THE DYNAMIC ANALYSIS AND CONTROL OF A

SELF-EXCITED INDUCTION GENERATOR DRIVEN

BY A WIND TURBINE

by

Dawit Seyoum

A thesis submitted to

The University of New South Wales for the Degree of

Doctor of Philosophy

School of Electrical Engineering and Telecommunications

March, 2003

ii

CERTIFICATE OF ORIGINALITY

I hereby declare that this submission is my own work and that, to the best of my

knowledge and belief, it contains no material previously published or written by another

person nor material which to a substantial extent has been accepted for the award of any

other degree or diploma of a university or other institute of higher learning, except

where due acknowledgment is made in the text.

_______________________

Dawit Seyoum

iii

ACKNOWLEDGEMENTS

First, thanks be to God who gave me the physical and spiritual health to pursue my

Ph.D. study.

I would like to thank my supervisors Associate Professor M.F. Rahman and Associate

Professor Colin Grantham for their guidance and financial assistance throughout this

study.

Special acknowledgement is due to Mr. Doug McKinnon for proof reading the thesis

and for sharing ideas. I thank Daniel Indyk from Energy Australia for his assistance to

visit a wind power site. Thank you to the laboratory staff for their logistical support.

Thanks also go to my colleagues in the Energy Systems Research Group for their

suggestions, Mr. Baburaj Karanayil, Mr. Chathura Mudannayake, Dr. Enamul Haque,

Mr. Lixin Tang, Mr. Phuc Huu To and Mr. Phop Chancharoensook.

I thank my late father who encouraged me to go to school when I was a little boy and

my mother who raised me and helped me to go to school as a single mother.

Last, but foremost, thanks go to my family. To my wife Abeba, thank you for your

patience, understanding, encouragement and help, especially when I was spending most

of the time doing research. And thanks to my little daughter, Lwam, for your patience in

enjoying the little time that I had to spend with you.

iv

ABSTRACT

This thesis covers the analysis, dynamic modelling and control of an isolated self-

excited induction generator (SEIG) driven by a variable speed wind turbine. The

voltage build up process of an isolated induction generator excited by AC capacitors

starts from charge in the capacitors or from a remnant magnetic field in the core. A

similar voltage build up is obtained when the isolated induction generator is excited

using an inverter/rectifier system with a single DC capacitor on the DC link of the

converter. In this type of excitation the voltage build up starts from a small DC voltage

in the DC link and is implemented using vector control.

The dynamic voltage, current, power and frequency developed by the induction

generator have been analysed, simulated and verified experimentally for the loaded and

unloaded conditions while the speed was varied or kept constant. Results which are

inaccessible in the experimental setup have been predicted using the simulation

algorithm.

To model the self excited induction generator accurate values of the parameters of the

induction machine are required. A detailed analysis for the parameter determination of

induction machines using a fast data acquisition technique and a DSP system has been

investigated. A novel analysis and model of a self-excited induction generator that takes

iron loss into account is presented in a simplified and understandable way.

The use of the variation in magnetising inductance with voltage leads to an accurate

prediction of whether or not self-excitation will occur in a SEIG for various capacitance

values and speeds in both the loaded and unloaded cases. The characteristics of

magnetising inductance, Lm, with respect to the rms induced stator voltage or

magnetising current determines the regions of stable operation as well as the minimum

generated voltage without loss of self-excitation.

In the SEIG, the frequency of the generated voltage depends on the speed of the prime

mover as well as the condition of the load. With the speed of the prime mover of an

isolated SEIG constant, an increased load causes the magnitude of the generated voltage

v

and frequency to decrease. This is due to a drop in the speed of the rotating magnetic

field. When the speed of the prime mover drops with load then the decrease in voltage

and frequency will be greater than for the case where the speed is held constant.

Dynamic simulation studies shows that increasing the capacitance value can

compensate for the voltage drop due to loading, but the drop in frequency can be

compensated only by increasing the speed of the rotor.

In vector control of the SEIG, the reference flux linkage varies according to the

variation in rotor speed. The problems associated with the estimation of stator flux

linkage using integration are investigated and an improved estimation of flux linkage is

developed that compensates for the integration error.

Analysis of the three-axes to two-axes transformation and its application in the

measurement of rms current, rms voltage, active power and power factor from data

obtained in only one set of measurements taken at a single instant of time is discussed.

It is also shown that from measurements taken at two consecutive instants in time the

frequency of the three-phase AC power supply can be evaluated. The three-axes to two-

axes transformation tool simplifies the calculation of the electrical quantities.

vi

CONTENTS

ACKNOWLEDGEMENTS....................................................................................... ...iii

ABSTRACT ........................................................................................................... ...iv

CONTENTS ........................................................................................................... ...vi

LIST OF FIGURES ................................................................................................... ..xii

LIST OF TABLES ..................................................................................................... .xix

LIST OF SYMBOLS ................................................................................................. ..xx

1 INTRODUCTION ............................................................................................... 1

1.1 General ........................................................................................................ 1

1.2 Thesis outline............................................................................................... 4

1.3 Literature review ......................................................................................... 8

1.3.1 Self-excited induction generator........................................................ 8

1.3.2 Capacitance and rotor speed for self-excitation ................................ ..11

1.3.3 Representation of magnetising inductance ........................................ ..11

1.3.4 Control of generated voltage and frequency...................................... ..13

1.3.5 Wind powered generators .................................................................. ..13

1.3.6 Cross saturation ................................................................................. ..15

1.4 References ................................................................................................... ..16

2 WIND POWER.................................................................................................... ..21

2.1 Source of wind............................................................................................. ..21

2.2 Wind Turbine............................................................................................... ..22

2.2.1 Vertical axis wind turbine.................................................................. ..22

vii

2.2.2 Horizontal axis wind turbine ............................................................. ..23

2.3 Power extracted from wind.......................................................................... ..24

2.4 Torque developed by a wind turbine ........................................................... ..31

2.5 Tip-Speed Ratio........................................................................................... ..35

2.6 Power control in wind turbines.................................................................... ..36

2.6.1 Pitch control....................................................................................... ..38

2.6.2 Yaw control ....................................................................................... ..38

2.6.3 Stall control........................................................................................ ..39

2.7 Wind powered electric generation............................................................... ..40

2.8 Economics of wind powered electric generation......................................... ..41

2.9 Summary...................................................................................................... ..42

2.10 References ................................................................................................... ..43

3 THREE AXES TO TWO AXES TRANSFORMATION AND ITS

APPLICATION ................................................................................................... ..44

3.1 Introduction ................................................................................................. ..44

3.2 General change of variables in transformation............................................ ..45

3.2.1 Transformation into a stationary reference frame ............................. ..46

3.2.2 Transformation into a rotating reference frame................................. ..51

3.3 Voltage measurement .................................................................................. ..53

3.4 Current measurement................................................................................... ..55

3.5 Power measurement..................................................................................... ..58

3.6 Power factor measurement .......................................................................... ..60

3.7 Frequency measurement .............................................................................. ..61

3.8 Measurement in a balanced non sinusoidal three phase system.................. ..63

3.9 Summary...................................................................................................... ..64

3.10 References ................................................................................................... ..64

4 INDUCTION MACHINE MODELING ........................................................... ..66

4.1 Introduction ................................................................................................. ..66

4.2 Conventional induction machine mode ....................................................... ..67

4.3 D-Q axes induction machine model ............................................................ ..70

viii

4.4 Simulation of induction machine................................................................. ..74

4.5 D-Q axes induction machine model in rotating reference frame ................ ..86

4.6 Development of D-Q axes induction machine model with Rm .................... ..87

4.7 Summary...................................................................................................... ..93

4.8 References ................................................................................................... ..93

5 DATA ACQUISITION AND DIGITAL SIGNAL PROCESSING ................ ..95

5.1 Introduction ................................................................................................. ..95

5.2 DS1102 DSP board...................................................................................... ..96

5.3 Data acquisition ........................................................................................... ..98

5.3.1 Voltage and Current measurement .................................................... ..98

5.3.1.1 Anti-aliasing filter................................................................. ..99

5.3.1.2 Voltage measurement ........................................................... 101

5.3.1.3 Current measurement............................................................ 102

5.4 Speed and angle measurement..................................................................... 103

5.4.1 Angle measurement ........................................................................... 105

5.4.2 Speed measurement ........................................................................... 107

5.5 Digital signal processing ............................................................................. 108

5.5.1 Digital filter ....................................................................................... 108

5.5.1.1 Infinite Impulse Response (IIR) filter .................................. 109

5.5.1.2 Finite Impulse Response (FIR) filter .................................... 110

5.5.1.3 Comparison of IIR and FIR filters........................................ 111

5.5.2 Digital filter design from analog filter............................................... 111

5.5.3 Implementation of a digital filter by approximating analog

filter circuits....................................................................................... 112

5.6 Summary...................................................................................................... 113

5.7 References ................................................................................................... 114

6 PARAMETER DETERMINATION FOR AN INDUCTION MACHINE.... 115

6.1 Introduction ................................................................................................. 115

6.2 Open-circuit and short-circuit test ............................................................... 117

6.2.1 Open-circuit test ................................................................................ 117

ix

6.2.2 Short-circuit test ................................................................................ 118

6.2.3 Induction machine with constant rotor parameters............................ 119

6.2.4 Induction machine with variable rotor parameters ............................ 120

6.2.5 Results for DSP based parameter determination .............................. 125

6.3 Sensitivity study on variable rotor parameters ............................................ 137

6.3.1 The effect of combining measurement errors ................................... 138

6.3.1.1 Percentage errors ................................................................. 138

6.3.1.2 Combining errors .................................................................. 139

6.3.2 Induction machine parameters for analysis of measurement error..... 139

6.3.3 Statistical tools.................................................................................... 140

6.3.4 Simulation of parameter determination with measurement error....... 142

6.4 Summary...................................................................................................... 146

6.5 References ................................................................................................... 147

7 EXCITATION OF THREE PHASE INDUCTION GENERATOR USING

THREE AC CAPACITORS ............................................................................... 149

7.1 Introduction ................................................................................................. 149

7.2 Model of self-excited induction generator .................................................. 151

7.3 Analysis of self-excitation process.............................................................. 153

7.3.1 RLC circuit characteristics ................................................................ 154

7.3.2 Conditions for self-excitation in induction generator........................ 156

7.3.2.1 Using matrix partition........................................................... 158

7.3.2.2 Direct matrix inversion......................................................... 162

7.4 Characteristics of magnetising inductance in induction machine ............... 164

7.5 Minimum speed and capacitance for self-excitation ................................... 166

7.6 Magnetising inductance and its effect on stability of generated voltage .... 170

7.7 Onset of self-excitation when the SEIG is loaded....................................... 173

7.8 Simulation of self-excited induction generator ........................................... 175

7.8.1 The modelling of self-excitation process........................................... 175

7.8.1.1 Determination of initial conditions....................................... 175

7.8.1.2 The dynamic representation of self-excitation at no load .... 176

7.8.2 The dynamic representation of a loaded SEIG.................................. 186

7.9 Characteristics of wind turbine and its effect on generator output.............. 194

x

7.10 Effect of rotor parameters variation on self-excitation................................ 199

7.11 Summary...................................................................................................... 205

7.12 References ................................................................................................... 207

8 MODELLNG OF AN ISOLATED SELF-EXCITED INDUCTION

GENERATOR TAKING IRON LOSS INTO ACCOUNT ............................. 208

8.1 Introduction ................................................................................................. 208

8.2 SEIG dynamic model including Rm ............................................................. 209

8.3 Characteristics of Lm and Rm........................................................................ 210

8.4 Analysis of SEIG including Rm ................................................................... 211

8.5 Simulation of dynamic self-excitation including Rm ................................... 213

8.5.1 Simulation of dynamic self-excitation at no load.............................. 213

8.5.2 Dynamics of SEIG during loading .................................................... 216

8.6 Summary...................................................................................................... 220

8.7 References ................................................................................................... 221

9 INVERTER/RECTIFIER EXCITATION OF A THREE-PHASE

INDUCTION GENERATOR ............................................................................. 222

9.1 Introduction ................................................................................................. 222

9.2 Vector control .............................................................................................. 224

9.2.1 Rotor flux oriented vector control ..................................................... 225

9.2.1.1 Direct (feedback) flux oriented vector control ..................... 227

9.2.1.2 Indirect (feed forward) flux oriented vector control............. 231

9.2.2 Rotor flux oriented control with voltage as the controlled variable.. 232

9.2.3 Stator flux oriented vector control..................................................... 234

9.3 System description....................................................................................... 239

9.4 Establishment of reference flux linkage ...................................................... 241

9.5 Details for the implementation of vector control ........................................ 243

9.5.1 Implementation of direct rotor flux oriented vector control.............. 244

9.5.2 Implementation of indirect rotor flux oriented vector control........... 245

9.5.3 Implementation of rotor flux oriented vector control with voltage as a

control variable .................................................................................. 246

xi

9.5.4 Implementation of stator flux oriented vector control....................... 247

9.6 Results ......................................................................................................... 248

9.7 Summary...................................................................................................... 254

9.8 References ................................................................................................... 256

10 FLUX LINKAGE ESTIMATION AND COMPENSATION IN

INDUCTION MACHINES ................................................................................ 258

10.1 Introduction ................................................................................................. 258

10.2 Theory of Integrator .................................................................................... 259

10.3 Numerical integrator.................................................................................... 263

10.4 Proposed integration offset adjustment ....................................................... 263

10.4.1 Strategy I - without input offset minimization ................................ 264

10.4.2 Strategy II - with input offset minimization .................................... 265

10.5 Stator flux linkage estimation with the proposed method ........................... 265

10.6 Summary...................................................................................................... 267

10.7 References ................................................................................................... 268

11 CONCLUSIONS AND SUGGESTION FOR FUTURE WORK.................... 269

11.1 Conclusions ................................................................................................. 269

11.2 Suggestions for future work ........................................................................ 277

APPENDICES

A DETERMINATION OF INERTIA AND FRICTION COEFIENT OF

THE INDUCTION GENERATOR SYSTEM ........................................ 278

B MEASUREMENT AND CONTROL SYTEMS HARDWARE............ 283

C DETAILS IN INDUCTION MACHINE MODELLING ...................... 289

C.1 Introduction ........................................................................................ 289

C.2 Relationship of parameters in steady state model and d-q model of

induction machines ............................................................................. 289

C.3 Expanded equations for induction machine modelling including Rm.. 292

D LIST OF PUBLICATIONS ...................................................................... 296

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LIST OF FIGURES

Fig. 1.1 Kooragang wind turbine generator, Newcastle, NSW, Australia ...............2

Fig. 1.2 Wind farm around San Francisco, California, USA (Photo 2002) .............3

Fig. 2.1 Vertical axis wind turbine ...........................................................................23

Fig. 2.2 Horizontal axis wind turbine (a) upwind machine (b) downwind machine24

Fig. 2.3 Detail of a wind turbine driven power generation system ..........................25

Fig. 2.4 Change of wind speed and wind pressure around the wind turbine ............ ..27

Fig. 2.5 Power coefficient versus V2/V1 .................................................................... . 30

Fig. 2.6 Wind turbine output power to shaft speed characteristic curve................... . 31

Fig. 2.7 Air flow around cross section of a blade of a wind turbine ......................... . 32

Fig. 2.8 Air flow around cross section of a blade during stall condition .................. . 32

Fig. 2.9 Wind turbine output torque to shaft speed characteristic curve................... . 33

Fig. 2.10 Detail of a twisted rotor blade...................................................................... . 34

Fig. 2.11 Cross section of a twisted rotor blade from tip to base................................ . 35

Fig. 2.12 Typical power coefficient versus tip speed ratio ......................................... . 36

Fig. 2.13 Histogram and Weibull function for the probability of a given wind

speed (data measured in 1m/s intervals) ...................................................... ..37

Fig. 2.14 Wind turbine control regions ....................................................................... ..38

Fig. 2.15 Power coefficient verses tip speed ratio under yaw control ........................ ..39

Fig. 2.16 Growth of wind energy capacity worldwide................................................ ..41

Fig. 2.17 Trend in the cost of electricity generated from wind energy ....................... ..42

Fig. 3.1 Three-axes and two-axes in the stationary reference frame......................... ..46

Fig. 3.2 Three-axes and two-axes in the stationary reference frame with d-axis

and a-axis aligned ........................................................................................ ..49

Fig. 3.3 Steps of the abc to rotating dq axes transformation..................................... ..52

Fig. 3.4 Voltage vector and its component in dq axes .............................................. ..54

Fig. 3.5 Current vector and its component in stationary dq axes .............................. ..58

Fig. 3.6 Voltage and current vectors with their components in the stationary

dq-axes ......................................................................................................... ..59

xiii

Fig. 4.1 Stator side of the per-phase equivalent circuit of a three-phase

induction machine ........................................................................................ ..67

Fig. 4.2a Rotor side of the per-phase equivalent circuit of a three-phase

induction machine ....................................................................................... ..68

Fig. 4.2b Rotor side of the induction machine with adjustment ................................. ..68

Fig. 4.3 Per-phase equivalent circuit of three-phase induction machine neglecting

core loss........................................................................................................ ..69

Fig. 4.4 Per-phase equivalent circuit of three-phase induction machine including

core loss........................................................................................................ ..69

Fig. 4.5 D-Q representation of induction machine.................................................... ..71

Fig. 4.6 Detailed d-q representation of induction machine in stationary reference

frame (a) d-axis circuit (b) q-axis circuit ..................................................... ..72

Fig. 4.7 Experimental setup to find the characteristics of induction machine

in the motoring and generating regions ....................................................... ..75

Fig. 4.8 Variation of stator phase current for constant supply voltage and frequency

(a) Current and voltage when the rotor speed is varied from standstill to

twice the synchronous speed (b) detail of motoring region (c) detail around

the synchronous speed (d) detail in the generating region........................... ..77

Fig. 4.9 Relationship between phase voltage vector and phase current vector (a) in

the motoring region (b) between motoring and generating (at synchronous

speed) (c) in the generating region............................................................... ..78

Fig. 4.10 Induction machine torque, power and efficiency characteristics (a) torque

(b) electrical power (c) mechanical power (Pm=ZmTe) (d) efficiency ......... ..79

Fig. 4.11 Space vector angles measured with respect to the stator voltage space

vector angle for (a) stator current Is (b) stator flux linkage Os (c) rotor current Ir (d) magnetising current Im.............................................. ..80

Fig. 4.12 Magnitude of space vector for (a) stator voltage (b) stator current Is

(c) stator flux linkage Os (d) rotor current Ir (e) magnetising current Im ...... ..81

Fig. 4.13 Space vector diagram for stator voltage, stator current, rotor current,

magnetising current and stator flux linkage (a) during motoring mode

(b) during generating mode.......................................................................... ..82

Fig. 4.14 Stator current in the de-q

e axes of the excitation reference frame

xiv

(a) qe-axis current (b) d

e-axis current........................................................... ..84

Fig. 4.15 Stator voltage in the de-q

e axes of the excitation reference frame (a) d

e-axis

voltage (b) qe-axis voltage ........................................................................... ..84

Fig. 4.16 Magnetising current in the de-q

e axes of the excitation reference frame

(a) de-axis magnetising current (b) q

e-axis magnetising current.................. ..85

Fig. 4.17 Rotor current in the de-q

e axes of the excitation reference frame

(a) de-axis rotor current (b) q

e-axis rotor current ......................................... ..85

Fig. 4.18 Rotor current in different reference frames (a) rotor current in a rotating

reference frame that is rotating at the rotor speed (b) rotor current in the

stator (stationary) reference frame ............................................................... ..86

Fig. 4.19 D-Q representation of induction machine in the excitation (Ze) reference

frame (a) d-axis circuit (b) q-axis circuit ..................................................... ..87

Fig. 4.20 D-Q model of induction machine including core loss represented by Rm (a) d-axis (b) q-axis ...................................................................................... ..90

Fig. 5.1 Block diagram for data acquisition and signal processing........................... ..95

Fig. 5.2 Hardware and software system configuration.............................................. ..96

Fig. 5.3 Block Diagram of the DS1102..................................................................... ..97

Fig. 5.4 Voltage measurement system (a) voltage sensor (b) signal conditioning

for the sensed voltage................................................................................... 101

Fig. 5.5 Current measurement system (a) current transducer (b) signal

conditioning for the sensed current in terms of voltage signal .................... 103

Fig. 5.6 Output signals of and incremental angle encoder ........................................ 104

Fig. 5.7 Block diagram of an incremental encoder interface .................................... 105

Fig. 5.8 Block diagram for FIR filter ........................................................................ 110

Fig. 5.9 Simple first order analog low pass filter ...................................................... 112

Fig. 6.1 The per-phase equivalent circuit with shunt magnetising branch

impedance represented in parallel................................................................ 115

Fig. 6.2 Per-phase equivalent circuit with shunt magnetising branch impedance

represented in series form ............................................................................ 116

Fig. 6.3 Per-phase equivalent circuit of three-phase induction machine under

no load test ................................................................................................... 117

Fig. 6.4 Per-phase equivalent circuit at standstill (short-circuit test)........................ 118

Fig. 6.5 Current displacement with rotor speed a) zero speed b) intermediate

xv

speed c) close to synchronous speed............................................................ 121

Fig. 6.6 Rotor parameter variations with slip for deep bar induction machine......... 123

Fig. 6.7 Per-phase equivalent circuit with variable rotor parameters ....................... 123

Fig. 6.8 Monitoring system for parameter determination ......................................... 126

Fig. 6.9 Three-phase induction motor input quantities as a function of time

(a) measured line voltage (b) measured line current (c) measured input

power............................................................................................................ 128

Fig. 6.10 Three-phase induction motor input quantities as a function of speed

(a) measured line voltage (b) measured line current (c) measured input

power............................................................................................................ 130

Fig. 6.11 Variation of rotor parameters for machine single-cage rotor....................... 131

Fig. 6.12 Variation of rotor parameters with slip and supply line to line voltage ...... 132

Fig. 6.13 Effect of temperature on rotor parameters ................................................... 134

Fig. 6.14 Variation of (a) magnetizing reactance with voltage at 95oC (b) iron loss

resistance with voltage at 95oC (c) magnetizing reactance with temperature

and voltage (d) iron loss resistance with temperature and voltage .............. 137

Fig. 6.15 Values of rotor resistance, Rr, and rotor leakage reactance, Xlr ...............................140

Fig. 6.16 Measurement error with a normal distribution ............................................ 141

Fig. 6.17 Data generated for simulation of measurement error................................... 143

Fig. 6.18 Error in rotor parameters due to 0.5% error in voltage current and/or

power............................................................................................................ 144

Fig. 6.19 Error in rotor parameters due to 1% error in voltage current and/or

power............................................................................................................ 144

Fig. 6.20Error in rotor parameters due to 1.5% error in voltage current and/or

power............................................................................................................ 145

Fig. 6.21 Simulated shaft torque for variable and constant rotor parameters .............. 146

Fig. 7.1 SEIG with a capacitor excitation system driven by a wind turbine............. 150

Fig. 7.2 D-Q representation of self-excited induction generator............................... 151

Fig. 7.3 Detailed d-q model of SEIG in stationary reference frame (a) q-axis circuit

(b) d-axis circuit ........................................................................................... 152

Fig. 7.4 RLC circuit................................................................................................... 154

Fig. 7.5 Current in series RLC circuit (a) for R = 1.2: and (b) for R = -1.2:......... 156G

xvi

Fig. 7.6 Variation of magnetising inductance with phase voltage at rated frequency

165

Fig. 7.7 Flow chart to determine the minimum speed and minimum capacitance

for SEIG at no load ...................................................................................... 167

Fig. 7.8 Values of minimum capacitance and rotor speed for self-excitation at

no load.......................................................................................................... 169

Fig. 7.9 Error in capacitance when calculated using the approximate method......... 170

Fig. 7.10 Measured unsuccessful self-excitation at C=60PF (a) generated phase

voltage (b) speed .......................................................................................... 171

Fig. 7.11 Measured self-excitation at C = 60PF and lower speed (a) generated

phase voltage (b)speed................................................................................. 172

Fig. 7.12 Measured self-excitation at C = 60PF with speed and generated voltage

close to rated values (a) generated phase voltage (b)speed ......................... 173G

Fig. 7.13 Required capacitance and speed for self-excitation with load, RL ............... 174

Fig. 7.14 Relationship between capacitance value, rotor speed and generated

voltage at no load ......................................................................................... 178

Fig. 7.15 Variation of magnetising inductance with phase voltage at different

frequencies ................................................................................................... 179

Fig. 7.16 Variation of magnetising inductance with magnetising current .................. 180

Fig. 7.17 DC motor speed regulator ............................................................................ 181

Fig. 7.18 Measured self-excitation at C = 60PF and with regulated speed

(a) generated phase voltage (b) speed (c) stator current .............................. 182G

Fig. 7.19 Simulated self-excitation at C = 60PF and with regulated speed

(a) generated phase voltage (b) speed (c) stator current .............................. 183

Fig. 7.20 Simulated self-excitation at C = 60PF and with regulated speed

(a) magnetising inductance (b) rms magnetising current (c) peak stator

flux-linkage .................................................................................................. 184G

Fig. 7.21 Three dimensional d-axis flux-linkage and q-axis flux-linkage as a

function of time during self-excitation process ........................................... 185

Fig. 7.22 Self-excitation process initiated by a charged capacitor of 60PF and

rotor speed of 1480rpm (a) experimental result (b) simulated result........... 186G

Fig. 7.23 d-q model of a loaded SEIG in a stationary reference frame (a) q-axis

xvii

circuit (b) d-axis circuit............................................................................... 187

Fig. 7.24 Relationship between rotor speed and synchronous speed in a SEIG ......... 189

Fig. 7.25 Experimental loading of SEIG after the voltage has developed to its steady

state value (a) phase voltage (b) speed (c) frequency (d) rms phase voltage

(e) generated power (f) rms stator current ................................................... 190

Fig. 7.26 Simulated loading of SEIG after the voltage has developed to its steady

state value (a) phase voltage (b) speed (c) frequency (d) rms phase voltage

(e) generated power (f) rms stator current ................................................... 191

Fig. 7.27 Simulated loading of SEIG (a) rms stator current (b) rms capacitor current

(c) rms load current ...................................................................................... 192

Fig. 7.28 Simulated loading of SEIG (a) Lm (b) peak flux-linkage (c) rms

magnetising current...................................................................................... 192

Fig. 7.29 Measured variation of generated voltage with load for a 60PF capacitance 193G

Fig. 7.30 Measured variation of generated frequency with load for a 60PF

capacitance ................................................................................................... 193G

Fig. 7.31 Wind turbine output torque as a function of rotor speed ............................. 195

Fig. 7.32 Simulated results for wind turbine with variable rotor speed (a) load

resistance (b) capacitance (c) rotor speed (d) phase voltage (e) frequency

as a function of time..................................................................................... 197

Fig. 7.33 Simulated results for wind turbine with variable rotor speed (a) rms stator

current (b) rms capacitor current (c) rms load current (d) electromagnetic

torque (e) output power as a function of time............................................. 198

Fig. 7.34 Input to the hypothetical SEIG (a) capacitance, PF (b) load resistance, :G

(c) speed, rpm............................................................................................... 200

Fig. 7.35 Comparison of constant and variable rotor parameters performance in

SEIG (a) rms phase voltage (b) rms stator current (c) rms capacitor current

(d) rms load current (e) rms magnetising current (f) magnetising

inductance .................................................................................................... 203

Fig. 7.36 Comparison of constant and variable rotor parameters performance in

SEIG (a) generated frequency (b) slip (c) electromagnetic torque

(d) electrical generated output power (e) mechanical input power

(f) efficiency................................................................................................. 204

xviii

Fig. 8.1 No load D-Q model of a SEIG including core loss represented by Rm (a) d-axis (b) q-axis........................................................................................ 210

Fig. 8.2 Values of capacitance and speed for self-excitation with and without Rm at no load........................................................................................................ 213

Fig. 8.3 No load RMS phase voltage during self-excitation with and without Rm ..... 216

Fig. 8.4 Variation of connected capacitor and resistor................................................ 218

Fig. 8.5 The dynamic rms generated voltage with variation of load and capacitance 218

Fig. 8.6 Dynamic currents in the load, capacitor and stator with variation in load

and capacitance .............................................................................................. 219

Fig. 8.7 The dynamic output power with variation in load and capacitance .............. 219

Fig. 8.8 The dynamic electromagnetic torque with variation in load and capacitance220

Fig. 9.1 Electrical and mechanical connections ........................................................ 224

Fig. 9.2 Vector diagram for rotor flux oriented vector control ................................. 226

Fig. 9.3 Vector diagram for stator flux oriented vector control ................................ 235

Fig. 9.4 System description ....................................................................................... 240

Fig. 9.5 Relationship between generator rotor speed and flux linkage ..................... 242

Fig. 9.6 Implementation of direct rotor flux oriented vector control with current

controlled PWM VSI ................................................................................................... 244

Fig. 9.7 Implementation of indirect rotor flux oriented vector control with current. 246

Fig. 9.8 Implementation of direct rotor flux oriented vector control with stator

voltage as a control variable ........................................................................ 247

Fig. 9.9 Implementation of stator flux oriented vector control with current

controlled PWM VSI ................................................................................... 248

Fig. 9.10 Generated DC voltage for different capacitance value ................................ 250

Fig. 9.11 Rotor speed and angular frequency of the generated voltage for different

capacitance value ......................................................................................... 250

Fig. 9.12 Flux linkage at different rotor speeds of the induction generator

for 1000PF ................................................................................................... 251

Fig. 9.13 Generated line to line voltage at the terminals of the induction generator .. 251

Fig. 9.14 Loading of the induction generator (a) RL (b) rotor speed (c) VDC (d) flux

linkage (e) edsi (f)

eqsi (g) Idc (h) Output power (i) Slip (j) Electromagnetic

torque ........................................................................................................... 254

xix

Fig. 10.1 Offset error equal to Am as a result of the integration initial condition........ 261

Fig. 10.2 No integrator error ....................................................................................... 261

Fig. 10.3 Error produced due to measurement offset .................................................. 262

Fig. 10.4 Error produced due to measurement offset and integration initial condition262

Fig. 10.5 Numerical integrator representation ............................................................ 263

Fig. 10.6 Proposed offset adjustment in a numerical integrator.................................. 265

Fig. 10.7 Proposed integrator with input offset adjustment ........................................ 265

Fig. 10.8 Detail for integration error compensation ................................................... 266

Fig. 10.9 Stator flux linkage estimation using the proposed method .......................... 267

Fig. A.1 Electromagnetic torque versus motor speed at steady state......................... 280

Fig. A.2 Variation of speed with time (a) DC motor field supply on

(b) DC motor field supply off ...................................................................... 280

Fig. B.1 Interconnection of hardware system ............................................................ 283

Fig. B.2 DSPACE DS1102 DSP controller board ..................................................... 283

Fig. B.3 Multiplexer board control to dSPACE DS1102 DSP card connection........ 283

Fig. B.4 DAC output for DC motor speed control..................................................... 284

Fig. B.5 Dead time Generator board and DS1102 DSP card connection .................. 284

Fig. B.6 Incremental encoder DS1102 DSP card connection .................................... 284

Fig. B.7 Four isolated 15V Power supply for optocoupler circuit............................. 285

Fig. B.8 Optocoupler to Mitsubishi PM50RVA120 IPM .......................................... 286

Fig. B.9 8 to 4 multiplexer with Sample and Hold .................................................... 287

Fig. B.10 Cross over protection board (dead time generator)...................................... 288

Fig. D.1 Student award............................................................................................... 300

LIST OF TABLES

Table 2.1 Rough Categories of Wind Generator Sizes ............................................... 39

xx

LIST OF SYMBOLS

Generally symbols are defined locally. The list of principal symbols is given below

V1 - Upwind velocity, m/s

V2 - Downwind velocity, m/s

VT - wind velocity at the wind turbine, m/s

U - density of air, Kg/m3

m - mass of air, Kg

V - velocity of air, m/s

F - force applied on rotor blades, N

PT - power extracted by the wind turbine, Watt

A - area swept by the blades of the wind turbine, m2

ZT - angular velocity of the wind turbine, rad/s

Vtn - tangential speed of the blades at the tips

TT - torque produced by the wind turbine, Nm

Vw - the undisturbed wind speed in the site, m/s

Ve - the maximum fraction of the undisturbed wind that can be absorbed by the rotor

blade for maximum capture of wind power, Ve = 2/3*Vw, m/s

Va - is the wind created due to rotation of the wind turbine and increases with radius (Vais perpendicular to Ve and Vw), m/s

Vres - the resultant incident wind speed due to Va and Ve, m/s

r - total radius the rotor blade respectively, m

r1, r2 and r3 - radiuses at points 1, 2 and 3 of the rotor blade respectively, m

TSR - Tip-Speed Ratio (dimensionless ratio of tip linear speed of blades to Vw)

Prf - Steady state wind pressure, which is equal to atmospheric air pressure, N/m2

Prf

- wind pressure just after the wind turbine, N/m2

Prf

- wind pressure just before the wind turbine, N/m2

m - Mass flow rate of air per unit time, Kg/s

Q - Volume flow rate of air per unit time, m3/s

Cp - Dimensionless power coefficient

fas, fbs, and fcs a b c axes instantaneous quantities in stationary reference frame

xxi

fqs, fds, and fos dq axes instantaneous quantities in stationary reference frame

fqe, and fde dq axes DC quantities in excitation reference frame

va, vb and vc phase voltages in three axes system (stationary reference frame), V

ia, ib and ic phase currents in three axes system (stationary reference frame), A

vqs, and vds phase voltages in two axes system (stationary reference frame), V

iqs, and ids phase currents in two axes system (stationary reference frame), A

iqe, and ide phase currents in two axes system (excitation reference frame), A

ds-q

s stationary dq axes

de-q

e dq axes in rotating reference frame (rotating at excitation frequency)

vds d-axis stator voltage, V

vqs q-axis stator voltage, V

vdr d-axis rotor voltage, V

vqr q-axis rotor voltage, V

ids d-axis stator current, A

iqs q-axis stator current, A

idr d-axis rotor current, A

iqr q-axis rotor current, A

imd d-axis magnetising current, A

imq q-axis magnetising current, A

Ods d-axis stator flux linkage, web-turn

Oqs q-axis stator flux linkage, web-turn

Odr d-axis rotor flux linkage, web-turn

Oqr q-axis rotor flux linkage, web-turn

Odm d-axis air gap flux linkage, web-turn

Oqm q-axis air gap flux linkage, web-turn

Vm peak phase voltage, V

Im peak phase current, A

Vrms rms phase voltage, V

Irms rms phase current, A

Vdq phase voltage space vector, V

Idq phase current space vector, A

Ts sampling time(period), seconds

xxii

T angle between the two axes and three axes, rad

I phase shift between current and voltage

Z angular speed of the space vector, speed of the general reference frame, rad/s

Ze angular speed of the excitation reference frame, synchronous speed, rad/s

Zr electrical rotor angular speed, rad/sec

Zm mechanical rotor (shaft) angular speed(Zm = Zr /Pp ), rad/sec

fe excitation frequency, Hz

s the slip of the rotor with respect to the stator magnetic field

Pp number of pole pairs of the induction machine

Ne synchronous speed in revolutions per minute (rpm)

Vs rms stator voltage, V

Is rms stator current, A

Ir rms rotor current, A

Rs stator winding resistance, :

Rr rotor winding resistance, :

Rm equivalent resistance representing iron loss or core loss, :

Lls stator leakage inductance, H

Llr rotor leakage inductance, H

Lm magnetising inductance, H

Ls stator leakage inductance (Lls) + magnetising inductance (Lm) , H

Lr rotor leakage inductance (Llr) + magnetising inductance (Lm), H

p d/dt, the differential operator

Es rms induced emf in the stator winding due to the rotating magnetic field that

links the stator and rotor windings, V

Er rms induced voltage in the rotor when the rotor is stationary, V

sZe rotor current angular frequency

Te electromagnetic torque, Nm

Tm mechanical torque

mOJJG

air gap flux linkage

rIJG

rotor current space vector

D friction coefficient, Nm/rad/sec

J inertia, Kg-m2

xxiii

Aincr incremental count of the position counter, incremental steps

Iincr incremental position, radians

Zres speed measurement resolution, rad/s

Tres angle measurement resolution, rad

VO the measured open-circuit phase voltage, V

IO the measured open-circuit phase current, A

PO the measured open-circuit three-phase power, W

Vsh the measured short-circuit input phase voltage, V

Ish the measured short-circuit input phase current, A

Psh the measured short-circuit three-phase input power, W

Superscript

* commanded variables

Abbreviations

SEIG Self-Excited Induction Generator

emf Electromotive force

PWM Pulse Width Modulation

IGBT Insulated Gate Bipolar Transistor

RMS root mean square

DSP Digital Signal Processor (Processing)

ADC Analog to digital converter

IIR Infinite impulse response

FIR Finite impulse response

PI Proportional and integral (PI controller)

VSI Voltage source inverter

IPM Intelligent power module

VAR Volt ampere reactive

1

CHAPTER 1

INTRODUCTION

1.1 General

Today, most of the electricity generated comes from fossil fuels (coal, oil, and natural

gas). These fossil fuels have finite reserves and will run out in the future. The negative

effect of these fossil fuels is that they produce pollutant gases when they are burned in

the process to generate electricity. Fossil fuels are a non-renewable energy source.

However, renewable energy resources (solar, wind, hydro, biomass, geothermal and

ocean) are constantly replaced, hence will not run out, and are usually less polluting [1].

Due to an increase in greenhouse gas emissions more attention is being given to

renewable energy. As wind is a renewable energy it is a clean and abundant resource

that can produce electricity with virtually no pollutant gas emission. Induction

generators are widely used for wind powered electric generation, especially in remote

and isolated areas, because they do not need an external power supply to produce the

excitation magnetic field. Furthermore, induction generators have more advantages such

as cost, reduced maintenance, rugged and simple construction, brushless rotor (squirrel

cage) and so on.

In the literature, starting in the 1930s, it is well known that a three-phase induction

machine can be made to work as a self-excited induction generator (SEIG) [2, 3]. In an

isolated application a three-phase induction generator operates in the self-excited mode

by connecting three AC capacitors to the stator terminals [2-4] or using a converter and

a single DC link capacitor [5]. The dynamic performance of an isolated induction

generator excited by three AC capacitors or a single DC capacitor with a converter is

discussed in detail in this work.

CHAPTER 1 INTRODUCTION

2

Induction machines are more robust and cheaper than other electrical machines for the

same rating. They need less maintenance when manufactured with a squirrel cage rotor.

Depending on the condition of operation the induction machine can be used as a motor

or generator. Induction machines are available in single-phase or three-phase

constructions. In this work the modelling and analysis given is only for the three-phase

induction machine and the induction machine is operated as a generator. The definition

of slip in this study is the usual one and is the same for the induction generator and

induction motor.

In a grid connected induction generator driven by a wind turbine the magnetic field is

produced by excitation current drawn from the grid. In different countries there are

many induction generators with high power ratings that use wind power as their prime

mover. These export electric power to the grid. The Kooragang wind turbine generator,

shown in Fig. 1.1, which is owned and operated by Energy Australia, in Newcastle,

NSW, Australia, is connected to the grid and has rated power of 600KW and the turbine

is a Vestas V44-600KW machine [6].

Fig. 1.1 Kooragang wind turbine generator, Newcastle, NSW, Australia (Photo 2002)

CHAPTER 1 INTRODUCTION

3

For this generating system the angular speed of the wind turbine rotor measured on the

wind turbine side is 28rpm. A gear box steps up the shaft speed and on the generator

side the angular speed of the generator rotor is approximately 1500rpm [6].

Multiple wind turbine generators can be installed at a given site to form a wind farm.

Fig. 1.2 shows part of a wind farm around San Francisco, California, USA.

Fig. 1.2 Wind farm around San Francisco, California, USA (Photo 2002)

The output voltage and frequency of an isolated induction generator vary depending on

the speed of the rotor and the load connected to the generator. This is due to a drop in

the speed of the rotating magnetic field [7]. The wind turbine can be designed to operate

CHAPTER 1 INTRODUCTION

4

at constant speed or variable speed. When the speed of the prime mover of the isolated

induction generator drops with load, then the decrease in voltage and frequency will be

greater than for the case where the speed is held constant. The AC voltage can be

compensated by varying the exciting AC capacitors or using a controlled inverter and a

DC capacitor. However the frequency can be compensated only if there is a change in

the rotor speed. Because the frequency of the three-phase isolated induction generator

varies with loading its application should be for the supply of equipment insensitive to

frequency deviations, such as heaters, water pumps, lighting, battery charging etc.

For applications that require constant voltage and frequency the rectified DC voltage of

the isolated induction generator should be controlled to remain at a given reference

value. Then the constant DC voltage can be converted to constant AC voltage and

frequency using an output inverter. In this way a control mechanism is implemented to

regulate the output voltage and frequency from an induction generator.

1.2 Thesis outline

There are eleven chapters and four appendices in this thesis. The thesis presents the

modelling of the dynamic characteristics of an isolated self-excited induction generator

driven by a wind turbine. To have a good understanding of the prime mover an

overview of the characteristics of wind turbines is presented. Analysis of an induction

generator is discussed using modelling and the theory of induction machines.

In Section 1.3 of this chapter the literature related to isolated induction generators and

wind turbines is reviewed. This involves clarifying the strengths and limitations of the

previous works and highlighting the advantages of the research covered in the thesis.

In Chapter 2 a detailed explanation about wind as a power source and the mechanism of

conversion of wind power to mechanical power is presented. The variation of output

power and output torque with rotor angular speed and wind speed is discussed. The

economics and growth of wind powered electric generation is given and the projection

for the future is also discussed.

CHAPTER 1 INTRODUCTION

5

The three-axes to two-axes transformation presented in Chapter 3 is applicable for any

balanced three-phase system. In electrical machines analysis a three-axes to two-axes

transformation is applied to produce simpler expressions that provide more insight into

the interaction of the different parameters. The D-Q model for dynamic analysis is

obtained using this transformation. It is shown that the three-axes to two-axes

transformation simplifies the calculation of dynamic rms current, rms voltage, active

power and power factor in a three-phase system and more specifically for this

application, the three-phase induction machine. Traditional methods of measuring these

quantities are unable to obtain peak values of current and voltage in less than one

quarter of a cycle. However using the three-axes to two-axes transformation in the

manner described in Chapter 3, it is possible to evaluate the rms or peak magnitudes of

three-phase AC currents and voltages from one set of measurements taken at a single

instant of time. Furthermore from measurements taken at two consecutive instants in

time the frequency of the three-phase AC power supply can be evaluated.

In Chapter 4 the modelling of an induction machine using the conventional or steady

state model and the D-Q or dynamic model are explained. The voltage, current and flux

linkage in the rotating reference frame and their phase relationships in the motoring

region and generating region are presented. Chapter 4 gives the fundamentals of

induction machine modelling and characteristics as a preparation of the modelling and

analysis of an isolated induction generator. The induction machine model in D-Q axes

has been improved to include the equivalent iron loss resistance, Rm. This improved

model is presented in a simple and understandable way. Using this model the dynamic

current, torque and power can be calculated more accurately.

In Chapter 5 the data acquisition system and signal processing are discussed. The

measurement of voltages, currents, rotor angle and angular speed with their appropriate

sensors is explained. The detail of the digital signal processing (DSP) card and

transducer board used in the experimental setup is given. The sensors for current and

voltage are Hall-Effect devices. Rotor speed and angle measurements are taken using an

optical incremental encoder. The resolution of angle and speed for a given encoder is

derived. Anti-aliasing filters are introduced in the analog signals of the sensor outputs to

prevent the high frequencies appearing as a low frequency when the analog signal is

CHAPTER 1 INTRODUCTION

6

digitised in the A/D converter. The advantage of digital signal processing is discussed

and different types of filter design are presented which are used in the simulation and

experimental procedures.

Machine modelling requires knowledge of the parameters of the machine. Whether the

three-phase induction machine is modelled using the conventional per-phase equivalent

circuit or the D-Q method the parameters of the machine are required. Chapter 6

discusses a rapid way of determining the parameters that is fast enough to determine the

parameters at rated voltage of the induction machine without damaging it due to

overheating. The error in the values of induction motor parameters arising from

measurement error in voltage, current and power have been presented. Rotor parameter

variations in squirrel cage induction machines and the cause of this variation is

examined. The variation of induction machine parameters with temperature is also

presented.

Chapter 7 deals with the modelling, analysis and dynamic performance of an isolated

three-phase induction generator excited by three AC capacitors connected at the stator

terminals. The mathematical model of a self-excited induction generator including the

representation of the remnant magnetic flux in the iron core and the initial charge in the

capacitor is given. The initiation and process of self-excitation is presented, starting

from a simple RLC circuit as an analogy to a complete dynamic representation of a self-

excited induction generator, i.e. the complete representation includes both steady state

and transient conditions. The variation of magnetising inductance of the induction

machine is important in the voltage build up and stabilisation of the generated voltage.

It is shown that the characteristics of magnetising inductance with respect to the rms

induced stator voltage or magnetising current determines the regions of stable operation

as well as the minimum generated voltage without loss of self-excitation. The variation

of the generated voltage and frequency for a self excited induction generator driven by a

wind turbine at constant and variable speeds has been investigated. Using simulation

algorithms more results which are not accessible in an experimental setup have been

predicted.

CHAPTER 1 INTRODUCTION

7

In Chapter 8 the modelling of an isolated self-excited induction generator taking iron

loss into account is discussed. Iron loss or core loss is represented in the induction

machine model using Rm, a resistance value which has the same power loss as the total

iron loss in the induction machine. The method presented here is a novel analysis and

modelling for the dynamics of the self-excited induction generator driven by a variable

speed prime mover taking iron loss into account. It is noted that this method is easily

understood, having drawn on many familiar concepts and using the standard

terminology and nomenclature of D-Q unified machine theory. This improved model

takes into consideration the variations of Rm with air gap voltage and, as in Chapter 7,

the variation of magnetising inductance. This model is then coupled to the

characteristics of a variable speed prime mover and the analysis of this system is

produced and discussed.

In Chapter 9 the voltage build up process and terminal voltage control in an isolated

wind powered induction generator using an inverter/rectifier excitation with a single

capacitor on the DC link is discussed. A vector control technique is developed to

control the excitation and the active power producing currents independently. That is,

the current control scheme causes the currents to act in the same way as in a DC

generator where the field current and the armature current are decoupled. When the

speed of the prime mover is varied the flux linkage in the induction generator is made to

vary inversely proportional to the rotor speed so that the generated voltage will remain

constant. Since the torque produced by a wind turbine drops at high turbine rotor speed

the induction generator will run at high generator rotor speed when loaded with a small

load and the rotor speeds decrease with an increase in load. As the turbine rotor shaft

and the generator rotor shaft are connected via a gear box, both rotor speeds will

increase and decrease proportionally at constant gear ratio. The flux linkage of the

induction generator is controlled by controlling the d-axis current in the synchronously

rotating reference frame. Two vector control strategies: rotor flux oriented vector

control and stator flux oriented vector control are presented. It is shown that the

estimation of rotor flux linkage is more dependent on the induction machine parameters

whereas estimation of stator flux linkage is dependent only on the stator resistance.

CHAPTER 1 INTRODUCTION

8

Chapter 10 investigates the problems and the solutions in the estimation of stator flux

linkage using integration of the voltage behind the stator resistance. This voltage is

calculated from the measured voltages and currents. Accurate flux estimation is very

crucial in the control of induction motor drives and induction generators using vector

control. The method of flux linkage estimation proposed in this chapter is new and

effective. It eliminates the error produced by the measurement offset error and

integrator output error due to initial integration in a continuous time integrator or

numerical/discrete time integrator. It is shown that if the integration ramp output due to

the existence of measurement offset error is large then subtracting the output of a low

pass filter of the signal from the signal to be integrated minimizes the offset. A signal

with small input offset will have a small increment of ramp that will appear at the

output of the integrator. As the time increases the ramp keeps on increasing and

eventually the distortion in flux will be unacceptable. However, if the ramp is

eliminated every cycle, the flux distortion due to the offset correction at the output is

insignificant.

In Chapter 11 conclusions and suggestions for future work are given.

1.3 Literature review

In this section previous work carried out in the area of self-excited induction generators

that are driven by variable speed prime movers and in particular by wind turbines are

reviewed. If there is a controller to regulate the output voltage and frequency, then an

isolated induction generator can be driven by a variable speed prime mover. However,

for loads which are insensitive to frequency, then the controller needs only to regulate

the generated voltage.

1.3.1 Self-excited induction generator

The early work on three-phase SEIGs excited by three capacitors was mainly

experimental analysis [2, 3]. The main methods of representing a SEIG are the steady

state model and the dynamic model. The steady state analysis of SEIG is based on the

steady state per-phase equivalent circuit of an induction machine with the slip and

angular frequency expressed in terms of per unit frequency and per unit angular speed.

The steady state analysis includes the loop-impedance method [8-13] and the nodal

CHAPTER 1 INTRODUCTION

9

admittance method [14-15]. The loop-impedance method is based on setting the total

impedance of the SEIG, i.e. including the exciting capacitance, equal to zero and then to

find the steady state operating voltage and frequency using an iteration process. In the

nodal admittance method the real and imaginary parts of the overall admittance of the

SEIG are equated to zero. The equations are formulated based on the steady state

conditions of the SEIG.

The main draw back of using the per-phase steady state equivalent circuit model is that

it cannot be used to solve transient dynamics because the model was derived from the

steady state conditions of the induction machine.

The dynamic model of a SEIG is based on the D-Q axes equivalent circuit or unified

machine theory. For analysis the induction machine in three axes is transformed to two

axes, D and Q, and all the analysis is done in the D-Q axes model. The results are then

transformed back to the actual three axes representation. In the D-Q axes if the time

varying terms are ignored the equations represent only the steady state conditions. The

SEIG represented in D-Q axes and analysed under steady state conditions are reported

in [16-17]. In [18-21] the dynamic equations for the representation of SEIG conditions

are given. In these papers the initial conditions that take into account the initial charge

in the exciting capacitors and the remnant magnetic flux linkage in the iron core are not

given and in some of the papers the complete dynamic equations are not presented.

The D-Q axes model of SEIG given in [20] reported that the dynamic generated voltage

varies with the applied load, but there are no results that show what happens to the

dynamic speed of the rotor when the generator is loaded. Hence it cannot be proven

whether the variation in voltage is exaggerated due to a change in speed or not. To

investigate this, the characteristic of the dynamic voltage is simulated and measured

keeping the speed at a constant value by applying a speed regulator to a DC motor

which is used as a prime mover for the SEIG. For the constant speed drive test a PI

(proportional and integrator) speed controller and an inner loop PI current controller is

used. The dynamic frequency of the generated voltage, during loading conditions, is

calculated from measured voltages or from measured voltages and currents. A three-

axes to two-axes transformation is used in the calculation of the dynamic frequency

CHAPTER 1 INTRODUCTION

10

value. Here the transformation is used to simplify the calculation. The measured and

simulated dynamic currents, active power and electromagnetic torque generated by the

SEIG are also given in this paper.

The normal connection of a SEIG is that the three exciting capacitors are connected

across the stator terminals and there is no electrical connection between the stator and

rotor windings. However, in the literature a SEIG with electrical connection between

rotor and stator windings is reported [22]. This paper deals with the steady state

performance of a SEIG realised by a series connection of stator and rotor windings of a

slip-ring type induction machine and solved using D-Q analysis. In this type of

connection it has been claimed that it has the advantage of operating at a frequency

independent of load conditions for a fixed rotor speed, however the angular frequency

of the output voltage is equal to half of the rotor electrical angular speed, which means

the prime mover should rotate at twice the normal speed to generate voltage with

standard frequency. There is also concern regarding the current carrying capability of

the rotor and stator windings because both of them are carrying the same current.

Whether any wound rotor induction machine can be used in this way or not is not

specified.

Shridhar et al reported that if a single valued capacitor bank is connected, i.e. without

voltage regulator, a SEIG can safely supply an induction motor rated up to 50% of its

own rating and with a voltage regulator that maintains the rated terminal voltage the

SEIG can safely feed an induction motor rated up to 75% of its own rating [23]. In this

case the SEIG can sustain the starting transients of the induction motor without losing

self-excitation.

Since a SEIG operates in the saturation region, it has been shown that to saturate the

core, the width of the stator yoke is reduced so that the volume and the weight of the

induction generator will be less than the corresponding induction motor [24]. The

voltage drop for a constant capacitor induction motor used as a generator was 30%

while the voltage drop of the corresponding designed induction generator was 6% [24].

CHAPTER 1 INTRODUCTION

11

A three-phase SEIG can be used as a single-phase generator with excitation capacitors

connected in C-2C mode where capacitors C and 2C connected across two phases

respectively and nil across the third phase [25].The steady state performance of an

isolated SEIG when a single capacitor is connected across one phase or between two

lines supplying one or two loads is presented in [26]. However in these applications the

capacity of the three-phase induction generator cannot be fully used.

1.3.2 Capacitance and rotor speed for self-excitation

The minimum and maximum values of capacitance required for self-excitation of a

three-phase induction generator have been analysed previously using a current model

[9, 11, 20]. Calculation of the minimum capacitance required for self excitation using a

flux model has also been reported [27].

In the calculation of capacitance required for self-excitation, economically and

technically, it is not advisable to choose the maximum value of capacitance. This is due

to the fact that for the same voltage rating the higher capacitance value will cost more.

In addition, if the higher capacitance value is chosen then there is a possibility that the

current flowing in the capacitor might exceed the rated current of the stator due to the

fact that the capacitive reactance reduces as the capacitance value increases.

It has been shown that a de-excited induction generator can re-excite even if the load is

already connected to it [30], but the relationship between the value of the load,

capacitance and speed has not been given. In this thesis the relationship between speed,

capacitance and load is given so that the characteristics of the induction generator for

self-excitation with a load can be established. This relationship is also important to find

the region where the induction generator can continue to operate without loss of self-

excitation.

Wind speed can change from the minimum set point to the maximum set point

randomly and the SEIG can be started at any point within the range of speed. It is

essential to find the minimum and maximum speed required for self-excitation, when

the generator is loaded. In this thesis the author has developed the analysis and

CHAPTER 1 INTRODUCTION

12

calculation of the minimum and maximum speeds for self-excitation to occur and for a

particular value of capacitance.

1.3.3 Representation of magnetising inductance

In the SEIG the variation of magnetising inductance is the main factor in the dynamics

of voltage build up and stabilisation. Several papers have reported on the representation

of the variation of magnetising inductance (Lm) or magnetising reactance (Xm) during

voltage build up.

One of the ways of representation is Xm as a function of Vg/f (V/Hz to relate to flux) [8-

9, 11-13, 15, 21], where Vg is the voltage across Xm and f is the frequency of excitation,

or Lm as a function of Vg [14, 26] for a known frequency of operation. In these papers it

has been shown that the value of Xm, as the value of Vg/f or Vg increases from zero,

starts at a given unsaturated value, remains constant at the unsaturated value for low

values of air-gap voltage or ratio of air gap voltage to frequency, and then starts to

decrease up to its rated value, which is a saturated value. In fact, in [9] the measured

values show the actual variation of magnetising reactance. This is the magnetizing

reactance as the air gap voltage increases from zero. It starts at a given value, increases

until it reaches its maximum value and then starts to decrease down to its rated value,

which is a saturated value. However, in the analysis of the SEIG the magnetising

reactance for values of air gap voltage close to zero were ignored. Since Xm is

dependent on frequency it is not good for transient dynamic analysis, rather Lm should

be used.

The other representation is Xm as a function of magnetising current [20, 28] or Lm as a

function of magnetising current [16, 29, 30]. In these papers it has been illustrated that

the magnetising inductance or magnetising reactance starts at a maximum unsaturated

value and then decreases when the iron core saturates, however in [16] the authors have

indicated that the value of magnetising inductance starts at a given unsaturated value,

increases and then finally decreases as the magnetising current increases from zero.

Although this representation depicts the actual variation of magnetising inductance, the

significance of this characteristic has not been presented.

CHAPTER 1 INTRODUCTION

13

The reason for this variation in magnetising reactance and the effect on self-excitation is

discussed in this thesis. As the magnetizing reactance is dependent on frequency,

magnetizing inductance is used in the analysis and its effect on the initiation of self-

excitation and stabilisation is discussed in detail and confirmed experimentally.

1.3.4 Control of generated voltage and frequency

The main problem in using a SEIG is the control of the generated voltage because the

voltage amplitude and frequency drops with loading as well as with a decrease in the

generator rotor speed [7]. The magnitude and frequency of the output voltage of a stand

alone induction generator driven by a variable speed rotor can be controlled by

employing the rotor excitation of a wound-rotor induction machine [31]. In a similar

way it can be controlled by varying the rotor resistance of a self-excited slip-ring

induction generator [32]. However a self-excited slip-ring induction generator will

require more maintenance than a squirrel cage rotor due to the slip-rings and brush gear.

The rms value of the generated voltage, irrespective of its frequency, can be controlled

using variable capacitance values [33], or a fixed capacitor thyristor controlled reactor

static VAR compensator [34], or continuously controlled shunt capacitors using

antiparallel IGBT switches across the fixed excitation capacitor [35].

It has been shown that copper loss decreases in the stator and increases in the rotor in

the generating mode when compared to the motoring mode [36]. In a SEIG, a squirrel

cage rotor is preferable to a wound rotor because the squirrel cage rotor has a higher

thermal withstand capability and requires less maintenance. Due to the higher thermal

withstand capability of the squirrel cage rotor, a higher copper loss in the rotor is

acceptable.

1.3.5 Wind powered generators

For a fixed speed wind turbine system that can be connected to the grid, maintaining a

constant frequency is not a problem, irrespective of whether an induction or

synchronous generator is used. Such systems typically employ induction machines

connected directly to the grid. In grid connected systems there are two generating

schemes for variable speed wind turbine systems [37-43]. The first scheme employs

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14

machine control using power electronics feeding the rotor circuit (wound rotor

induction machine) or a second winding in the stator of an induction machine (squirrel

cage rotor or wound rotor) to adjust the frequency and generated voltage when the

generator rotor speed is varied. The second scheme applies to single stator winding fed

induction generators which produce a constant DC output voltage that is then inverted

to have an output of constant rms voltage and frequency. The generation of constant DC

voltage is implemented using scalar or vector control [44-45] or using a DC-DC

converter to produce constant DC voltage from the variable rectified DC voltage [46].

In a variable speed wind turbine system the mechanical stresses caused in the structural

elements by gusts and varying wind speed are diminished by letting the rotor follow the

wind. Also when the rotor speed is allowed to vary with the wind the turbine can be

operated at peak efficiency. However, the necessary power electronics can be

expensive.

Brushless doubly-fed induction machines have two stator windings of different pole

number [39-42]. Although the system has reduced size and cost of the power

electronics, the induction machine is expensive because it is specially made. A double

output induction generator is a wound rotor induction machine with the control power

electronics connected on the rotor circuit [43, 45]. In this arrangement the induction

generator gives more than its rated power without being overheated. The power

generation can be realised for a wide range of wind speed. They have a rotor inverter

and front end converter while the stator is linked directly to the grid.

The methods discussed above can also be used to control the output voltage from a

stand alone induction generator. In the literature it is reported that a stand alone

induction generator excited by a single DC capacitor and inverter/rectifier system can

be used instead of the AC capacitor excited system. If a constant DC voltage is achieved

then a load side inverter is used to produce a constant rms voltage and frequency. For

this application an inverter/rectifier can be shunt connected so that it carries only the

exciting current [47-49] or a converter can be connected in series so that it carries the

full current [50-51], i.e. the exciting and load current. In both cases the initiation of

voltage build up is the same. However in these papers the details of the control

mechanism and the generation of reference currents are not given. The minimum DC

CHAPTER 1 INTRODUCTION

15

capacitance required for the initiation of voltage build up has been discussed [50].

When the converter carries only the exciting current an additional rectifier is required to

produce the DC voltage that supplies the load.

Artificial Intelligence is the branch of science that concentrates on making computers or

computer-based technology to function like humans. Advanced intelligent control of a

variable speed wind generation system has been reported in the literature [52-57].

Artificial intelligence techniques include fuzzy logic, neural network, and genetic

algorithm, etc [56-57]. The evolving adaptive and elastic versions of fuzzy logic

control in combination with the artificial neural network algorithms promise to

revolutionize the applicability of fuzzy logic control in reference trajectory tracking,

state estimation and parameter adaptation of control strategies [52]. It has been shown

that fuzzy control algorithms are universal, give fast convergence, are parameter

insensitive, and accept noisy and inaccurate signals [57]

It has been reported that artificial intelligent has been used extensively to optimize

efficiency and