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TRANSCRIPT
DIRECT TORQUE CONTROLLED INDUCTION MACHINES FOR INTEGRATED
STARTER/ALTERNATOR 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
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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
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Dedicated to the memory of my grandmother
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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.
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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
voltage 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
direct torque control (DTC) concept can be successfully extended to the ISA
application.
An improved DTC of the ISA based on direct stator 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 rotor 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 vector control 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.
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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.
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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
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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
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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
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9.1.3 Direct torque controlled ISA based on permanent magnet 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
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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 INDUCTION MOTOR ......................................................................................................... 18 FIG. 1.19 DTC OF INDUCTION GENERATOR ................................................................................................. 19
FIG. 2.1 DYNAMIC e ed q− EQUIVALENT CIRCUITS OF MACHINE (A)
eq AXIS CIRCUIT, (B) ed 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
FIG. 2.6 STARTING OF ISA WITH RFOC: (A) TORQUE, SPEED AND STATOR FLUX (B) TORQUE e
di AND e
qi 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
AND STATOR CURRENT (B) TORQUE, edi AND
eqi ........................................................................ 34
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FIG. 2.10 LOAD DUMP OF ISA WITH BATTERY CONNECTED: (A) BUS VOLTAGE, TORQUE, STATOR FLUX AND
STATOR CURRENT (B) TORQUE, edi AND
eqi ................................................................................ 35
FIG. 2.11 ISA PERFORMANCE AT ACCELERATION: (A) BUS VOLTAGE, SPEED, STATOR FLUX AND STATOR
CURRENT (B) SPEED, edi AND
eqi ................................................................................................ 37
FIG. 2.12 ISA PERFORMANCE AT DECELERATION: (A) BUS VOLTAGE, SPEED, STATOR FLUX AND STATOR
CURRENT (B) SPEED, edi AND
eqi ................................................................................................ 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 sμ (B) TS =50 sμ .......................................................... 48
FIG. 3.7 ISA GENERATING WITH FULL LOAD (A) TS =150 sμ (B) TS =50 sμ .............................................. 49
FIG. 3.8 SPECTRUM ANALYSIS OF THE STATOR CURRENT WITH FFT (A) TS =150 sμ (B) TS =50 sμ .......... 50
FIG. 3.9 LOAD DUMPING PERFORMANCE OF ISA (A) TS =150 sμ (B) TS =50 sμ ........................................ 51
FIG. 3.10 ISA PERFORMANCE AT SPEED RAMP (TS =50 sμ ) (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
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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) aNV WITH
DEAD-TIME EFFECT ONLY(D)CONSIDERING ont AND offt 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
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FIG. 6.9 FORWARD COMPENSATION STRUCTURE ....................................................................................... 117 FIG. 6.10 THE CONTROL SYSTEM 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 VOLTAGES 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 sR ................................................. 141
FIG. 7.3 SLIDING MODE FLUX OBSERVER WITH 50% ERROR IN sR ............................................................ 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% sR ERROR................................................... 147
FIG. 7.11 SLIDING MODE FLUX OBSERVER WITH 50% sR ERROR.............................................................. 147
FIG. 7.12 OPEN-LOOP STATOR FLUX ESTIMATION WITH 3A DC CURRENT OFFSET...................................... 148
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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
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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 ( 0ai > ; 0bi > ; 0ci < ) ....................................................... 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
xvii
LIST OF SYMBOLS
α −β stationary reference frame
d q− stator flux reference frame
e ed q− 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
sR stator resistance of the induction machine
sL stator inductance
rL rotor winding self-inductance
mL mutual inductance
lsL stator leakage inductance
lrL rotor leakage inductance
sΨ Stator flux vector
rΨ rotor flux vector
eT electromagnetic torque, Nm
TL load torque
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Test, T 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 alternating current
dc, DC direct current
DSP digital signal processor
DTC direct torque control
DTFC direct torque and flux control
DFC direct flux vector control
EKF extended kalman filter
emf electromagnetic force
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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 synchronous motor
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.
Chapter 1 Introduction 1
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 2
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 3
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 4
• 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 5
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 6
• 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.
Integrated starter/alternator
DC starter Motor
Eng
ine
spee
d (r
pm)
Starting time (ms)
200 400 600 800 10000
0
200
400
600
800
1000
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 7
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 8
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
commutator brush makes it is impossible to be used in an ISA application due to the
Chapter 1 Introduction 9
limitation of speed and reliability. The conventional synchronous machine used in
today’s alternators 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 magnets (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 10
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
N
N
S
SN S N
S
N
N
S
SN S N
(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 11
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 12
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 13
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 14
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 15
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 16
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 17
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 18
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.
e dc dcT V Iω = (1-1)
where ω is the speed of AC machine, which is determined by the engine. eT is the
electromagnetism torque of AC machine; dc dcV ,I 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:
a
dcb s e
c
uV
u V TSwitching Signal
u
⎧⎧ ⎪→ → →Ψ →⎨ ⎨⎩ ⎪
⎩
(1-2)
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.
dcV
Fig. 1.18 DTC of induction motor
Chapter 1 Introduction 19
The concept of DTC for motor drive 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:
a
bs e dc
c
uu
V T VuSwitching Signal
⎧⎪⎪→ Ψ → → →⎨⎪⎪⎩
(1-3)
dcU
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 20
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 21
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 2 An induction machine based ISA using RFOC with SVM 22
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 ( e ed q− ), the dynamic of the induction
machine can be expressed as
Chapter 2 An induction machine based ISA using RFOC with SVM 23
( )
( )
ssd s sd e sq
sqsq s sq e sd
rdrd r rd e r rq
rqrq r rq e r rd
dv R idt
dv R i
dtdv R i
dtd
v R idt
αψ⎧ = + − ω ψ⎪⎪
ψ⎪ = + + ω ψ⎪⎨ ψ⎪ = + − ω −ω ψ⎪⎪ ψ⎪ = + + ω −ω ψ⎩
(2-1)
where
sdv and sqv are the stator voltages;
eω and rω are synchronous and rotor rotating frequency;
sdi , sqi , rdi and rqi are stator and rotor currents in d- and q-axis;
sdψ , sqψ , rdψ and rqψ are the stator and rotor flux linkages in d- and q-axis;
sR 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:
sd s sd m rd
sq s sq m rq
rd m sd r rd
rq m sq r rq
L i L iL i L i
L i L iL i L i
ψ = +⎧⎪ψ = +⎪⎨ψ = +⎪⎪ψ = +⎩
(2-2)
where sL , rL and mL are the stator self, rotor self and mutual inductances, respectively.
Chapter 2 An induction machine based ISA using RFOC with SVM 24
sqi rqi
sR
sqψmL
rR
ls s mL L L= −( )e r rdω ω ψ−
lr r mL L L= −
rqψ
e sdωψ
sqV rqV
(a)
sdi rdi
sR
sdψmL
rR
ls s mL L L= −( )e r rqω ω ψ−
lr r mL L L= −
rdψ
e sqωψ
sdV rdV
(b)
Fig. 2.1 Dynamic e ed q− equivalent circuits of machine (a) eq axis circuit, (b) ed 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 startingT . In the
generating mode, torque reference is connected to the output of the dc bus voltage
controller 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 25
in proportional to 1 rω 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 ( e ed q− ),
which are transformed to the stationary frame (α −β ) by e ed q− 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 ).
r∠Ψ
−
Current Model Estimator
SVM IMPI
rω
PI
Encorder
sqV
sdV
e ed q−
α β−
,V Vα βPI
*sdi
*sqi
sqisdi
TK−
rΨ
dcV
*T
*dcV
startingT +
−
+
r∗Ψ
rω
bω
Fig. 2.2 Rotor flux oriented controlled ISA with SVM
2 23
r esq
m r est
L Tip L ψ
∗∗ = (2-3)
Chapter 2 An induction machine based ISA using RFOC with SVM 26
rω
sAisBisCi
si α
si β
11 rT s+
sdi
sqirje− θ
rθrT
mL
∫rθ
rψ
÷ +
Fig. 2.3 flux model in the rotor-flux-oriented reference frame [74]
de e
qe e
V Vcos sinV Vsin cosα
β
θ − θ⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥θ θ⎣ ⎦⎣ ⎦ ⎣ ⎦
(2-4)
where eθ is the angle between the rotor flux frame ( e ed q− ) and stationary frame
(α −β ), i.e. the angle of rotor flux linkage vector as shown in Fig. 2.4
rΨ
eθ α
β
eq edsI
sdisqi
eω
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 27
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 sR ( mΩ ) 25.1
Rotor resistance rR ( mΩ ) 18.2
Mutual inductance (mH) 1.8
Stator leakage inductance lsL (mH) 0.07618
Rotor leakage inductance lrL (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.
2 3 2 30.7855 42 25.7 V2 2l l dcV m V
π π−⎛ ⎞ ⎛ ⎞≤ ⋅ ⋅ = × × × =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
(2-5)
where m (=0.7855) is the modulation factor with sinusoidal PWM [75], dcV 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 28
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 feedback 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 29
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 30
(a)
(b)
Fig. 2.6 Starting of ISA with RFOC: (a) torque, speed and stator flux (b) torque edi and e
qi
Chapter 2 An induction machine based ISA using RFOC with SVM 31
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 sμ .
Fig. 2.7 ISA generating with full load
Chapter 2 An induction machine based ISA using RFOC with SVM 32
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 33
changed from -5 Nm to about -1 Nm during load dumping. The edi 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 34
(b)
Fig. 2.9 Load dump of ISA without battery connected: (a) bus voltage, torque, stator flux and
stator current (b) torque, edi and e
qi
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 35
(a)
(b)
Fig. 2.10 Load dump of ISA with battery connected: (a) bus voltage, torque, stator flux and
stator current (b) torque, edi and e
qi
Chapter 2 An induction machine based ISA using RFOC with SVM 36
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 37
(b)
Fig. 2.11 ISA performance at acceleration: (a) bus voltage, speed, stator flux and stator current
(b) speed, edi and e
qi
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 38
(a)
(b)
Fig. 2.12 ISA performance at deceleration: (a) bus voltage, speed, rotor flux and stator current
(b) speed, edi and e
qi
Chapter 2 An induction machine based ISA using RFOC with SVM 39
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 40
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 3 Analysis and implementation of the classical direct torque controlled ISA 41
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 42
the classic DTC controlled induction generator with 150 sμ (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:
ss s s
dV R IdtΨ
= + (3-1)
0 rr r m r
dR I jdtΨ
= + − ω Ψ (3-2)
s s s m r
r m s r r
L I L I
L I L I
⎧Ψ = +⎪⎨Ψ = +⎪⎩
(3-3)
( )3 3
2 232
m me r s r s s r
s r s r
mr s
s r
L LT P P sinL L L LLP sinL L
= Ψ ×Ψ == Ψ Ψ θ − θσ σ
= Ψ Ψ γσ
(3-4)
where
2
1 m
s r
LL L
σ = − (3-5)
where sR and rR are the stator and rotor resistances, sL , rL and mL are the stator, rotor
and mutual inductances, respectively. And mω is rotor speed, P is the number of pole
pairs, sθ and rθ are the angles of stator and rotor flux vectors, respectively, and γ
(equal to s rθ − θ ) 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 43
voltage space vectors according to (3-1). The voltage vector can be selected from eight
basic vectors including six non-zero active voltage ( )1 6V V→ vectors and two zero
voltage vectors ( )0 7,V V as shown in Fig. 3.1.
1AS =
0CS =
1CS =
0BS =0AS =
1BS =
2V3V
4V
5V 6V
0V7V
1Vα
β
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.
1V
2V3V
4V
5V 6V
sψ
rψ
α
βsω
γ
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 44
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.
sθ∠
eT
eT ∗
sψ ∗
sψ
dcV
Fig. 3.3 Structure of classical direct torque control
Table 3.1 Switching table of inverter vectors
dψ edT Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6
1 V2 V3 V4 V5 V6 V1
0 V7 V0 V7 V0 V7 V0 1
1− V6 V1 V2 V3 V4 V5
1 V3 V4 V5 V6 V1 V2
0 V0 V7 V0 V7 V0 V7 0
1− V5 V6 V1 V2 V3 V4
The output of flux hysteresis comparator with two-level is dψ
1
0
s ref s
s ref s
d if
d if
⎧ ψ = ψ ≤ ψ − Δψ⎪⎨
ψ = ψ ≥ ψ + Δψ⎪⎩ (3-6)
where sΔψ is the error band of the flux comparator.
The output of torque hysteresis comparator with three-level is edT
Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 45
1
0
1
0
e e ref e
e e ref
e e ref e
e e ref
dT if T T Tanticlockwise rotation :
dT if T T
dT if T T Tclockwise rotation :
dT if T T
⎧ ⎧ = ≤ − Δ⎪⎪ ⎨⎪ = ≥⎪⎩⎪⎪⎨⎪ ⎧ = ≥ − Δ⎪ ⎪
⎨⎪ = ≤⎪⎪ ⎩⎩
(3-7)
where eTΔ is the error band of the torque comparator.
3.3 ISA with classical DTC
γ
β
αMotoring State
sψ
rψ
γ
β
αGenerating State
sψ
rψ
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 46
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.
dcV
*T
eT
sψ ∗
*dcV
sψ
startingT +
−
−
+
sθ∠
dcV
−
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)
( )
32
s s s s
e s s
V R I dt
T P I
⎧Ψ = −⎪⎨
= Ψ ×⎪⎩
∫ (3-8)
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 47
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 sμ
Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 48
(b) Ts =50 sμ
Fig. 3.6 Starting process of ISA (a) Ts =150 sμ (b) Ts =50 sμ
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 sμ than that of the case with
sampling time as 150 sμ .
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 sμ ).
Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 49
(a) Ts =150 sμ
(b) Ts =50 sμ
Fig. 3.7 ISA generating with full load (a) Ts =150 sμ (b) Ts =50 sμ
Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 50
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 sμ ).
(a) Ts =150 sμ (b) Ts =50 sμ
Fig. 3.8 Spectrum analysis of the stator current with FFT (a) Ts =150 sμ (b) Ts =50 sμ
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 sμ or 50 sμ .
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 51
(a) Ts =150 sμ
(b) Ts =50 sμ
Fig. 3.9 Load dumping performance of ISA (a) Ts =150 sμ (b) Ts =50 sμ
Chapter 3 Analysis and implementation of the classical direct torque controlled ISA 52
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 53
(b)
Fig. 3.10 ISA performance at speed ramp (Ts =50 sμ ) (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.
( )11s s s s
c
V R Is T
Ψ = −+
(3-9)
Where ( )1 2c cT f= π and cf 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 54
hysteresis comparator is different with analog hysteresis comparator by using a fixed
sampling time sT 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.
2e
eTT ∗ Δ
+
2e
eTT ∗ Δ
−1t 3t2t
eT ∗
2e
eTT ∗ Δ
+
2e
eTT ∗ Δ
−eT ∗
/S H
sT
sTsTsT
(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 sμ ) 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 sμ .
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 55
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 56
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 sμ ) 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 4 Direct flux vector controlled ISA with space vector modulation 57
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 58
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:
ss s s
dV R IdtΨ
= + (4-1)
0 rr r m r
dR I jdtΨ
= + − ω Ψ (4-2)
s s s m r
r m s r r
L I L I
L I L I
⎧Ψ = +⎪⎨Ψ = +⎪⎩
(4-3)
32
me r s
s r
LT PL L
= Ψ ×Ψσ
(4-4)
where
2
1 m
s r
LL L
σ = − (4-5)
where sR and rR are the stator and rotor resistances, sL , rL and mL are the stator self,
rotor self and mutual inductances, respectively. And mω is rotor speed, P is the number
of pole pairs.
Chapter 4 Direct flux vector controlled ISA with space vector modulation 59
The relationship between stator and rotor flux vectors sΨ and rΨ respectively is
derived from (4-2) and (4-3)
r r m rs m r
s r r
d R L R( j )dt L L LΨ
= Ψ + ω − Ψσ σ
(4-6)
By using Laplace transform of (4-6) and assuming the rotor speed mω is changing
slowly, the relationship between stator and rotor flux vectors sΨ and rΨ in the
frequency domain can be obtained
1
m
sr s
r rm
r r
LL( s ) ( s )
L Ls jR R
Ψ = Ψ⎛ ⎞
σ + − ω σ⎜ ⎟⎝ ⎠
(4-7)
(Please refer to Appendix B for further details of the derivation included in this chapter)
Assuming that s sj j t* *s s se eθ ωΨ = Ψ = Ψ and the amplitude of sΨ is kept constant, and
that sΨ rotates at an angular speed sω ,
1 *s s
s
( s )s j
Ψ = Ψ− ω
(4-8)
By substituting (4-8) into (4-7) and taking inverse Laplace transform
1 1
1
m
*sr s
r r sm
r r
L
L( t )
L L s js j
R R
−Ψ = Ψ− ω
σ + − ω σ
⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬
⎛ ⎞⎪ ⎪⎜ ⎟⎪ ⎪⎩ ⎭⎝ ⎠
L (4-9)
Thus
( )( )
( )( )( )( )
21 2
21
1 1
mr
s
s
tt
e cos te s m( t )
s my* j tan tane s mx
LL
−τ−+ − ω − ωτ
Ψ =
+ τ ω − ω
− −− τ ω − ω× Ψ
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(4-10)
Chapter 4 Direct flux vector controlled ISA with space vector modulation 60
where
r
rt
s m
t
s m
LR
x cos( t ) cos( t )
y sin( t ) sin( t )
ee
−τ
−τ
⎧τ = σ⎪⎪⎪ = ω − ω⎨⎪⎪ = ω − ω⎪⎩
(4-11)
With small slip, (4-10) can be simplified as
( )( )1 11
tm s mr ss
* j( t ) eyL tan tane xL
− − −τΨ ≈ × Ψ
⎡ ⎤⎛ ⎞⎛ ⎞ − τ ω − ω⎜ ⎟− ⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦⎝ ⎠ (4-12)
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
( )( )1 1m s mr ss
* j( t ) eyL tan tanxL
− −Ψ ≈ Ψ
⎡ ⎤⎛ ⎞ − τ ω − ω⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (4-13)
From (B-4), the torque can be expressed as
32
sj t*me r s
s r
LT ( t ) P ( t )L L e ω= Ψ × Ψ
σ (4-14)
By substituting (4-13) into (4-14), we obtain
( )( )
2
1 1
32
*m me s
s r s
s s m
L LT ( t ) PL L L
ysin t tan tanx
− −
⎧ ⎫= Ψ⎨ ⎬σ⎩ ⎭⎧ ⎫⎡ ⎤⎛ ⎞× ω − − τ ω − ω⎨ ⎬⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎩ ⎭
(4-15)
where
Chapter 4 Direct flux vector controlled ISA with space vector modulation 61
r
rt
s m
t
s m
LR
x cos( t ) cos( t )
y sin( t ) sin( t )
ee
−τ
−τ
⎧τ = σ⎪⎪⎪ = ω − ω⎨⎪⎪ = ω − ω⎪⎩
(4-16)
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
vector sΨ 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 tan smallθ ≈ θ ≈ θ θ (4-17)
By considering (4-15) and (4-16) at same time, torque expression can be further
simplified as
( )2
2
2
31
2
t*m
e s s mr s
LT ( t ) P
R L e −τ≈ Ψ − ω − ω
⎧ ⎫⎛ ⎞⎨ ⎬ ⎜ ⎟
⎝ ⎠⎩ ⎭ (4-18)
Therefore
( )1t
e s mT ( t ) K e −τ= − ω − ω⎛ ⎞
⎜ ⎟⎝ ⎠
(4-19)
where
2 2
2
32
*ms
r s
r
r
LK PR L
LR
⎧= Ψ⎪⎪
⎨⎪τ = σ⎪⎩
(4-20)
By Laplace transform of (4-19), we have
{ }11e s mT ( s ) K
s⎛ ⎞= ω − ω⎜ ⎟τ +⎝ ⎠
L (4-21)
Chapter 4 Direct flux vector controlled ISA with space vector modulation 62
where { }s mω − ωL is the Laplace form of { }s mω − ω
The transfer function of the torque loop with input as { }s mω − ω can be written as
{ } 1
ep
s m
T ( s ) KG ( s )s
= =ω − ω τ +L
(4-22)
Equation (4-22) shows that the relationship between eT and sω is equivalent to a first
order system with a disturbance mω . The equivalent system block is shown as follows:
( )s sω ( )eT s
1Ksτ +
( )m sω−
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:
( )s sω ( )eT s1
Ksτ +
( )m sω−
( )cG s−
eT ∗
Fig.4.2 PI control of the equivalent system
where
p ic
K s KG ( s )
s+
= (4-23)
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 63
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)
( )
32
s s s s
e s s
V R I dt
T P I
⎧Ψ = −⎪⎨
= Ψ ×⎪⎩
∫ (4-24)
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
* *s s
s s
s s s
T∗
∗
⎧⎪⎪⎨⎪⎪⎩
ψ = Ψ
Δθ = ω Δθ = θ + Δθ
(4-25)
where TΔ is the sampling time, sΔθ is the increased angle of stator flux vector during
sampling period and sθ 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
vector sΔΨ . With given sΔΨ , 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
sref s sV R I
TΔΨ
= +Δ
(4-26)
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 s∗ω has to be limited to ensure that the reference voltage is lower or equal to the
maximum inverter voltage:
ref maxV V≤ (4-27)
Chapter 4 Direct flux vector controlled ISA with space vector modulation 64
where maxV is the maximum available inverter voltage. For under-modulation of SVM,
maxV equals to 1
3dcV , where dcV is the dc bus voltage of the inverter.
Therefore the limitation of the torque PI controller should be:
1
3dc
maxs * *
s s
VV∗ω ≤ =ψ ψ
(4-28)
*rω
*sψ
sΔΨsω∗
sθ
1TΔ
sψ
refV*
eT
eT
sψ ∗
TΔsθΔ sθ
∗ s sψ θ∗ ∗∠−
− +
&Torque Stator Flux Estimator
SVM IMPI
rω
PI
Encorder
Vdc
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 pG ( s ) 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
11
1G ( s )
s=λ +
(4-29)
where λ is the desired time constant.
thus
Chapter 4 Direct flux vector controlled ISA with space vector modulation 65
11
1 1c p
c p
G ( s )G ( s )G ( s )
s G ( s )G ( s )= =λ + +
(4-30)
1
p
i
KK
KK
τ⎧ =⎪⎪ λ⇒ ⎨⎪ =⎪ λ⎩
(4-31)
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 mL 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
2
2
1
1
c p
c p
p i
p i
G ( s )G ( s )G ( s )
G ( s )G ( s )
KK s KK
( KK ) KKs s
= =+
+τ=
++ +
τ τ
(4-32)
As presented in [92], the optimum coefficients of the performance index ITAE are
2 21 4 n ns . s+ ω + ω (4-33)
where nω is the natural frequency of the closed-loop system.
nω is selected to meet the settling time requirement. And the settling time is
4s
n
t =ζω
(4-34)
where ζ is the damping ratio.
Thus
Chapter 4 Direct flux vector controlled ISA with space vector modulation 66
2 2 211 4p i
n n
( KK ) KKs s s . s+
+ + = + ω + ωτ τ
(4-35)
Then
2
1 4 1np
ni
.KK
KK
ω τ −⎧ =⎪⎪⎨
ω τ⎪ =⎪⎩
(4-36)
To remove the zero of closed-loop system, a pre-filter fG ( s ) is added to 2G ( s ) . Then
the closed-loop transfer function changes to
3 2fG ( s ) G ( s )G ( s )= (4-37)
Since the desired closed-loop transfer function is
2
3 2 22 1 1 4
i
n
p i n n
KK
G ( s ) ( KK ) KK s . ss s
ωτ= =+ + ω + ω+ +τ τ
(4-38)
The pre-filter fG ( s ) is designed as
( )1
1fp i
G ( s )K K s
=+
(4-39)
With pre-filter fG ( s ) , the system change to
( )s sω ( )eT s
1Ksτ +
( )m sω−
( )cG s−
eT ∗
( )fG s
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 67
( )s sω ( )eT s1
dsTK esτ
−
+
( )m sω−
( )cG s−
eT ∗
Fig.4.5 PI control of equivalent torque loop
where
p ic
K s KG ( s )
s+
= (4-40)
and dT is the delay time
1
dsTp
KG ( s ) es
−=τ +
(4-41)
4.2.3.1 Direct synthesis of PI controller
Because pG ( s ) 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)
11
1dsTG ( s ) e
s−=
λ + (4-42)
where λ is the desired time constant
thus
11
1 1d c psT
c p
G ( s )G ( s )G ( s ) e
s G ( s )G ( s )−= =
λ + + (4-43)
So
1
1
1 1 11 1
1dc sT
p
G ( s )G ( s ) KG ( s ) G ( s ) s es
−= =− λ + −
τ +
(4-44)
Suppose that dsTe− is approximated by a 1st order Taylor series expansion, i.e.
Chapter 4 Direct flux vector controlled ISA with space vector modulation 68
1dsTde T s− ≈ − (4-45)
So (4-44) is simplified as
( ) ( )
1 1 1 1 11 1
1 1
cd d d
sG ( s ) K Ks T s s T s K T ss s
τ += = =
λ + − − λ + λ +τ + τ +
(4-46)
Compared (4-46) with (4-40)
( )
( )1
pd
id
KK T
KK T
τ⎧ =⎪ λ +⎪⇒ ⎨⎪ =⎪ λ +⎩
(4-47)
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
21
1 11
d
d
p i sT
c p
p i sTc p
K s K K eG ( s )G ( s ) s sG ( s ) K s K KG ( s )G ( s ) es s
−
−
+τ += =
++ +τ +
(4-48)
Chapter 4 Direct flux vector controlled ISA with space vector modulation 69
( ) ( ) ( )2 2
2 2
2 2
2
111 1
1
1
d d
d
d
p i
p isT sT
p i p i dd
p i sT
p p d i i d
p i sT
p d p i d i
p i
p d
p i d
p d
K s K KK Ks K Ks sG ( s ) e eK s K K s s K Ks K K T sT s
s sK Ks K K
es s K Ks K KT s K K K KT s
K Ks K Ke
s K KT s s K Ks K KT s K K
K Ks K KK KT
K K K KTs s
K KT
− −
−
−
++τ += =
+ τ + + + −+ −τ ++
=τ + + − + −
+=τ − + + − +
+τ −
=+ −
+ +τ −
dsT
i
p d
eK KK KT
−
τ −
(4-49)
As presented in [14], the optimum coefficients of the performance index ITAE are
2 21 4 n ns . s+ ω + ω (4-50)
where nω is the natural frequency of the closed-loop system.
nω is selected to meet the settling time requirement. And the settling time is
4s
n
t =ζω
(4-51)
where ζ is the damping ratio.
Thus
2 2 211 4p i d i
n np d p d
K K K KT K Ks s s . sK KT K KT
+ −+ + = + ω + ω
τ − τ − (4-52)
Then
Chapter 4 Direct flux vector controlled ISA with space vector modulation 70
( )
( )
2
2 2
2 2
2
11 4
1 1 4 1 4 1 4
1 4 1 4 1
1 4 1 4 1
p i dn
p d
in
p d
p i d n p d n n p d
i n p d n
p n p d i d n
p d n i n
n d p i d n
p d n i
K K K KT.
K KT
K KK KT
K K K KT . K KT . . K KT
K K K KT
K K . K KT K KT .
K KT K K
K . KT K K KT .
K KT K K
+ −⎧= ω⎪ τ −⎪
⎨⎪ = ω⎪τ −⎩⎧ + − = ω τ − = ω τ − ω⎪⎨
= ω τ − ω⎪⎩+ ω − = ω τ −⎧⎪
⎨ω + = ω τ⎪⎩
+ ω − = ω τ −
ω + = 2
2 2
1 4 1 4 1n
n d d p n
d n i n
K . KT KT K .KT K K
⎧⎪⎨
ω τ⎪⎩+ ω − ω τ −⎡ ⎤ ⎡ ⎤ ⎡ ⎤
=⎢ ⎥ ⎢ ⎥ ⎢ ⎥ω ω τ⎣ ⎦ ⎣ ⎦ ⎣ ⎦
(4-53)
1
2 2
1 4 1 4 1p n d d n
i d n n
K K . KT KT .K KT K
−+ ω − ω τ −⎡ ⎤ ⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥ ⎢ ⎥ω ω τ⎣ ⎦ ⎣ ⎦ ⎣ ⎦
(4-54)
To remove the zero of closed-loop, a pre-filter fG ( s ) is added to 2G ( s ) . Then the
closed-loop transfer function changes to
3 2fG ( s ) G ( s )G ( s )= (4-55)
Since the desired closed-loop transfer function is
32 1
d
i
p d sT
p i d i
p d p d
K KK KT
G ( s ) eK K K KT K Ks sK KT K KT
−τ −==
+ −+ +
τ − τ −
(4-56)
The pre-filter fG ( s ) is designed as
( )1
1fp i
G ( s )K K s
=+
(4-57)
With pre-filter fG ( s ) , the system change to
Chapter 4 Direct flux vector controlled ISA with space vector modulation 71
( )s sω ( )eT s
1Ksτ +
( )m sω−
( )cG s−
eT ∗
( )fG s
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 sR ( mΩ ) 25.1
Rotor resistance rR ( mΩ ) 18.2
Mutual inductance (mH) 1.8
Stator inductance sL (mH) 0.07618
Rotor inductance rL (mH) 0.07618
Inertia (Kg.m²) 0.00824
Using these parameters, the equivalent torque open-loop transfer function can be
express as follows
-3
0.49291 8.2 10 1p
KG ( s )s s
= =τ + × +
(4-58)
Chapter 4 Direct flux vector controlled ISA with space vector modulation 72
where
2 2
2
-3
3 0.49292
8 2 10
0 057
*ms
r s
r
r
*s
LK PR L
L .R
.
⎧= Ψ =⎪
⎪⎪τ = σ = ×⎨⎪⎪ Ψ =⎪⎩
(4-59)
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
1 -4
1 11 4 10 1
G ( s )s s
= =λ + × +
(4-60)
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
1
31
41.5940
1 5.0716 10
p
i
KK
KK
τ⎧ = =⎪⎪ λ⎨⎪ = = ×⎪ λ⎩
(4-61)
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 73
Closed torque loop performance of proposed scheme with above PI controller is
investigated. The torque reference is 6 Nm and the sampling time is 150 sμ . 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 74
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, nω can be obtained by selecting ζ with (4-
34). For example
0 8
4 2500ns
.
t
ζ =⎧⎪⎨ω = =⎪ ζ⎩
(4-62)
then
2
25
2
1 4 1 56.2029
1.0398 10
np
ni
.KK
KK
ω τ −⎧ = =⎪⎪⎨
ω τ⎪ = = ×⎪⎩
(4-63)
-4
1 15.4049 10 11
fp
i
G ( s ) K ssK
= =× ++
(4-64)
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 75
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 76
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 77
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 dcV (V) 42
Stator flux reference sΨ for DFC (Wb) 0.057
Rotor flux reference rΨ for RFOC (Wb) 0.0547
Sampling time ( sμ ) 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 78
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
*rω
r∠Ψ
rψ ∗
−
Current Model
SVM IMPI
rω
PI
Encorder
qV
dVα β−
,V Vα βPI
*di
*qi
qi
di
PI−
rΨ
e ed q−
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 79
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 80
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.
( )11s s s s
c
V R Is T
Ψ = −+
(4-65)
where ( )1 2c cT f= π and cf 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 150 sμ .
Chapter 4 Direct flux vector controlled ISA with space vector modulation 81
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 82
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 83
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 84
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 85
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
dcU
*T
eT
sψ ∗
*dcU
*sψ sψΔ
sψ
refV
startingT
sω∗
1TΔ
+
−
−−
+
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 86
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 excitation 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)
( )
32
s s s s
e s s
V R I dt
T P I
⎧Ψ = −⎪⎨
= Ψ ×⎪⎩
∫ (4-66)
The above scheme uses only one PI torque regulator to control the rotating speed of
stator flux vector. The desired reference stator flux vector *sψ is generated by Flux-
Vector-Combination block in Fig. 3.5, whose amplitude and angle is given by
s
**s s
s s
s s s
T∗∗
⎧⎪⎪⎨⎪⎪⎩
ψ = Ψ
Δθ = ωθ = θ + Δθ
(4-67)
where sT is the sampling time, sΔθ is the angular movement of the stator flux vector
during sampling period and sθ is the present angle of the stator flux vector. The
reference stator flux reference vector is compared with the estimated flux to obtain error
flux vector sΔΨ . With given sΔΨ , 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
sref s s
s
V R ITΔΨ
= + (4-68)
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 s∗ω 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 87
ref maxV V≤ (4-69)
where maxV is the maximum available inverter voltage. For under-modulation of SVM,
maxV equals to 1
3dcV , where dcV is the dc bus voltage of the inverter.
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.
2V3V
4V
6V
0V
7V1V
refV
5V
refV TΔ
sΨ*
sΨ α
sθ
α
β
α
β
Fig. 4.24 Reference space voltage vector
For example, when refV locates between 1V and 2V , it can be expressed as
0 1 20 1 2ref
s s s
T T TV V V VT T T
= + + (4-70)
where 0T , 1T , and 2T are the effective time intervals of 0V , 1V and 2V , respectively
within the sampling period sT .
From Fig. 4.24, the following can be obtained
1 21 2
22
3
3
refs s
refs
T TV cos V V cosT TTV sin V sinT
π⎧ α = +⎪⎪⎨ π⎪ α =⎪⎩
(4-71)
Thus
Chapter 4 Direct flux vector controlled ISA with space vector modulation 88
1
1
2
2
3
3
3
ref
s
refs
V sin( )T T
V sin
V sinT T
V sin
π⎧ − α⎪=⎪ π
⎪⎨⎪ α
=⎪ π⎪⎩
(4-72)
Hence
0 1 2sT T T T= − − (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 89
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
sμ .
Chapter 4 Direct flux vector controlled ISA with space vector modulation 90
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 91
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 92
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 93
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 94
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 95
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 5 Direct torque and flux controlled ISA with space vector modulation 96
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 feedbacks 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 97
5.2 Direct torque and flux control principle
sΨ
sθ α
β
q d
rΨ
sI
sdisqi
Fig. 5.1 Vector diagram of the induction machine
In stator flux reference frame ( )d q− shown in Fig. 5.1, the dynamic behavior of
induction machine can be described as following equations:
( )0
32
ss s s s s
rr r s m r
e sd sq
dV R I jdt
dR I jdt
T P i
⎧ Ψ= + + ω Ψ⎪
⎪Ψ⎪
= + + ω −ω Ψ⎨⎪⎪ = Ψ ⋅⎪⎩
(5-1)
and
s s s m r
r m s r r
L I L I
L I L I
⎧Ψ = +⎪⎨Ψ = +⎪⎩
(5-2)
Therefore,
Chapter 5 Direct torque and flux controlled ISA with space vector modulation 98
( )1
2
1
ss s s s s
rs m r r r
s s ss m r m
m r m ss r mr r r
d V R I jdt
d j R IdtI L L L L
L L L LL L LI
−
⎧ Ψ⎪ = − − ω Ψ⎪⎪ Ψ⎪ = − ω −ω Ψ −⎨⎪⎪ ⎡ ⎤ ⎡ ⎤⎡ ⎤ Ψ Ψ−⎡ ⎤ ⎡ ⎤
= =⎪ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥−−Ψ Ψ⎪⎢ ⎥ ⎣ ⎦ ⎣ ⎦⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎩
(5-3)
Equation (5-3) can be simplified as
( )
10
s s ms ss s r s
sr m rr r
s ms r r
R R Ld jL L Ldt V
R L Rd jL L Ldt
⎡ ⎤⎡ ⎤Ψ − − ω⎢ ⎥⎢ ⎥ ⎡ ⎤σ σ Ψ ⎡ ⎤⎢ ⎥⎢ ⎥ = +⎢ ⎥ ⎢ ⎥⎢ ⎥Ψ Ψ⎢ ⎥ ⎣ ⎦⎢ ⎥⎣ ⎦− ω −ω −⎢ ⎥⎢ ⎥ σ σ⎣ ⎦ ⎣ ⎦
(5-4)
where
2
1 m
s r
LL L
σ = − (5-5)
(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)
( )( )( ) ( )
1
m
sr s
s m
LLs s
s jΨ = Ψ
τσ + ω − ω τ + (5-6)
where r
r
LR
τ = .
It is known in the stator flux reference frame that
0
s ds qs
qs
j⎧Ψ = Ψ + Ψ⎪⎨Ψ =⎪⎩
(5-7)
The rotor flux vector in the stator flux reference frame can be expressed as
r rd rqjΨ = Ψ + 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 99
( )( )
( )
( ) ( )( )
( )
2
2
r m
s rrd sd
s m r
r r
r
r m
s m s rrq sd
r s m r
r r r
r
R LL Ls s
Rs R LsL
R LL Ls sR Rs sL R Ls
L
⎧⎪ σ⎪Ψ = Ψ
ω − ω⎪+ +⎪ σ⎪ +
σ⎪⎨⎪
− ω − ω⎪ σΨ = Ψ⎪
ω − ω⎪ + + +σ⎪ σ+⎪ σ⎩
(5-9)
The expression of stator current with stator and rotor flux vector is already shown in (5-
3), which is restated as
[ ]2
1 ss r m
s r m r
I L LL L L
⎡ ⎤Ψ⎡ ⎤ = − ⎢ ⎥⎣ ⎦ − Ψ⎢ ⎥⎣ ⎦
(5-10)
By substituting (5-9) into (5-10), it is derived that
( )
( )
( )
2
2
22 2 2 2 2
2
2
2 1
2 1
ms m
s rsq sd
s m
ms m
s rsd
LL LI ( s ) ( s )
s s
LL L ( s )
s
ω −ω τ= Ψτ σ + τσ + τ σ ω −ω +
ω −ω τ≈ Ψ
τσ +
(5-11)
The simplification in (5-11) is based on small τ and σ .
By inverse Laplace transform, the expression of sqI is time domain is obtained as
{ }
( )
( ) { }
2
21 1
22
2
2 1
1
ms m
s r sdsq sq
tms m sd
s r
LL LI ( t ) I ( s )
s s
L eL L
∗− −
−∗ τσ
⎧ ⎫ω − ω τ⎪ ⎪Ψ⎪ ⎪= = ⎨ ⎬τσ +⎪ ⎪
⎪ ⎪⎩ ⎭
= ω − ω τ Ψ −
L L (5-12)
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 100
( ) ( ){ }222
2
3 3 12 2
tm
e sd sq sd s ms r
LT ( t ) P ( t ) i ( t ) P eL L
−∗ τστ= Ψ ⋅ = Ψ ω −ω − (5-13)
By (5-1), the voltage equation in dq frame is
sd sd
sd s sd
sq s sq s sd s sd
d dV R idt dt
V R i
Ψ Ψ⎧ = + ≈⎪⎨⎪ = + ω Ψ ≈ ω Ψ⎩
(5-14)
By substituting (5-14) into (5-13), the relationship between the q voltage component
and the torque is developed as
{ } ( )2
22
3 12
tm
e sd sq ms r
LT ( t ) P e V fL L
−∗ τστ= ⋅Ψ − − ω (5-15)
where
( ) ( ) { }222
2
3 12
tm
m sd ms r
Lf P eL L
−∗ τστω = Ψ − ω (5-16)
Therefore, it is clear shown in (5-15) that the torque of induction machine can be
directly regulated by the q voltage component considering ( )mf ω 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.
s sds s
s sqs s
V Vcos sinV Vsin cos
α
β
θ − θ⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥θ θ⎣ ⎦⎣ ⎦ ⎣ ⎦
(5-17)
where sθ 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
ref s sV V jVα β= + (5-18)
Chapter 5 Direct torque and flux controlled ISA with space vector modulation 101
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.
dcV
*T
eT
sψ ∗
*dcV
sψ
refV
startingT +
−
−
+sqV
sdV
d q−
α β−
sθ
dcV
−
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 102
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.
( )( )1
32
s s s s
s s s
e s s
V R I dt
tan
T P I
−β α
⎧Ψ = −⎪⎪⎪θ = Ψ Ψ⎨⎪⎪ = Ψ ×⎪⎩
∫ (5-19)
In (5-19), current vector sI is constructed by the two line current with Park
transformation. And voltage vector sV can be obtained by
1refsV ( k ) V ( k )= − (5-20)
The time delay between refV and sV results from the SVM generating time sT .
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:
ref maxV V≤ (5-21)
where maxV is the maximum available inverter voltage.
For under-modulation of SVM,
1
3max dcV V= (5-22)
where dcV 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 103
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 104
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 sμ .
Fig. 5.4 ISA generating with full load
Chapter 5 Direct torque and flux controlled ISA with space vector modulation 105
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 106
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 107
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 108
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 109
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 6 Non-linear behaviour of the converter and its compensation 110
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 111
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.
+
dcV
+A
−A
+D
−D
ai-
P
N
0>
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 112
dt
+A
−A
+A
−A
aNV
)a
)b
)c
dt
)d
sT
dt
dt
aNV ′ 0>ai
0<aiaNV ′
ond tt +
offt ond tt +
aNV 0>ai
0<ai
offt
Fig. 6.2(a) ideal gate signal (b)practical gate signal with dead-time (c) aNV with dead-
time effect only(d)considering ont and offt 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 sT is given in Fig. 6.4.
IM
Ai Bi Ci
1AS =
0CS =
1CS =
0BS =0AS =
1BS =dcV
2V3V
4V
6V
0V
7V1V
refV
5V
α
β
α
(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 113
AS
CS
BS
sT
0 0 0 1 0 0 11 0 111 11 0 1 0 0 0 0 0
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 0ai > , 0bi > and
0ci < .
AS
CS
BS
sT
0 0 0 1 0 0 11 0 111 11 0 1 0 0 0 0 0
ond tt +
ond tt +
offtond tt +
offt
offt
Chapter 6 Non-linear behaviour of the converter and its compensation 114
Fig. 6.5 Gate signal with dead-time
Table 6.1 Dead-time effect analysis ( 0ai > ; 0bi > ; 0ci < )
Lost parts
(shadowed
parts)
duration Extra Parts
(Non-shadowed
parts)
duration
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. 0ai > ; 0bi > ; 0ci < . Then the actual
output voltage vector is
( )( )
( ) ( )
( ) ( )( ) ( )( )
1 3 5
1 3 5
2 5
5 5
52
ref s d on off
off d on
ref s d on off d on off
ref s d on off d on off
ref s d on off
V T V V t t V t
V V t V t t
V T V t t t V t t t
V T V t t t V t t t
V T V t t t
− + + −
+ + + +
= − + − + + −
= + + − + + −
= + + −
(6-1)
So, the error voltage vector for this case is ( ) ( )2
5423
d on off d on offdc
s s
t t t t t tV V a
T T+ − + −
=
where 2 3α j /e π= .
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 115
Table 6.2 Error voltage vectors under different current polarities
( )Asgn i ( )Bsgn i ( )Csgn i Error
vector 1
Error
vector 2
Error vector
3
total
+(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 116
indicates the switching state of the top power device on the leg A. For example, 0ai > ;
0bi > ; 0ci <
AS
CS
BS
sT
0 0 0 1 0 0 11 0 111 11 0 1 0 0 0 0 0
dV−
dV−
ceV
dc ceV V−
dc dV V+
dc ceV V−
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
2 22 41 α α α3 3ref th ref thV V [ )] V V− + − = + (6-2)
where 2 3α j /e π= .
so, the error voltage vector is 222 α3
thdc
dc
VVV
⎛ ⎞⎜ ⎟⎝ ⎠
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 117
Table 6.3 Error voltage vectors under different current polarities
Asgn( i ) Bsgn( i ) Csgn( i ) 1 a a2 total total
+(0) +(0) -(1) -1 -1 1 2a2 2V5
+ - + -1 1 -1 2a 2V3
+ - - -1 1 1 -2 2V4
- + + 1 -1 -1 2 2V1
- + - 1 -1 1 -2a 2V6
- - + 1 1 -1 -2a2 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)
( ) ( )d on off d on offth th
error error errors dc s dc
t t t t t tu uV V V VT V T V
⎡ ⎤+ − + −Δ = + = +⎢ ⎥
⎢ ⎥⎣ ⎦ (6-3)
Where errorV 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
refV
realVVΔ
Fig. 6.8 Backward compensation structure
Chapter 6 Non-linear behaviour of the converter and its compensation 118
For the backward compensation structure, the error voltage vector VΔ is fed after
command voltage vector refV being applied to the SVM block. The real voltage vector
applied to the machine through the DC-AC converter will be
real refV V V= + Δ (6-4)
After compensation, the real voltage vector realV can be used for the estimation of the
flux vector and the controllers.
6.4.2 Forward compensation
refV
realV
VΔ
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
forward compensation. For forward compensation, the error voltage vector VΔ is fed
before command voltage vector refV 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
real refV V= (6-5)
The new command voltage vector of the SVM block changes to
ref new refV V V− = − Δ (6-6)
Similarly, the real voltage vector realV can be used for the estimation and the controller.
Chapter 6 Non-linear behaviour of the converter and its compensation 119
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.
ˆsΨ
eT
θ
*sΨ
*eT
r e fV
realV
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 120
rω
sAisBisCi
si α
si β
rθ
rψ
Polar to Cartesian
+
+
lrLlsL
m rL L +
+m rL L
lrL lsL
rαψ
rβψ
sαψ
sβψRotor flux estimator
(a) Stator flux estimation
( )32e s s s sT P i iα β β α= ψ −ψ
sαψ
sβψ
si α
si β
eT
(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.
( )
( )
( )32
ms ls s r lr s
r
ms ls s r lr s
r
r r r
r r r
e s s s s
LL i L iLLL i L iL
cos
sin
T P i i
α α α α
β β β β
α
β
α β β α
⎧ψ = + ψ +⎪⎪⎪ψ = + ψ +⎪⎪⎪ψ = ψ θ⎨⎪ψ = ψ θ⎪⎪
= ψ −ψ⎪⎪⎪⎩
(6-7)
Chapter 6 Non-linear behaviour of the converter and its compensation 121
where lsL , lrL and mL are the stator leakage, rotor leakage and mutual inductances,
respectively; sαψ , sβψ , rαψ , rβψ , si α and si β 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.
( )32e s s s sT P i iα β β α= ψ − ψ
sαψ
sβψ
si α
si β
eT( )
( )s s s s
s s s s
v R i dt
v R i dt
α α α
β β β
⎧ψ = −⎪⎨ψ = −⎪⎩
∫∫
sv α
sv β
si α
si β
Fig. 6.12 Voltage mode stator flux and torque estimator
where sv α and sv β are the stator voltages in stationary frame, si α , si β , sαψ and sβψ 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.
( )
( )
1111
s s s sc
s s s sc
v R is T
v R is T
α α α
β β β
⎧ψ = −⎪ +⎪⎨⎪ψ = −⎪ +⎩
(6-8)
where ( )1 2c cT f= π and cf 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 122
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 123
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 torques with current mode and
voltage mode estimators are overlapped.
Chapter 6 Non-linear behaviour of the converter and its compensation 124
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 125
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 VαΔ and VβΔ 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 feed forward 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 126
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 127
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.
( )( ) ( ) 100
current voltages ,s s ,s
,ref
errors %α β α β
α β
ψ −ψ= ×
ψ (6-9)
Where refψ is the magnitude of the flux reference, ( )current
s ,sα βψ is the estimated flux
with current mode estimator, and ( )voltage
s ,sα βψ is the estimated flux with voltage mode
estimator.
Chapter 6 Non-linear behaviour of the converter and its compensation 128
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 129
(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 130
(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 131
(a) without compensation
(b) with backward compensation
Chapter 6 Non-linear behaviour of the converter and its compensation 132
(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 133
(a) without compensation
(b) with backward compensation
Chapter 6 Non-linear behaviour of the converter and its compensation 134
(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 135
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 7 Direct torque controlled ISA with sliding mode observer 136
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 137
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
ss s s
ss s s
dv R idt
dv R i
dt
αα α
ββ β
ψ⎧ = +⎪⎪⎨ ψ⎪ = +⎪⎩
(7-1)
0
0
rr r m r
rr r m r
dR idt
dR i
dt
αα β
ββ α
ψ⎧ = + −ω ψ⎪⎪⎨ ψ⎪ = + + ω ψ⎪⎩
(7-2)
s s s m r
s s s m r
r m s r r
r m s r r
L i L iL i L i
L i L iL i L i
α α α
β β β
α α α
β β β
ψ = +⎧⎪ψ = +⎪⎨ψ = +⎪⎪ψ = +⎩
(7-3)
( )32e s s s sT P i iα β β α= ψ −ψ (7-4)
where sv α and sv β are the stator voltages in stationary frame, si α , si β , ri α and ri β are the
stator and rotor current in stationary frames, respectively, sαψ , sβψ rαψ and rβψ are the
stator and rotor fluxes, respectively, sR and rR are the stator and rotor resistances, sL ,
rL and mL are the stator, rotor and mutual inductances, respectively. And mω is rotor
speed, P is the number of pole pairs.
Thus
Chapter 7 Direct torque controlled ISA with sliding mode observer 138
0 0 00 0 0
1 0
10
1 00 1
r s r mm
r s s r ss s
s sr s m rm
s sr s s s r
s ss
s
s
s
s s
R R RL L L L Li i
i id R R Rdt L L L L L
RR
Lv
L v
α α
β β
α α
β β
α
β
⎡ ⎤⎛ ⎞ ω− + −ω⎢ ⎥⎜ ⎟σ σ σ σ⎡ ⎤ ⎡ ⎤⎝ ⎠⎢ ⎥
⎢ ⎥ ⎢ ⎥⎢ ⎥⎛ ⎞ ω⎢ ⎥ ⎢ ⎥⎢ ⎥= ω − + −⎜ ⎟ψ ψ⎢ ⎥ ⎢ ⎥σ σ σ σ⎢ ⎥⎝ ⎠⎢ ⎥ ⎢ ⎥⎢ ⎥ψ ψ−⎣ ⎦ ⎣ ⎦⎢ ⎥⎢ ⎥−⎣ ⎦
⎡ ⎤⎢ ⎥σ⎢ ⎥
⎡ ⎤⎢ ⎥+ ⎢ ⎥⎢ ⎥σ ⎣ ⎦⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
(7-5)
where
2
1 m
s r
LL L
σ = − (7-6)
In direct torque control scheme, the magnitude of stator flux vector sΨ will be
controlled as constant, that is sΨ = constant, or sddt
Ψ is equal to zero. So,
( )
( )
s s s s s s
s s s s s s
d sin tdtd cos tdt
α β
β α
⎧ ψ ≈ Ψ − ω ω = −ω ψ⎪⎪⎨⎪ ψ ≈ Ψ ω ω = ω ψ⎪⎩
(7-7)
Comparing with (7-1), it is found that
ss s s s s
ss s s s s
d v R idt
dv R i
dt
αα α β
ββ β α
ψ⎧ = − ≈ −ω ψ⎪⎪⎨ ψ⎪ = − ≈ ω ψ⎪⎩
(7-8)
Equation (7-5) can be reorganized as
Chapter 7 Direct torque controlled ISA with sliding mode observer 139
1 0
10
sr r mm
r s r ss s
s sr m rm
sr s s r
s s s
s s
s
iR RL L L Li id
idt R RL L L L
L
L
α
α β
β α
β
β
α
⎡ ⎤⎛ ⎞ ω ⎡ ⎤− −ω⎢ ⎥⎜ ⎟ ⎢ ⎥σ σ σ⎡ ⎤ ⎝ ⎠⎢ ⎥ ⎢ ⎥≈⎢ ⎥ ⎢ ⎥ ψ⎢ ⎥⎛ ⎞ ω⎣ ⎦ ⎢ ⎥ω − − ⎢ ⎥⎜ ⎟ ψσ σ σ⎢ ⎥ ⎣ ⎦⎝ ⎠⎣ ⎦⎡ ⎤⎢ ⎥σ −ω ψ⎡ ⎤⎢ ⎥+ ⎢ ⎥ω ψ⎢ ⎥ ⎣ ⎦⎢ ⎥σ⎣ ⎦
(7-9)
With small slip, sω is close to mω . So, (7-9) can be simplified as
0
0
sr rm
r s rs s
s sr rm
sr s r
iR RL L Li id
idt R RL L L
α
α β
β α
β
⎡ ⎤⎛ ⎞ ⎡ ⎤− −ω⎢ ⎥⎜ ⎟ ⎢ ⎥σ σ⎡ ⎤ ⎝ ⎠⎢ ⎥ ⎢ ⎥≈⎢ ⎥ ⎢ ⎥ ψ⎢ ⎥⎛ ⎞⎣ ⎦ ⎢ ⎥ω − ⎢ ⎥⎜ ⎟ ψσ σ⎢ ⎥ ⎣ ⎦⎝ ⎠⎣ ⎦
(7-10)
The error between sω and mω 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 mω as
1
2
1
2
r rs s s
r s r
r rs s s
r s r
ss s s
ss s s
d R Rˆ ˆ ˆ ˆi i ndt L L L
d R Rˆ ˆ ˆ ˆi i ndt L L L
ˆd v R i c signSdtˆd
v R i c signSdt
α α α
β β β
αα α
ββ β
⎧ ⎛ ⎞= − + ψ +⎪ ⎜ ⎟σ σ⎝ ⎠⎪
⎪ ⎛ ⎞⎪ = − + ψ +⎜ ⎟⎪ σ σ⎝ ⎠⎨⎪ ψ
= − + ⋅⎪⎪
ψ⎪ = − + ⋅⎪⎩
(7-11)
1
2
1 1
2 2
s s
s s
ˆS i iˆS i i
n k sign Sn k sign S
α α
β β
⎧ = −⎪
= −⎪⎨
= ⋅⎪⎪ = ⋅⎩
(7-12)
Chapter 7 Direct torque controlled ISA with sliding mode observer 140
where si α , si β , sˆ αψ and sˆ βψ are the estimated stator currents and fluxes. c is a positive
number to be chosen. 1S and 2S are the current errors between measured and estimated
stator currents. 1n and 2n are discontinuous functions of the current errors and 0k > .
From (7-10) and (7-11), the error dynamics for current are obtained
r rs s s m s s
r s r
r rs s s m s s
r s r
d R Ri i i k sign idt L L L
d R Ri i i k sign idt L L L
α α α β α
β β β α β
⎧ ⎛ ⎞= − + ψ −ω −⎪ ⎜ ⎟σ σ⎪ ⎝ ⎠
⎨⎛ ⎞⎪ = − + ψ + ω −⎜ ⎟⎪ σ σ⎝ ⎠⎩
(7-13)
where
s s s
s s s
ˆi i iˆi i i
α α α
β β β
⎧ = −⎪⎨
= −⎪⎩ (7-14)
By choosing Lyapunov candidate function as
( )2 212 s sV i iα β+= (7-15)
The time derivative of Lyapunov function V is
2 2
V i i i is s s s
Rr i i i f i f k i is s s s s sLr
= ⋅ + ⋅α α β β
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟= − + + + − +⎜ ⎟ ⎜ ⎟α β α α β β α β⎜ ⎟σ ⎝ ⎠ ⎝ ⎠⎝ ⎠
(7-16)
where
rs m s
s r
rs m s
s r
Rf iL LRf iL L
α α β
β β α
⎧ = ψ −ω⎪ σ⎪⎨⎪ = ψ + ω⎪ σ⎩
(7-17)
if k large enough, i.e. { }k max f , fα β> , then 0V < , until si α and si β 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 si α and si β are equal to
zero.
Chapter 7 Direct torque controlled ISA with sliding mode observer 141
After sliding mode motion occurs, the error dynamics for flux estimation is obtained
from (7-1) and (7-11)
1
2
s
s
d c signSdt
dc signS
dt
α
β
ψ⎧ = − ⋅⎪⎪⎨ ψ⎪ = − ⋅⎪⎩
(7-18)
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.
ˆsΨ
( )3 ˆ ˆ2e s s s sT P i iα β β αψ ψ= −
( )7 11Equation −
eT
θ
*sΨ
2 2
1
ˆ ˆ
ˆˆˆ
s s s
s
stg
α α β
β
α
ψ ψ ψ
ψθ ψ
−⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
= +
=
*eT
,s sv vα β
,s si iα β
3 2
ˆ ˆ,s sα βψ ψ
ˆ ˆ,s si iα β
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 142
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 sR 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 sR variation.
Fig. 7.2 Open-loop stator flux estimation with 50% error in sR
Chapter 7 Direct torque controlled ISA with sliding mode observer 143
Fig. 7.3 Sliding mode flux observer with 50% error in sR
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 144
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 145
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 sR 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 146
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 147
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 sR variation.
Chapter 7 Direct torque controlled ISA with sliding mode observer 148
Fig. 7.10 Open-loop stator flux estimation with 50% sR error
Fig. 7.11 Sliding mode flux observer with 50% sR error
Chapter 7 Direct torque controlled ISA with sliding mode observer 149
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 150
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 151
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 152
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 153
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 154
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 155
(b) with backward compensation
Chapter 7 Direct torque controlled ISA with sliding mode observer 156
(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 157
(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 158
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 8 Efficiency improvement for ISA with power factor control 159
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 160
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
ss s s
ss s s
dv R idt
dv R i
dt
αα α
ββ β
ψ⎧ = +⎪⎪⎨ ψ⎪ = +⎪⎩
(8-1)
0
0
rr r m r
rr r m r
dR idt
dR i
dt
αα β
ββ α
ψ⎧ = + −ω ψ⎪⎪⎨ ψ⎪ = + + ω ψ⎪⎩
(8-2)
Chapter 8 Efficiency improvement for ISA with power factor control 161
s s s m r
s s s m r
r m s r r
r m s r r
L i L iL i L i
L i L iL i L i
α α α
β β β
α α α
β β β
ψ = +⎧⎪ψ = +⎪⎨ψ = +⎪⎪ψ = +⎩
(8-3)
( )32e s s s sT P i iα β β α= ψ −ψ (8-4)
where sv α and sv β are the stator voltages in stationary frame, si α , si β , ri α and ri β are the
stator and rotor current in stationary frames, respectively, sαψ , sβψ , rαψ and rβψ are
the stator and rotor fluxes, respectively, sR and rR are the stator and rotor resistances,
sL , rL and mL are the stator, rotor and mutual inductances, respectively. And mω is
rotor speed, P is the number of pole pairs.
The total copper loss is
( ) ( )2 2 2 232copper s s s r r rP i i R i i Rα β α β⎡ ⎤= + + +⎣ ⎦ (8-5)
The core loss contains hysteresis and eddy current losses, whose density [122] can be
express as
2
2 2
h h m
e e m
P K fB W kg
P K f B W kg
⎧ =⎪⎨
=⎪⎩ (8-6)
where hK and eK are the hysteresis and eddy current loss coefficients, f is the
frequency, mB is the maximum flux density.
mB 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 162
dcV
*dcV
startingT +
−
dcV
ˆsΨ
( )3ˆ ˆ ˆ2e s s s sT P i iα β β αψ ψ= −
eT
θ
*sΨ
1
2 2ˆ ˆ ˆ
ˆˆˆ
s s s
s
stg
α β
β
α
ψ ψ
ψθ ψ
−⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
Ψ
=
= +
*eT
,s sv vα β
,s si iα βˆ ˆ,s sα βψ ψ
3 2( )8 1Equation −
*PF
PF∧
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 163
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.
*PF
PF∧
PI1−*
sΨ
+−
+
Rated Flux
Minmum Flux
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]
( ) ( )2 2 2 2 2 2
s s s s
s s s s
v i v iPPFP Q v v i i
α α β β
α β α β
+= =
+ + + (8-7)
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 164
Power factor@1500 rpm
00.10.20.30.40.50.60.70.80.9
0 0.2 0.4 0.6 0.8 1Load ( 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 165
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).
( ) ( )( ) ( )
2
2 2
2 2
100
100
100
100
core
core _ rated
m
m _ rated
copper
copper _ rated
s s r r
s rated s r rated r
Pcore loss% %P
%
Pcopper loss% %
P
i R i R%
i R i R− −
⎧ = ×⎪⎪⎪ ⎛ ⎞ψ⎪= ×⎜ ⎟⎪ ⎜ ⎟ψ⎪ ⎝ ⎠⎨⎪ = ×⎪⎪⎪ +⎪= ×
+⎪⎩
(8-8)
where core _ ratedP and copper _ ratedP 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
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2
Load (x100% rated Te)
core loss%-with PFcontrolcore loss%-withoutPF control
Fig. 8.5 Core loss percentage with and without power factor control
Chapter 8 Efficiency improvement for ISA with power factor control 166
Copper loss% @1500rpm
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2
Load (x100% rated Te)
copper loss%-with PFcontrolcopper loss%-withoutPF control
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)
( )
( )
Analyzer Analyzer
Analyzer Analyzer
100 100
100 100
DCM friction mreal mM
Greal m DCM friction m
T TT % %P P
P P% %
T T T
⎧ + ωωη = × = ×⎪⎪⎨⎪η = × = ×⎪ ω − ω⎩
(8-9)
where Mη and Gη are the efficiencies of the induction machine in motoring and
generating modes; AnalyzerP is the electrical power measured from the power analyzer;
mω is the rotor speed of the induction machine in rad/s; realT , DCMT and frictionT 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 167
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 168
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 169
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 9 Conclusions 170
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 171
• 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 sμ 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 ( d q− ) to stationary frame (α β− ). However, the
Chapter 9 Conclusions 172
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 173
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
Torque control
Directly torque
control by
hysteresis
comparator
Directly torque
control by PI
action
Directly torque
control by PI
action
Indirectly torque
control by PI
control of q axis
current
Flux control
Directly flux
control by
hysteresis
comparator
Indirectly flux
control by PI
action
Directly flux
control by PI
action
Indirectly flux
control by PI
control of d axis
current
dc bus voltage
control
Satisfied ISA
specifications
Satisfied ISA
specifications
Satisfied ISA
specifications
Satisfied ISA
specifications
PWM
generation Not required SVM SVM SVM
Switching
frequency
Variable (could
be constant with
discrete
hysteresis
comparator)
Constant Constant Constant
Current &
Torque ripples
Highest (the
maximum peak-
peak torque
low(the maximum
peak-peak torque
ripple is 16.7 % of
low(the maximum
peak-peak torque
ripple is 16.7 % of
low(the maximum
peak-peak torque
ripple is 14.7 % of
Chapter 9 Conclusions 174
ripple is 183.3 %
of rated torque
with 150sT sμ= )
rated torque with
150sT sμ= )
rated torque with
150sT sμ= )
rated torque with
150sT sμ= )
Current
controller Not required Not required Not required Required
Coordinate
transformation
using rotor
speed signal
Not required Not required Not required
Rotor flux vector
frame to stationary
frame ( e ed q to
αβ
Induction
machine’s
parameters
involved
sR sR sR sR , rR , sL ,
rL and mL
Flux orientation
and decoupling
algorithm
Not required Not required Not required required
Implementation
Complexity simplest Medium Medium complex
Flux estimation Voltage mode:
LPF; SMO
Voltage mode:
LPF; SMO
Voltage mode:
LPF; SMO
current mode;
could be voltage
mode, but it still
involves many
induction machine
parameters ( sR ,
rR , sL , rL and
mL )
High speed
performance Good Good Good
Good, but has
instability during
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 175
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 176
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.
References 177
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Appendix A 187
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 188
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 B Modelling of the direct flux vector control 189
APPENDIX B
MODELLING OF THE DIRECT FLUX VECTOR
CONTROL
In stationary frame, the dynamic behaviour of induction machine can be described as
following equations:
ss s s
dV R IdtΨ
= + (B-1)
0 rr r m r
dR I jdtΨ
= + − ω Ψ (B-2)
s s s m r
r m s r r
L I L I
L I L I
⎧Ψ = +⎪⎨Ψ = +⎪⎩
(B-3)
32
me r s
s r
LT PL L
= Ψ ×Ψσ
(B-4)
where
2
1 m
s r
LL L
σ = − (B-5)
where sR and rR are the stator and rotor resistances, sL , rL and mL are the stator, rotor
and mutual inductances, respectively. And mω 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.
1
21s s ss m r m
m r m ss r mr r r
I L L L LL L L LL L LI
− ⎡ ⎤ ⎡ ⎤⎡ ⎤ Ψ Ψ−⎡ ⎤ ⎡ ⎤= =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥−−Ψ Ψ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
(B-6)
By considering (B-1), (B-2) and (B-6), we get
Appendix B Modelling of the direct flux vector control 190
1
21
rm r r r
s s ss m r m
m r m ss r mr r r
d j R IdtI L L L L
L L L LL L LI
−
⎧ Ψ= Ψ −⎪
⎪⎨ ⎡ ⎤ ⎡ ⎤⎡ ⎤ Ψ Ψ−⎡ ⎤ ⎡ ⎤⎪ = =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎪ −−Ψ Ψ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎩
ω
(B-7)
The relationship between stator and rotor flux vectors sΨ and rΨ is derived from (B-7)
r r m rs m r
s r r
d R L R( j )dt L L LΨ
= Ψ + ω − Ψσ σ
(B-8)
where
2
1 m
s r
LL L
σ = − (B-9)
By using Laplace transform of (B-8) and assuming the rotor speed mω is changing
slowly, the relationship between stator and rotor flux vectors sΨ and rΨ in the
frequency domain can be obtained
1
r m m
s r sr s s
r r rm m
r r r
R L LL L L( s ) ( s ) ( s )
R L Ls j s jL R R
σΨ = Ψ = Ψ
⎛ ⎞ ⎛ ⎞− ω − σ + − ω σ⎜ ⎟ ⎜ ⎟σ⎝ ⎠ ⎝ ⎠
(B-10)
Assuming that s sj j t* *s s se eθ ωΨ = Ψ = Ψ and the amplitude of sΨ is kept constant, and
that sΨ rotates at an angular speed sω , the Laplace form of the stator flux vector sΨ is
1 *s s
s
( s )s j
Ψ = Ψ− ω
(B-11)
By substituting (B-10) into (B-11) and taking inverse Laplace transform
1 1
1
m
*sr s
r r sm
r r
L
L( t )
L L s js j
R R
−Ψ = Ψ− ω
σ + − ω σ
⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬
⎛ ⎞⎪ ⎪⎜ ⎟⎪ ⎪⎩ ⎭⎝ ⎠
L (B-12)
Thus
Appendix B Modelling of the direct flux vector control 191
( )
( )
1 *
1 *
1
1
1
1 1
1 1
1 1
1 1
m
sr s
sr rm
r r
r
m rs
s sr r r rm s m
r r r r
r
m r
rs s rs m
r r
LLL
s jL Ls jR R
LL RLL s jL L L Lj j s j
R R R R
LL RL LL s j Lj sR R
−
−
−
⎧ ⎫⎪ ⎪⎪ ⎪Ψ = Ψ⎨ ⎬−⎛ ⎞⎪ ⎪+ −⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭⎧ ⎫⎛ ⎞⎪ ⎪⎜ ⎟⎪ ⎪⎜ ⎟= − Ψ⎨ ⎬⎜ ⎟−⎛ ⎞ ⎛ ⎞⎪ ⎪− − − + −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎪ ⎪⎝ ⎠ ⎝ ⎠⎝ ⎠⎩ ⎭
= −−+ − +
ωσ ω σ
σ
ωω σ σ ω σ ω σ
σ
ωσ ω ω σ
( )
( )
( )
*
1
*
1a*
2
ar g
1
1
rm
rs
r
r
rr ms mrr s
r
r
r
sr
mr
m LjRt ts L
s Rrs m
r
LL jj rctg RR t tm Ls R
sr
s mr
Lj ctR
m
s
LjR
LL
LjR
LL L
R
LL
e e
e e e
−−
⎛ ⎞ −− −⎜ ⎟⎝ ⎠ −
−
⎧ ⎫⎛ ⎞⎪ ⎪⎜ ⎟⎪ ⎪⎜ ⎟ Ψ⎨ ⎬⎜ ⎟⎛ ⎞⎪ ⎪−⎜ ⎟⎜ ⎟⎜ ⎟⎪ ⎪⎝ ⎠⎝ ⎠⎩ ⎭
⎧ ⎫⎪ ⎪= Ψ −⎨ ⎬⎪ ⎪+ − ⎩ ⎭
⎧ ⎫⎪ ⎪= Ψ −⎨ ⎬⎪ ⎪⎛ ⎞ ⎩ ⎭+ −⎜ ⎟
⎝ ⎠
=
ω σω
σ
ω σσ ω ωω
σ
σ
ω σ
σ ω ω
σ ω ω
( )
( )( )
( )
( )( )
1*
2
ar g 1*
2
cos( ) sin( ) cos( ) sin( )
1
cos( ) sin( ) cos( ) sin( )
1
s mr
r r
rs m
r
r r
tL Rs s s m m
rs m
r
Lj ctR tm L Rs s s m m
sr
s mr
t j t t j tLR
L t j t t j tL L
R
e e
e e
⎛ ⎞−⎜ ⎟
⎝ ⎠ −
⎛ ⎞− −⎜ ⎟
⎝ ⎠ −
⎧ ⎫Ψ + − +⎨ ⎬⎩ ⎭⎛ ⎞
+ −⎜ ⎟⎝ ⎠
⎧ ⎫= Ψ + − +⎨ ⎬⎩ ⎭⎛ ⎞
+ −⎜ ⎟⎝ ⎠
ω ω
σ
σ ω ω
σ
ω ω ω ω
σ ω ω
ω ω ω ω
σ ω ω
(B-13)
Equation (B-13) can be further simplified as
Appendix B Modelling of the direct flux vector control 192
( )
( )
( )( )
( )
( )
2 2ar g ar g*
2
2
ar g ar g*
2
( )
1
1 2 cos
1
rs m
r
r r
rr r s mr
y Lj ct j ctm x Rr ss
rs m
r
t tL L
s m y LR R j ct ctm x Rss
rs m
r
tx yL
L LR
tLL L
R
e e
e ee
⎛ ⎞⎛ ⎞ − −⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠
− −
⎛ ⎞⎛ ⎞⎛ ⎞− −⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠
Ψ+
= Ψ⎛ ⎞
+ −⎜ ⎟⎝ ⎠
⎛ ⎞+ − −⎜ ⎟⎝ ⎠= Ψ
⎛ ⎞+ −⎜ ⎟⎝ ⎠
σ ω ω
σ σσ ω ω
σ ω ω
ω ω
σ ω ω
(B-14)
where
cos( ) cos( )
sin( ) sin( )
r
r
r
r
tL
s mR
tL
s mR
x t t
y t t
e
e
−
−
⎧ = −⎪⎪⎨⎪ = −⎪⎩
σ
σ
ω ω
ω ω (B-15)
That is
( )( )
( )( )( )( )
21 2
21
1 1
mr
s
s
tt
e cos te s m( t )
s my* j tan tane s mx
LL
−τ−+ − ω − ωτ
Ψ =
+ τ ω − ω
− −− τ ω − ω× Ψ
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(B-16)
where
r
rt
s m
t
s m
LR
x cos( t ) cos( t )
y sin( t ) sin( t )
ee
−τ
−τ
⎧τ = σ⎪⎪⎪ = ω − ω⎨⎪⎪ = ω − ω⎪⎩
(B-17)
With small slip, (B-16) can be simplified as
Appendix B Modelling of the direct flux vector control 193
( )( )
( )( )1 1
21 2
1 1
1
1
mr s
s
tm s mss
tt
eey* j tan tan( t ) e s mx
* je
LL
yL tan tane xL− − −τ
−τ−+ −τ − −− τ ω − ωΨ ≈ × Ψ
× Ψ
⎛ ⎞⎜ ⎟⎜ ⎟ ⎛ ⎞⎛ ⎞⎝ ⎠ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
⎡ ⎤⎛ ⎞⎛ ⎞ − τ ω − ω⎜ ⎟= − ⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦⎝ ⎠
(B-18)
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
( )( )1 1m s mr ss
* j( t ) eyL tan tanxL
− −Ψ ≈ Ψ
⎡ ⎤⎛ ⎞ − τ ω − ω⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (B-19)
From (B-4), the torque can be expressed as
32
sj t*me r s
s r
LT ( t ) P ( t )L L e ω= Ψ × Ψ
σ (B-20)
By substituting (B-19) into (B-20), we obtain
( )( )
( )( )
1 1
2 1 1
32
32
sj t*m m s me s ss r s
*m ms s s m
s r s
* jeyL L tan tanT ( t ) P xL L L
L L yP sin t tan tanL L L x
e− − ω
− −
Ψ⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪− τ ω − ω⎜ ⎟= × Ψ⎢ ⎥⎨ ⎬⎝ ⎠⎣ ⎦σ ⎪ ⎪⎩ ⎭
⎧ ⎫⎧ ⎫ ⎡ ⎤⎛ ⎞≈ Ψ × ω − − τ ω − ω⎨ ⎬ ⎨ ⎬⎜ ⎟⎢ ⎥σ ⎝ ⎠⎣ ⎦⎩ ⎭ ⎩ ⎭
(B-21)
where
r
rt
s m
t
s m
LR
x cos( t ) cos( t )
y sin( t ) sin( t )
ee
−τ
−τ
⎧τ = σ⎪⎪⎪ = ω − ω⎨⎪⎪ = ω − ω⎪⎩
(B-22)
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 194
vector sΨ 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 tan smallθ ≈ θ ≈ θ θ (B-23)
So, torque expression can be further simplified as
( )( )
( )( )
2 1
2
32
32
*m me s s s m
s r s
*m ms s s m
s r s
L L yT ( t ) P sin t tanL L L x
L L yP tL L L x
−⎧ ⎫⎧ ⎫ ⎡ ⎤⎛ ⎞= Ψ × ω − − τ ω − ω⎨ ⎬ ⎨ ⎬⎜ ⎟⎢ ⎥σ ⎝ ⎠⎣ ⎦⎩ ⎭ ⎩ ⎭⎧ ⎫ ⎧ ⎫⎛ ⎞= Ψ × ω − + τ ω − ω⎨ ⎬ ⎨ ⎬⎜ ⎟σ ⎝ ⎠⎩ ⎭⎩ ⎭
(B-24)
By considering (B-24) and (B-22) at same time, we obtain
( )( )
( )2
2
2
2
31
2
3 12e
t*m
s s mr s
t*m m
s s ms r s
T ( t )
LP
R L
L LPL L L
e
e−τ
−τ≈
= Ψ − ω − ω
⎧ ⎫ ⎧ ⎫⎛ ⎞Ψ − τ ω − ω⎨ ⎬ ⎨ ⎬⎜ ⎟σ ⎝ ⎠⎩ ⎭⎩ ⎭⎧ ⎫⎛ ⎞⎨ ⎬ ⎜ ⎟
⎝ ⎠⎩ ⎭
(B-25)
The simplification in (B-25) is based on the fact that
( )( ) ( )1t
s ms s mytx e −
τ− ω − ω⎧ ⎫⎛ ⎞ ⎛ ⎞ω − + τ ω − ω ≈⎨ ⎬ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎩ ⎭
(B-26)
by considering the dynamic in (B-22).
Therefore
( )
( )
22
2
31
2
1
t*m
e s s mr s
t
s m
LT ( t ) P
R L
K
e
e
−τ
−τ
≈ Ψ − ω − ω
= − ω − ω
⎧ ⎫⎛ ⎞⎨ ⎬ ⎜ ⎟
⎝ ⎠⎩ ⎭⎛ ⎞⎜ ⎟⎝ ⎠
(B-27)
where
Appendix B Modelling of the direct flux vector control 195
2 2
2
32
*ms
r s
r
r
LK PR L
LR
⎧= Ψ⎪⎪
⎨⎪τ = σ⎪⎩
(B-28)
By Laplace transform of (B-27), we have
{ }11e s mT ( s ) K
s⎛ ⎞= ω − ω⎜ ⎟τ +⎝ ⎠
L (B-29)
where { }s mω − ωL is the Laplace form of { }s mω − ω .
The transfer function of the torque loop with input as { }s mω − ω can be written as
{ } 1
ep
s m
T ( s ) KG ( s )s
= =ω − ω τ +L
(B-30)
Equation (B-30) shows that the relationship between eT and sω is equivalent to a first
order system with a disturbance mω . The equivalent system block is shown as follows:
( )s sω ( )eT s
1Ksτ +
( )m sω−
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:
( )s sω ( )eT s1
Ksτ +
( )m sω−
( )cG s−
eT ∗
Fig.B.2 PI control of the equivalent system
Appendix B Modelling of the direct flux vector control 196
where
p ic
K s KG ( s )
s+
= (B-31)
Fig.B.2 is the equivalent torque loop of the direct flux vector control scheme discussed
in Chapter 4.
197
APPENDIX C
MODELLING OF THE DIRECT TORQUE AND
FLUX CONTROL
sΨ
sθ α
β
q d
rΨ
sI
sdisqi
Fig. C.1 Vector diagram of the induction machine
In stator flux reference frame ( )d q− shown in Fig. C.1, the dynamic behavior of
induction machine can be described as following equations:
( )0
32
ss s s s s
rr r s m r
e sd sq
dV R I jdt
dR I jdt
T P i
⎧ Ψ= + + ω Ψ⎪
⎪Ψ⎪
= + + ω −ω Ψ⎨⎪⎪ = Ψ ⋅⎪⎩
(C-1)
and
s s s m r
r m s r r
L I L I
L I L I
⎧Ψ = +⎪⎨Ψ = +⎪⎩
(C-2)
198
Therefore,
( )1
2
1
ss s s s s
rs m r r r
s s ss m r m
m r m ss r mr r r
d V R I jdt
d j R IdtI L L L L
L L L LL L LI
−
⎧ Ψ⎪ = − − ω Ψ⎪⎪ Ψ⎪ = − ω −ω Ψ −⎨⎪⎪ ⎡ ⎤ ⎡ ⎤⎡ ⎤ Ψ Ψ−⎡ ⎤ ⎡ ⎤
= =⎪ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥−−Ψ Ψ⎪⎢ ⎥ ⎣ ⎦ ⎣ ⎦⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎩
(C-3)
Equation (C-3) can be simplified as
( )
( ) 2
0 010 00
0 01 10 00
10
s
s s s ss
s m r rr r
s s sr mss
s m m sr s r mr r
dj R Idt V
j R Iddt
j L LRV
j L LR L L L
⎡ ⎤Ψ⎢ ⎥ ⎡ ⎤− Ψ ⎡ ⎤⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ = + −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ − −⎢ ⎥Ψ Ψ⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦⎢ ⎥⎣ ⎦
⎡ ⎤ ⎡ ⎤− Ψ Ψ−⎡ ⎤ ⎡ ⎤⎡ ⎤⎡ ⎤= + −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ − − −−Ψ Ψ⎣ ⎦ ⎣ ⎦⎢ ⎥ ⎣ ⎦ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
=
ωω ω
ωω ω
( )
( )
0 0 10 0
10 01
0 00 1
s s sr mss
s m m sr s rr r
m
s s s rs sss
s m r mr r
s r r
j L LRV
j L LR L L
Lj L L LR
Vj R L
L L L
⎡ ⎤ ⎡ ⎤− Ψ Ψ−⎡ ⎤ ⎡ ⎤⎡ ⎤⎡ ⎤+ −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ − − −Ψ Ψ⎣ ⎦ ⎣ ⎦⎢ ⎥ ⎣ ⎦ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
⎡ ⎤−⎢ ⎥⎡ ⎤ ⎡− Ψ Ψ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎢ ⎥= + −⎢ ⎥ ⎢⎢ ⎥ ⎢ ⎥⎢ ⎥ − − ⎢ ⎥Ψ Ψ⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣−⎢ ⎥⎣ ⎦
ωω ω σ
ω σ σω ω
σ σ
( )
( )
0100
10
s s m
s s s rs ss
s m r m rr r
s r r
s s ms
s s r ss
r m r rs m
s r r
R R Lj L L L
Vj R L R
L L L
R R LjL L L
VR L RjL L L
⎤⎥
⎢ ⎥⎦
⎡ ⎤−⎢ ⎥⎡ ⎤ ⎡ ⎤− Ψ Ψ⎡ ⎤⎡ ⎤ ⎢ ⎥= + +⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ − − ⎢ ⎥Ψ Ψ⎣ ⎦ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦−⎢ ⎥⎣ ⎦
⎡ ⎤− −⎢ ⎥ ⎡ ⎤Ψ ⎡ ⎤⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥ Ψ ⎣ ⎦⎢ ⎥⎣ ⎦− − −⎢ ⎥⎣ ⎦
ω σ σω ω
σ σ
ωσ σ
ω ωσ σ
(C-4)
where
2
1 m
s r
LL L
σ = − (C-5)
So, the relationship between stator and rotor flux vector can be obtained by Laplace
transform from (C-4)
199
( )r m rr s s m r
s r r
R L Rs jL L L
⎛ ⎞Ψ = Ψ + − − − Ψ⎜ ⎟
⎝ ⎠ω ω
σ σ (C-6)
thus
( ) ( )
( )( ) ( )( )
1
1 1
r m m
s r sr s s
r r rs m s m
r r r
m m
s ss s
s m s m
R L LL L L
R L Ls j s jL R R
L LL L
s j s j
σΨ = Ψ = Ψ
⎛ ⎞ ⎛ ⎞− − ω − ω − σ − − ω − ω σ −⎜ ⎟ ⎜ ⎟σ⎝ ⎠ ⎝ ⎠
= Ψ = Ψτσ − − ω − ω τ − τσ + ω − ω τ +
(C-7)
where r
r
LR
τ = .
It is known in the stator flux reference frame that
0
s ds qs
qs
j⎧Ψ = Ψ + Ψ⎪⎨Ψ =⎪⎩
(C-8)
The rotor flux vector in the stator flux reference frame can be expressed as
r rd rqjΨ = Ψ + Ψ (C-9)
With (C-6), (C-8) and (C-9), the dq component of rotor flux vector can be obtained
200
( )
( ) ( ) ( )
( )
( )
( )
r m rr s s m r
s r r
r m rrd rq sd s m rd rq
s r r
r m rrd sd s m rq rd
s r r
rrq s m rd rq
r
r m rrd sd s m rq
s r
R L Rs jL L L
R L Rs j j jL L L
R L RsL L L
RsL
R L RsL L L
⎛ ⎞Ψ = Ψ + − ω − ω − Ψ⎜ ⎟σ σ⎝ ⎠
⎛ ⎞⇒ Ψ + Ψ = Ψ + − ω − ω − Ψ + Ψ⎜ ⎟σ σ⎝ ⎠
⎧ ⎛ ⎞Ψ = Ψ + ω − ω Ψ − Ψ⎪ ⎜ ⎟σ σ⎪ ⎝ ⎠⇒ ⎨
⎛ ⎞⎪ Ψ = − ω − ω Ψ − Ψ⎜ ⎟⎪ σ⎝ ⎠⎩
Ψ = Ψ + ω − ω Ψ −σ
⇒ ( )
( )
( )
( )
( )
2
2
rdr
s mrq rd
r
r
s mr m rrd sd rd rd
rs r r
r
s mrq rd
r
r
s m r mrrd sd
r r s r
r
s mrq rd
r
r
RsL
R L Rs RL L LsL
RsL
R LRs R L L LsL
RsL
⎧ ⎛ ⎞Ψ⎪ ⎜ ⎟σ⎝ ⎠⎪⎪
⎨ − ω − ωΨ = Ψ⎪⎪ +
σ⎪⎩⎧ ⎛ ⎞⎪ ⎜ ⎟− ω − ω⎪ ⎜ ⎟Ψ = Ψ + Ψ − Ψ
σ σ⎪ ⎜ ⎟+⎪ ⎜ ⎟σ⇒ ⎝ ⎠⎨⎪ − ω − ω⎪Ψ = Ψ⎪ +⎪ σ⎩⎧⎛ ⎞⎜ ⎟ω − ω⎜ ⎟+ + Ψ = Ψ
σ σ⎜ ⎟+⎜ ⎟σ⇒ ⎝ ⎠⎨− ω − ω
Ψ = Ψ+
σ
( )
( )( )
2
2
r m
s rrd sd
s m r
r r
r
r m
s m s rrq sd
r s m r
r r r
r
R LL L
Rs R LsL
R LL L
R Rs sL R LsL
⎪⎪⎪⎪
⎪⎪⎪⎪⎩⎧⎪ σ⎪Ψ = Ψ
ω − ω⎪+ +⎪ σ⎪ +
σ⎪⇒ ⎨⎪
− ω − ω⎪ σΨ = Ψ⎪
ω − ω⎪ + + +σ⎪ σ+⎪ σ⎩
(C-10)
201
The expression of stator current with stator and rotor flux vector is already shown in (C-
3), which is restated as
[ ]2
1 ss r m
s r m r
I L LL L L
⎡ ⎤Ψ⎡ ⎤ = − ⎢ ⎥⎣ ⎦ − Ψ⎢ ⎥⎣ ⎦
(C-11)
By substituting (C-10) into (C-11), it is derived that
( )( )
( )( )
( )
( )
2
2
2
2
1
1 11
1 1 1
m rqsq r sq m rq
s r m s r
r m
s mm s rsq sd
rs r s m r
r r r
r
m
s mm ssq sd
s r s m
s mm m
s r ss m
LI L L
L L L L LR L
L L LI RL L Rs sL R LsL
LL LI
L L s ss
L LL L L s s s
− Ψ⎡ ⎤⇒ = Ψ − Ψ =⎣ ⎦−
− −−⇒ = Ψ
−+ + ++
−⇒ = Ψ
−+ + ++
−=
⎛ ⎞ ⎛ ⎞+ + − + +⎜ ⎟ ⎜⎝ ⎠ ⎝ ⎠
σ
ω ω σσ ω ω
σ σσ
ω ω τσσ ω ω
τσ τστσ
ω ωσ τσ ω ω
τσ τσ τσ( )
( )
( )( )
2
2 2 222 2
2 22
22 2 2 2 2 2 2
1 1 1
2 1
sd
s mmsq sd
s rs m
s mmsq sd
s r s m
LIL L s s s
LIL L s s
Ψ
⎟
−⇒ = Ψ
+ + − + +
−⇒ = Ψ
+ + − +
ω ωτσ ω ω
τσ τσ τ σω ω τ σ
τσ τ σ τσ τ σ ω ω
(C-12)
Thus
( )
( )
( )
( )
( )
2
2
22 2 2 2 2
2
2
22 2
2
2
2 1
2 1
2 1
ms m
s rsq sd
s m
ms m
s rsq sd
s m
ms m
s rsq sd
LL LI
s s
LL LI
s
LL LI
s
ω − ω τ⇒ = Ψ
τ σ + τσ + τ σ ω − ω +
ω − ω τ⇒ ≈ Ψ
τσ + τ σ ω − ω +
ω − ω τ⇒ ≈ Ψ
τσ +
(C-13)
202
where
2
1 m
s r
r
r
LL L
LR
⎧σ = −⎪⎪⎨⎪τ =⎪⎩
(C-14)
The simplification in (C-13) is based on small τ and σ .
By inverse Laplace transform, the expression of sqI is time domain is obtained as
{ }( )
( )
( ) { }
2
21 1
2
21
22
2
2 1
2 1
1
ms m
s rsq sq sd
ms m
s r sd
tms m sd
s r
LL LI ( t ) I ( s ) ( s )
s
LL L
s s
L eL L
− −
∗−
−∗ τσ
⎧ ⎫ω − ω τ⎪ ⎪⎪ ⎪= = Ψ⎨ ⎬τσ +⎪ ⎪
⎪ ⎪⎩ ⎭⎧ ⎫ω − ω τ⎪ ⎪Ψ⎪ ⎪= ⎨ ⎬τσ +⎪ ⎪
⎪ ⎪⎩ ⎭
= ω − ω τ Ψ −
L L
L (C-15)
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.
( ) { }( ) ( ){ }
22
2
222
2
32
3 12
3 12
e sd sq
tmsd s m sd
s r
tmsd s m
s r
T ( t ) P ( t ) i ( t )
LP eL L
LP eL L
−∗ ∗ τσ
−∗ τσ
= Ψ ⋅
= Ψ ω − ω τ Ψ −
τ= Ψ ω − ω −
(C-16)
By (C-1), the voltage equation in dq frame is
sd sd
sd s sd
sq s sq s sd s sd
d dV R idt dt
V R i
Ψ Ψ⎧ = + ≈⎪⎨⎪ = + ω Ψ ≈ ω Ψ⎩
(C-17)
By substituting (C-17) into (C-16), the relationship between the q voltage component
and the torque is developed as
203
{ } ( )2
22
3 12
tm
e sd sq ms r
LT ( t ) P e V fL L
−∗ τστ= ⋅Ψ − − ω (C-18)
where
( ) ( ) { }222
2
3 12
tm
m sd ms r
Lf P eL L
−∗ τστω = Ψ − ω (C-19)
Therefore, it is clear shown in (C-18) that the torque of induction machine can be
directly regulated by the q voltage component considering ( )mf ω 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.