Ψ=rmsrrLI + LI

33LLG GGG TP=Ψ×Ψ==ΨΨθ−θmm P sin() ersrssr22σσLL LL sr sr (3-4) GG 3 Lm =ΨΨγPsinrs 2 σLLsr where

L 2 σ=1 − m (3-5) LLs r

where Rs and Rr are the stator and rotor resistances, Ls , Lr and Lm are the stator, rotor and mutual inductances, respectively. And ωm is rotor speed, P is the number of pole pairs, θs and θr are the angles of stator and rotor flux vectors, respectively, and γ

(equal to θ−θs r ) is the angle between the stator and rotor flux vectors.

The rotor flux vector changes slowly compared to the stator flux vector with a large time constant. So it can be assumed to be constant. The stator flux vector can be changed by applying proper stator voltage. Therefore, the torque can be rapidly changed by varying γ in the required direction which is determined by the required torque reference. This is the basic idea of the classic direct torque control scheme. With voltage source inverter, the angle γ can be easily changed by producing appropriate stator

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 42

voltage space vectors according to (3-1). The voltage vector can be selected from eight basic vectors including six non-zero active voltage (VV16→ ) vectors and two zero voltage vectors ()VV07, as shown in Fig. 3.1.

β

V3 V2

S = 1 S = 1 V A B SC = 1 4 V0 α V 7 V1

SA = 0 SB = 0 SC = 0 V5 V6

Fig. 3.1 Eight switching states and the voltage space vectors

By applying different voltage vectors, the stator flux vector will move forward or backward as indicated in Fig. 3.2.

β V V ωs 3 2

V4 V1

V V K 5 6 ψ s K ψ r

γ α

Fig. 3.2 Movement of stator flux vector by selection different voltage space vectors

The structure of classical direct torque control for voltage-source inverter-fed induction machine is shown in Fig. 3.3. Proper voltage vectors are selected from the switching table by considering different output states of the torque and flux comparators and the sectors where the stator flux vectors are located. The optimum switching table is shown

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 43

in Table 3.1, which is referred to [74, 75]. The torque and flux are independently controlled by the torque and flux hysteresis comparators, respectively.

G ∗ ψ s

∗ Te

Vdc ∠θs

Te G ψ s

Fig. 3.3 Structure of classical direct torque control

Table 3.1 Switching table of inverter vectors

dψ dTe Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6

1 V2 V3 V4 V5 V6 V1

1 0 V7 V0 V7 V0 V7 V0

−1 V6 V1 V2 V3 V4 V5

1 V3 V4 V5 V6 V1 V2

0 0 V0 V7 V0 V7 V0 V7

−1 V5 V6 V1 V2 V3 V4

The output of flux hysteresis comparator with two-level is dψ

⎧ ⎪difψ =ψ≤ψ−Δψ1 s ref s ⎨ (3-6) difψ =ψ≥ψ+Δψ0 ⎩⎪ s ref s

where Δψs is the error band of the flux comparator.

The output of torque hysteresis comparator with three-level is dTe

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 44

⎧ ⎧ ⎪dTeerefe= 1 if T≤−Δ T T ⎪anticlockwise rotation : ⎨ ⎪ dT=≥0 if T T ⎩⎪ eeref ⎪ ⎨ (3-7) ⎪ ⎧ ⎪ ⎪dTeerefe=≥−Δ1 if T T T ⎪clockwise rotation : ⎨ dT=≤0 if T T ⎩⎪ ⎩⎪ eeref

where ΔTe is the error band of the torque comparator.

3.3 ISA with classical DTC

β β G G ψ s ψ r

G G ψ r ψ s γ γ

α α Motoring State Generating State

Fig. 3.4 stator and rotor flux vector at motoring and generating states

The idea of the direct torque control can be extended from motoring mode to generation mode with same control structure. The only difference in generation mode is that the torque reference is negative and the stator flux vector lags to rotor flux vector as shown in Fig. 3.4.

Based on above analysis, a complete scheme of classic direct torque controlled ISA is developed and it is indicated in Fig. 3.5. It includes starting/generating state switch which simulates the operation of ISA from stating mode to generating mode. During starting mode, the induction acts as a motor to provide high torque for the starting of the engine. During generating mode, the torque reference is switched to the output of voltage controller to maintain the dc bus voltage with negative torque. As shown in Fig. 3.5, the dc load of ISA is connected at dc side of the DC-AC converter with the battery. The converter of the induction machine supplies active power to the dc load during

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 45

generation state while it provides reactive power to the machine. In this scheme, one voltage sensor for dc bus voltage and two current sensors for the stator current of the induction machine are used for the controller.

* Vdc Tstarting + Vdc −

Vdc T * +

∗ − ψ s

− G ∠θs ψ s

Te

Fig. 3.5 Classic DTC scheme for ISA

The stator flux vector is estimated in the stationary frame avoiding co-ordination transformation and involvement of more machine parameters. The estimation algorithm is given in (3-8) G JJG G ⎧Ψ=VRIdt − ⎪ ssss∫ ( ) ⎨ 3 G G (3-8) ⎪TPI=Ψ× ⎩ ess2

3.4 Simulation results

The proposed scheme has been modeled with Matlab/Simulink in order to evaluate its performance. The model of the induction machine in Simulink is modified to include the engine speed as an input variable. The simulation results present in this chapter is for 1.0 kW/22 V induction machine supplied by voltage source inverter with 42 V dc bus. The parameters of the induction machine are shown in Table 2.1. The 42 V batteries also modeled to provide dc voltage for starting. In the simulation, it is assumed that the engine starts at 1200 rpm. After starting, the speed of induction machine is

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 46

determined by the engine. In order to illustrate the proposed scheme for the generator, the simulation has been carried out under the following conditions.

3.4.1 Starting mode

During the starting period, the induction machine produces full torque to drive the DC machine, which simulates the engine. The starting torque is set as 6 Nm and the engine starting speed is 1200 rpm. As shown in Fig. 3.6, the full induction machine’s torque run the whole set from 0 to 1200 rpm. After the speed reaches 1200 rpm, the engine speed in the model is set as 1500 rpm. At the same time, the reference of the induction machine is switched from torque to the output of the voltage regulator. The induction machine now begins to act as a generator and provide power to the battery and the dc load. The stator flux of the induction machine is kept as constant with proposed direct torque control method.

(a) Ts =150 μs

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 47

(b) Ts =50 μs

Fig. 3.6 Starting process of ISA (a) Ts =150 μs (b) Ts =50 μs

Two sampling times are used for the modeling. As shown in Fig. 3.6, the torque and flux ripples are much less with sampling time as 50 μs than that of the case with sampling time as 150 μs .

3.4.2 Generating mode- steady state

The steady state performance with full load of the induction machine is shown in Fig. 3.7. With voltage regulator the dc voltage of the ISA system is kept as 42 V when the induction machine provides full torque to the load. Moreover, the stator flux of the induction machine is kept constant within the error band. Similarly, small torque and flux ripples are obtained with shorter sampling time (50 μs ).

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 48

(a) Ts =150 μs

(b) Ts =50 μs

Fig. 3.7 ISA generating with full load (a) Ts =150 μs (b) Ts =50 μs

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 49

The spectrum analysis diagrams of the stator current Fig. 3.8 show the switching frequency is variable with DTC-ST. in addition, the harmonic components is lower with shorter sampling time (50 μs ).

(a) Ts =150 μs (b) Ts =50 μs

Fig. 3.8 Spectrum analysis of the stator current with FFT (a) Ts =150 μs (b) Ts =50 μs

3.4.3 Generating mode - dynamic response

The dynamic performance of the ISA is also studied in this section. The performances of the ISA system under load dump and engine speed acceleration or deceleration are presented below.

3.4.3.1 Performance during Load dump

The dc load of the ISA is removed suddenly at the generating state when the speed is 1500 rpm. As shown in Fig. 3.9, the dc bus voltage of the ISA is almost fixed at 42 V when the dc load is dumping no matter the sampling time is 150 μs or 50 μs . Certainly, high sampling frequency is preferred for lower torque and flux ripples. The induction machine’s torque is changed from -6 Nm to about 0 Nm during load dumping.

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 50

(a) Ts =150 μs

(b) Ts =50 μs

Fig. 3.9 Load dumping performance of ISA (a) Ts =150 μs (b) Ts =50 μs

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 51

3.4.3.2 Dynamic performance during acceleration/deceleration

In this section, the DC machine’s speed reference is increased suddenly from 1500 rpm to 2500 rpm and back to simulate the rapid change of the engine speed. During these acceleration and deceleration, the induction machine is generating with full dc load. As shown in Fig. 3.10, the dc bus voltage of the ISA is kept as 42 V whenever the simulated engine is accelerated or decelerated. The stator flux of the induction machine is reduced when the rotor speed is higher than the base speed (1500 rpm).

(a)

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 52

(b)

Fig. 3.10 ISA performance at speed ramp (Ts =50 μs ) (a) accelerating (b) deceleration

3.5 Experimental results

Voltage mode stator flux estimator is used in the experiment. Due to the noise or measurement error inherently present in the current sensor, the pure integrator in (3-8) can to be saturated. Therefore, a low pass filter is used instead for the flux estimation.

G 1 JJG G Ψ=s ()VRIsss − (3-9) sT+1 c

Where Tfcc=π()12 and fc is the cut-off frequency of the filter.

3.5.1 DTC-ST with constant switching frequency

The hysteresis comparator based classic DTC has the disadvantages of variable switching frequency. With a digital signal processor (DSP), the switching frequency can be fixed with discrete hysteresis comparator as shown in Fig. 3.11. The discrete

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 53

hysteresis comparator is different with analog hysteresis comparator by using a fixed sampling time Ts for the output of the comparator. Moreover, the output voltage vector selected from the Switching-Table is applied to the induction machine with equal switching period. Therefore, the switching frequency is constant. The discrete hysteresis comparator will operate like an analog hysteresis with low enough smaller sampling time. However, it requires a fast DSP.

Ts SH/

ΔT ΔT ∗ e ∗ e Te + Te + 2 2 ∗ ∗ Te Te ∗ ΔTe ∗ ΔT T − T − e e e t t t 2 T T T 2 1 2 3 s s s (a) (b)

Fig. 3.11 Analog (a) and discrete (b) hysteresis comparator [63]

In the experimental system, DSP slave processor TMS320F240 is used. It cannot implement the control algorithm with low sampling time (50 μs ) as mentioned in simulation. Therefore, only the steady state experimental results with Classic DTC based induction generator is given in this chapter with sampling time 150 μs .

3.5.2 Generating mode- steady state

It shows in Fig. 3.12 that the torque of the induction machine is negative with large ripples. The power generated by the induction machine transfers through the converter to charge the batteries. The locus of the stator flux vector was shown in Fig. 3.13, which indicates the vector is moving along a circle with an error band.

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 54

Fig. 3.12 ISA generating with DTC-ST

Fig. 3.13 Stator flux vector diagram

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 55

3.6 Conclusion

The classic direct torque controlled induction generator for integrated starter alternator application has been analyzed and verified with simulation and experiments. The results show that the direct torque control concept had been successfully extended to the control of induction generator for an ISA. Although the torque and flux ripples are rather large, their mean values are same as the RFOC based ISA for similar operating conditions.

A discrete method was implemented to keep the switching frequency of the inverter constant. High flux and torque ripples results from look-up table of the voltage vectors and the hysteresis comparators of the torque and flux. Therefore, short sampling time (as low as 25 μs ) of the control system should be used [73].

The drawbacks of high torque and flux ripples of the classical DTC can be reduced by using a voltage pulse width modulator instead of the switching table [81-91]. The DTC strategies operating at constant switching frequency can be implemented by means of PI controlled closed-loop schemes. The controllers calculate the required stator voltage vector, averaged over a sampling period. The voltage vector is finally synthesized by a PWM technique, which in most cases is the space-vector modulation (SVM).

The improved DTC schemes with SVM for ISA application have been proposed during this study [29, 55]. One of improved DTC schemes with direct flux vector control is presented in the next chapter.

Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 56

CHAPTER 4 DIRECT FLUX VECTOR CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SPACE VECTOR MODULATION

4.1 Introduction

Since direct torque control (DTC) was introduced in 1980’s, many schemes were proposed to overcome the problems associated with the basic DTC [66, 67]: operation with variable switching frequency and large torque ripple, due to the hysteresis control and the switching table method. The variable switching frequency problem can be addressed by Proportional-Integral (PI) controllers plus PWM instead of hysteresis controller and the torque ripple can be reduced with space vector modulation (SVM) technique [81-91]. However, few papers present the analytical design principle of the PI controller parameters for DTC with SVM. The PI controllers seem to be determined mainly by trial and error.

This chapter also presents the theory of direct flux vector control (DFC) scheme for an induction machine, which is based on the basic DTC concept. The scheme proposed in this chapter extends the works reported in [89], in which the relationships between controlled variables and the torque were not fully developed. This DFC scheme controls the electromagnetic torque of the induction machine by regulating the amplitude and the rotating speed of the flux vector with only one Proportional-Integral (PI) controller and the required voltage vector is applied to the induction machine by space vector modulation. The speed sensor is eliminated and the torque and stator flux is estimated with voltage mode estimator. This DFC scheme controls the torque of induction machine with high dynamic performance. This thesis is concerned with the dc bus

Chapter 4 Direct flux vector controlled ISA with space vector modulation 57

voltage control in an ISA application to meet the specification of the 42 V PowerNet using an induction machine under DFC.

This chapter analyzes the concept of proposed scheme in detail and presents the design principle of the PI controller parameters. Two types of PI controller design schemes are presented with direct synthesis and robust optimization methods based on the analysis of the inner relationships between the control variables and the torque. Modeling results show that the dynamic performance is not sensitive to the variation of the rotor resistance. Fixed switching frequency and low torque ripple are obtained with SVM technique. All the algorithms are based on stationary frame, and only stator resistance is used for calculation of the stator flux vector. Modeling and experimental results for the proposed direct flux vector control are presented for a 1.0 kW induction machine with a PI controller.

4.2 Direct flux vector control

In stationary frame, the dynamic behaviour of induction machine can be described as following equations: G JJG G dΨ VRI=+s (4-1) sssdt G G dΨ G 0 = RI+−ωΨr j (4-2) rrdt m r G G G ⎪⎧Ψ=s LIss + L mr I ⎨ G G G (4-3) ⎩⎪Ψ=rmsrrLI + LI

G G 3 Lm TPers= Ψ×Ψ (4-4) 2 σLLsr where

L 2 σ=1 − m (4-5) LLs r

where Rs and Rr are the stator and rotor resistances, Ls , Lr and Lm are the stator self, rotor self and mutual inductances, respectively. And ωm is rotor speed, P is the number of pole pairs.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 58

G G The relationship between stator and rotor flux vectors Ψs and Ψr respectively is derived from (4-2) and (4-3) G G G dRLΨrrm R r = Ψ+s (j ω−mr ) Ψ (4-6) dt Lsr Lσσ L r

By using Laplace transform of (4-6) and assuming the rotor speed ωm is changing G G slowly, the relationship between stator and rotor flux vectors Ψs and Ψr in the frequency domain can be obtained

Lm GG Ls Ψ=rs(s) Ψ (s) (4-7) LLrr⎛⎞ sjσ+−ωσ⎜⎟1 m RRrr⎝⎠

(Please refer to Appendix B for further details of the derivation included in this chapter) G G Assuming that Ψ=Ψ**jjtθs =Ψ ωs and the amplitude of Ψ is kept constant, and ssee s s G that Ψs rotates at an angular speed ωs ,

G 1 * Ψs(s)=Ψs (4-8) sj−ωs

By substituting (4-8) into (4-7) and taking inverse Laplace transform

⎧ Lm ⎫ G ⎪ ⎪ −1 ⎪ Ls 1 * ⎪ Ψ=r (t) L ⎨ Ψs ⎬ (4-9) LL⎛⎞sj−ω ⎪ sjσ+−ωσrr1 s ⎪ ⎪ ⎜⎟m ⎪ ⎩⎭RRrr⎝⎠

Thus

2 t ⎛⎞t − 12+−⎜⎟e− ecosτ ω−ω t G ⎜⎟τ (()sm) Lm ⎝⎠ Ψ=r (t) Ls 2 (4-10) 1 +τω−ω ( ()sm) ⎛⎞−−11⎛⎞y ×Ψ* jtan⎜⎟⎜⎟−τω−ω tan s e ⎝⎠⎝⎠x ( ()sm)

Chapter 4 Direct flux vector controlled ISA with space vector modulation 59

where

⎧ L τ=σ r ⎪ R ⎪ r t ⎪ − x cos( t )τ cos( t ) (4-11) ⎨ =ω−sme ω ⎪ t − τ ⎪ y =ω−sin(sm t ) sin( ω t ) ⎪ e ⎩

With small slip, (4-10) can be simplified as

t G ⎛⎞− ⎡ −−11⎛⎞y ⎤ Lm τ * j Ψ≈(t) 1 − e ×Ψe ⎢tan⎜⎟−τω−ω tan ()()sm⎥ (4-12) rs⎜⎟ ⎣ ⎝⎠x ⎦ Ls ⎝⎠

It shows that the rotor flux vector tracks stator flux vector in its amplitude and rotating speed with a time constant, given by τ . Once the stator flux is built up and kept constant, the rotor flux will also be kept constant. Therefore, the amplitude of the rotor flux can be considered as fixed after establishing of the stator flux. Equation (4-12) can be further simplified as

G ⎡ −−11⎛⎞y ⎤ Lm * Ψ≈Ψ(t) j ⎢tan⎜⎟−τω−ω tan ()()sm⎥ (4-13) rse ⎝⎠x Ls ⎣ ⎦

From (B-4), the torque can be expressed as

3 L G jtω T(t) Pm (t) * s (4-14) ers=Ψ×Ψe 2 σLLsr

By substituting (4-13) into (4-14), we obtain

2 ⎧⎫3 LLmm* T(t)es=Ψ⎨⎬ P ⎩⎭2 σLLsr L s (4-15) ⎧⎫⎡ −−11⎛⎞y ⎤ ×ω−sin⎨⎬ssm t⎢ tan⎜⎟ − tan () τω−ω()⎥ ⎩⎭⎣ ⎝⎠x ⎦ where

Chapter 4 Direct flux vector controlled ISA with space vector modulation 60

⎧ L τ=σ r ⎪ R ⎪ r t ⎪ − x cos( t )τ cos( t ) (4-16) ⎨ =ω−sme ω ⎪ t − τ ⎪ y =ω−sin(sm t ) sin( ω t ) ⎪ e ⎩

It clear that the dynamic response of torque is determined by the amplitude and rotating speed of the stator flux vector with the non-linear relationship of (4-15). The torque of the induction machine can be regulated by controlling rotating speed of the stator flux G vector Ψs as long as its amplitude is kept constant. As rotor flux vector tracks the stator flux vector, its amplitude is also kept constant after establishing of constant stator flux amplitude. In addition, the sin or tan computation results of a small angle is very close to the angle by itself (in rad) as shown in (4-17). Therefore, the above torque expression can be simplified to (4-18) in which the slip is small.

sin()θ ≈θ≈θ tan( ) ( ) ( small θ) (4-17)

By considering (4-15) and (4-16) at same time, torque expression can be further simplified as

2 t 2 ⎧⎫3 Lm * ⎛⎞− T(t)≈ P Ψ−ω−ω1 τ (4-18) essm⎨⎬2 ⎜⎟e () ⎩⎭2 RLrs ⎝⎠

Therefore

t ⎛⎞− τ T(t)esm= K⎜⎟1 −ω−ω() (4-19) ⎝⎠e where

2 2 ⎧ 3 Lm * ⎪KP=Ψ2 s ⎪ 2 RLrs ⎨ (4-20) L ⎪τ=σ r ⎪ ⎩ Rr

By Laplace transform of (4-19), we have

⎛⎞1 T(s)esm= K⎜⎟L{}ω−ω (4-21) ⎝⎠τ+s 1

Chapter 4 Direct flux vector controlled ISA with space vector modulation 61

where L{ω−ωs m } is the Laplace form of {ωs −ωm }

The of the torque loop with input as {ωs −ωm } can be written as

T(s)e K G(s)p == (4-22) L{}ωsm−ω τs +1

Equation (4-22) shows that the relationship between Te and ωs is equivalent to a first order system with a disturbance ωm . The equivalent system block is shown as follows:

−ωm ()s

Ts() ω ()s e s K τ s +1

Fig. 4.1 Equivalent system model of the torque loop

In order to achieve good performance of tracking a reference torque signal and disturbance rejection, the PI controller of Fig.4.2 may be employed:

−ωm ()s ∗ ω ()s Ts() Te s K e Gsc () − τ s +1

Fig.4.2 PI control of the equivalent system where

Ks+ K G(s)= pi (4-23) c s

4.2.1 Direct flux vector control scheme

From above analysis, it is clear that a direct relationship exists between the torque and the rotational speed of the stator flux vector when its amplitude is kept constant. This means that it is possible to control the machine torque by directly controlling the

Chapter 4 Direct flux vector controlled ISA with space vector modulation 62

amplitude and rotating speed of stator flux vector. This is the basic idea of direct flux vector control for induction machine. A complete scheme of direct flux vector control that allows effective torque control has been developed and it is indicated in Fig.4.3. The stator flux vector is estimated in the stationary frame avoiding co-ordination transformation and involvement of more machine parameters. The estimation algorithm is given in (3-8) G JJG G ⎧Ψ=VRIdt − ⎪ ssss∫ ( ) ⎨ 3 G G (4-24) ⎪TPI=Ψ× ⎩ ess2

The above scheme uses only one PI torque regulator to control the rotating speed of stator flux vector. The desired amplitude and angle of the stator flux vector is given by G ⎧ ψ=Ψ** ⎪ ss ⎪ ∗ ⎨Δθ=ωΔssT (4-25) ⎪θ ∗ =θ +Δθ ⎩⎪ s ss

where ΔT is the sampling time, Δθs is the increased angle of stator flux vector during sampling period and θs is the current angle of the stator flux vector. The reference stator flux reference vector is compared with the estimated flux to obtain error flux G G vector ΔΨs . With given ΔΨs , the exact stator voltage vector that changes the rotating speed of stator flux vector to generate required torque while keeping its amplitude constant is given by G G ΔΨ G VRI=+s (4-26) refΔT s s

The space vector modulation method is used to apply the required stator voltage vector with fixed switching frequency. In transient state, the reference voltage will be larger than the available inverter voltage when the torque error is too large. In that case, the

∗ speed ωs has to be limited to ensure that the reference voltage is lower or equal to the maximum inverter voltage: G VVref≤ max (4-27)

Chapter 4 Direct flux vector controlled ISA with space vector modulation 63

where Vmax is the maximum available inverter voltage. For under-modulation of SVM,

1 Vmax equals to Vdc , where Vdc is the dc bus voltage of the inverter. 3

Therefore the limitation of the torque PI controller should be:

1 Vdc ∗ Vmax 3 ω≤s ** = (4-28) ψψss

∗ ψ s G * G G ψ s V * ∗ ∗ ΔΨ s 1 ref * ∗ ∗ Δθ ψ s ∠θs SVM IM ω r Te ωs s θs ΔT PI PI ΔT − G − + ψ ω s Vdc r Te θs

Torque& Stator Flux Estimator

Encorder

Fig.4.3 Direct flux vector control scheme for induction machine

4.2.2 Design of the PI controller for torque regulation

In this section, two different methods are presented for the design of PI controller in the closed torque loop.

4.2.2.1 Direct synthesis of PI controller

Because G(s)p is a stable first order system, the PI can be synthesized for the desired closed-loop transfer function. Assuming the desired close loop transfer function of torque is

1 G(s)= (4-29) 1 λs +1 where λ is the desired time constant. thus

Chapter 4 Direct flux vector controlled ISA with space vector modulation 64

1 Gcp (s)G(s) G(s)1 == (4-30) λ+s11 + G(s)G(s)cp

⎧ τ K = ⎪ p Kλ ⇒ ⎨ (4-31) 1 ⎪K = ⎪⎩ i Kλ

4.2.2.2 Robust PI controller

Equations (4-30) and (4-31) show that direct synthesized PI controller is very sensitive to the parameters of the system, which are included in (4-20) and (4-21). Practically, the rotor resistance Rr may vary up to 100% of the nominal value due to the rotor heating and the mutual inductance Lm may also changes in the case of magnetic saturation. If any parameter changes, the desired closed-loop characteristic cannot be realized by designed PI controller parameters in (4-31). Therefore, robust control design method based on performance index is used in this section.

The closed-loop transfer function of the system in Fig.4.2 is

G(s)G(s)cp G(s)2 = = 1+ Gcp (s)G(s)

KKpi s+ KK (4-32) = τ (KK)1+ KK ss2 ++p i τ τ

As presented in [92], the optimum coefficients of the performance index ITAE are

22 s.s+14ω+ωnn (4-33)

where ωn is the natural frequency of the closed-loop system.

ωn is selected to meet the settling time requirement. And the settling time is

4 ts = (4-34) ζωn where ζ is the damping ratio.

Thus

Chapter 4 Direct flux vector controlled ISA with space vector modulation 65

(KK)1+ KK sss.s222++=+ω+ωp i 14 (4-35) ττ nn

Then

⎧ 14. ω τ− 1 K = n ⎪ p K ⎨ (4-36) ωτ2 ⎪K = n ⎩⎪ i K

To remove the zero of closed-loop system, a pre-filter G(s)f is added to G(s)2 . Then the closed-loop transfer function changes to

G(s)32= Gf (s)G(s) (4-37)

Since the desired closed-loop transfer function is

KKi ω 2 G(s)==τ n (4-38) 3 (KK)1+ KK s.s22+14ω+ω ss2 ++p i nn ττ

The pre-filter G(s)f is designed as

1 G(s)f = (4-39) ()KKspi+1

With pre-filter G(s)f , the system change to

−ωm ()s ∗ T ωs ()s Tse () e K Gsf () Gsc () − τ s +1

Fig.4.4 PI control of equivalent system with pre-filter

4.2.3 Design of the PI controller with control delay

Due to digital control structure, the control signal would be delayed for 1 to 1.5 times of the sampling time. In this section, two different methods are presented for the design of PI controller with considering the delay effect.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 66

−ωm ()s ∗ T ωs ()s Tse () e K −sTd Gsc () e − τ s + 1

Fig.4.5 PI control of equivalent torque loop where

Ks+ K G(s)= pi (4-40) c s

and Td is the delay time

K G(s)= e−sTd (4-41) p τ+s 1

4.2.3.1 Direct synthesis of PI controller

Because G(s)p is a stable first order system, the PI can be synthesized for the desired closed-loop transfer function. Assuming the desired close loop transfer function of torque is (as the time delay cannot be removed from the process)

1 G(s)= e−sTd (4-42) 1 λ+s 1 where λ is the desired time constant thus

G(s)G(s) 1 −sTd cp G(s)1 == e (4-43) λ+s11 + G(s)G(s)cp So

111G(s)1 G(s)c == (4-44) K −sTd Gp (s)11−λ+− G(s)1 s e τ+s 1

Suppose that e−sTd is approximated by a 1st order Taylor series expansion, i.e.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 67

−sTd eTs≈−1 d (4-45)

So (4-44) is simplified as

11 111τ+s G(s)=== (4-46) c KK λ+−sTssTsKTs11() −ddd λ+() λ+ τ+ss11 τ+

Compared (4-46) with (4-40)

⎧ τ K = ⎪ p ⎪ KT()λ+ d ⇒ ⎨ (4-47) ⎪ 1 Ki = ⎩⎪ KT()λ+ d

4.2.3.2 Robust PI controller

Equations (4-46) and (4-47) also show that direct synthesized PI controller is very sensitive to the parameters of the system. If any parameter changes, the desired closed- loop characteristic cannot be realized by designed PI controller parameters in (4-47). Therefore, robust control design method based on performance index is used in this section.

The closed-loop transfer function of the system in Fig.4.2 is

Ks+ K piK −sTd G(s)G(s) e G(s)==cp ssτ+1 (4-48) 2 1+ G (s)G(s) Ks+ K K cp 1+ pi e−sTd ssτ+1

Chapter 4 Direct flux vector controlled ISA with space vector modulation 68

Kspi+ K K KKsKK+ ssτ+1 −−sTsTd pi d G(s)2 == e2 e Kspi+ K K τ++ssKKsKKTs +1 − 11+−()Ts ()pi() d ssτ+1 d KKsKK+ pi −sTd = 22e τ++ssKKsKKTsKKKKTsppdiid − + − KKsKK+ (4-49) pi −sTd = 22 e τ−sKKTssKKsKKTsKKpd ++ p − id + i

KKsKKpi+

τ−KKTpd = e−sTd 1+−KK KKT KK ss2 ++pid i τ−KKTpd τ−KKTpd

As presented in [14], the optimum coefficients of the performance index ITAE are

22 s.s+14ω+ωnn (4-50)

where ωn is the natural frequency of the closed-loop system.

ωn is selected to meet the settling time requirement. And the settling time is

4 ts = (4-51) ζωn where ζ is the damping ratio.

Thus

2221+−KKpid KKT KKi sss.s++=+ω+ω14 nn (4-52) τ−KKTpd τ− KKT pd

Then

Chapter 4 Direct flux vector controlled ISA with space vector modulation 69

⎧1+−KKpid KKT ⎪ =ω14. n ⎪ τ−KKTpd ⎨ KK ⎪ i =ω 2 ⎪ n ⎩τ−KKTpd ⎧ ⎪1141414+KKpidn − KKT =ωτ− .() KKT pdn =ωτ−ω . . npd KKT ⎨ 22 ⎩⎪KKinpdn=ω τ− K KT ω

⎪⎧KKpnpdidn+ω14 . KKT − KKT =ωτ− 14 . 1 ⎨ 22 (4-53) ⎩⎪KKTpdnω+ KK i =ωτ n

⎪⎧()K+ω14 .nd KT K p − K id KT =ωτ− 14 . n 1 ⎨ 2 2 ⎩⎪KKTpdnω+ KK i =ωτn

⎡⎤⎡⎤⎡⎤K+ω14 .nd KT − KT d K p 14 . ωτ− n 1 ⎢⎥⎢⎥⎢⎥22= ⎣⎦⎣⎦⎣⎦KTdnωωτ K K i n

−1 ⎡⎤⎡KK.KTKT.pnddn+14ω− ⎤⎡ 14 ωτ− 1 ⎤ ⎢⎥⎢= 22 ⎥⎢ ⎥ (4-54) ⎣⎦⎣KKTKidnnωωτ ⎦⎣ ⎦

To remove the zero of closed-loop, a pre-filter G(s)f is added to G(s)2 . Then the closed-loop transfer function changes to

G(s)32= Gf (s)G(s) (4-55)

Since the desired closed-loop transfer function is

KKi

τ−KKTpd G(s)== e−sTd (4-56) 3 1+−KK KKT KK ss2 ++pid i τ−KKTpd τ− KKT pd

The pre-filter G(s)f is designed as

1 G(s)f = (4-57) ()KKspi+1

With pre-filter G(s)f , the system change to

Chapter 4 Direct flux vector controlled ISA with space vector modulation 70

−ωm ()s ∗ T ωs ()s Tse () e K Gsf () Gsc () − τ s +1

Fig.4.6 PI control of equivalent system with pre-filter

Based on above analysis, the modified PI controller parameters can be obtained by considering the delay effect. The modified PI controller parameters have been used in the experiments.

4.2.4 Modeling results

A 1.0 kW, 22 V, 4-pole induction machine is considered to illustrate proposed direct flux vector control scheme. The parameters of the induction machine are shown in Table 4.1, which are same as that in Table 2.1. The whole system is modelled by Simulink/Matlab.

Table 4.1 Parameters of the Induction Machine

Rated output power(W) 1000 Rated Voltage (Volt) 22 Rated frequency (Hz) 50 Poles number P 4

Stator resistance Rs ( mΩ ) 25.1

Rotor resistance Rr ( mΩ ) 18.2 Mutual inductance (mH) 1.8

Stator inductance Ls (mH) 0.07618

Rotor inductance Lr (mH) 0.07618 Inertia (Kg.m²) 0.00824 Using these parameters, the equivalent torque open-loop transfer function can be express as follows

K 0.4929 G(s)== (4-58) p τss+×+18.2101-3

Chapter 4 Direct flux vector controlled ISA with space vector modulation 71

where

2 ⎧ 3 L 2 KP=Ψ=m * 0.4929 ⎪ 2 RL2 s ⎪ rs ⎪ L -3 ⎨τ=σr =82. × 10 (4-59) ⎪ Rr ⎪ Ψ=* 0. 057 ⎪ s ⎩

4.2.4.1 Direct synthesis of PI controller

The PI controller is designed with desired close loop performance and the machine parameters by (4-31). For example, the desired close loop transfer function is

11 G(s)== (4-60) 1 λss+×+14101-4

It is corresponding to a first order system whose setting time is chosen as 2 ms for a Step-function input.

Thus, the PI controller parameters are

⎧ τ K ==41.5940 ⎪ p1 Kλ ⎨ (4-61) 1 ⎪K ==5.0716 × 103 ⎩⎪ i1 Kλ

Fig.4.7 Torque dynamic performance of direct flux vector control with rotor resistance variation of 50% and 100%

Chapter 4 Direct flux vector controlled ISA with space vector modulation 72

Closed torque loop performance of proposed scheme with above PI controller is investigated. The torque reference is 6 Nm and the sampling time is 150μs . Practically, rotor resistance varies due to heating. The sensitivity of the system to parameter variation should be studied. Fig.4.7 shows the torque dynamic response for square-wave torque reversal reference input. It takes into account the effect of rotor resistance Rr variation, which varies by 50% and 100% of the original value in Table 4.1. The desired response time of torque is achieved (2 ms) and the torque tracks the reference well without steady state error as long as the parameters of the induction machine are accurate. However, there will be a tracking error when the rotor resistance Rr is changed. The inaccurate Rr results in the desired closed-loop behavior is not being achieved.

Fig.4.8 Performance of direct flux vector control with speed loop

Closed speed loop performance of the system is also tested. Fig.4.8 shows the speed of induction machine rises from standstill to 600 rpm, and then accelerates to rated speed

Chapter 4 Direct flux vector controlled ISA with space vector modulation 73

1500 rpm. There is an overshoot in torque which is caused by establishing of stator flux during starting period (0-600 rpm).

Fig.4.8 also shows the amplitude of stator flux vector is kept constant by the controller and that of rotor flux vector tracks stator flux with a time delay. After establishing of stator and rotor flux, their amplitudes can be kept constant by the controller during accelerating period (600-1500rpm). This indicates that the previous assumption of constant rotor flux amplitude is valid. The stator flux and current diagram shows that less torque ripple and current harmonics are obtained with the proposed scheme using the designed PI controller by comparing with the classic direct torque control scheme.

4.2.4.2 Robust PI controller

Assuming the desired settling time is 2 ms, ωn can be obtained by selecting ζ with (4- 34). For example

⎧ζ=08. ⎪ 4 (4-62) ⎨ω= =2500 ⎪ n ⎩ ζts then

⎧ 14. ωτ− 1 K ==n 56.2029 ⎪ p2 K ⎨ (4-63) ωτ2 ⎪K ==n 1.0398 × 105 ⎩⎪ i2 K

11 G(s)== (4-64) f K 5.4049× 10-4s + 1 p s +1 Ki

Under same condition, closed torque loop performance of proposed scheme with PI controller parameters in (4-63) is investigated. The effect of pre-filter is also studied. Fig.4.9 shows that large torque overshoot occurs resulting from the zero of the closed- loop transfer function. Therefore, pre-filter is required to remove the overshoot. As shown in Fig.4.10, the system is very robust to the variation of rotor resistance even it changes to two times of original value. Unlike the rotor flux oriented control scheme,

Chapter 4 Direct flux vector controlled ISA with space vector modulation 74

direct flux vector control need few parameters of the machine for the controller, which increases its robust ability to parameters variation.

Fig.4.9 Torque dynamic performance of direct flux vector control with and without Pre-filter

Fig.4.10 Torque dynamic performance of direct flux vector control with rotor resistance variation of 50% and 100% (pre-filter added)

Chapter 4 Direct flux vector controlled ISA with space vector modulation 75

Fig.4.11 Performance of direct flux vector control with speed loop – No pre-filter added

Similar with above section, closed speed loop performance of the system is also investigated. Fig.4.11 and Fig.4.12 show the speed of induction machine rises from standstill to 600 rpm, and then accelerates to rated speed 1500 rpm. There is an overshoot in torque which is caused by establishing of stator flux during starting period (0-600 rpm). With pre-filter added to the torque controller, the torque overshoot is less in Fig.4.12.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 76

Fig.4.12 Performance of direct flux vector control with speed loop –pre-filter added

4.2.4.3 Comparison with rotor flux oriented control (RFOC)

Table 4.2 Parameters of the control scheme

Inverter dc bus voltage Vdc (V) 42

Stator flux reference Ψ s for DFC (Wb) 0.057

Rotor flux reference Ψr for RFOC (Wb) 0.0547

Sampling time ( μs ) 150

The direct flux vector control (DFC) is compared with rotor flux oriented control (RFOC) presented in Chapter 2. The control structure of RFOC with SVM is shown in Fig.4.14. The torque dynamic response of RFOC under same conditions is given in Fig.4.13. The parameters of induction machine are same with Table 4.1 and the control parameters are shown in Table 4.2. The torque response of RFOC is better than DFC without overshoot. In this chapter, the settling time of DFC is designed as 2 ms as an

Chapter 4 Direct flux vector controlled ISA with space vector modulation 77

example, which is a little slower than that of RFOC. Under same design principle, the torque response of DFC can be faster than 2 ms with difference PI parameters.

Fig.4.13 Torque dynamic response of RFOC

ω* i * r q V ee q dq− PI PI VV, ∗ * − αβ ψ r i SVM IM id q Vd PI PI α − β − i d G ∠Ψr

G Current Model Ψr

ωr Encorder

Fig.4.14 Rotor flux oriented control scheme with SVM

The sensitivity of RFOC is also investigated for comparison. As show in Fig.4.15, RFOC is very sensitive to the variation of rotor resistance. Its torque performance is poor even when the rotor resistance changes only by 20% of the original value. The torque is totally out of control when the rotor resistance increases by 50%. Comparing

Chapter 4 Direct flux vector controlled ISA with space vector modulation 78

Fig.4.15 and Fig.4.10, it is obvious that DFC is more robust than RFOC to the variation of rotor resistance Rr . The DFC is more robust than RFOC to the variation of the rotor resistance because of the following two facts. Firstly, the rotor resistance is not involved in the control system of DFC whereas it is a critical parameter for the decoupling controller of the RFOC. Secondly, the DFC with robust PI controller is not sensitive to the variation of machine parameters.

Fig.4.15 Torque dynamic performance of rotor flux oriented control with varied rotor resistance

Chapter 4 Direct flux vector controlled ISA with space vector modulation 79

4.2.5 Experimental results

Fig. 4.16 The experiment setup of the system

As shown in Fig. 4.16, the system was implemented on a dSPACE DS1104 Controller Board with TMS320F240 slave processor. A three phase VSI inverter is connected to supply 42 V dc bus voltage, which is supplied from a rectifier.

Voltage mode stator flux estimator based on (4-1) is used in the system. Due to the noise or measurement error inherently present in the current sensor, the pure integrator in can lead to saturation. To avoid that, a low pass filter is used in stead for the flux estimation.

G 1 JJG G Ψ=s ()VRIsss − (4-65) sT+1 c

where Tfcc=π()12 and fc is the cut-off frequency of the filter.

4.2.5.1 Direct synthesis of PI controller

Closed-loop torque performance of proposed scheme with above the PI controller is investigated. The torque reference is square wave signal with ± 6 Nm magnitudes and the sampling time is 150μs .

Chapter 4 Direct flux vector controlled ISA with space vector modulation 80

Fig.4.17 Torque dynamic performance of direct flux vector control with direct synthesis of PI controller

Closed-loop speed performance of the system is also tested. Fig.4.18 shows the speed of induction machine rises from 600 rpm to rated speed 1500 rpm. The amplitude of stator flux vector is kept constant by the controller.

Fig.4.18 Performance of direct flux vector control with speed loop

Chapter 4 Direct flux vector controlled ISA with space vector modulation 81

4.2.5.2 Robust PI controller

Fig.4.19 Torque dynamic performance of direct flux vector control with pre-filter

Under same condition, closed torque loop performance of proposed scheme with PI controller parameters in (4-63) is investigated. The torque response is shown in Fig.4.19.

Similar with the above section, closed-loop speed performance of the system is also investigated. Fig.4.20 shows the speed of induction machine rises from 600 rpm to rated speed 1500 rpm. The amplitude of stator flux vector is kept constant by the controller.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 82

Fig.4.20 Performance of direct flux vector control with speed loop

Fig.4.21 shows the speed, torque and stator flux at steady state. Less torque and flux ripples are obtain with proposed control method.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 83

Fig.4.21 steady state performance with speed-loop

Fig.4.22 Spectrum analysis of the stator current

Chapter 4 Direct flux vector controlled ISA with space vector modulation 84

The spectrum of the stator current is analyzed by FFT algorithm by using the data captured by a digital oscilloscope (Lecroy 364TL). The 6.67 kHz part of the frequency in Fig.4.22 is corresponding to the sampling frequency of the system, which indicates the switching frequency of the inverter is fixed by space vector modulation.

4.3 Direct flux vector controlled induction generator for an ISA

4.3.1 Induction generator with DFC

* Udc Tstarting + U dc −

T * + ω ∗ s G * JJJJG G ψ Δψ s s 1 Vref ∗ − ψ s ΔT − G ψ s

Te

Fig. 4.23 DFC scheme for ISA

From above analysis, it becomes clear that a direct relationship exists between the torque and the rotation speed of stator flux vector when its amplitude is kept constant. This means that it is possible to control the machine torque by directly controlling the amplitude and rotating speed of stator flux vector. This is the basic idea of direct flux vector control for induction machine. A complete scheme of direct flux vector controlled ISA that allows effective dc bus voltage and torque control has been developed and it is indicated in Fig. 4.23. It includes a starting/generating mode switch which simulates the operation mode of ISA from starter to generator. During starting mode, the induction machine acts as a motor to provide high torque for the starting of the engine. As shown in Fig. 4.23, the dc load of ISA is connected at dc side of the DC-

Chapter 4 Direct flux vector controlled ISA with space vector modulation 85

AC converter with the battery. The VSI converter for the induction machine supplies active power to the dc load during generation state while the same converter also provides reactive power to the machine for the of its field.

The stator flux vector is estimated in the stationary frame avoiding co-ordination transformation and involvement of more machine parameters. The estimation algorithm is given in (3-8) G JJG G ⎧Ψ=VRIdt − ⎪ ssss∫ ( ) ⎨ 3 G G (4-66) ⎪TPI=Ψ× ⎩ ess2

The above scheme uses only one PI torque regulator to control the rotating speed of

G * stator flux vector. The desired reference stator flux vector ψs is generated by Flux- Vector-Combination block in Fig. 3.5, whose amplitude and angle is given by

G * ⎧ ψ=Ψ* ⎪ ss ⎪ ∗ ⎨Δθss = ω Ts (4-67) ⎪ ∗ θs =θss +Δθ ⎩⎪

where Ts is the sampling time, Δθs is the angular movement of the stator flux vector during sampling period and θs is the present angle of the stator flux vector. The reference stator flux reference vector is compared with the estimated flux to obtain error G G flux vector ΔΨs . With given ΔΨs , the exact stator voltage vector that changes the rotating speed of stator flux vector to generate required torque while keeping its amplitude constant is given by G G G ΔΨs VRIref=+ s s (4-68) Ts

The space vector modulation method is used to apply the required stator voltage vector with fixed switching frequency. In transient state, the reference voltage will be larger than the available inverter voltage when the torque error is too large. In that case, the

∗ speed ωs has to be limited to ensure the reference voltage is lower or equal to the maximum inverter voltage:

Chapter 4 Direct flux vector controlled ISA with space vector modulation 86

G VVref≤ max (4-69)

where Vmax is the maximum available inverter voltage. For under-modulation of SVM,

1 Vmax equals to Vdc , where Vdc is the dc bus voltage of the inverter. 3

With SVM technique, the demand space voltage vector can be composed by two active and one zero voltage vectors, which is illustrated in right part of Fig. 4.24.

β β G G V V3 2 G G Vref VTref Δ JJJG * G G G V V α α Ψ s 4 G0 G V Ψ s 7 V1

α G G θs V5 V6

Fig. 4.24 Reference space voltage vector

G G G For example, when Vref locates between V1 and V2 , it can be expressed as

G GGG T0 TT12 VVref =++012 V V (4-70) TTTs ss G G G where T0 , T1 , and T2 are the effective time intervals of V0 , V1 and V2 , respectively within the sampling period Ts .

From Fig. 4.24, the following can be obtained

⎧ TTπ VcosVα=12 + V cos ⎪ ref 12 ⎪ TTss3 ⎨ (4-71) ⎪ T2 π Vref sinα= V2 sin ⎩⎪ Ts 3

Thus

Chapter 4 Direct flux vector controlled ISA with space vector modulation 87

⎧ π Vsin(−α ) ⎪ ref TT= 3 ⎪ 1 π s ⎪ Vsin1 ⎨ 3 (4-72) ⎪ Vsinα TT= ref ⎪ 2 π s ⎪ Vsin ⎩ 2 3

Hence

TTTT012= s −− (4-73)

4.3.2 Experimental results

4.3.2.1 Starting mode

During the starting period, the induction machine produces full torque to drive the DC machine, which simulates the engine. In this experimental setup, the starting torque is set as 6 Nm and the engine starting speed is 500 rpm to reflect the idle speed of the engine. After DC machine simulated engine is started, both the DC machine and induction machine are accelerated from 500 rpm to 1200 rpm. For the study in this thesis, 1200 rpm was chosen as the simulated ISA generating speed because of the limitation of the DC machine simulating the engine.

As shown in Fig. 4.25, the full induction machine’s torque runs the whole set from 0 to 1200 rpm. After the speed reaches 1200 rpm, the DC machine simulated engine sets its speed reference as 1500 rpm and regulated by its own controller. In this study, 1500 rpm is the base speed of the induction machine. At the same time, the reference of the induction machine is switched from torque to voltage to reflect the transition from motoring to generating. The induction machine now begins to act as a generator and provide power to the battery and the dc load. The torque of the induction machine thus changes from positive torque to negative torque as in (i) of Fig. 4.25. The stator flux [(iii) in Fig. 4.25] of the machine is kept constant in this proposed direct flux vector control method.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 88

Fig. 4.25 Starting process of ISA

4.3.2.2 Generating mode - steady state

The steady state performance with full load of the induction machine is shown in Fig. 4.26. With voltage regulator the dc voltage of the ISA system is kept as 42 V when the induction machine provides full torque to the load. And the stator flux of the induction machine is still constant. The stator current waveform is captured by a digital oscilloscope (LeCroy LT364L) and the data is analysed by FFT algorithm. The current spectrum analysis in Fig. 4.27 indicates that the DC-AC converter of the ISA system runs at constant frequency 6.67 kHz, which is corresponding to the sampling time 150 μs .

Chapter 4 Direct flux vector controlled ISA with space vector modulation 89

Fig. 4.26 ISA generating with full load

Fig. 4.27 Spectrum analysis of the stator current of ISA

Chapter 4 Direct flux vector controlled ISA with space vector modulation 90

4.3.2.3 Generating mode - dynamic response.

The dynamic performance of the ISA is studied in this section. The performance of the ISA system under load dump and engine speed acceleration or deceleration is presented as follows.

4.3.2.3.1 Performance during load dump

The dc load of the ISA is removed suddenly in the generating mode when the speed is 1500 rpm. Two conditions are considered for the load dump of the ISA. They are load dump without battery connected and load dump with battery connected as shown in Fig. 4.28 and Fig. 4.29, respectively.

As shown in Fig. 4.28 and Fig. 4.29, the peak dc bus voltage of the ISA is well controlled below the limitation of the 42 V PowerNet standard (58 V) [6] when the dc load is dumped. The settling time of the dc bus voltage is only 100 ms. The induction machine’s torque is changed from -6 Nm to about -1 Nm during load dumping. The torque of the induction machine varies slower in Fig. 4.29 because of the charging of the batteries.

Fig. 4.28 Load dump of ISA without battery connected

Chapter 4 Direct flux vector controlled ISA with space vector modulation 91

Fig. 4.29 Load dump of ISA with battery connected

4.3.2.3.2 Dynamic performance during speed acceleration/deceleration

In this section, the DC machine’s speed reference is increased suddenly from 1500 rpm to 3000 rpm, while the induction machine is generating with full dc load. As shown in Fig. 4.30, the dc bus voltage of the ISA is well controlled as 42 V during speed acceleration. The stator flux of the machine is weakened when the speed is above the base speed (1500 rpm).

Chapter 4 Direct flux vector controlled ISA with space vector modulation 92

Fig. 4.30 ISA performance at acceleration

The deceleration of the ISA also tested by dropping the speed suddenly from 3000 rpm to 1500 rpm, while the induction machine is generating with full dc load. As shown in Fig. 4.31, the dc bus voltage of the ISA is dropped a little from 42 V during speed deceleration, but it still in the allowed voltage range of 42 V PowerNet [6]. Fig. 4.31 (iii) shows the flux of the machine is increased when the speed returns to base speed (1500 rpm).

Fig. 4.31 ISA performance at deceleration

Chapter 4 Direct flux vector controlled ISA with space vector modulation 93

4.3.2.4 High speed operation

The operation of proposed ISA system in high speed range is also tested. When the speed of the induction machine exceeds the base speed (1500 rpm), the stator flux reference is weaken by the inverse proportional with the rotor speed. Fig. 4.32 shows the ISA performance at 4000 rpm with full load. The induction machine’s torque is less than 6 Nm due to the high speed operation. The stator flux of the induction machine is reduced for field weakening.

In this thesis, the ISA only runs up to 4000 rpm due to limitation of the induction machine in the laboratory.

Fig. 4.32 ISA with field weakening at high speed

4.4 Conclusion

In this chapter, an improved torque controller of induction machine based on direct control of stator flux linkage vector is presented. The fundamental relationship between the rotating speed of the stator flux linkage and torque is analyzed and the design

Chapter 4 Direct flux vector controlled ISA with space vector modulation 94

principle of controller is presented. A simple structure with only one Proportional- Integral (PI) controller is shown to implement the torque and flux control adequately. Parameters of PI controller are easily found in the proposed design principle. Robust design of the controller ensures the system is not sensitive to the variation of rotor resistance. Fixed switching frequency and low torque ripple are obtained with PI control and space vector modulation (SVM) method. Satisfactory modeling and experimental results indicate the feasibility of the proposed direct flux vector control scheme for induction machines. The control scheme employs encoderless torque control structure, and eliminates the disturbance of speed to the torque controller successfully. The controller gives good torque and flux control performance.

A direct flux vector controlled scheme of induction generator has been proposed and verified in this chapter for future 42 V automobiles application. A simple structure with only one Proportional-Integral (PI) controller is shown to implement the torque and flux control adequately. By controlling the electromagnetic torque of the induction machine, the required dc bus voltage can be well regulated within the 42 V PowerNet specifications. Simulation and experimental results indicate that the proposed scheme provides a practical solution for an integrated starter alternator, avoiding the drawback of rotor flux oriented control scheme.

However, the calculation of the commanded voltage vector requires the derivative of the stator flux vector, which is kept moving. Thus, it is a potential source of error. Actually, the stator flux linkage will be a dc quantity when the reference frame is fixed to the stator flux vector. It should thus be possible to avoid calculation of the derivative of the flux vector. In the next chapter, a control scheme of ISA based this on idea will be presented.

Chapter 4 Direct flux vector controlled ISA with space vector modulation 95

CHAPTER 5 DIRECT TORQUE AND FLUX CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SPACE VECTOR MODULATION

5.1 Introduction

The direct flux vector control presented in Chapter 4 controls the rotating speed of the stator flux vector by a torque feedback loop. No direct control for the amplitude of the stator flux vector is included. In this chapter, the of the torque and the flux are both used in two independent control loops. It is a direct torque and flux control (DTFC) scheme based on the basic DTC concept. In effect, the two hysteresis comparators are replaced by two PI controllers.

A similar scheme to DTFC for induction motor drives application has been presented in [83]. But its application in generators or the ISA has not been reported. This chapter proposes a direct torque and flux control scheme for an induction generator in ISA application. The relationships between controlled variables and the torque are fully developed. Constant switching frequency and lower torque ripple are achieved with Proportional-Integral (PI) controller and space vector modulation (SVM). The speed sensor is eliminated and the torque and stator flux are estimated with voltage mode estimator. As the torque of induction machine is controlled with DTFC with high dynamic performance, the dc bus voltage can be regulated to meet the specification of the 42 V PowerNet.

This chapter is organized as follows. Section 5.2 presents the detailed analysis of the principle for direct torque and flux control based ISA system. In Section 5.4, experimental results are presented. Finally, the conclusion is drawn in Section 5.5.

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 96

5.2 Direct torque and flux control principle

β

q G d G Is Ψ s

G isd Ψr isq

θs α

Fig. 5.1 Vector diagram of the induction machine

In stator flux reference frame (dq− ) shown in Fig. 5.1, the dynamic behavior of induction machine can be described as following equations: G ⎧JJG G dΨ G VRI=+s +ωΨ j ⎪ sssdt ss ⎪ G G G ⎪ dΨr ⎨0 = RIrr++ω−ωΨ j() s m r (5-1) ⎪ dt ⎪ 3 TPi=Ψ⋅ ⎪ esdsq ⎩ 2 and G G G ⎪⎧Ψ=s LIss + L mr I ⎨ G G G (5-2) ⎩⎪Ψ=rmsrrLI + LI

Therefore,

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 97

⎧ G dΨ JJG G G ⎪ s =−VRIj −ωΨ ⎪ dt sssss G ⎪ G G ⎪dΨr ⎨ =−jRI() ωsmrrr −ω Ψ − (5-3) dt ⎪ G G G ⎪ −1 ⎡⎤I s ⎡⎤LLsm⎡Ψss⎤⎡⎤1 ⎡ L r− L m ⎤Ψ ⎪⎢⎥GG==⎢ ⎥⎢⎥ G ⎢⎥LLLL− L 2 ⎢− L L ⎥ ⎩⎪⎣⎦⎢⎥Ir ⎣⎦mr⎣⎢Ψrr⎦⎣⎦⎥⎢⎥sr m ⎣ m s ⎦Ψ

Equation (5-3) can be simplified as G ⎡⎤RRL ⎡⎤dΨs ssm −−ωj s G ⎢⎥⎢⎥LLLσσ⎡⎤Ψ ⎡⎤1 JJG dt ⎢⎥ssrs ⎢⎥G =+⎢⎥G ⎢⎥Vs (5-4) ⎢⎥dΨΨ⎢⎥RLrm R r 0 r −ω−ω−j ⎣⎦⎢⎥r ⎣⎦ ⎢⎥⎢⎥()sm ⎣⎦dt ⎣⎦LLsrσσ L r where

L 2 σ=1 − m (5-5) LLs r

(The further details of the derivation included in this chapter can be found in Appendix C)

So, the relationship between stator and rotor flux vector can be obtained from (5-4)

Lm GG Ls Ψ=rs()ss Ψ() (5-6) sjτσ +()() ωsm − ω τ + 1

L where τ= r . Rr

It is known in the stator flux reference frame that G ⎪⎧Ψs =Ψds +j Ψ qs ⎨ (5-7) ⎩⎪Ψ=qs 0

The rotor flux vector in the stator flux reference frame can be expressed as G Ψrrdrq=Ψ +j Ψ (5-8)

With (5-6), (5-7) and (5-8), the dq component of rotor flux vector can be obtained

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 98

⎧ RLrm ⎪ LLsrσ ⎪Ψ=rd()ss2 Ψ sd () ⎪ ()ω−ω R s ++sm r ⎪ R L σ ⎪ s + r r ⎪ Lr σ ⎨ (5-9) ⎪ RLrm

⎪ −ω−ω()sm LLsrσ ⎪Ψ=rq()ss2 Ψ sd () Rr ω−ω ⎪ s + ()sm Rr L σ s ++ ⎪ r Rr L σ ⎪ s + r ⎩ Lr σ

The expression of stator current with stator and rotor flux vector is already shown in (5- 3), which is restated as G G 1 ⎡Ψs ⎤ ⎡⎤ILL=−[]⎢ G ⎥ (5-10) ⎣⎦srmLL− L 2 sr m ⎣⎢Ψr ⎦⎥

By substituting (5-9) into (5-10), it is derived that

2 Lm ()ω−ωsm τ 2 LLsr Isq(s)=Ψ sd (s) τσ222ss +21 τσ+τσ 22 ω −ω2 + ()sm (5-11) L 2 ()ω−ω τ m smLL2 ≈Ψsr (s) 21τσ+s sd

The simplification in (5-11) is based on small τ and σ .

By inverse Laplace transform, the expression of Isq is time domain is obtained as

2 ⎧ Lm ⎫ ⎪()ω−ωsm τ 2 ∗ ⎪ −−11⎪ LLsrΨ sd⎪ I(t)sq==LL{} I(s) sq ⎨ ⎬ 21τσss + ⎪ ⎪ (5-12) ⎪⎩⎭⎪ 2 L −t =ω−ωτm Ψ∗ 1 −e 2τσ ()sm2 sd{} LLsr

It is assumed that the magnitude of the stator flux vector is kept constant with flux regulator in axis d . By considering (5-1) and (5-12), the torque is obtained as follows.

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 99

2 332 τL −t T(t)=Ψ P (t) ⋅ i (t) = P Ψ∗ m ω−ω−1 e 2τσ (5-13) esdsqsdsm()2 (){ } 22LLsr

By (5-1), the voltage equation in dq frame is

⎧ ddΨΨsdsd ⎪VRisd=+ s sd ≈ ⎨ dt dt (5-14) ⎪ ⎩VRisq= s sq+ωΨ s sd ≈ωΨ s sd

By substituting (5-14) into (5-13), the relationship between the q voltage component and the torque is developed as

2 3 τL −t T(t)=⋅Ψ P∗ m 1 − e2τσ V −ω f (5-15) esdsqm2 { } () 2 LLsr where

2 3 2 τL −t fPω= Ψ∗ m 1 − e2τσ ω (5-16) ()msdm()2 { } 2 LLsr

Therefore, it is clear shown in (5-15) that the torque of induction machine can be directly regulated by the q voltage component considering f (ωm ) as a disturbance to the system. Similarly, the amplitude of stator flux vector can be regulated by the d component of stator voltage directly as shown in (5-14). Above analysis forms the principle of the direct torque and flux control (DTFC) scheme for the induction machine.

The voltage vector should be transferred from the stator flux reference frame to the stationary frame by (5-17) before using SVM algorithm.

⎡VV⎤⎡⎤⎡⎤cosθ− sin θ sα = sssd (5-17) ⎢VV⎥⎢⎥⎢⎥ ⎣ sβ ⎦⎣⎦⎣⎦sinθθss cos sq

where θs is the angle between the stator flux frame ( dq ) and stationary frame ( αβ ), i.e. the angle of stator flux linkage vector as shown in Fig. 5.1.

Then the reference voltage vector is G VVjVref=+ sα sβ (5-18)

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 100

The gating signals can be generated by SVM algorithm as discuss in Section 4.3.1 by inputting reference voltage vector.

5.3 Direct torque and flux controlled induction generator for an ISA

Based on above analysis, a complete scheme of direct torque and flux control for ISA that allows effective torque control has been developed and it is indicated in Fig. 5.2. The torque and flux are regulated by two PI controllers. The design of this two PI controller is based on (5-13) and (5-14). With same approaches discussed in Section 4.2.2, the PI controller parameters of the torque can also be found. The ISA system includes starting/generating mode switch which simulates the operation of ISA from starter to generator. After the switch changes to generating mode, the voltage regulator will take effect to keep the dc bus voltage as 42 V and the torque reference will be negative.

* Vdc Tstarting + Vdc −

Vdc T * + Vsq G dq− Vref ∗ − V ψ s sd α − β − G θs ψ s

Te

Fig. 5.2 Direct torque and flux controlled induction generator for ISA

As shown in Fig. 5.2, only one voltage sensor for dc bus voltage and two current sensors for stator current are adopted in proposed scheme. The voltage and current signals are used for stator flux estimation. The stator flux vector is estimated in the stationary frame avoiding co-ordination transformation and involvement of more

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 101

machine parameters. The estimation algorithm is given in (5-19). And the voltage signal is also used as voltage feedback to maintain the dc bus voltage as 42 V.

⎧ G JJG G Ψ=VRIdt − ⎪ ssss∫ () ⎪ −1 ⎨θ=ssstan () Ψβ Ψα (5-19) ⎪ 3 G G ⎪TPI=Ψ× ⎩⎪ ess2 G In (5-19), current vector Is is constructed by the two line current with Park JJG transformation. And voltage vector Vs can be obtained by JJGJG V(k)s = Vref (k−1 ) (5-20) JG JJG The time delay between V ref and Vs results from the SVM generating time Ts .

In transient state, the reference voltage will be larger than the available inverter voltage when the torque error is too large. In that case, the reference voltage has to be limited to ensure the reference voltage is lower or equal to the maximum inverter voltage: G VVref≤ max (5-21)

where Vmax is the maximum available inverter voltage.

For under-modulation of SVM,

1 VVmax= dc (5-22) 3

where Vdc is the dc bus voltage of the inverter.

5.4 Experimental results

5.4.1 Starting mode

During the starting period, the induction machine produces full torque to drive the DC machine, which simulates the engine. In this experimental setup, the starting torque is set as 6 Nm and the engine starting speed is 500 rpm to reflect the idle speed of the engine. After DC machine simulated engine is started, both the DC machine and

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 102

induction machine are accelerated from 500 rpm to 1200 rpm. For the study in this thesis, 1200 rpm was chosen as the simulated ISA generating speed because of the limitation of the DC machine simulating the engine.

As shown in Fig. 5.3, (i) of the full induction machine’s torque runs the whole set from 0 to 1200 rpm. After the speed reaches 1200 rpm, the DC machine simulated engine sets its speed reference as 1500 rpm and regulated by its own controller. In this study, 1500 rpm is the base speed of the induction machine. At the same time, the reference of the induction machine is switched from torque to voltage to reflect the transition from motoring to generating. The induction machine begins to act as a generator to provide power to the battery and the dc load. The torque of the induction machine is thus changed from positive to negative torque as in (i) of Fig. 5.3. As shown in Fig. 5.3 (iii), there is an overshoot of the stator flux when the rotor speed rises from standstill state. This overshoot results from the PI regulation of the flux controller. The proposed design of the PI parameters of the flux controller may eliminate the overshoot. After starting, the stator flux is controlled as constant.

Fig. 5.3 Starting process of ISA

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 103

5.4.2 Generating mode - steady state

The steady state performance with full load of the induction machine is shown in Fig. 5.4. With voltage regulator the dc voltage of the ISA system is kept as 42 V when the induction machine provides full torque to the load. And the stator flux of the induction machine is still constant. The stator current waveform is captured by a digital oscilloscope (LeCroy LT364L) and the data is analysed by FFT algorithm. It indicates in Fig. 5.5 that the DC-AC converter of the ISA system runs at constant frequency 6.67 kHz, which is corresponding to the sampling time 150 μs .

Fig. 5.4 ISA generating with full load

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 104

Fig. 5.5 Spectrum analysis of the stator current of ISA

5.4.3 Generating mode - dynamic response.

The dynamic performance of the ISA also studied in this section. The performance of the ISA system under load dumping and engine speed acceleration or deceleration is presented as follows.

5.4.3.1.1 Performance during load dump

The dc load of the ISA is removed suddenly at the generating state when the speed is 1500 rpm. Two conditions are considered for the load dump of the ISA. They are load dump without battery connected and load dump with battery connected as shown in Fig. 5.6 and Fig. 5.7, respectively.

As shown in Fig. 5.6 and Fig. 5.7, the peak dc bus voltage of the ISA is well controlled below the limitation of the 42 V PowerNet standard (58 V) [6] when the dc load is dumped. The settling time of the dc bus voltage is only 100 ms. The induction machine’s torque is changed from -6 Nm to about -2 Nm during load dumping. The

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 105

torque of the induction machine varies slower in Fig. 5.7 because of the charging of the batteries. The stator flux of the induction machine is dropped a little resulting from the load dump.

Fig. 5.6 Load dump of ISA without battery connected

Fig. 5.7 Load dump of ISA with battery connected

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 106

As shown in Fig. 5.6 and Fig. 5.7 it is found that the torque ripples are at same frequency of stator current (voltage). The torque ripple is caused by the estimation error in the stator flux. The stator flux is estimation by integration of the stator voltage as shown in (3-8). That is why the torque error is at the same frequency of the stator current (voltage).

5.4.3.2 Performance during speed acceleration/deceleration

In this section, the DC machine’s speed reference is increased suddenly from 1500 rpm to 3000 rpm, while the induction machine is generating with full dc load. As shown in Fig. 5.8, the dc bus voltage of the ISA is well controlled as 42 V during speed acceleration. The stator flux of the machine is weakened when the speed is above the base speed (1500 rpm).

Fig. 5.8 ISA performance at acceleration

The deceleration of the ISA also tested by dropping the speed suddenly from 3000 rpm to 1500 rpm, while the induction machine is generating with full dc load. As shown in Fig. 5.9, the dc bus voltage of the ISA is dropped a little from 42 V during speed

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 107

deceleration, but it still in the allowed voltage range of 42 V PowerNet [6]. Fig. 5.9 (iii) shows the flux of the machine is increased when the speed returns to base speed (1500 rpm).

Fig. 5.9 ISA performance at deceleration

5.4.4 Performance High speed operation

The operation of proposed ISA system in high speed range is also tested. When the speed of the induction machine exceeds the base speed (1500 rpm), the stator flux reference is weaken by the inverse proportional with the rotor speed. Fig. 5.10 shows the ISA performance at 4000 rpm with full load. The induction machine’s torque is less than 6 Nm due to the high speed operation. The stator flux of the induction machine is reduced for field weakening.

In this thesis, the ISA only runs up to 4000 rpm due to limitation of the induction in the laboratory.

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 108

Fig. 5.10 ISA with field weakening at high speed

5.5 Conclusion

This chapter presents a direct torque and flux control of the integrated starter/alternator. This control scheme has been analyzed and verified with simulation and experiments. The simulation and experimental results show that the direct torque control concept had also been successfully extended to generator application. Simplicity of the system structure and lower ripples of current and torque are both achieved with proposed scheme. The modeling and experimental results confirm the effectiveness of the proposed scheme to be a strong candidate for ISA system.

Compared to the direct flux vector control scheme proposed in last chapter, this scheme is a little bit complex due to transformation computation. However, the calculation of the commanded voltage vector by (5-14) requires the derivative of the stator flux magnitude, which is a dc quantity. Thus, this scheme is less noisy [63] than the flux vector calculation based direct flux vector control scheme.

Chapter 5 Direct torque and flux controlled ISA with space vector modulation 109

CHAPTER 6 NON-LINEAR BEHAVIOUR OF THE DC-AC CONVERTER AND ITS COMPENSATION

6.1 Introduction

In the direct torque control scheme, the stator flux can be estimated by sensing the stator voltage and current of the machine. Sensing of line-line voltage waveforms required filtering in order to eliminate the harmonics and noise created by PWM modulation, and offset as well. Alternatively, it is preferred to reconstruct the stator voltage vector from the gating signals and the dc link voltage which is in turn regarded as the reference voltage vector. However, the reference voltage vector does not exactly represent the voltage vector at the machine terminals due to the non-linear behaviour of the converter, which are caused by the dead-time effect [93-95] and voltage drops on the power devices [96, 97].

Specially, this case becomes critical in the 42 V ISA application because the machine’s voltage is very low with the one-stage structure as stated in 1.2.3.3. For example, the voltage of the induction machine used in this study is only 22 V. therefore; even 1 V error for a power device will cause about 10% percentages of the reconstructed voltage. The total effect of the dead-time and voltage drop introduce a large error of the reference voltage. The inaccurate reference voltage can cause wrong stator flux estimation, and further degrade the control ability of the DTC. Therefore, the non-linear behaviour of the DC-AC converter has to be compensated.

This chapter analyzed the total effects of dead-time and voltage drops and developed a combined compensation methods to compensate these two effects together, which are normally considered separately in the existing literature [94-97]. Generally, the dead-

Chapter 6 Non-linear behaviour of the converter and its compensation 110

time and voltage drop compensation are based on normal PWM or SPWM fed inverters [93, 96-98]. At present, the space vector PWM technique is widely used in voltage source inverters. For the 42 V ISA, it is necessary to study the compensation method also with space vector PWM of DC-AC converter. A novel dead-time compensation method has been studied for space vector PWM in [95] based on time error resulting from the dead-time. In this chapter, the effects of dead-time and voltage drops on the three phase DC-AC converter with space vector modulation are both analyzed. An error voltage vector based compensation method is proposed to reduce those two effects together. Two compensation structures are developed and compared with feed-forward and feed-backward manners.

6.2 Effect of Dead-time

To avoid direct short circuit across the dc bus voltage source, a blanking time or dead- time is inserted into the gating signal of the switch that is to be turned on. There is a time in each switching cycle where both the high and low side switches in the same leg are off and the current flow is through the diodes.

P

+ A+ D + > 0 - ia Vdc − A− D

N

Fig. 6.1 one leg of the converter

The voltage level of each phase during dead-time is determined by the current direction of each phase. As shown in Fig. 6.1, the positive direction is defined as the phase current is flowing from converter to the load. By assuming the sign of phase current doesn't change during the sampling period, the effect of the dead-time for PWM is presented in Fig. 6.2. The shadow stands for the losing area due to the dead-time and turn-on or turn-off time of the power device.

Chapter 6 Non-linear behaviour of the converter and its compensation 111

A+ a) A−

td A+

b) td A−

td i > 0 VaN′ a c) i < 0 td VaN′ a

toff td + ton V ia > 0 d) aN t td + ton ia < 0 off VaN

Ts

Fig. 6.2（a） ideal gate signal （b）practical gate signal with dead-time （c）VaN with dead-

time effect only（d）considering ton and toff of the power device

With space vector PWM, the voltage vectors diagram is shown in Fig. 6.3. The reference voltage vector is synthesized by the two adjacent basic voltage vectors. The gate signal of the converter in one sampling period Ts is given in Fig. 6.4.

β G G V V3 2

S A = 1 S B = 1 SC = 1 Vdc G Vref

S = 0 S = 0 S = 0 G G A B C V V 4 G0 α G α iB V iA iC 7 V1

G G V V IM 5 6

(a) (b)

Fig. 6.3 Switching state of VSI (a) and space voltage vectors (b)

Chapter 6 Non-linear behaviour of the converter and its compensation 112

Ts

SA

SB

SC 000 100 110 111 110 100 000

Fig. 6.4 Gate signal without dead-time

Similar with PWM case in Fig. 6.2, the duration of the gate signal is reduced and increased with dead-time effect. Table 6.1 shows a example with ia > 0 , ib > 0 and ic < 0 .

Ts

td + ton toff

SA

td + ton toff

SB

t off td + ton

SC 000 100 110 111 110 10 0 000

Chapter 6 Non-linear behaviour of the converter and its compensation 113

Fig. 6.5 Gate signal with dead-time

Table 6.1 Dead-time effect analysis (ia > 0 ; ib > 0 ; ic < 0 )

Lost parts duration Extra Parts duration

(shadowed (Non-shadowed parts) parts)

A (1 0 0) =V1 td+ton (1 0 0) =V1 toff

B (0 1 0) =V3 td+ton (0 1 0) =V3 toff

C (0 0 1) =V5 toff (0 0 1) =V5 td+ton

The changes of the duration will introduce an error vector. The error vector is determined by sign of the phase current. For example, the reference voltage vector is in sector 1 and the sign of current are (+ +−) , i.e. ia > 0; ib > 0 ; ic < 0 . Then the actual output voltage vector is GGG G VTref s−+( V13 V)( t d + t on) − Vt 5 off GG G ++()VVt13off + Vtt 5() d + on GG G =−+−++−VTVtttrefs25()() donoff Vttt donoff (6-1) GG G =++−++−VTref s Vt55()() d t on t off Vt d t on t off GG =+VTref s2 Vt5 () d +− t on t off

G (ttdonoff+− t) 4 2 () tt donoff +− t So, the error voltage vector for this case is 2VVa5 = dc TTss3 where α = e j/23π .

Table 6.2 summarizes the error voltage vectors caused by dead-time effect different current polarities.

Chapter 6 Non-linear behaviour of the converter and its compensation 114

Table 6.2 Error voltage vectors under different current polarities

Error Error Error vector total sgn( iA ) sgn( iB ) sgn( iC ) vector 1 vector 2 3

+(0) +(0) -(1) -100(V1) -010(V3) +001(V5) 2V5

+ - + -100 +010 -001 2V3

+ - - -100 +010 +001 2V4

- + + +100 -010 -001 2V1

- + - +100 -010 +001 2V6

- - + +100 +010 -001 2V2

6.3 Effect of voltage drop on the power device

Fig. 6.6 analysis of the voltage drop on the power device

The effect of voltage drop on the output voltage vector depends on the polarity of the current and the switching state of the power device as shown in Fig. 6.6. The letter s

Chapter 6 Non-linear behaviour of the converter and its compensation 115

indicates the switching state of the top power device on the leg A. For example, ia > 0; ib > 0 ; ic < 0

Ts

VVdc− ce

SA

−Vd

VVdc− ce

SB −Vd

VVdc+ d

SC 000 100 110 111 110 10 0 000

Vce

Fig. 6.7 Gate signal with voltage drop

By assuming Vth=(Vce+Vd)/2, the error voltage vector will be only determined by the sign of the current in each phase and it has nothing to do with switching state.

Therefore, the actual output voltage vector is

GG24 VV[)]VV−+−=+1 αα22 α (6-2) ref33 th ref th where α = e j/23π .

⎛⎞2 2 Vth so, the error voltage vector is 2⎜⎟Vdcα ⎝⎠3 Vdc

Table 6.3 lists the error voltage vectors caused by the voltage drop under different current polarities.

Chapter 6 Non-linear behaviour of the converter and its compensation 116

Table 6.3 Error voltage vectors under different current polarities

2 sgn( iA ) sgn( iB ) sgn( iC ) 1 a a total total

2 +(0) +(0) -(1) -1 -1 1 2a 2V5

+ - + -1 1 -1 2a 2V3

+ - - -1 1 1 -2 2V4

- + + 1 -1 -1 2 2V1

- + - 1 -1 1 -2a 2V6

2 - - + 1 1 -1 -2a 2V2

6.4 Compensation algorithm

By comparing Table 6.2 and Table 6.3, it is found that the total error voltage vectors are identical in terms of the sign of current for both dead-time and voltage drop effects. Therefore, their compensation can be combined together as shown in (6-3)

⎡ ⎤ GG()ttdonoff+− t Guu G ( tt donoff +− t) Δ=VV + Vth = V ⎢ + th ⎥ (6-3) errorTV error error TV s dc⎣⎢ s dc ⎦⎥ G Where Verror is the error vector obtained from Table 6.2 and Table 6.3.

Basically, the error voltage vector can be compensated in backward and forward manners.

6.4.1 Backward compensation G G Vreal ΔV

G Vref

Fig. 6.8 Backward compensation structure

Chapter 6 Non-linear behaviour of the converter and its compensation 117

G For the backward compensation structure, the error voltage vector ΔV is fed after G command voltage vector Vref being applied to the SVM block. The real voltage vector applied to the machine through the DC-AC converter will be G GG VVreal= ref +Δ V (6-4) G After compensation, the real voltage vector Vreal can be used for the estimation of the flux vector and the controllers.

6.4.2 Forward compensation G Vreal

G G ΔV Vref

Fig. 6.9 Forward compensation structure

With backward compensation structure, the compensation process depends on the controller of the system. In fact, the pressure of the controller can be eased by using G forward compensation. For forward compensation, the error voltage vector ΔV is fed G before command voltage vector Vref being applied to the SVM block. Therefore, the predicted error voltage vector can eliminate the effect of the dead-time and voltage drop in advance. The real voltage vector applied to the machine through the DC-AC converter will be G G VVreal= ref (6-5)

The new command voltage vector of the SVM block changes to G GG VVVref− new= ref −Δ (6-6) G Similarly, the real voltage vector Vreal can be used for the estimation and the controller.

Chapter 6 Non-linear behaviour of the converter and its compensation 118

6.5 Experimental results

The effectiveness of the compensation schemes for the voltage drop and dead-time is tested experimentally. Compensation logics are integrated with the real-time controller of the induction machine as shown in Fig. 6.10. Only two current sensors and one dc bus voltage sensor for the SVM DTC drive are used. No extra hardware is needed for these schemes.

* Te

* Ψ s

G V θˆ ref

G Vreal ˆ Ψ s ˆ T e

Fig. 6.10 The control system with voltage drop and dead-time compensation.

In order to evaluate the performance of the compensation method for the ISA, both motoring and generating modes are studied in this section.

6.5.1 Motoring mode

In order to compare the accuracy of the stator flux estimation in DTC-SVM with the actual stator flux of the induction machine, two possible methods could be used. One would involve installing sensor coil in the stator frame. This would still not be very accurate because of the stator resistance and leakage fluxes. The other method would involve estimating stator flux from the rotating rotor flux frame using a current model. The last approach was used in this thesis. Fig. 6.11 shows a current mode stator flux and torque estimator based on the rotor flux estimator in the conventional rotor-oriented reference frame as discussed in Chapter 2 (see Fig. 2.3).

Chapter 6 Non-linear behaviour of the converter and its compensation 119

isα

Llr Lls

G ψsα ψ ψrα r LL isA + mr + i sB Rotor flux Polar to i sC estimator Cartesian ψ ψrβ sβ θ LL r + mr + ωr

L lr Lls

isβ

(a) Stator flux estimation

ψsα

ψsβ Te 3 TPiessss=ψ−ψ()α ββα i isα 2

isβ

(b) Torque estimation

Fig. 6.11 Current mode stator flux and torque estimator

The current mode stator flux and torque estimator in Fig. 6.11 are based on the following equations.

⎧ L ψ=Li +m () ψ+ Li ⎪ slssα αααL rlrs ⎪ r ⎪ L ψ=Li +m ψ+ Li ⎪ slssββ() rlrs ββ Lr ⎪ G ⎨ψ=ψrrrα cos θ (6-7) ⎪ G ψ=ψsin θ ⎪ rrrβ ⎪ 3 ⎪TPiessss=ψ−ψ()αβ βα i ⎪ 2 ⎩⎪

Chapter 6 Non-linear behaviour of the converter and its compensation 120

where Lls , Llr and Lm are the stator leakage, rotor leakage and mutual inductances, respectively; ψsα , ψsβ , ψrα , ψrβ , isα and isβ are the stator flux linkages, rotor flux linkages and stator currents in stationary frame (α − β ) , respectively.

In DTC-SVM schemes, a voltage mode stator flux and torque estimator is used for the feedback signals of the controller as shown in Fig. 6.12.

ψsα vsα ψ vsβ sβ ⎧ψ=vRidt − ⎪ ssssααα∫ () T 3 e ⎨ i TPi=ψ−ψ i isα ψ=vRidt − sα essss()α ββα ⎩⎪ ssssβββ∫ () 2 i isβ sβ

Fig. 6.12 Voltage mode stator flux and torque estimator

where vsα and vsβ are the stator voltages in stationary frame, isα , isβ , ψsα and ψsβ are the stator and rotor current in stationary frames, respectively.

In practical, a low pass in (6-8) for stator fluxes is used instead of pure integration in Fig. 6.12 to avoid saturation effect.

⎧ 1 ψ=vRi − ⎪ ssssα ()αα ⎪ sT+1 c ⎨ (6-8) ⎪ 1 ψ=ssssβββ()vRi − ⎩⎪ sT+1 c

where Tfcc=π()12 and fc is the cut-off frequency of the filter.

Therefore, the voltage mode stator flux and torque estimator in Fig. 6.12 is used for the control of DTC-SVM while the current mode stator flux and torque estimator in Fig. 6.11 is working in parallel to verify the estimation accuracy of the voltage mode estimation.

6.5.1.1 Results without compensation

Fig. 6.13 illustrates the rotor speed, stator current, and estimated torque and stator flux at no-load state without compensation when the induction machine runs in the motoring

Chapter 6 Non-linear behaviour of the converter and its compensation 121

mode at 600 rpm. The torque estimated by the voltage mode estimator has large error compared to the torque estimated by current mode estimator. It is shown in Fig. 6.14, large stator flux estimation errors exist when compensation is not used. There is a six- step like distortion in the current waveform. Due to inaccurate flux estimation, the torque has large ripples.

Fig. 6.13 Rotor speed, stator current, and estimated torque and flux at no-load -without compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 122

Fig. 6.14 Estimation errors of the stator flux- without compensation

6.5.1.2 Results with backward compensation

The rotor speed, stator current, and torque at no-load state are plotted in Fig. 6.15 when the induction machine is running at 600 rpm. With backward compensation, the estimation errors of the stator flux are less as shown in Fig. 6.16 at same condition as above section. The measured current waveforms were corrected and appeared the most sinusoidal and the torque ripple is lower. The estimated with current mode and voltage mode estimators are overlapped.

Chapter 6 Non-linear behaviour of the converter and its compensation 123

Fig. 6.15 Rotor speed, stator current, and estimated torque at no-load - with backward compensation

Fig. 6.16 Estimation errors of the stator flux- with backward compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 124

Fig. 6.17 Reference voltages and error voltages - with backward compensation

The reference voltages and error voltages are plotted in Fig. 6.17 with backward compensation. The error voltages ΔVα and ΔVβ are used for the calculation of the flux.

6.5.1.3 Results with forward compensation

Compared with backward compensation, the forward compensation method is also tested under the same conditions. With forward compensation, the estimation of the stator flux is further improved. The torque ripple is lower with improved stator current waveform. The estimated torques with current mode and voltage mode estimators are overlapped. Fig. 6.18 shows the speed, torque, stator current and stator flux results at no-load with compensation. Fig. 6.19 shows the estimation errors of stator flux with forward compensation.

Chapter 6 Non-linear behaviour of the converter and its compensation 125

Fig. 6.18 Rotor speed, stator current, and estimated torque at no-load - with forward compensation

Fig. 6.19 Estimation errors of the stator flux- with forward compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 126

Fig. 6.20 Reference voltages and error voltages - with forward compensation

Similar with backward compensation, the reference voltages and error voltages are plotted in Fig. 6.20 with forward compensation.

6.5.1.4 Comparison

The stator flux estimation errors are calculated in percentage using (6-9) for the above three cases.

current voltage ψ−ψ()s,sαβ () s,s αβ errors()αβ, =×100 % (6-9) ψ ref

current Where ψ ref is the magnitude of the flux reference, ψ ()sα,sβ is the estimated flux

voltage with current mode estimator, and ψ ()sα,sβ is the estimated flux with voltage mode estimator.

Chapter 6 Non-linear behaviour of the converter and its compensation 127

As shown in Fig. 6.21, the flux estimation errors are limited within 10% with those two compensation methods, whereas the error is nearly 30% without compensation.

Fig. 6.21 Flux estimation errors comparison for with and without compensation

The dynamic performance of the compensation is also studied by comparing both simulation and experimental results with and without compensation when the induction machine speed is changed rapidly from 600 rpm to 1200 rpm. As shown in Fig. 6.22, large torque and flux estimation error exists without compensation (part a), which makes the dynamic response slower than that of with backward (part b) or forward (part c) compensation. In the experiments, it takes 0.65 seconds for the speed rising from 600 rpm to 1200 rpm without compensation (part a), whereas only 0.5 seconds with backward (part b) or forward (part c) compensation. The torque response is important for the ISA during starting period. Therefore, compensation should be integrated into the controller of the ISA.

Chapter 6 Non-linear behaviour of the converter and its compensation 128

(i) simulation results (ii) experimental results

(a) Without compensation

(i) simulation results (ii) experimental results

(b) With backward compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 129

(i) simulation results (ii) experimental results

(c) With forward compensation

Fig. 6.22 dynamics of the torque and flux for the DTC-SVM with and without compensation

6.5.2 Generating mode

The performance of the compensation methods is also studied for both steady and dynamic states under generating operation of the ISA.

6.5.2.1 Steady State performance

Fig. 6.23 compares the dc bus voltage, estimated torque, stator flux and stator current at no-load state for with and without compensation when the ISA runs with generating mode at 1500 rpm (rated speed). Although the torque is smoother and its estimation error is smaller with backward or forward compensations, there is no significant improvement in the dc bus voltage in the steady state. This is expected because the dc bus voltage is regulated by PI feedback control action. The stator voltage is very much larger at 1500 rpm than that at low speed range. Therefore, the error caused by the voltage drop and the dead-time is no longer comparable with the stator voltage and their effects on the performance of the system can be ignored at high speed range.

Chapter 6 Non-linear behaviour of the converter and its compensation 130

(a) without compensation

(b) with backward compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 131

(c) with forward compensation

Fig. 6.23 performance comparison with and without compensation while ISA is generating at 1500 rpm with no-load

6.5.2.2 Dynamic performance

The dynamic performance of the compensation is studied by comparing the experimental results with and without compensation during load dump. As shown Fig. 6.24, the torque of the induction machine changes from -6 Nm (full load) to about -1 Nm when the load dump happens at 1500 rpm. Very larger torque (almost 4 Nm) and stator flux estimation errors exist when the compensation methods is not used in part (a) of Fig. 6.24. However, the dc bus voltage is well regulated by the closed-loop control of the voltage even without compensation.

Chapter 6 Non-linear behaviour of the converter and its compensation 132

(a) without compensation

(b) with backward compensation

Chapter 6 Non-linear behaviour of the converter and its compensation 133

(c) with forward compensation

Fig. 6.24 performance comparison with and without compensation during load dump at 1500 rpm

6.6 Conclusion

In this chapter, the effects of switch voltage drops and dead-time on the space vector modulated DC-AC converter are analyzed. This analysis is necessary because of the low voltage rating of the induction machine for ISA application. The experimental results show that the effects of voltage drops and dead-time cause errors in estimated flux and torque, lead to current distortion and generate oscillation in torque and flux linkage.

The proposed compensation schemes can reduce the above mentioned effects. No extra hardware is needed for these compensators. Both steady state and dynamic performance have been analyzed. Experimental results confirm their effectiveness in low speed range and the torque response has been improved when the ISA runs in motoring mode. This compensation algorithm has been integrated in the controllers which were described in the Chapters 4 and 5. In the generating mode of ISA, the improvement of the

Chapter 6 Non-linear behaviour of the converter and its compensation 134

compensation on the dc bus voltage regulation is not significant because of closed-loop control of the voltage. However, the estimation errors of the torque and flux can be reduced with compensation, which could reduce the torque and flux ripples and increase the stability of the control system. Therefore, the compensation is necessary for both motoring and generating modes of the ISA.

The stator flux estimation with compensation is an open-loop type estimator, which is sensitive to the noise and parameter variations. In addition, the compensation cannot self-adjust due to open-loop structure. Therefore, a close-loop type estimator is needed to improve the flux estimation further with self-adaptive ability. Next chapter describes a close-loop estimator with a sliding mode observer for the ISA system discussed in this thesis.

Chapter 6 Non-linear behaviour of the converter and its compensation 135

CHAPTER 7 AN IMPROVED STATOR FLUX ESTIMATION OF DIRECT TORQUE CONTROLLED INTEGRATED STARTER/ALTERNATOR WITH SLIDING MODE OBSERVER

7.1 Introduction

According to the operation principle of the direct torque control, the stator flux linkage is estimated by integrating the stator voltage. However, a pure integrator has dc offset and initial value problems. Moreover, uneven voltage drops on the power devices also introduce errors in stator flux estimation even the compensation method is used. To solve the problems, digital and programmable-cascaded low-pass filter is developed [99-101]. These approaches are still open loop flux estimation methods, which are sensitive to the noise, sensors offset and variation of stator resistance. Therefore, close- loop flux estimation method is preferred in high performance applications, which are generally known as flux observers [102]. Many research efforts have been made with different observers, such as Kalman filter [103], Luenberger observer [104], etc. These observers have some disadvantages, such as the complex matrix computation algorithm and sensitivity to noise. Among different close-loop flux estimation schemes, sliding mode observers have gained much research interests due to their order reduction, disturbance rejection, simple implementation, and less computational burden [105-111].

In this chapter, a new sliding mode observer is developed to estimate the stator flux for direct torque controlled integrated starter/alternator based on a simplified induction machine model in the stationary reference frame. The sliding mode observer without requiring any speed information is analyzed in detail. The simulation and experimental

Chapter 7 Direct torque controlled ISA with sliding mode observer 136

results show that the proposed observer is able to deliver more accurate estimation than open-loop integrator estimator for the stator flux.

7.2 Dynamic Model of Induction Machines

In stationary frame ( α−β ), the dynamic behavior of induction machine can be described as

⎧ dψ vRi=+sα ⎪ sssααdt ⎨ (7-1) dψ ⎪vRi=+sβ ⎩⎪ sssββdt

⎧ dψ 0 = Ri +−ωψrα ⎪ rrα dt m rβ ⎨ (7-2) dψ ⎪0 = Ri ++ωψrβ ⎩⎪ rrβ dt m rα

⎧ψ=sα Lissαα + L mr i ⎪ ⎪ψ=sβ Lissββ + L mr i ⎨ (7-3) ⎪ψ=rmsrrα Liαα + Li ⎪ ⎩ψ=rmsrrβ Liββ + Li

3 TPiessss=ψ−ψ()α ββα i (7-4) 2

where vsα and vsβ are the stator voltages in stationary frame, isα , isβ , irα and irβ are the stator and rotor current in stationary frames, respectively, ψsα , ψsβ ψrα and ψrβ are the stator and rotor fluxes, respectively, Rs and Rr are the stator and rotor resistances, Ls ,

Lr and Lm are the stator, rotor and mutual inductances, respectively. And ωm is rotor speed, P is the number of pole pairs.

Thus

Chapter 7 Direct torque controlled ISA with sliding mode observer 137

⎡⎤ ⎛⎞RRrs R rω m ⎢⎥−+⎜⎟ −ωm σσLL σ LLL σ ⎡ iisα ⎤⎡⎤⎢⎥⎝⎠rs srssα ⎢ ⎥⎢⎥⎢⎥ d iisβ ⎛⎞RRω R sβ ⎢ ⎥⎢⎥= ⎢⎥ω−+−rs m r dt ⎢ψψ⎥⎢⎥m ⎜⎟ sα ⎢⎥⎝⎠σσLLrs σσ LLL ssrsα ⎢ ⎥⎢⎥⎢⎥ ψψsβ −R 000sβ ⎣ ⎦⎣⎦⎢⎥s ⎢⎥000−R ⎣⎦s (7-5) ⎡⎤1 0 ⎢⎥σL ⎢⎥s ⎢⎥1 ⎡⎤v + 0 sα ⎢⎥σL ⎢⎥v ⎢⎥s ⎣⎦sβ ⎢⎥10 ⎢⎥ ⎣⎦01 where

L 2 σ=1 − m (7-6) LLs r G In direct torque control scheme, the magnitude of stator flux vector Ψs will be G d G controlled as constant, that is Ψ = constant, or Ψ is equal to zero. So, s dt s

⎧ d G ψ ≈Ψ() −sin ω t ω =−ωψ ⎪dt sα sssssβ ⎨ (7-7) d G ⎪ ψ≈Ψ()cos ω t ω=ωψ ⎩⎪dt ssβα ssss

Comparing with (7-1), it is found that

⎧dψ sα = vRi−≈−ωψ ⎪ dt sα ssαβ s s ⎨ (7-8) dψ ⎪ sβ =−vRi ≈ωψ ⎩⎪ dt sssssββ α

Equation (7-5) can be reorganized as

Chapter 7 Direct torque controlled ISA with sliding mode observer 138

⎡⎤ ⎛⎞RRrrmω ⎡ isα ⎤ ⎢⎥−−ω⎜⎟ m ⎢ ⎥ d ⎡⎤iissαβ⎝⎠σσσLLLLrsrs ≈ ⎢⎥⎢ ⎥ ⎢⎥⎢⎥ dt issβα⎛⎞RRω ⎢ψ ⎥ ⎣⎦⎢⎥rmr ω−m ⎜⎟ − ⎢ ⎥ ⎢⎥σσσLLLLψsβ ⎣⎦⎝⎠rssr⎣ ⎦ (7-9) ⎡⎤1 ⎢⎥0 σLs ⎡⎤−ωss ψ β + ⎢⎥⎢⎥ ⎢⎥1 ⎣⎦ωψssα ⎢⎥0 ⎣⎦σLs

With small slip, ωs is close to ωm . So, (7-9) can be simplified as

⎡⎤ ⎛⎞RRrr⎡ isα ⎤ ⎢⎥−−ω⎜⎟ m 0 ⎢ ⎥ d ⎡⎤iissαβ⎝⎠σσLLLrsr ≈ ⎢⎥⎢ ⎥ (7-10) ⎢⎥⎢⎥ dt ⎣⎦issβα⎛⎞RR⎢ψ ⎥ ⎢⎥ω−rr0 ⎢ ⎥ m ⎜⎟ ψ ⎢⎥⎣⎦⎝⎠σσLLLrsr⎣ sβ ⎦

The error between ωs and ωm can be considered as the disturbance to the system, which can be compensated by the robust ability of a sliding mode observer.

7.3 Sliding mode stator flux observer

Based on (7-10), the encoder-less sliding mode observer can be designed without speed signals ωm as

⎧ ⎛⎞ dRRˆˆrr ⎪ iisssααα= −+ψ+⎜⎟ ˆ nˆ1 dtσσ L L L ⎪ ⎝⎠rsr ⎪ dRR⎛⎞ ⎪ ˆˆrr iisssβββ= −+ψ+⎜⎟ ˆ nˆ 2 ⎪dtσσ L L L ⎨ ⎝⎠rsr (7-11)

⎪dψˆ sα ⎪ =−vsssαα R i +⋅ c signS1 ⎪ dt ⎪dψˆ sβ =−v R i +⋅ c signS ⎩⎪ dt sssββ 2

ˆ ⎧Si1 =−ssαα i ⎪ ⎪Sii=−ˆ ⎨ 2 ssββ (7-12) ⎪nksignSˆ11=⋅ ⎪ ⎩nksignSˆ 22=⋅

Chapter 7 Direct torque controlled ISA with sliding mode observer 139

ˆ ˆ where isα , isβ , ψˆ sα and ψˆ sβ are the estimated stator currents and fluxes. c is a positive number to be chosen. S1 and S2 are the current errors between measured and estimated stator currents. nˆ1 and nˆ 2 are discontinuous functions of the current errors and k > 0 .

From (7-10) and (7-11), the error dynamics for current are obtained

⎧ dRR⎛⎞rr ⎪ iisαααβα=−⎜⎟ssmss + ψ −ω iksigni − ⎪⎝⎠dtσσ Lrsr L L ⎨ (7-13) dRR⎛⎞ ⎪ ii=−rr + ψ +ω iksigni − ⎪ sβββαβ⎜⎟ssmss ⎩dt⎝⎠σσ Lrsr L L where

ˆ ⎪⎧iiisα = ssαα− (7-14) ⎨ ˆ ⎩⎪iiisβ = ssββ−

By choosing Lyapunov candidate function as

1 22 V = iissα + β (7-15) 2 ( )

The time derivative of Lyapunov function V is

Vi =⋅+⋅ i i i ssαα ss ββ ⎛⎞R (7-16) r ⎛⎞22 ⎛⎞ =−⎜⎟⎜⎟ii + + ififkii + −⎜⎟ + ⎜⎟σL ⎝⎠ssα βααββαβ s s s s ⎝⎠r ⎝⎠ where

⎧ R f =ψ−ωr i ⎪ α sαβms ⎪ σLLsr ⎨ (7-17) ⎪ Rr fβ =ψ+ωsβαmsi ⎩⎪ σLLsr

 if k large enough, i.e. kmaxf,f> { α β }, thenV < 0, until isα and isβ are equal to zero, which means that the estimated currents will converge to their actual values. So, the sliding mode will occur in the intersection of the surfaces, and isα and isβ are equal to zero.

Chapter 7 Direct torque controlled ISA with sliding mode observer 140

After sliding mode motion occurs, the error dynamics for flux estimation is obtained from (7-1) and (7-11)

⎧dψ sα =−c ⋅ signS ⎪ dt 1 ⎨ (7-18) dψ ⎪ sβ =−c ⋅ signS ⎩⎪ dt 2

The equation (7-18) ensures that the flux errors converge to zero when c is a positive gain. The valued of c is chosen for the desired convergence rates of the flux error. It should be noted that a low-pass filter is used instead of direct integration to calculate the fluxes in (7-11). This approach is introduced to overcome the problems of an ideal integration such as the initial value effect.

Based on above analysis, the sliding mode observer is developed. Fig. 7.1 shows the overall structure of direct torque controlled induction machine with sliding mode observer.

* Te

* Ψ s

θˆ vvsα , sβ ˆˆ iisα , sβ ˆ ψ ˆˆ22 Ψ s sα =+ψψsα sβ ⎛⎞ψˆ θˆ = tg −1 ⎜⎟sβ ⎜⎟ψˆ ⎝⎠sα Equation (711− ) ψψˆˆsα , sβ

iisα , sβ Tˆ e 3 TPiessss=−()ψψˆˆα ββα i 32 2

Fig. 7.1 The overall structure of the direct torque controlled induction machine with sliding mode observer

Chapter 7 Direct torque controlled ISA with sliding mode observer 141

7.4 Simulation Results

The proposed sliding mode flux observer is compared with the open-loop flux estimator, which obtains stator flux by direct integration in (7-1). The performance of these two types of stator flux estimators is investigated under the following cases when the induction machine runs at 1200 rpm.

1. Stator resistance Rs variation Fig. 7.2 shows that there is a fixed estimation error with the open-loop estimator when stator resistance varies by 50%. In comparison, the flux estimation error is converged with sliding mode observer as shown in Fig. 7.3. It indicates that the sliding mode observer is not sensitive to the Rs variation.

Fig. 7.2 Open-loop stator flux estimation with 50% error in Rs

Chapter 7 Direct torque controlled ISA with sliding mode observer 142

Fig. 7.3 Sliding mode flux observer with 50% error in Rs

2. dc offset in current measurement The effect of dc offset in current for flux estimation is also studied. A 3A dc current offset is deliberately added to stator current iα for open-loop estimator and sliding mode observer. Due to the effect of integration in open-loop estimator, the estimation error of stator flux keeps increased with time. Fig. 7.5 shows that the estimation error can be limited in a small range with sliding mode observer.

Chapter 7 Direct torque controlled ISA with sliding mode observer 143

Fig. 7.4 Open-loop stator flux estimation with 3A dc current offset

Fig. 7.5 Sliding mode flux observer with 3A dc current offset

Chapter 7 Direct torque controlled ISA with sliding mode observer 144

3. Dynamic performance The dynamics of direct torque controlled induction machine with open-loop estimator and sliding mode observer are compared in Fig. 7.6 and Fig. 7.7. The speed of machine is accelerated from 600 rpm to 1200 rpm under constant stator flux. They exhibit similar dynamic response of the torque when there is no Rs variation or current offset.

Fig. 7.6 Direct torque controlled induction machine with open-loop stator flux estimator

Fig. 7.7 Direct torque controlled induction machine with sliding mode flux observer

Chapter 7 Direct torque controlled ISA with sliding mode observer 145

7.5 Experimental Results

In order to compare the performance of the sliding mode observer and open-loop estimator (i.e. voltage mode estimator in Fig. 6.12), the current mode torque and stator flux estimators described in Chapter 6 (see Fig. 6.11) are used as reference of the flux estimation. Therefore, the sliding mode flux observer is used for the control of DTC- SVM while the current mode stator flux and torque estimator is working in parallel to verify the estimation accuracy of the stator flux estimation.

In the following sections, the flux estimation error is the difference between current mode estimator and sliding mode observer (SMO), or open-loop estimator with low pass filter (voltage mode estimator).

7.5.1 Stator flux and torque estimation in motoring mode

7.5.1.1 Steady state performance of the sliding mode flux observer

The steady state performance of direct torque controlled induction machine with open- loop estimator and sliding mode observer are compared at 600 rpm with no-load. These results in Fig. 7.8 and Fig. 7.9 indicate that the flux estimation with sliding mode observer is more accurate than that of open-loop estimator.

Fig. 7.8 Rotor speed, stator current, and estimated torque and flux at no-load with open-loop stator flux estimation

Chapter 7 Direct torque controlled ISA with sliding mode observer 146

Fig. 7.9 Rotor speed, stator current, and estimated torque and flux at no-load with sliding mode flux observer

7.5.1.2 Estimation error with Stator resistance variation

Fig. 7.10 shows that there is a fixed estimation error with the open-loop estimator when stator resistance varied by 50%. In comparison, the flux estimation error is smaller with sliding mode observer as presented in Fig. 7.11. It indicates that the sliding mode observer is not sensitive with the Rs variation.

Chapter 7 Direct torque controlled ISA with sliding mode observer 147

Fig. 7.10 Open-loop stator flux estimation with 50% Rs error

Fig. 7.11 Sliding mode flux observer with 50% Rs error

Chapter 7 Direct torque controlled ISA with sliding mode observer 148

7.5.1.3 Estimation error with dc offset in current measurement

The effect of current dc offset for flux estimation is also studied. 3 A dc current offset is deliberately added to stator current iα for open-loop estimator and sliding mode observer. With open-loop estimator, there exist constant errors at steady state. Fig. 7.13 shows that the estimation error can be limited in a small range with sliding mode observer.

Fig. 7.12 Open-loop stator flux estimation with 3A dc current offset

Chapter 7 Direct torque controlled ISA with sliding mode observer 149

Fig. 7.13 Sliding mode flux observer with 3A dc current offset

7.5.1.4 Effect of estimation errors on the dynamic performance

The dynamics of direct torque controlled induction machine with open-loop estimator and sliding mode observer are compared in Fig. 7.14 and Fig. 7.16. The speed of machine is accelerated from 600 rpm to 1200 rpm under constant stator flux. During torque transient, the actual torque oscillates and deviates from the reference due to inaccurate flux estimation by open-loop estimator. In comparison, the torque dynamic behavior is better and the estimation error is small.

Chapter 7 Direct torque controlled ISA with sliding mode observer 150

Fig. 7.14 Dynamic performance with open-loop stator flux estimation

Fig. 7.15 Estimation errors with open-loop stator flux estimation

Chapter 7 Direct torque controlled ISA with sliding mode observer 151

Fig. 7.16 Dynamic performance with sliding mode flux observer

Fig. 7.17 Estimation errors with sliding mode flux observer

Chapter 7 Direct torque controlled ISA with sliding mode observer 152

Fig. 7.18 Current estimation with sliding mode flux observer

As shown in Fig. 7.15 and Fig. 7.17, the estimation error of the open-loop estimator is larger than that of the sliding mode observer. Fig. 7.18 shows the stator current estimation of the sliding mode observer, which proves its tracking ability. The oscillation of the estimated current results from the sliding mode operation of the observer.

7.5.2 Stator flux and torque estimation in generating mode

The performance of the Sliding Mode Observer (SMO) is also studied for both steady and dynamics states under generating operation of the ISA.

7.5.2.1 Steady State performance of the sliding mode flux observer

Fig. 7.19 compares the dc bus voltage, estimated torque, stator flux and stator current at no-load state for with and without compensation, and with SMO when the ISA runs with generating mode at 1500 rpm (rated speed). Compared to the cases of without/with backward, the torque and flux estimation errors are greatly reduced. However, there is no significant improvement in the dc bus voltage in the steady state due to the feedback

Chapter 7 Direct torque controlled ISA with sliding mode observer 153

regulation of the voltage. The stator voltage is larger at 1500 rpm than that at low speed range. Therefore, the error caused by the voltage drop and the dead-time is no longer comparable with the stator voltage and their effects on the performance of the system are not significant at high speed range.

(a) without compensation

Chapter 7 Direct torque controlled ISA with sliding mode observer 154

(b) with backward compensation

Chapter 7 Direct torque controlled ISA with sliding mode observer 155

(c) with SMO

Fig. 7.19 performance comparison without and with compensation, and SMO while ISA is generating at 1500 rpm

7.5.2.2 Effect of estimation errors on the dynamic performance

The dynamic performance of the SMO is also studied by comparing the experimental results during load dump. As shown Fig. 7.20, the torque of the induction machine is increased from -6 Nm (full load) to about -1 Nm when the load dump happens at 1500 rpm. Very large torque (almost 4 Nm) and stator flux estimation errors exist when the compensation method is not used in part (a) of Fig. 7.20. However, the dc bus voltage is well regulated by the closed-loop control of the voltage even without compensation. Compared to open-loop estimator with/without compensation, the torque and stator flux estimation errors are reduced, which is helpful to stabilize the control system.

(a) without compensation

Chapter 7 Direct torque controlled ISA with sliding mode observer 156

(b) with backward compensation

(c) with SMO

Fig. 7.20 performance comparison with/without compensation and with SMO during load dump at 1500 rpm

Chapter 7 Direct torque controlled ISA with sliding mode observer 157

7.6 Conclusion

This chapter presents a sliding mode flux observer for a direct torque controlled integrated starter/alternator. The stator flux estimation accuracy is guaranteed when the error between the actual current and observed current converges to zero. The algorithm of the sliding mode observer is based on simple computation in the stationary frame, which cost less time. Both simulation and experimental results confirm that the proposed sliding mode observer is robust to the stator resistance variation and sensor offset.

Experimental results confirm the effectiveness of SMO in low speed range and the torque response has been improved when the ISA runs in motoring mode. Fast starting of an ISA can thus be achieved with SMO. In the generating mode of ISA, the improvement of the compensation on the dc bus voltage regulation is not significant because of closed-loop control of the voltage. However, the estimation errors of the torque and flux can be reduced with SMO, which could reduce the torque and flux ripples and increase the stability of the control system. In addition, SMO is a close-loop type estimator with self-adaptive ability and it is not sensitive to the variation of parameters. Therefore, SMO can further improve the performance of the ISA for both motoring and generating modes.

Chapter 7 Direct torque controlled ISA with sliding mode observer 158

CHAPTER 8 EFFICIENCY IMPROVEMENT FOR INTEGRATED STARTER/ALTERNATOR WITH POWER FACTOR CONTROL

8.1 INTRODUCTION

For the application of ISA, the induction machine works on both motoring and generating state. The efficiency is an important factor to evaluate the performance. The efficiency of induction machine is low at light load with rated flux. Because the ISA operates in a wide load range, the efficiency can be improved significantly by optimal control. The loss of an induction machine includes copper (Winding) losses; Core losses and friction & windage losses. The copper and core losses belong to electromagnetic losses, which can be minimized by optimal control of the flux level in the machine [112].

Extensive work has been done previously for the adaptation of the flux. Most of them are based on the following three methods.

1) Search method, where the output power of the machine is kept constant while the flux level is iteratively adapted to find a minimum input power [21, 113-115]. It is not a good choice for industry application because the slow adaptation, continuous disturbances in the torque and the need for precise load information.

2) Loss model based method [116, 117] is a nature solution for field oriented controlled machine whose control is already based on the knowledge of the machine. Model-based control provides fast adaptation of the flux, but it requires knowledge of the machine parameters, and it requires more computation than the other methods.

Chapter 8 Efficiency improvement for ISA with power factor control 159

3) Power factor control method is based on cos(ϕ) control. Compared with the above two methods, it is a simple method requiring any speed or load information, and its regulation speed is faster. Power factor control is implemented in both scalar controlled (V/f) [118] and vector controlled drives [119-121]. It shows the drive loss with power factor control is very close to the minimized loss. However, the application of power factor control in direct torque control has not been reported yet.

In this chapter, a novel efficiency-optimized scheme based on power factor tuning for direct torque controlled integrated starter/alternator is proposed. The power factor of the induction machine is controlled to track the pre-determined power factor reference. A new structure of the power factor controller is proposed. The power loss is reduced with proper power factor under difference conditions. It is a simple method without requiring any speed or load information, and it is a fast adaptation method. So, it is a good choice for industry application.

This chapter is organized as follows. Section 8.2 introduced the loss model of the induction machine. The principle of power factor control for direct controlled ISA is presented in Section 8.3. Modeling analysis and experimental results are given in Section 8.4-8.5. The conclusion is drawn in Section 8.6.

8.2 Induction Machine Loss Model

In stationary frame ( α−β), the dynamic behaviour of induction machine can be described as

⎧ dψ vRi=+sα ⎪ sssααdt ⎨ (8-1) dψ ⎪vRi=+sβ ⎩⎪ sssββdt

⎧ dψ 0 = Ri +−ωψrα ⎪ rrα dt m rβ ⎨ (8-2) dψ ⎪0 = Ri ++ωψrβ ⎩⎪ rrβ dt m rα

Chapter 8 Efficiency improvement for ISA with power factor control 160

⎧ψ=sα Lissαα + L mr i ⎪ ⎪ψ=sβ Lissββ + L mr i ⎨ (8-3) ⎪ψ=rmsrrα Liαα + Li ⎪ ⎩ψ=rmsrrβ Liββ + Li

3 TPiessss=ψ−ψ()α ββα i (8-4) 2

where vsα and vsβ are the stator voltages in stationary frame, isα , isβ , irα and irβ are the stator and rotor current in stationary frames, respectively, ψsα , ψsβ , ψrα and ψrβ are the stator and rotor fluxes, respectively, Rs and Rr are the stator and rotor resistances,

Ls , Lr and Lm are the stator, rotor and mutual inductances, respectively. And ωm is rotor speed, P is the number of pole pairs.

The total copper loss is

3 ⎡ 22 22⎤ PiiRiiRcopper=+++()() sαβ s s r αβ r r (8-5) 2 ⎣ ⎦

The core loss contains hysteresis and eddy current losses, whose density [122] can be express as

2 ⎪⎧PKfBhhm= Wkg (8-6) ⎨ 22 ⎩⎪PKfBeem= Wkg

where Kh and Ke are the hysteresis and eddy current loss coefficients, f is the frequency, Bm is the maximum flux density.

Bm is determined by the flux level in the magnetic field. Therefore, the flux level has significant effect on the core loss with higher speed at light load. That is the case when the integrated starter/alternator is generating at high speed.

8.3 Principle of Power Factor Control

Fig. 8.1 shows the complete structure of the direct torque controlled integrated starter/alternator.

Chapter 8 Efficiency improvement for ISA with power factor control 161

* Vdc Tstarting + Vdc −

Vdc * Te

PF *

* Ψ s

∧ vv, PF ˆ ˆ sαβs Ψ s θ

ˆ 22 Ψs =+ψψˆˆsα sβ ⎛⎞ ψˆsβ θˆ = tg −1 ⎜⎟ Equation (81− ) ⎜⎟ˆ 32 ⎝⎠ψ sα

ψˆˆsα ,ψ sβ iisα , sβ ˆ T e ˆ 3 TPiessss=−()ψψˆˆα ββα i 2

Fig. 8.1 The overall structure of the direct torque controlled integrated starter/alternator

The torque and flux are regulated by the controllers. The ISA system includes starting/generating state switch which simulates the operation of ISA from starter to generator. After the switch changes to generating mode, the voltage regulator will take effect to keep the dc bus voltage as 42 V and the torque reference will be negative. As shown in Fig. 8.1, only one voltage sensor for dc bus voltage and two current sensors for stator current are adopted in proposed scheme. The voltage and current signals are used for stator flux estimation. The stator flux vector is estimated in the stationary frame avoiding co-ordination transformation and involvement of more machine parameters. The estimation algorithm is given in (8-1). In practice, the pure integrator in (8-1) could be saturated due to the noise or measurement error inherently present in the current sensor. Therefore, a low pass filter should be used in stead for the flux estimation. In Fig. 8.1, the voltage signal is also used as voltage feedback to maintain the dc bus voltage as 42 V.

Chapter 8 Efficiency improvement for ISA with power factor control 162

As shown in Fig. 8.1, the reference flux is obtained from the Power Factor (PF) controller by maintaining the power factor at given PF reference.

In this scheme, the power factor controller is design as in Fig. 8.2. A negative gain is used because power factor will be increased with lower flux level.

Rated Flux * * Ψ PF + s −1 PI − + Minmum Flux ∧ PF Rated Flux Fig. 8.2 Power factor controller

The reference voltage vector is adopted for the estimation of power factor without using line voltage sensors. The power factor can be calculated by [123, 124]

P vi+ vi PF ==ssαα ss ββ (8-7) 22 2222 PQ+ ()()vviissssαβαβ++ where P and Q are the instantaneous active power and reactive power of the induction machine, respectively.

8.4 Modeling Results

A 1kW/22V integrated starter/alternator is modelled by Simulink/Matlab to verify the proposed power factor scheme. The parameter of the induction machine is given in Appendix. The rated flux used in simulation is 0.0572. Constant PF reference is chosen as 0.75.

Fig. 8.3 shows the variation of the power factor under different loads when the induction machine is running at 1500 rpm with constant flux. The power factor is low when the load is small. So, the efficiency of the induction machine is low under smaller load.

Chapter 8 Efficiency improvement for ISA with power factor control 163

Power factor@1500 rpm 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Load ( x100% rated Te)

Fig. 8.3 Power factor of the induction under different loads

Fig. 8.4 Stator voltage, stator and rotor currents with 30% rated load

Chapter 8 Efficiency improvement for ISA with power factor control 164

Fig. 8.4 shows the stator voltage, stator current and rotor current when the power factor controller is added to the system. With power factor control, the flux level is reduced with decreased stator voltage. The rotor current is increased with low flux level.

In order to evaluate the performance of the power factor control under different loads, the power loss is calculated in percentage by (8-8) with considering of (8-5) and (8-6).

⎧ P core loss%=×core 100 % ⎪ P ⎪ core _ rated ⎪ 2 ⎛⎞ψ ⎪=×⎜⎟m 100% ⎪ ⎜⎟ψ ⎪ ⎝⎠m_rated ⎨ (8-8) P ⎪copper loss%=×copper 100 % ⎪ P ⎪ copper _ rated ⎪ 22 ()iRss+ () iR rr ⎪=×100% iRiR22+ ⎩⎪ ()()srated−− s rrated r

where Pcore _ rated and Pcopper _ rated are the core loss and copper loss at rated load, respectively.

It is shown in Fig. 8.5 that the core loss is greatly reduced by power factor control. More power is saved by power factor control under lower load. Fig. 8.6 indicates that the copper loss also deceased by power factor control within low load range (< 50% rated load). Because more current is required to maintain the higher electromagnetic torque, the copper loss is increased with power factor control when the load is larger than 50% rated load.

Core loss% @ 1500rpm 120

100

80

60

40 core loss%-with PF control core loss%-without 20 PF control

0 0 0.2 0.4 0.6 0.8 1 1.2 Load (x100% rated Te)

Fig. 8.5 Core loss percentage with and without power factor control

Chapter 8 Efficiency improvement for ISA with power factor control 165

Copper loss% @1500rpm 120

100 copper los s %-with P F control copper los s %-without 80 PF control

60

40

20

0 00.20.40.60.811.2 Load (x100% rated Te)

Fig. 8.6 Copper loss percentage with and without power factor control

8.5 Experimental results

In order to evaluate the power factor controller, the efficiency of the induction machine is tested with the ISA experimental platform as shown in Fig. 2.5. The electrical power of the induction machine is obtained with YOKOGAWA Power Analyzer (PZ4000). The mechanical torque of the induction machine is calculated by the torque of the DC drive machine and the torque to overcome friction loss.

Both motoring and generating modes are investigated for the efficiency improvement. The efficiencies in different modes are calculated by (8-9)

⎧ TT+ω Trealω m ( DCM friction) m ⎪η=M ×100%% = × 100 ⎪ PPAnalyzer Analyzer ⎨ (8-9) PP ⎪η=Analyzer ×100%% = Analyzer × 100 ⎪ G T ω TT−ω ⎩ real m ()DCM friction m

where ηM and ηG are the efficiencies of the induction machine in motoring and generating modes; PAnalyzer is the electrical power measured from the power analyzer;

ωm is the rotor speed of the induction machine in rad/s; Treal ,TDCM and Tfriction are the real torque of the induction machine, the real torque of the dc drive machine, and the torque caused by the friction loss, respectively.

Chapter 8 Efficiency improvement for ISA with power factor control 166

8.5.1 Motoring mode

It is shown in Fig. 8.7 that the efficiency of the induction machine in motoring mode is improved by power factor controller. Specially, the efficiency is increased almost 10 % at small load range (0 - 30% rated load).

Fig. 8.7 Efficiency comparison of the induction machine with and without Power Factor (PF) control in motoring mode at 1200 rpm and 1500 rpm

Similar with modeling, the transients of the regulation of the power factor controller is also recorded in experiment at 1200 rpm. As shown in Fig. 8.8, the stator voltage is reduced gradually while the power factor controller is taking effect. Therefore, the core loss of the machine will be minimized with reduced flux level.

Chapter 8 Efficiency improvement for ISA with power factor control 167

Fig. 8.8 Transients of the regulation of the power factor controller

8.5.2 Generating mode

In generating mode, the efficiencies of the induction machine are compared in Fig. 8.9 when it is running at 1500 rpm and 2100rpm. It is indicated that the efficiency of the induction machine in generating mode is also improved by power factor controller. The efficiency improvements are significant in the low load range (0-30% rated load) as expected from the analysis.

Chapter 8 Efficiency improvement for ISA with power factor control 168

Fig. 8.9 Efficiency comparison of the induction machine with and without power factor control in generating mode at 1500 rpm and 2100 rpm

8.6 Conclusion

A loss minimization scheme for the direct torque controlled integrated starter/alternator is proposed in this chapter. With proper power factor control, both core loss and copper loss are minimized under different loads. It provides a simple solution for the efficiency improvement of the induction machine without speed or load information. The results confirm the effectiveness of the proposed control scheme.

Chapter 8 Efficiency improvement for ISA with power factor control 169

CHAPTER 9 CONCLUSIONS

In this thesis, an integrated starter/alternator (ISA) for automobiles based on direct torque controlled induction machines has been modeled, analyzed, designed and implemented. The simulation and experimental results show that effective control of the ISA has been achieved for both starting and generating modes. This study provides a high performance control solution for an ISA in the future 42-V PowerNet application, other than the widely applied rotor flux oriented control scheme [16, 20, 24-26, 38] which is sensitive to the variation of machine parameters and requires accurate speed sensor signal for the flux orientation and decoupling. Considering the moist, hot and severe environment in automobiles, direct torque control scheme is more reliable and attractive without involving many machine parameters and requiring speed sensor signal for the control of torque and flux.

In summary, the contributions made in this thesis are:

• Investigation on a classical direct torque controlled integrated starter/alternator based on switching table

• Investigation and experimental verification of two improved direct torque controlled integrated starter/alternator schemes based on space vector modulation (DTC-SVM)

• Theoretical analysis of two improved DTC-SVM schemes and design of their controllers

• Design, analysis and implementation of an encoder-less sliding mode observer for the stator flux estimation

• Design, analysis and implementation of a power factor control structure to improve the efficiency of the induction machine in a prototype ISA system

Chapter 9 Conclusions 170

• Development of compensation methods of the non-linear characteristics of the inverter used in an ISA

The classic direct torque controlled induction generator for integrated starter alternator application has been analyzed and verified with simulation and experiments in Chapter 3. Discrete hysteresis comparator is used to keep the switching frequency of the inverter constant. High flux and torque ripples results from the look-up table of the voltage vectors and the hysteresis comparators of the torque and flux. Therefore, higher sampling time of the control system has to be used (25 μs or less) [73]. All the above difficulties can be eliminated by using a voltage space vector modulator instead of the switching table [81-91].

In this thesis, an improved torque controller of induction machine based on direct control of stator flux linkage vector is presented in Chapter 4. The fundamental relationship between the rotating speed of the stator flux linkage and torque is analyzed and the design principle of controller is presented. Parameters of PI controller are easily found using the proposed design principle. Robust design of the controller ensures the system is not sensitive to the variation of rotor resistance. Fixed switching frequency and low torque ripple are obtained with the combination of PI control and space vector modulation (SVM) method. Satisfactory modeling and experimental results indicate the feasibility of the proposed direct flux vector control scheme for induction machines. The control scheme employs encoderless torque control structure, and eliminates the disturbance of speed to the torque controller successfully. The controller gives good torque and flux control performance. The direct flux vector controlled scheme of induction generator has been proposed and verified for the future 42 V automobiles application. A simple structure with only one Proportional-Integral (PI) controller is shown to implement the torque and flux control adequately. By controlling the electromagnetic torque of the induction machine, the required dc bus voltage can be well regulated within the 42 V PowerNet specifications.

Another DTC concept based improved direct torque and flux control of the integrated starter/alternator is also proposed in Chapter 5. This control scheme has been analyzed and verified with simulation and experiments. Compared to the direct flux vector control scheme proposed in Chapter 4, this scheme is a little more complex due to transformation from stator flux frame ( dq− ) to stationary frame (α − β ). However, the

Chapter 9 Conclusions 171

extra complexity is minor because no mechanical sensor signal is required. The direct flux vector control presented in Chapter 4 controls the rotating speed of the stator flux vector by a torque feedback loop. The amplitude of the stator flux vector is regulated indirectly. In Chapter 5, the torque and the amplitude of the stator flux are regulated by two independent control loops. In addition, only derivative of a dc quantity is involved in the calculation of the commanded voltage vector, whereas derivative of an ac quantity is involved in the direct flux vector control scheme. Thus, this scheme is not sensitive to the noise which is generated when the flux vector is differentiated [63]. The simulation and experimental results show that the scheme has achieved similar performance to the direct flux vector control scheme. This scheme provides an alternative solution for the ISA application with direct torque control concept.

The voltage rating of the induction machine used in this study is very low (22 V). The effects of voltage drops on the power devices and dead-time of the converter are significant when the stator flux is estimated by reconstruction of the stator voltage vector from the gating signals and the dc link voltage. This non-linear behaviour introduces large error in the stator flux estimation leading to slower dynamic response and instability due to the oscillation of torque and flux. The effects of voltage drops and dead-time on the space vector modulated DC-AC converter are analyzed in Chapter 6. Compensation schemes have been proposed to reduce the abovementioned effects. Moreover, the compensation of the non-linear behaviour of the converter has been implemented through experimental works. No extra hardware is needed for these compensators. Experimental results confirm that the compensation is necessary for both motoring and generating modes of the ISA. These compensation algorithms have been integrated in the controller in the direct torque controlled ISA system discussed in the Chapters 4 and 5.

The stator flux estimation with compensation discussed in Chapter 3-6 is an open-loop type estimator, which is sensitive to the offset in sensors and variation of stator resistance. In Chapter 7, a closed-loop sliding mode stator flux observer for a direct torque controlled integrated starter/alternator has been developed to improve the stator flux estimation. The sliding mode stator flux observer is based on the error between the actual current and observed current converging to zero. The algorithm of the sliding mode observer is simple and all computation is in the stationary frame, which leads to

Chapter 9 Conclusions 172

low computation burden of the DSP. Both Simulation and experimental results confirm that the proposed sliding mode observer is insensitive to the stator resistance variation and measurement offset in sensor outputs.

In this study, DTC schemes for the control of the integrated starter/alternator are compared with a rotor flux oriented scheme (RFOC-ISA). Three direct torque controlled induction machine for ISA system are presented. They are: Classic DTC-ST in Chapter 3 (DTC-ST-ISA), two DTC-SVM schemes in Chapter 4 (DFC-ISA) and Chapter 5 (DTFC-ISA). These schemes are compared with RFOC for ISA application.

Table 9.1 lists general comparison of the control schemes for the ISA discussed in this thesis in terms of the control ability, structure, etc. The shadowed parts indicate the drawbacks of the schemes.

Table 9.1 Comparison of different control schemes for the ISA

DTC-ST-ISA DFC-ISA DTFC-ISA RFOC-ISA

Directly torque Indirectly torque Directly torque Directly torque control by control by PI Torque control control by PI control by PI hysteresis control of q axis action action comparator current

Directly flux Indirectly flux Indirectly flux Directly flux control by control by PI Flux control control by PI control by PI hysteresis control of d axis action action comparator current dc bus voltage Satisfied ISA Satisfied ISA Satisfied ISA Satisfied ISA control specifications specifications specifications specifications

PWM Not required SVM SVM SVM generation

Variable (could be constant with Switching discrete Constant Constant Constant frequency hysteresis comparator)

Highest (the low(the maximum low(the maximum low(the maximum Current & maximum peak- peak-peak torque peak-peak torque peak-peak torque Torque ripples peak torque ripple is 16.7 % of ripple is 16.7 % of ripple is 14.7 % of

Chapter 9 Conclusions 173

ripple is 183.3 % rated torque with rated torque with rated torque with

of rated torque Tss = 150μ ) Tss = 150μ ) Tss = 150μ )

with Tss = 150μ )

Current Not required Not required Not required Required controller

Rotor flux vector Coordinate frame to stationary transformation Not required Not required Not required ee using rotor frame ( dq to speed signal αβ

Induction machine’s Rs , Rr , Ls , Rs Rs Rs parameters Lr and Lm involved

Flux orientation and decoupling Not required Not required Not required required algorithm

Implementation simplest Medium Medium complex Complexity

current mode; could be voltage mode, but it still involves many Voltage mode: Voltage mode: Voltage mode: Flux estimation induction machine LPF; SMO LPF; SMO LPF; SMO parameters ( Rs ,

Rr , Ls , Lr and

Lm )

Good, but has High speed instability during Good Good Good performance high-speed generation [125]

It can be concluded that both DTC and RFOC schemes can effectively control the induction machine for the ISA application. By considering the parameters dependency, complexity of the structure and cost, it is clear that DTC is superior to FOC.

Chapter 9 Conclusions 174

A tradeoff between performance and simplicity is needed for the comparison of DTC- ST and DTC-SVM schemes (DFC-ISA, DTFC-ISA). Although lower flux & torque ripples and constant switching frequency are achieved with DTC-SVM scheme, SVM unit makes the control structure complex. On the other hand, DTC-ST scheme require fast sampling frequency to minimize the flux & torque ripples within acceptable limits. Therefore, DSP interfaced with hardware to determine the switching logic of the inverter, such as ASIC (Application-Specific Integrated Circuit) [73], FPGA (Field- Programmable Gate Array), and CPLD (Complex Programmable Logic Device) is needed for DTC-ST scheme.

High efficiency of the automotive electrical system is required for the economy of fuel. A loss minimized scheme for the direct torque controlled integrated starter/alternator is thus proposed in Chapter 8. With proper power factor control, both core loss and copper loss are minimized under different loads. It provides a simple solution for the efficiency improvement of the induction machine without requiring speed or load information when the load is small. The experimental results confirm the effectiveness of the proposed control scheme.

The effectiveness of the direct torque controlled induction machine for an integrated starter/alternator system has thus been confirmed and well supported by the studies presented in this thesis.

9.1 Suggestions for future work

9.1.1 Machine

The induction machine used in an ISA runs in both motoring and generating modes. Therefore, special design of the induction machine is needed to satisfy the requirement of the ISA during starting (high torque) and generating (constant power over a wide speed range). In addition, higher voltage rating than 22 V of the machine is worthy of further investigation in an ISA application with different topologies. The power losses on the connection and winding of an induction machine and semiconductor switches could be reduced with higher voltage rating.

Chapter 9 Conclusions 175

9.1.2 Power converter

High electrical power requirement (6–15 kW) of the future 42-V PowerNet imposes great challenge on the bidirectional power converter in an ISA system. The bidirectional power converter has to handle several hundred-amperes of the current with compact size due to the limited space in automobiles. Thermal design of the converter is also an important issue for the environment of a vehicle, which can be very hostile. Research related to this area has been reported in papers [60].

With higher voltage rating of the machine, investigation on new bidirectional DC-DC- AC converter topologies is required for the ISA application. Comparison study on this topic has been presented in paper [33].

9.1.3 Direct torque controlled ISA based on permanent magnet synchronous machine

High efficiency makes the permanent magnet synchronous machine (PMSM) also a strong candidate for an ISA system. The direct torque control for PMSM drives has been studied in the last decade [80, 85, 86, 88, 126-129], but not for an ISA application. Direct torque controlled ISA based on PMSM is worthy of investigation. Recently, direct torque and flux control of a permanent magnet-assisted reluctance synchronous machine (PM–RSM) for the ISA system in hybrid electric vehicles has been reported [30].

Many new innovations in machine design, converter and control may therefore be possible.

Chapter 9 Conclusions 176

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APPENDIX A LIST OF PUBLICATIONS

Journal publications:

1. Jun Zhang, M. F. Rahman, “A Direct Flux Vector Controlled Induction Generator with Space Vector Modulation for Integrated Starter Alternator”, fully accepted by the IEEE Transactions on Industrial Electronics. 2. Jun Zhang, M. F. Rahman, “Direct Torque and Flux Controlled Induction Generator for Integrated Starter/alternator with Minimized Sensor Numbers”, under review of the IEEE Transactions on Vehicular Technology.

Conference publications:

3. Jun Zhang, M.F. Rahman, "Non-Linear Behaviour Compensation of the Converter for Direct Torque Controlled Induction Machines ", proceeding of Australasian Universities Power Engineering Conference, Melbourne, Australia, December 10 - 13, 2006.

4. Jun Zhang, M. F. Rahman, “A Sliding Mode Flux Observer for Direct Torque Controlled Integrated Starter/Alternator”, proceeding of 41st Annual Meeting of the IEEE Industry Applications Society, October 8 - 12, 2006, Tampa Florida, USA (IAS 2006).

5. Jun Zhang, M. F. Rahman, “Efficiency-Optimized Direct Torque Controlled Integrated Starter/Alternator with Power Factor Control”, the 37th IEEE Power Electronics Specialists Conferences, June 18 - 22, 2006, Jeju, Korea (PESC 2006).

6. Jun Zhang, M. F. Rahman, “A New Scheme to Direct Torque Control of Interior Permanent Magnet Synchronous Machine Drives for Constant Inverter Switching Frequency and Low Torque Ripple”, the 5th International the Power Electronics and Motion Control Conference, 13-16 August, 2006 Shanghai, P. R. China (IPEMC 2006).

7. Jun Zhang, Zhuang Xu, Lixin Tang and M. F. Rahman, “A Novel Direct Load Angle Control for Interior Permanent Magnet Synchronous Machine Drives with

Appendix A 187

Space Vector Modulation”,The Sixth IEEE International Conference on Power Electronics and Drive Systems, 28 Nov – 1 Dec 2005, Kuala Lumpur, Malaysia (PEDS 2005).

8. Jun Zhang, M. F. Rahman, “Direct Flux Vector Control Scheme for Induction Machine Drives with Space Vector Modulation”, IEEE Industry Applications Society, 40th Annual General Meeting, October 2-6, 2005, Hong Kong (IAS 2005).

9. Jun Zhang, M. F. Rahman, “Sliding Mode Controlled Low Voltage Induction Machine for 42V Automotive Systems”, Australasian Universities Power Engineering Conference, The University Of Tasmania, Hobart, Australia, 25 September – 28 September 2005.

10. Jun Zhang, M. F. Rahman, “Direct Torque and Flux Controlled Induction Generator for Integrated Starter Alternator with Minimized Sensor Numbers”, 2005 IEEE Vehicle Power and Propulsion Conference, September 7-9, 2005, Illinois Institute of Technology, Chicago, Illinois, USA (VPP 2005).

11. Jun Zhang, M. F. Rahman , “Analysis and Design of a Novel Direct Flux Control Scheme for Induction Machine”, Proceeding of IEEE International Electric Machines and Drives Conference, San Antonio, USA, May 15 – 18, 2005, ISBN: 0- 7803-8988-3 (CD ROM) (IEMDC 2005).

12. Jun Zhang, M.F. Rahman and L. Tang, “A direct flux controlled induction generator with space vector modulation for integrated starter alternator”, Industrial Electronics Society, 2004. 30th Annual Conference of IEEE, Vol.1, Iss., 2-6 Nov. 2004, Pages: 330- 334 Vol. 1 (IECON 2004).

13. Jun Zhang, M.F. Rahman and L. Tang, "A Direct Torque Controlled Integrated Starter Alternator with Space Vector Modulation", Proc. AUPEC 2004, Brisbane, Australia, 29 Sept. - 2 Oct. 2004.

14. Jun Zhang, M.F. Rahman and L. Tang, “Modified direct torque controlled induction generator with space vector modulation for integrated starter alternator”, Power Electronics and Motion Control Conference, 2004. The 4th International, Vol.1, Iss., 14-16 Aug. 2004, Pages: 405- 408 Vol.1, (IPEMC 2004).

Appendix A 188

APPENDIX B MODELLING OF THE DIRECT FLUX VECTOR CONTROL

In stationary frame, the dynamic behaviour of induction machine can be described as following equations: G JJG G dΨ VRI=+s (B-1) sssdt G G dΨ G 0 = RI+−ωΨr j (B-2) rrdt m r G G G ⎪⎧Ψ=s LIss + L mr I ⎨ G G G (B-3) ⎩⎪Ψ=rmsrrLI + LI

G G 3 Lm TPers= Ψ×Ψ (B-4) 2 σLLsr where

L 2 σ=1 − m (B-5) LLs r

where Rs and Rr are the stator and rotor resistances, Ls , Lr and Lm are the stator, rotor and mutual inductances, respectively. And ωm is rotor speed, P is the number of pole pairs.

The stator and rotor current vectors can be denoted by the stator and rotor flux vectors from (B-3), respectively.

G −1 G G ⎡⎤I s ⎡⎤LLsm⎡Ψss⎤⎡⎤1 ⎡ L r− L m ⎤Ψ ⎢⎥GG==⎢ ⎥⎢⎥ G (B-6) ⎢⎥LLLL− L 2 ⎢− L L ⎥ ⎣⎦⎢⎥Ir ⎣mr ⎦⎢⎥⎣Ψrr⎦⎣⎦sr m ⎣ m s ⎦⎢⎥Ψ

By considering (B-1), (B-2) and (B-6), we get

Appendix B Modelling of the direct flux vector control 189

G G G ⎧dΨr ⎪ =Ψ−jRIωmr rr ⎪ dt ⎨ G −1 G G (B-7) ⎡⎤I s ⎡⎤LLsm⎡Ψss⎤⎡⎤1 ⎡ L r− L m ⎤Ψ ⎪⎢⎥GG==⎢ ⎥⎢⎥ G ⎪ ⎢⎥LLLL− L 2 ⎢− L L ⎥ ⎩⎣⎦⎢⎥Ir ⎣mr ⎦⎢⎥⎣Ψrr⎦⎣⎦sr m ⎣ m s ⎦⎢⎥Ψ G G The relationship between stator and rotor flux vectors Ψs and Ψr is derived from (B-7) G G G dRLΨrrm R r = Ψ+s (j ω−mr ) Ψ (B-8) dt Lsr Lσσ L r where

L 2 σ=1 − m (B-9) LLs r

By using Laplace transform of (B-8) and assuming the rotor speed ωm is changing G G slowly, the relationship between stator and rotor flux vectors Ψs and Ψr in the frequency domain can be obtained

RLrm L m GG G LLsrσ L s Ψ=rs(s) Ψ= (s) Ψ s (s) (B-10) ⎛⎞RLLrrr ⎛ ⎞ sj−ω−⎜⎟mm s σ +−ωσ ⎜1 j ⎟ ⎝⎠LRRrrrσ ⎝ ⎠ G G Assuming that Ψ=Ψ**jjtθs =Ψ ωs and the amplitude of Ψ is kept constant, and ssee s s G G that Ψs rotates at an angular speed ωs , the Laplace form of the stator flux vector Ψs is

G 1 * Ψs(s)=Ψs (B-11) sj−ωs

By substituting (B-10) into (B-11) and taking inverse Laplace transform

⎧ Lm ⎫ G ⎪ ⎪ −1 ⎪ Ls 1 * ⎪ Ψ=r (t) L ⎨ Ψs ⎬ (B-12) LL⎛⎞sj−ω ⎪ sjσ+−ωσrr1 s ⎪ ⎪ ⎜⎟m ⎪ ⎩⎭RRrr⎝⎠

Thus

Appendix B Modelling of the direct flux vector control 190

⎧⎫ Lm G ⎪⎪ −1*⎪⎪Ls 1 Ψ=rsL ⎨⎬ Ψ LL⎛⎞sj− ω ⎪⎪sjσωσrr+−1 s ⎪⎪⎜⎟m ⎩⎭RRrr⎝⎠ ⎧⎫⎛⎞L ⎪⎪⎜⎟σ r Lm −1 ⎪⎪11⎜⎟Rr * =−ΨL ⎨⎬s Lsj⎜⎟− ω ss⎪⎪⎛⎞LLrr L r ⎛⎞ L r ⎜⎟11−−−jjsjωσms σ() ω⎜⎟ σ +− ⎜⎟ ωσ m ⎪⎪RR⎜⎟ R R ⎩⎭⎝⎠rr⎝⎠ r ⎝⎠ r ⎧⎫⎛⎞L ⎪⎪⎜⎟σ r Lm −1 ⎪⎪11⎜⎟Rr * =−L ⎨⎬Ψs LsjLr ⎜⎟− ω L ⎛⎞L ss⎪⎪1 +−jσωω() r r sm⎜⎟sσ + ⎜⎟1 − jωσm ⎪⎪Rr ⎜⎟R R ⎩⎭⎝⎠r ⎝⎠r L m Lr ⎧⎫1− jωσm R L ω tt− r s * ⎪⎪s L =Ψ−s ⎨⎬σ r L eeR 1 +−jσωωr ⎪⎪r ()sm ⎩⎭ Rr L ⎛⎞Lr r −−jrctga σωω ⎧⎫1− jωσm ⎜⎟()sm R L ⎝⎠Rr ω tt− r m e * ⎪⎪s L =Ψ−σ r 2 s ⎨⎬ee L Rr s ⎛⎞L ⎪⎪ r ⎩⎭ 1 +−⎜⎟σωω()sm ⎝⎠Rr ⎛⎞L − jctar g σ r ωω− ⎜⎟()sm 1 ⎝⎠Rr Lm e * ⎧ − t ⎫ = Ψ+−cos(ωωtj ) sin( t )σ LRrr() cos( ω tj ) + sin( ω t ) 2 ss⎨ se m m⎬ Ls ⎩⎭ ⎛⎞Lr 1 +−⎜⎟σωω()sm ⎝⎠Rr ⎛⎞L −−jctar g⎜⎟σωωr () R sm 1 Lm e ⎝⎠r * ⎧ − t ⎫ =Ψ+−+cos(ωωtj ) sin( t )σ LRrr() cos( ω tj ) sin( ω t ) 2 ss⎨ se m m⎬ Ls ⎩⎭ ⎛⎞Lr 1 +−⎜⎟σωω()sm ⎝⎠Rr (B-13)

Equation (B-13) can be further simplified as

Appendix B Modelling of the direct flux vector control 191

22 G ⎛⎞yL⎛⎞r Lm xy+ * jctar g⎜⎟ −− jct ar g⎜⎟σωω()sm Ψ ()t =Ψ⎝⎠xR⎝⎠r rs2 ee Ls ⎛⎞Lr 1 +−⎜⎟σωω()sm ⎝⎠Rr

tt2 (B-14) −− ⎛⎞LL 12cos+−σσrr()ωωsm −t ⎜⎟ee()⎛⎞⎛⎞yL⎛⎞ RRrr jctar g−− ar ct g σωωr Lm ⎝⎠ * ⎜⎟⎜⎟ ⎜⎟()sm =Ψ⎝⎠⎝⎠xR⎝⎠r 2 s e Ls ⎛⎞Lr 1 +−⎜⎟σωω()sm ⎝⎠Rr where

t ⎧ − x cos(tt )Lr cos( ) ⎪ =−ωωsme σ ⎪ Rr (B-15) ⎨ t − ⎪ sin( )Lr sin( ) y =−ωωsmtte σ ⎩⎪ Rr

That is

2 t ⎛⎞t − 12+−⎜⎟e− ecosτ ω−ω t G ⎜⎟τ (()sm) Lm ⎝⎠ Ψ=r (t) Ls 2 (B-16) 1 +τω−ω ( ()sm) ⎛⎞−−11⎛⎞y ×Ψ* jtan⎜⎟⎜⎟−τω−ω tan s e ⎝⎠⎝⎠x ( ()sm) where

⎧ L τ=σ r ⎪ R ⎪ r t ⎪ − x =ω−cos( t )τ cos( ω t ) (B-17) ⎨ sme ⎪ t − τ ⎪ y =ω−sin(sm t ) sin( ω t ) ⎪ e ⎩

With small slip, (B-16) can be simplified as

Appendix B Modelling of the direct flux vector control 192

2 t ⎛⎞t − 12+−− e τ ⎜⎟e τ G L ⎝⎠ ⎛⎞−−11⎛⎞y Ψ≈(t) m ×Ψ* jtan⎜⎟⎜⎟−τω−ω tan rse ⎝⎠⎝⎠x ( ()sm) (B-18) Ls 1

t ⎛⎞− ⎡⎤−−11⎛⎞y Lm τ * j =−1 e ×Ψ e ⎢⎥tan⎜⎟−τω−ω tan ()()sm ⎜⎟s ⎣⎦⎝⎠x Ls ⎝⎠

It shows that the rotor flux vector tracks stator flux vector in its amplitude and rotating speed with a time constant, given by τ . Once the stator flux is built up and kept constant, the rotor flux will also be kept constant. Therefore, the amplitude of the rotor flux can be considered as fixed after establishing of the stator flux. Equation (B-18) can be further simplified as

G ⎡ −−11⎛⎞y ⎤ Lm * Ψ≈Ψ(t) j ⎢tan⎜⎟−τω−ω tan ()()sm⎥ (B-19) rse ⎝⎠x Ls ⎣ ⎦

From (B-4), the torque can be expressed as

3 L G jtω T(t) Pm (t) * s (B-20) ers=Ψ×Ψe 2 σLLsr

By substituting (B-19) into (B-20), we obtain

⎧⎫ 3 LL⎪⎪⎡⎤−−11⎛⎞y jtω mm* j tan−τω−ω tan () * s T(t)es=×Ψ P ⎨⎬Ψ e ⎢⎥⎜⎟ ()sm s 2 σLL L ⎣⎦⎝⎠x e sr⎩⎭⎪⎪ s (B-21) 2 ⎧⎫3 LLmm* ⎧ ⎡ −−11⎛⎞y ⎤⎫ ≈Ψ×ω−−τω−ω⎨ Pss⎬⎨ sin t⎢ tan⎜⎟ tan ()() sm⎥ ⎬ ⎩⎭2 σLLsr L s ⎩⎭⎣ ⎝⎠ x ⎦ where

⎧ L τ=σ r ⎪ R ⎪ r t ⎪ − x =ω−cos( t )τ cos( ω t ) (B-22) ⎨ sme ⎪ t − τ ⎪ y =ω−sin(sm t ) sin( ω t ) ⎪ e ⎩

It clear that the dynamic response of torque is determined by the amplitude and rotating speed of the stator flux vector with the non-linear relationship of (B-21). The torque of the induction machine can be regulated by controlling rotating speed of the stator flux

Appendix B Modelling of the direct flux vector control 193

G vector Ψs as long as its amplitude is kept constant. As rotor flux vector tracks the stator flux vector, its amplitude is also kept constant after establishing of constant stator flux amplitude. In addition, the sin or tan computation results of a small angle is very close to the angle by itself (in rad) as shown in (B-23). Therefore, the above torque expression can be simplified to (B-25) in which the slip is small.

sin()θ ≈θ≈θ tan( ) ( ) ( small θ) (B-23)

So, torque expression can be further simplified as

2 ⎧⎫3 LLmm* ⎧ ⎡ −1 ⎛⎞y ⎤⎫ T(t)esssm=Ψ×ω−−τω−ω⎨⎬⎨⎬ P sin t⎢ tan ⎜⎟()()⎥ ⎩⎭2 σLLsr L s ⎩⎭⎣ ⎝⎠ x ⎦ (B-24) 2 ⎧⎫3 LLmm* ⎧⎫⎛⎞y =Ψ×ω−+τω−ω⎨⎬⎨⎬Ptss⎜⎟()() sm ⎩⎭2 σLLsr L s ⎩⎭⎝⎠ x

By considering (B-24) and (B-22) at same time, we obtain

t ⎧⎫3 LL * 2 ⎧⎛⎞− ⎫ T(t)≈ P mmΨ−τω−ω1 τ e ⎨⎬⎨⎬ssm⎜⎟e ()() ⎩⎭2 σLLsr L s ⎩⎭⎝⎠ (B-25) 2 t 2 ⎧⎫3 Lm * ⎛⎞− =Ψ−ω−ωP 1 τ ⎨⎬2 ssm⎜⎟e () ⎩⎭2 RLrs ⎝⎠

The simplification in (B-25) is based on the fact that

t ⎧⎫⎛⎞y ⎛⎞− ω−t +τω−ω ≈1 − τ ω−ω (B-26) ⎨⎬ssm⎜⎟()()⎜⎟e ()sm ⎩⎭⎝⎠x ⎝⎠ by considering the dynamic in (B-22).

Therefore

2 t 2 ⎧⎫3 Lm * ⎛⎞− τ T(t)essm≈ ⎨⎬ P 2 Ψ−ω−ω⎜⎟1 () 2 RL ⎝⎠e ⎩⎭rs (B-27) t ⎛⎞− τ =−K ⎜⎟1 () ω−ωsm ⎝⎠e where

Appendix B Modelling of the direct flux vector control 194

2 2 ⎧ 3 Lm * ⎪KP=Ψ2 s ⎪ 2 RLrs ⎨ (B-28) L ⎪τ=σ r ⎪ ⎩ Rr

By Laplace transform of (B-27), we have

⎛⎞1 T(s)esm= K⎜⎟L{}ω−ω (B-29) ⎝⎠τ+s 1

where L{ω−ωs m } is the Laplace form of {ωs −ωm }.

The transfer function of the torque loop with input as {ωs −ωm } can be written as

T(s)e K G(s)p == (B-30) L{}ωsm−ω τs +1

Equation (B-30) shows that the relationship between Te and ωs is equivalent to a first order system with a disturbance ωm . The equivalent system block is shown as follows:

−ωm ()s

Ts() ω ()s e s K τ s +1

Fig. B.1 Equivalent system model of the torque loop

In order to achieve good performance of tracking a reference torque signal and disturbance rejection, a PI controller of Fig.B.2 can be employed:

−ωm ()s ∗ ω ()s Ts() Te s K e Gsc () − τ s +1

Fig.B.2 PI control of the equivalent system

Appendix B Modelling of the direct flux vector control 195

where

Ks+ K G(s)= pi (B-31) c s

Fig.B.2 is the equivalent torque loop of the direct flux vector control scheme discussed in Chapter 4.

Appendix B Modelling of the direct flux vector control 196

APPENDIX C MODELLING OF THE DIRECT TORQUE AND FLUX CONTROL

β

q G d G Is Ψ s

G isd Ψr isq

θs α

Fig. C.1 Vector diagram of the induction machine

In stator flux reference frame (dq− ) shown in Fig. C.1, the dynamic behavior of induction machine can be described as following equations: G ⎧JJG G dΨ G VRI=+s +ωΨ j ⎪ sssdt ss ⎪ G G G ⎪ dΨr ⎨0 = RIrr++ω−ωΨ j() s m r (C-1) ⎪ dt ⎪ 3 TPi=Ψ⋅ ⎪ esdsq ⎩ 2 and G G G ⎪⎧Ψ=s LIss + L mr I ⎨ G G G (C-2) ⎩⎪Ψ=rmsrrLI + LI

197

Therefore,

⎧ G dΨ JJG G G ⎪ s =−VRIj −ωΨ ⎪ dt sssss G ⎪ G G ⎪dΨr ⎨ =−jRI() ωsmrrr −ω Ψ − (C-3) dt ⎪ G G G ⎪ −1 ⎡⎤I s ⎡⎤LLsm⎡Ψss⎤⎡⎤1 ⎡ L r− L m ⎤Ψ ⎪⎢⎥GG==⎢ ⎥⎢⎥ G ⎢⎥LLLL− L 2 ⎢− L L ⎥ ⎪⎩⎣⎦⎢⎥Ir ⎣⎦mr⎣⎢Ψrr⎦⎣⎦⎥⎢⎥sr m ⎣ m s ⎦Ψ

Equation (C-3) can be simplified as G ⎡⎤ dΨs G G ⎢⎥⎡⎤1 JJG ⎡⎤− jω 0 ⎡⎤Ψ ⎡⎤R 0 ⎡⎤I ⎢⎥dt s s s s GG=+Vs ⎢⎥⎢⎥ −⎢⎥⎢⎥G ⎢⎥0 0 −−j ()ωω 0 R I ⎢⎥dΨΨrr⎣⎦ ⎣⎦sm⎣⎦⎢⎥⎣⎦r ⎣⎦r ⎣⎦⎢⎥dt G G JJG ⎡⎤1 ⎡⎤− jωs 0 ⎡Ψs ⎤⎡⎤⎡⎤Rs 0 1 ⎡⎤LLrm− Ψs =+Vs ⎢⎥⎢ G ⎥⎢⎥ − 2 G ⎢⎥0 0 −−j ()ωω ⎢⎥0 R LL− L ⎢⎥−LL ⎣⎦ ⎣⎦sm⎣⎢Ψrr⎦⎣⎦⎥⎣⎦⎢⎥⎣⎦r sr m msΨ GG JJG ⎡⎤1 ⎡⎤− jωs 0 ⎡⎤ΨΨss⎡⎤Rs 0 1 ⎡⎤LLrm− ⎡⎤ = Vs +−⎢⎥⎢⎥GG ⎢⎥ ⎢⎥0 0 −−j ()ωω ⎢⎥0 R LLσ ⎢⎥−LL ⎣⎦ ⎣⎦sm⎣⎦⎢⎥ΨΨrr⎣⎦r sr ⎣ms ⎦⎢⎥ ⎣⎦ ⎡⎤1 L GG− m 1 JJG ⎡⎤− jω 0 ⎡⎤ΨΨ⎡⎤R 0 ⎢⎥LLLσσ ⎡⎤ ⎡⎤ s sss ⎢⎥ssr =+⎢⎥Vs ⎢⎥⎢⎥GG −⎢⎥ ⎢⎥ 0 0 −−j ()ωω 0 R ⎢⎥L 1 ⎣⎦ ⎣⎦sm⎣⎦⎢⎥ΨΨrr⎣⎦r m ⎣⎢⎥⎦ ⎢⎥− ⎣⎦LLsrσσ L r ⎡⎤RRL GG− ssm ⎡⎤1 JJG ⎡⎤− jω 0 ⎡⎤ΨΨ⎢⎥LLLσσ ⎡⎤ s ss⎢⎥ssr =+⎢⎥Vs ⎢⎥⎢⎥GG + ⎢⎥ 0 0 −−j ()ωω ⎢⎥RL R ⎣⎦ ⎣⎦sm⎣⎦⎢⎥ΨΨrrrm r ⎣⎦⎢⎥ ⎢⎥− ⎣⎦LLsrσσ L r ⎡⎤RRL −−ssmjω G (C-4) ⎢⎥s JJG LLLssrsσσ⎡⎤Ψ ⎡⎤1 =+⎢⎥⎢⎥G V ⎢⎥RL R ⎢⎥0 s rm r ⎣⎦⎢⎥Ψr ⎣⎦ ⎢⎥−−−j ()ωωsm ⎣⎦LLsrσσ L r where

L 2 σ=1 − m (C-5) LLs r

So, the relationship between stator and rotor flux vector can be obtained by Laplace transform from (C-4)

198

GG G RLrm ⎛⎞Rr sjΨ=rssmr Ψ+−⎜⎟()ωω − − Ψ (C-6) LLsrσσ⎝⎠ L r thus

RLrm L m GG G LLsrσ L s Ψ=rs Ψ= Ψ s ⎛⎞⎛⎞RLrr L r sj−⎜⎟⎜⎟ −() ωsm −ω − s σ− − j() ω sm −ω σ−1 ⎝⎠⎝⎠LRrrσ R r (C-7)

LLmm GG LLss =Ψ=Ψss sjτσ−−()() ω−ωsm τ−11 sj τσ+()() ω−ω sm τ+

L where τ= r . Rr

It is known in the stator flux reference frame that G ⎪⎧Ψs =Ψds +j Ψ qs ⎨ (C-8) ⎩⎪Ψ=qs 0

The rotor flux vector in the stator flux reference frame can be expressed as G Ψrrdrq=Ψ +j Ψ (C-9)

With (C-6), (C-8) and (C-9), the dq component of rotor flux vector can be obtained

199

GG G RLrm ⎛⎞Rr sjΨ=rssmr Ψ+−⎜⎟() ω−ω− Ψ LLsrσσ⎝⎠ L r

RLrm ⎛⎞Rr ⇒sj() Ψrd +Ψ rq = Ψ sd +−⎜⎟ j() ω−ω− s m() Ψ rd +Ψ j rq LLsrσσ⎝⎠ L r ⎧ RLrm ⎛⎞Rr ⎪sΨ=rd Ψ+ω−ωΨ− sd⎜⎟() s m rq Ψ rd ⎪⎝LLsrσσ L r ⎠ ⇒ ⎨ ⎛⎞R ⎪sΨ=−ω−ωΨ−r Ψ ⎪ rq⎜⎟() s m rd rq ⎩ ⎝⎠Lr σ ⎧ RLrm ⎛⎞Rr ⎪sΨ=rd Ψ+ω−ωΨ− sd⎜⎟() s m rq Ψrd LLsrσ ⎝⎠ Lr σ ⎪ ⇒ ⎨ −ω−ω() Ψ=sm Ψ ⎪ rqR rd ⎪ s + r ⎩⎪ Lr σ ⎧ ⎛⎞ 2 ⎪ RL ⎜⎟−ω−ω() R ⎪sΨ=rm Ψ+⎜⎟sm Ψ−r Ψ rd sdR rd rd ⎪ LLsrσσ⎜⎟r L r ⎪ ⎜⎟s + ⇒ ⎨ ⎝⎠Lr σ ⎪ −ω−ω() ⎪Ψ=sm Ψ rqR rd ⎪ s + r ⎪ ⎩ Lr σ ⎧⎛⎞ 2 ⎪⎜⎟()ω−ω R RL ⎪⎜⎟s ++Ψ=Ψsm r rm R rd sd ⎪⎜⎟r LLLrsrσσ ⎪⎜⎟s + ⇒ ⎨⎝⎠Lr σ ⎪ −ω−ω() ⎪Ψ=sm Ψ rqR rd ⎪ s + r ⎪ ⎩ Lr σ

⎧ RLrm ⎪ LLsrσ ⎪Ψ=rd2 Ψ sd ⎪ ()ω−ω R s ++sm r ⎪ R L σ ⎪ s + r r ⎪ Lr σ ⇒ ⎨ (C-10) ⎪ RLrm

⎪ −ω−ω()sm LLsrσ ⎪Ψ=rq2 Ψ sd Rr ω−ω ⎪ s + ()sm Rr L σ s ++ ⎪ r Rr L σ ⎪ s + r ⎩ Lr σ

200

The expression of stator current with stator and rotor flux vector is already shown in (C- 3), which is restated as G G 1 ⎡Ψs ⎤ ⎡⎤ILL=−[]⎢ G ⎥ (C-11) ⎣⎦srmLL− L 2 sr m ⎣⎢Ψr ⎦⎥

By substituting (C-10) into (C-11), it is derived that

1 −ΨL ⇒=ILL⎡⎤ Ψ−Ψ=mrq sq2 ⎣⎦ r sq m rq LLsr− L m LL srσ

RLrm −LLL−−()ωω σ ⇒=I msrsm Ψ sq R 2 sd LLsrσ r ()ωω− R s + s ++sm r Lrσ R L σ s + r r Lrσ

Lm LL()ωω− τσ ⇒=I mssm Ψ sq1 2 sd LLsrσ ()ωω− 1 s + s ++sm τσ 1 s + τσ τσ

LLmm ()ωωsm− = Ψsd LLsrστσ L s ⎛⎞1112 ⎛⎞ ss⎜⎟++−+()ωωsm ⎜ s +⎟ ⎝⎠τσ τσ ⎝⎠ τσ 2 Lm ()ωωsm− ⇒=I sq 22 Ψsd LLτσ 2 1112 sr ss++−++()ωω s τσsm τσ τ22 σ (C-12) L 2 ()ωωτσ− 22 ⇒=I m sm Ψ sq LL22τσ 222 22 2 sd sr τσss++21 τσ τσ() ωsm −+ ω

Thus

L 2 ()ω−ω τ m smLL2 ⇒=I sr Ψ sqsd222 22 2 τσss +21 τσ+τσ() ωsm −ω + L 2 ()ω−ω τ m smLL2 ⇒≈I sr Ψ (C-13) sq22 2 sd 21τσs + τ σ() ωsm − ω + L 2 ()ω−ω τ m smLL2 ⇒≈I sr Ψ sq21τσ+s sd

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where

2 ⎧ Lm ⎪σ=1 − ⎪ LL ⎨ s r (C-14) L ⎪τ= r ⎪ ⎩ Rr

The simplification in (C-13) is based on small τ and σ .

By inverse Laplace transform, the expression of Isq is time domain is obtained as

2 ⎧ Lm ⎫ ⎪()ω−ωsm τ 2 ⎪ −−11⎪ LLsr ⎪ I sq(t)==LL{} I sq (s)⎨ Ψ sd (s)⎬ ⎪ 21τσs + ⎪ ⎪⎩⎭⎪ 2 ⎧⎫Lm ⎪⎪()ω−ωsm τ 2 ∗ −1⎪⎪LLΨ = L ⎨⎬sr sd (C-15) ⎪⎪21τσss + ⎩⎭⎪⎪ 2 L −t =ω−ωτm Ψ∗ 1 −e 2τσ ()sm2 sd{} LLsr

It is assumed that the magnitude of the stator flux vector is kept constant with flux regulator in axis d . By considering (C-1) and (C-15), the torque is obtained as follows.

3 T(t)=Ψ P (t) ⋅ i (t) esdsq2 2 3 L −t =Ψω−ωτPe∗∗m Ψ1 −2τσ (C-16) sd() s m2 sd {} 2 LLsr 2 3 2 τL −t =ΨPe∗ m ω−ω−1 2τσ ()sd2 () s m {} 2 LLsr

By (C-1), the voltage equation in dq frame is

⎧ ddΨΨsdsd ⎪VRisd=+ s sd ≈ ⎨ dt dt (C-17) ⎪ ⎩VRisq= s sq+ωΨ s sd ≈ωΨ s sd

By substituting (C-17) into (C-16), the relationship between the q voltage component and the torque is developed as

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2 3 τL −t T(t)=⋅Ψ P∗ m 1 − e2τσ V −ω f (C-18) esdsqm2 { } () 2 LLsr where

2 3 2 τL −t fPω= Ψ∗ m 1 − e2τσ ω (C-19) ()msdm()2 { } 2 LLsr

Therefore, it is clear shown in (C-18) that the torque of induction machine can be directly regulated by the q voltage component considering f (ωm ) as a disturbance to the system. Similarly, the amplitude of stator flux vector can be regulated by the d component of stator voltage directly as shown in (C-17). Above analysis forms the principle of the direct torque and flux control (DTFC) scheme for the induction machine.

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